Do electrons have structure?
Frederick Seelig
considered point particles at today's colliders' energy levels. But
wouldn't it be reasonable to suppose that electrons were composite
particles, too? If hadrons consist of fractional charge thingies, oughtn't
one to suppose that leptons do too?
Doesn't the Standard Model consider leptons to be elementary particles? Is
there a simple to understand reason for this? Do any extensions of the
Standard Model treat leptons as composite particles? At what energy levels
would electrons show internal structure?
--
Fred Seelig
J. J. Lodder
> Do electrons have structure? From what I have read, electrons are still
> considered point particles at today's colliders' energy levels. But
> wouldn't it be reasonable to suppose that electrons were composite
> particles, too? If hadrons consist of fractional charge thingies, oughtn't
> one to suppose that leptons do too?
Nature doesn't listen to our reason. It not even ought to,
it being far cleverer than we are :-)
However, the idea of composite electrons has severe problems;
electrons would have to consist of components -very- much heavier
than themselves, the remainder being supplied by a very large negative
binding energy.
While possible in principle, it would be hard to invent an 'elegant'
theory with such nearly, but not quite perfect, cancallations.
It would not be 'reasonable' :-)
> Doesn't the Standard Model consider leptons to be elementary particles?
Yes.
> Is there a simple to understand reason for this?
Yes, because the standard model is phenomenological.
It doesn't care for unobserved properties.
>Do any extensions of the
> Standard Model treat leptons as composite particles? At what energy levels
> would electrons show internal structure?
Won't know 'till seen,
Jan
Phil Gardner
Does the "evidence" that they are point particles include anything
more than the facts that:
(a) the cross-section for elastic scattering of electrons through
angles exceeding (say) pi/2 decreases without limit as the electron
energy is increased.
(b) in the last 70 years or more no-one has constructed a plausible
model of an extended electron with a mass-energy density that is
everywhere finite and continuous.
Phil Gardner <pej...@oznetcom.com.au>
Moataz Emam
The only known reasonable theory of electronic structure is within the
context of String theory, where electrons are extended strings in
spacetime. That is only apparent on the level of the Planck energy, or
length scale, about 10^-33 cm. This, of course, is quite unattainable
with today's technology. Some late ideas put the Planck scale much more
closer than that, making it possible to reach it in near future
accelerators.
--
Moataz H. Emam
URL: http://continue.to/emam
The Department of Physics
1129, Lederle Graduate Research Tower C,
University of Massachusetts, Amherst, 01003
e-mail : em...@physics.umass.edu
Tel. : (413) 545 0559
============================================
"I do not like it, and I am sorry I ever had anything to do with it."
Erwin Schrödinger, speaking of quantum
mechanics
"Those who are not shocked when they first come across quantum mechanics
cannot possibly have understood it."
Niels Henrik David Bohr
Matthew Nobes
> Do electrons have structure?
To the best of our ablility to test, no.
> From what I have read, electrons are still considered point
> particles at today's colliders' energy levels. But wouldn't
> it be reasonable to suppose that electrons were composite
> particles, too? If hadrons consist of fractional charge
> thingies, oughtn't one to suppose that leptons do too?
People have tried to make theories like this. Look up
``preons''.
If you like string theory, then electrons (and other leptons) are
some sort of excited modes of tiny little strings. I not sure if
string theorists count this as substructure or not.
> Doesn't the Standard Model consider leptons to be elementary
> particles?
Yes.
> Is there a simple to understand reason for this?
No, in the SM that's just the way things are.
> Do any extensions of the Standard Model treat leptons as
> composite particles?
String theory is probably the best known contender.
> At what energy levels would electrons show internal
> structure?
That depends on the theory. THe current experimental bound is
pretty high (~5 TeV IIRC). Of course there could be more subtle
effects. For example, muon substructure could possibly explain
the recent magentic moment anomoly measurment.
--
"Neutral kaons are even more crazy than silly putty"
-G. 't Hooft
Matthew Nobes, c/o Physics Dept. Simon Fraser University, 8888 University
Drive Burnaby, B.C., Canada, http://www.sfu.ca/~manobes
Ralph E. Frost
Matthew Nobes <man...@sfu.ca> wrote in message
news:Pine.GSO.4.30.010804...@fraser.sfu.ca...
> On Sun, 5 Aug 2001, Frederick Seelig wrote:
>
> > Do electrons have structure?
>
> To the best of our ablility to test, no.
I think this needs a bit of clarification. Consider that in our local
region/energy density, ALL imagery is created, conveyed and communicated in
terms of whole electron units. We can't leak one third of an electron out
of some membrane and then have that scuttle across into a detector.
In fact, when we power up the fields and equipment used to look for electron
substructure, folks do so in units of whole electrons. When we develop
photographs. we do so in terms of whole electrons.
So, since the result of ALL electron substructure queries will ultimately be
reduced down to ambient energy levels, is it POSSIBLE to have a resolved
image of a fractional electron?
I don't think so.
>
> > From what I have read, electrons are still considered point
> > particles at today's colliders' energy levels. But wouldn't
> > it be reasonable to suppose that electrons were composite
> > particles, too? If hadrons consist of fractional charge
> > thingies, oughtn't one to suppose that leptons do too?
>
> People have tried to make theories like this. Look up
> ``preons''.
>
> If you like string theory, then electrons (and other leptons) are
> some sort of excited modes of tiny little strings. I not sure if
> string theorists count this as substructure or not.
>
> > Doesn't the Standard Model consider leptons to be elementary
> > particles?
>
> Yes.
>
> > Is there a simple to understand reason for this?
>
> No, in the SM that's just the way things are.
>
> > Do any extensions of the Standard Model treat leptons as
> > composite particles?
>
> String theory is probably the best known contender.
>
> > At what energy levels would electrons show internal
> > structure?
>
> That depends on the theory. THe current experimental bound is
> pretty high (~5 TeV IIRC). Of course there could be more subtle
> effects. For example, muon substructure could possibly explain
> the recent magentic moment anomoly measurment.
>
Again, I don't think it matters WHAT energy level the equipment runs at.
The result will still be brought down and funnelled through local machinery.
This machinery only computes in units of whole electrons. Powering a
bigger system to higher energies is still not going to influence the ambient
outcome.
Er, don't some HEP test smash electrons into pieces?
J. J. Lodder
> Frederick Seelig <fse...@mitre.org> wrote in message news:<3B69516A.FC1FA863@
"Point particle" is a phenomenological concept anyway.
It means: particles that are described adequately
by a theory containing no structure-related parameters.
Jan
Gordon D. Pusch
Many people have attempt to construct such ``composite'' theories (e.g.,
the class of so-called ``technicolor'' models), but all have failed.
There is a fundamental problem in that the ``natural'' energy scale for
an object of size on the order of R is M*c^2 ~= (\hbar c) / R. The current
experimental upper-bound on the sizes of an electron, muon, or `u' and `d'
quark is less that 1e-18 m, so the natural mass of these quarks and leptons
if they were composite would have been expected to be much greater than
~200 GeV --- which is about five orders of magnitude too large for the
``first generation'' quarks and the electron, three orders of magnitude too
large for the muon and `s' quark, and at least nine orders of magnitude too
large for the electron and muon neutrinos. All attempts at construct a
``composite'' theory of quarks and lepton have foundered on this problem
of being unable to provide a natural reason why the first and second
generation quarks and leptons should be so light compared to the
``natural'' scale for their masses if they were composite.
Another problem most of these composite theories suffer from is the quantum
field theoretic disease called ``anomolies.'' I won't say anything about
anomolies except that they are viewed as Very Bad Things...
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
Lubos Motl
> Do electrons have structure? From what I have read, electrons are still
> considered point particles at today's colliders' energy levels.
Yes, according to all the experimental data as well as the Standard Model,
the electrons are point-like. It means that if they have a structure, the
distance between the components must be smaller than 10^{-18} meters or
so.
> But wouldn't it be reasonable to suppose that electrons were composite
> particles, too? If hadrons consist of fractional charge thingies,
> oughtn't one to suppose that leptons do too?
No, it would not be reasonable. First of all, there is absolutely no
motivation to do it. There are hundreds of different hadron species and
the discovery of quarks improved our understanding of physics in many
ways. Instead of hundreds of "elementary" hadrons, people could suddenly
deal with 6 fundamental quarks (and 6 antiquarks).
In the case of electrons, there is one electron only and it looks exactly
as fundamental as a quark. Electron is not as composite as a hadron!
Electron is as elementary as a quark. In the Standard Model, leptons (such
as electron) and quarks (up, down etc.) form families. Protons and
electrons don't! ;-) In the Grand Unified Theories, electrons and quarks
form multiplets that can be transformed into each other, not only
families.
More importantly, there is no observation that suggests a "parton"
structure of electrons. Parts of protons (quarks) can be seen at typical
distances of order 10^{-15} meters. On the contrary, electrons are safely
point-like even at distances of the order 10^{-18} meters or so. This is
the distance that current accelerators can "see".
There is also no new force to be explained. Protons and neutrons attract
each other in the nuclei. Today, we explain this force by a more
fundamental force between the quarks. This force is mediated by gluons.
The fact that quarks can have three colors essentially implies that there
must be a force that guarantees the colors to be equally good (the strong
force described by Quantum Chromodynamics).
On the contrary, electrons interact with the electromagnetic and weak
force (as well as gravity which is negligible in particle physics) and
there is no new force that could justify a substructure of electrons.
To summarize, hadrons are composites of quarks but electrons are not.
Electrons are as fundamental as quarks. It would be easy if we could take
an idea in physics and recycle it 20 times and make some progress 20
times. But physics is fortunately not that simple. You must find something
new to be famous. ;-) The method to explain a particle as a composite of
several smaller point-like particles has been probably exhausted. The only
exception could be the Higgs boson that could be a composite of
techniquarks - but even this possibility seems very unlikely.
Elementary particles have a deeper structure to explain. Perturbative
string theory shows every elementary particle (such as an electron, a
quark or a photon) to be a loop of string in a specific vibrational
pattern. Nonperturbatively, the nature of each particle can be even more
interesting (containing branes of various dimensions etc.) and there may
be several "dual" descriptions of the same thing. However, the simple way
to divide a particle into smaller particles cannot be done indefinitely.
There is a cutoff. Distances smaller than the Planck length do not make
any sense, for example. And therefore this is the last possible scale
where the old strategy must certainly break down.
> Doesn't the Standard Model consider leptons to be elementary particles? Is
> there a simple to understand reason for this? Do any extensions of the
> Standard Model treat leptons as composite particles? At what energy levels
> would electrons show internal structure?
No, there are no extensions like that. For instance, in the Standard
Model, electrons and neutrinos form doublets of SU(2) symmetry. This
symmetry cannot be "broken" in any way because it is a local gauge
symmetry. A composite electron implies a composite neutrino, too.
Neutrinos are almost massless and it is extremely difficult to imagine
that they are composite particles. Such subparticles would probably have
to be very light - but then their wavelength would be too large, it would
determine the "size" of the electrons - and it would contradict the
experiments. The experiments agree with the "point-like" Standard Model up
to energies 1 TeV or so.
In the conventional stringy scenarios, the electrons are loops of
vibrating string as large as 10^{-35} meters or so. In the newer scenarios
with large dimensions, such an electron can be larger. But in both cases
there is no point-like substructure.
Best wishes
Lubos
______________________________________________________________________________
E-mail: lu...@matfyz.cz Web: http://www.matfyz.cz/lumo tel.+1-805/893-5025
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Superstring/M-theory is the language in which God wrote the world.
Frederick Seelig
>
> Matthew Nobes <man...@sfu.ca> wrote in message
> news:Pine.GSO.4.30.010804...@fraser.sfu.ca...
> > On Sun, 5 Aug 2001, Frederick Seelig wrote:
> >
> > > Do electrons have structure?
> >
> > To the best of our ablility to test, no.
>
> I think this needs a bit of clarification. Consider that in our local
> region/energy density, ALL imagery is created, conveyed and communicated in
> terms of whole electron units. We can't leak one third of an electron out
> of some membrane and then have that scuttle across into a detector.
>
> In fact, when we power up the fields and equipment used to look for electron
> substructure, folks do so in units of whole electrons. When we develop
> photographs. we do so in terms of whole electrons.
>
> So, since the result of ALL electron substructure queries will ultimately be
> reduced down to ambient energy levels, is it POSSIBLE to have a resolved
> image of a fractional electron?
>
> I don't think so.
Not true. Electrons can resolve the internal structure of hadrons, even
though
quarks have only fractional charge.
Kevin A. Scaldeferri
Ralph E. Frost <ref...@dcwi.com> wrote:
>
>Matthew Nobes <man...@sfu.ca> wrote in message
>news:Pine.GSO.4.30.010804...@fraser.sfu.ca...
>> On Sun, 5 Aug 2001, Frederick Seelig wrote:
>>
>> > Do electrons have structure?
>>
>> To the best of our ablility to test, no.
>
> I think this needs a bit of clarification. Consider that in our local
>region/energy density, ALL imagery is created, conveyed and communicated in
>terms of whole electron units. We can't leak one third of an electron out
>of some membrane and then have that scuttle across into a detector.
>
>In fact, when we power up the fields and equipment used to look for electron
>substructure, folks do so in units of whole electrons. When we develop
>photographs. we do so in terms of whole electrons.
>
>So, since the result of ALL electron substructure queries will ultimately be
>reduced down to ambient energy levels, is it POSSIBLE to have a resolved
>image of a fractional electron?
Of course it is. Hadronic colliders do this all the time.
>
>Er, don't some HEP test smash electrons into pieces?
in some sense, but that's a terribly misleading way of describing what
happens.
--
======================================================================
Kevin Scaldeferri Calif. Institute of Technology
The INTJ's Prayer:
Lord keep me open to others' ideas, WRONG though they may be.
Charles Francis
They have no substructure. Their structure consists of the manner in
which they interact with photons.
> From what I have read, electrons are still
>considered point particles at today's colliders' energy levels. But
>wouldn't it be reasonable to suppose that electrons were composite
>particles, too? If hadrons consist of fractional charge thingies, oughtn't
>one to suppose that leptons do too?
>
>Doesn't the Standard Model consider leptons to be elementary particles?
Yes.
>Is
>there a simple to understand reason for this?
Dirac originally searched for a relativistic first order equation of
motion to describe a fundamental particle. He found only the Dirac
equation. Then we can conclude that particles which obey the Dirac
equation are actually fundamental.
Regards
--
Charles Francis
Maury Markowitz
> ``preons''.
Speaking of preons, can anyone give me a yeah/neah on "PREONS
Models of Leptons, Quarks and Gauge Bosons as Composite Objects"?
Maury
Maury Markowitz
news:tmtp3l9...@corp.supernews.com...
> I think this needs a bit of clarification. Consider that in our local
> region/energy density, ALL imagery is created, conveyed and communicated
in
> terms of whole electron units.
The issue isn't in terms of "whole/half electron units". You can do this
test without any measure of the units at all.
> Er, don't some HEP test smash electrons into pieces?
About a year ago right? Humphrey Maris's conclusions from a liquid-helium
experiment?
If it's the one I'm thinking of I remember reading the reasoning behind it
and thinking "this is completely bogus". Now of course I don't do this for a
living, and it's entirely possible that the entirely bogus part was horrid
simplification needed in order to get it into the form that I was reading.
Still, my BS detector was ringing loud. Here, you tell me:
"I found that the force exerted by the electron was enough to elongate the
bubble until it formed a thin neck," he says. "If the pressure in the liquid
was great enough, there was the possibility of it pinching off the neck so
that the bubble might actually split in two."
Ummm, ok.
There was also some work at KEK, but that was screening experiments and
nothing like fractional charge or anything.
Maury
Aaron Bergman
gdp...@NO.xnet.SPAM.com (Gordon D. Pusch) wrote:
> Many people have attempt to construct such ``composite'' theories (e.g.,
> the class of so-called ``technicolor'' models), but all have failed.
Technicolor is a composite Higgs theory as I remember it, not a
composite electron theory. They're pretty much ruled out by the lack of
appreciable FCNCs.
Aaron
Gerry Quinn
>
>No, there are no extensions like that. For instance, in the Standard
>Model, electrons and neutrinos form doublets of SU(2) symmetry. This
>symmetry cannot be "broken" in any way because it is a local gauge
>symmetry. A composite electron implies a composite neutrino, too.
>Neutrinos are almost massless and it is extremely difficult to imagine
>that they are composite particles. Such subparticles would probably have
>to be very light - but then their wavelength would be too large, it would
>determine the "size" of the electrons - and it would contradict the
>experiments. The experiments agree with the "point-like" Standard Model up
>to energies 1 TeV or so.
>
But surely one can always make the argument (at least above the Planck
scale) that for any given seemingly elementary particle, the
subparticles are heavy and the binding energy is high. Is it that
neutrinos are special because of neutrino oscillations, which presumably
involve any possible sub-particles and therefore speak against them
being 'locked' together in this fashion?
- Gerry Quinn
Matthew Nobes
> "Ralph E. Frost" <ref...@dcwi.com> wrote in message
> news:tmtp3l9...@corp.supernews.com...
[snip]
> > Er, don't some HEP test smash electrons into pieces?
>
> About a year ago right? Humphrey Maris's conclusions from a
> liquid-helium experiment?
>
> If it's the one I'm thinking of I remember reading the
> reasoning behind it and thinking "this is completely bogus".
> Now of course I don't do this for a living, and it's entirely
> possible that the entirely bogus part was horrid
> simplification needed in order to get it into the form that I
> was reading. Still, my BS detector was ringing loud. Here,
> you tell me:
>
> "I found that the force exerted by the electron was enough to
> elongate the bubble until it formed a thin neck," he says.
> "If the pressure in the liquid was great enough, there was
> the possibility of it pinching off the neck so that the
> bubble might actually split in two."
>
> Ummm, ok.
We had a talk on Maris' work a few months back by a student here
at SFU. I'm summerizing from mememory, but here's the essence of
it.
Maris' rigged it up so that the electron's wave function looked
like an ovoid
_______
/ \
| |
\_______/
Then, via some method, which I don't remeber, he managed to
``squeeze'' the wavefunction
__ __
/ \/ \
| |
\__/\__/
Then by increaseing the ``pressure'' via the misremebered
techniqe he managed to ``pinch'' the two lobes off.
__ __
/ \ / \
| | | |
\__/ \__/
I stress that up to this point, *nothing* here violates QM.
Maris invented a clever technique in order to do this, nothing
more. This result actually explains some prior experimental
anomlies IIRC.
The problem lies in Maris' interpretation of what he did. He
claims that he ``split'' the electron into two particles. (at
least, this is what was claimed in the popular press, and the
talk I saw). But as far as I can tell this both violates QM and
hasn't really been tested.
What conventional QM says is quite clear. The electron is now in
a superpostion state (albeit a bizzare one). Say I whip one of
these ``double bubble'' wavefunctions up, then send each bubble
off in different directions
<- B1 B2 -> X
Let's say I put a charge dector at the point marked by the X.
Conventional QM is very clear as to what will happen. Assumeing
a totally even ``split'' 50% of the time my detector will se
nothing, and the other 50% of the time it will see a charge e.
So in that sense the electron has not been ``split'' at all.
The popular reports seemed to be suggesting that Maris claims
that the detector will see 1/2e. I have no idea if they got his
postion correct or not. If they did then what he says violates
conventional QM, if they didn't then he hasn't really ``split''
the electron (though he did come up with an extremely clever way
to put it in a superposition state).
Maury Markowitz
> We had a talk on Maris' work a few months back by a student here
> at SFU. I'm summerizing from mememory, but here's the essence of
> it.
Excellent summary.
> Then, via some method, which I don't remeber, he managed to
> ``squeeze'' the wavefunction
> __ __
> / \/ \
> | |
> \__/\__/
>
> Then by increaseing the ``pressure'' via the misremebered
> techniqe he managed to ``pinch'' the two lobes off.
This is the basic problem I have. I'd like to avoid the debate on what the
wavefunction "is", but I can't think of any version of it that means that
it's physical and can be sqeezed. The wavefunction isn't a thing, the shape
of the wavefunction isn't physical. Regardless of the shape of the
wavefunction, the electron inside is still a point (after measurement).
It all comes down to this: what does it mean to squeeze a wavefunction? If
you apply pressure to the electron, the wavefunction changes en mass.
> Let's say I put a charge dector at the point marked by the X.
> Conventional QM is very clear as to what will happen. Assumeing
> a totally even ``split'' 50% of the time my detector will se
> nothing, and the other 50% of the time it will see a charge e.
> So in that sense the electron has not been ``split'' at all.
Right.
> The popular reports seemed to be suggesting that Maris claims
> that the detector will see 1/2e.
Yes, but his claim is based on something very different, the fact that the
charge transport rate increased. He explains this by suggesting that these
"double bubble" wavefunctions are 1/2 the size of the originals, and thus
they can move through the He faster than a single large one.
Let's put it this way, what's the difference between a wavefunction with
widely separated lobes, and what he's talking about from a experimental
standpoint? Nothing. If you take the copenhagen-ish approach to
understanding what the wavefunction means , then this split wavefunction is
no mystery at all, the electron is here or there. There doesn't seem to be
any reason to suggest it's a half electron, and I'd be surprised if there
was any way to tell the difference.
Of course this all rests on the interpretation that that bubble size the
electron forms in the He is indeed dependant on the shape of the
wavefunction. I can't say one way or the other.
Maury
Phil Gardner
> Phil Gardner <pej...@oznetcom.com.au> wrote:
>
> > Does the "evidence" that they are point particles include anything
> > more than the facts that:
> > (a) the cross-section for elastic scattering of electrons through
> > angles exceeding (say) pi/2 decreases without limit as the electron
> > energy is increased.
> > (b) in the last 70 years or more no-one has constructed a plausible
> > model of an extended electron with a mass-energy density that is
> > everywhere finite and continuous.
>
> "Point particle" is a phenomenological concept anyway.
> It means: particles that are described adequately
> by a theory containing no structure-related parameters.
>
> Jan
To any classical physicist the best available quantum mechanical
models provide no physical description at all of electrons and other
leptons, let alone an adequate one. They are very successful at
predicting a considerable range of experimental outcomes but that is
all. They can give no answer at all to such simple questions as:
How is the mass-energy of the particle distributed in space? Within
what radius is 50% of it contained?
Phil Gardner (pej...@oznetcom.com.au)
Phil Gardner
>
> There is a fundamental problem in that the ``natural'' energy scale for
> an object of size on the order of R is M*c^2 ~= (\hbar c) / R. The current
> experimental upper-bound on the sizes of an electron, muon, or `u' and `d'
> quark is less that 1e-18 m,
>
>
Do these meaurements of the "size of the electron" measure anything
more than the size of the scattering cross-section and how it varies
with the kinetic energy of the electron. What grounds have we for
assuming they tell us any more about the real size of the electron
than the Rayleigh scattering cross-section (one that goes to zero as
the photon energy) tells us about the size of a molecule or dielectric
sphere, ie nothing at all?
Phil Gardner <pej...@oznetcom.com.au>
Kevin A. Scaldeferri
Phil Gardner <pej...@oznetcom.com.au> wrote:
>nos...@de-ster.demon.nl (J. J. Lodder) wrote in message news:<1exqp5q.18i...@de-ster.demon.nl>...
>> Phil Gardner <pej...@oznetcom.com.au> wrote:
>>
>> "Point particle" is a phenomenological concept anyway.
>> It means: particles that are described adequately
>> by a theory containing no structure-related parameters.
>
>models provide no physical description at all of electrons and other
>leptons, let alone an adequate one.
I don't know what you mean by "adequate" if not:
> They are very successful at
>predicting a considerable range of experimental outcomes
At any rate, this is wrong:
> They can give no answer at all to such simple questions as:
>
>How is the mass-energy of the particle distributed in space? Within
>what radius is 50% of it contained?
The models claim the particles are pointlike.
Experiment tells us that the radius is less than 10^-18 m
Lubos Motl
> To any classical physicist the best available quantum mechanical
> models provide no physical description at all of electrons and other
> leptons, let alone an adequate one.
Well, most of the developments of 20th century physics would sound useless
or absurd to any "classical physicist". The energy of any radiation is
discrete; the atoms are stable; the electrons in atoms are described by
wave functions; time and space are perceived differently by observers in
relative motion. Fortunately, it is the classical physicist, not modern
physics, who is missing something. ;-) And modern physics also knows much
better which questions are well-defined and which questions are not.
> They are very successful at predicting a considerable range of
> experimental outcomes but that is all. They can give no answer at all
> to such simple questions as:
>
> How is the mass-energy of the particle distributed in space? Within
> what radius is 50% of it contained?
Well, similar questions have often a refined meaning in quantum field
theory; we can read answers from the correlators of the energy-momentum
tensor etc. While the electrons in path integrals etc. are truly
point-like, the correlators including quantum corrections show some
nontrivial smoothed behaviour at distances like the Compton wavelength and
the classical radius of the electron. But one would have to make the
question quantitative before we can deduce some quantitative answers. The
question formulated above neglects the uncertainty principle and does not
make much sense.
If we consider a state in the Hilbert space containing one electron, we
cannot localize it to a space smaller than the Compton wavelength and
therefore the expectation value of the energy density will be distributed
over a comparable volume and will depend on the precise shape of the wave
packet. A more localized idea about the "shape" of the electron's mass
density can be calculated from electron-graviton scattering.
Lubos Motl
> But surely one can always make the argument (at least above the Planck
> scale) that for any given seemingly elementary particle, the
> subparticles are heavy and the binding energy is high.
Yes, there exists a limited possibility of heavy fundamental particles
whose binding energy is huge and negative and therefore the resulting
composite particle is light. This possibility requires a strongly coupled
theory. For example, pieces of string have essentially Planckian mass and
the cancellations between the kinetic energy and the tension of the string
(one of them can be negative due to the quantum zeta function miracles)
can lead to exactly massless particles (such as the photon) or
approximately massless ones (such as the electron); see the Chapter 6 of
The Elegant Universe. ;-)
But this logic is not true in theories similar to QCD. If the concept of
"partons" is meaningful, they should be weakly coupled at some scale. In
the case of QCD, this is the QCD scale 300 MeV corresponding to the
distances 1 fermi or so (the size of a small nucleus etc.). It is the same
scale that determines both the size (1 fermi) and the mass (1 GeV) of the
composite particles (such as the proton). All the scales agree, everything
is natural. Proton's mass is what you expect from such an interaction that
becomes weakly coupled at sub-fermi distances.
I wanted to say that a corresponding "compositeness scale" in the case of
electrons must be greater than approximately 1 TeV - because we know that
they look point-like (as in QED) at distances 10^{-18} meters. Then it is
extremely unnatural to get particles as light as electrons and especially
neutrinos (fractions of eV) from such a theory that is strongly coupled at
all the distance scales longer than 10^{-18} meters, a scale corresponding
to 1 TeV. This would require a cancellation which is extremely unlikely in
the case of quantum field theories.
Compositeness is fine, but in the case of electrons and neutrinos,
compositeness from several point-like subparticles is unreasonable. The
capacity of this simple paradigm has been exhausted. We must study strings
to see deeper into the particles that we call "elementary" today.
J. J. Lodder
> To any classical physicist the best available quantum mechanical
> models provide no physical description at all of electrons and other
> leptons, let alone an adequate one. They are very successful at
> predicting a considerable range of experimental outcomes but that is
> all. They can give no answer at all to such simple questions as:
> How is the mass-energy of the particle distributed in space? Within
> what radius is 50% of it contained?
Guess I should take you up on that:
The classical theories of the electron did not do anything like that
either. For the state of the art you should consult:
H. A. Lorentz: "Theory of Electrons"
(last decades of the 19th century, final form ą 1905)
(real heavy stuff; never underestimate the ancient massters :-)
More up to date textbooks, Jauch's for example,
are easier going, but do not added major conceptual advances.
Lorentz considered extended electrons, with an assumed charge
distribution, and calculated it all using Maxwell's eqns,
including the selfinteractions,
and inventing the Lorentz transformations on the way.
Next L. dealt with the classical divergencies
like in the 'modern' renormalization group methods:
keep only terms independent of the assumed charge distribution
to obtain the physically relevant observable term,
like electromagnetic mass, mass dependence on velocity, etc.
And he obtained the correct result for the mass/velocity relation first,
which was originally known as the Lorentz-Einstein mass formula.
As far as physics is concerned there is no difference
between 'real' point particles and particles with a structure
that is far too small to observe.
Best,
Jan
Jim Carr
in message news:<3B69516A...@mitre.org>...
}
} Do electrons have structure? From what I have read, electrons are still
} considered point particles at today's colliders' energy levels.
In article <744cb7cd.01080...@posting.google.com>
>
>Does the "evidence" that they are point particles include anything
>more than the facts that:
>(a) the cross-section for elastic scattering of electrons through
>angles exceeding (say) pi/2 decreases without limit as the electron
>energy is increased.
>(b) in the last 70 years or more no-one has constructed a plausible
>model of an extended electron with a mass-energy density that is
>everywhere finite and continuous.
Yes.
It includes the fact that the energy and momentum transfer
dependence of scattering data agree (to within experimental
uncertainties) with the predictions of QED without any need
for a size correction (called a form factor). This is much
more than the qualitative statement you gave, and places
a quantitative limit around 10^{-18} m for substructure.
It also inlcudes plausible models (some named in other replies),
but you do not need a model to measure a model-independent
quantity like a form factor.
--
James Carr <j...@scri.fsu.edu> http://www.scri.fsu.edu/~jac/
SirCam Warning: read http://www.cert.org/advisories/CA-2001-22.html
e-mail info: new...@fbi.gov pyr...@ftc.gov enfor...@sec.gov
John Baez
Ralph E. Frost <ref...@dcwi.com> wrote:
>Er, don't some HEP tests smash electrons into pieces?
No: if they did, we wouldn't all be telling you that there's
no evidence for substructure in electrons!
John Baez
Matthew Nobes <man...@sfu.ca> wrote:
>Maris rigged it up so that the electron's wave function looked
>like an ovoid
_______
/ \
| |
\_______/
>Then, via some method, which I don't remember, he managed to
>``squeeze'' the wavefunction
__ __
/ \/ \
| |
\__/\__/
>Then by increaseing the ``pressure'' via the misremembered
>technique he managed to ``pinch'' the two lobes off.
__ __
/ \ / \
| | | |
\__/ \__/
>I stress that up to this point, *nothing* here violates QM.
>The problem lies in Maris' interpretation of what he did. He
>claims that he ``split'' the electron into two particles.
Ugh! I guess he just wanted to get on the front cover of
some popular science magazines. Do an experiment, get the
result quantum mechanics predicts... but then make up a completely
crazy way of explaining it in words, and you can have your
15 minutes of fame. It seems by now to be an established
technique - for example, all the results which supposedly
demonstrate "superluminal communication", but which actually
rely on the confusion between group velocity, phase velocity
and signal velocity:
http://www.netspace.net.au/~gregegan/APPLETS/20/20.html
As long as reporters keep falling for scientists who try to
make their work sound cooler than it is, certain scientists
will keep doing it.
John Baez
Aaron Bergman <aber...@Princeton.EDU> wrote:
>Technicolor is a composite Higgs theory as I remember it, not a
>composite electron theory. They're pretty much ruled out by the lack of
>appreciable FCNCs.
What the f**k is a FCNC?
Frederick Seelig
Jim Carr wrote:
[snip]
> It includes the fact that the energy and momentum transfer
> dependence of scattering data agree (to within experimental
> uncertainties) with the predictions of QED without any need
> for a size correction (called a form factor). This is much
> more than the qualitative statement you gave, and places
> a quantitative limit around 10^{-18} m for substructure.
>
> It also inlcudes plausible models (some named in other replies),
> but you do not need a model to measure a model-independent
> quantity like a form factor.
Jim,
Current experimental evidence aside, would you care to speculate
on what physicists in 10 or 50 years will see? In 2050, will we
be taught that electrons are still point particles? Or will they
have substructure? What do you guess?
Fred
Aaron J. Bergman
Flavor Changing Neutral Current. The bane of all attempts to go beyond
the standard model.
And I might be wrong about the last statement, too. It might be that
technicolor is ruled out by neutron dipole moment experiments. I can't
remember now. It's probably both, although (does some checking)
hep-ph/0007304 seems to lean towards FCNCs, but I only glanced. It's a
shame that technicolor is pretty much ruled out, though -- it's quite
the pretty theory.
Aaron
--
Aaron Bergman
<http://www.princeton.edu/~abergman/>
Jeff Berryhill
Flavor Changing Neutral Current interactions, usually pertaining to
quarks. The experimental data regarding them severely restrict any
kind of model which directly connects two up-like quarks (or two
down-like quarks) of differing flavors. Examples of FCNC phenomena
are
K^0, B^0, or D^0 mixing
K^0, D^0 or B^0 \rightarrow \ell\ell
B \rightarrow K^* \gamma or \rho \gamma
D \rightarrow \rho \gamma
B \rightarrow K^* \ell\ell or \rho \ell\ell
\mu \rightarrow e \gamma is an FCNC involving leptons.
In the standard model the quark flavor transitions b to d, b to s, c
to u, t to c, etc., are forbidden at tree level but they can sneak in
via second order electroweak diagrams like "boxes" and "penguins"
(don't ask me to draw one in ASCII). Being second order in the
electroweak coupling, the standard model rates are quite small, so
*any* new physics which introduces FCNCs at tree level will
substantially enhance the rates above the SM predictions, even if it's
suppressed by some large mass scale, as high as tens of TeV.
Lots of mesons of the types listed above have been produced and
studied in laboratories, and no deviations from SM predictions have
been observed. Charged higgses, technimesons, squarks, just about any
physics beyond the standard model may contribute to FCNCs and so
phenomenologists have to go through all kinds of (otherwise
unmotivated) contortions to evade the experimental constraints placed
by FCNCs. They're a very powerful probe of the electroweak scale.
--Jeff Berryhill
Paul D. Shocklee
Flavor-Changing Neutral Currents.
Like s -> d + X^0.
--
Paul Shocklee
Graduate Student, Department of Physics, Princeton University
Researcher, Science Institute, Dunhaga 3, 107 Reykjavik, Iceland
Phone: +354-525-4429
Kevin A. Scaldeferri
Flavor changing neutral current
And, while the above it true of the most simple technicolor models,
the proponent of technicolor are as clever as any one else about
finding variations that aren't ruled out.
John Baez
Moataz Emam <em...@physics.umass.edu> wrote:
>The only known reasonable theory of electronic structure is within the
>context of String theory, where electrons are extended strings in
>spacetime. That is only apparent on the level of the Planck energy, or
>length scale, about 10^-33 cm.
I consider preon models to be almost as reasonable as string
theory, and in these models, quarks and leptons are bound states of
"preons", with compositenss becoming manifest at length scales
far exceeding the Planck length. Sure, preon models have their
problems, but so does string theory! Anyway, my point is not to
advocate these models so much as to remind people of their existence.
They are not popular these days, but they do have their charms.
One can probably read about them in Mohapatra's or Ross' books on
grand unified theories.
Matthew Nobes
Flavour changing neutral current.
Ralph E. Frost
news:9lrvam$gdj$1...@glue.ucr.edu...
What was I thinking? Gellman said things are made of quarks, electrons, and
photons. I guess he must have meant there were structured out of quarks,
electrons and photons, huh?
Oops, what are the neutrino things then, debris that's caught in
back-eddies?
Lubos Motl
> I consider preon models to be almost as reasonable as string
> theory, and in these models, quarks and leptons are bound states of
> "preons", with compositenss becoming manifest at length scales
> far exceeding the Planck length.
Preon models are simple quantum field theories based on a simple idea that
leptons, quarks and even gauge bosons (!!) can be composite particles. All
of them should compose of spin-1/2 preons. There is nothing such as "preon
theory". This class of models does not contain gravity; they look less
natural than the Standard Model itself. The models not solve a single
serious problem of physics today - with a possible exception of the chance
to explain some hierarchies in QFT. As far as I know, they essentially do
not offer anything that the Standard Model cannot. In my opinion, it
sounds funny to compare the preon proposal with string theory. To see how
unrealistic and unorthodox the models are, see
http://arXiv.org/abs/hep-ph/9909569
> Sure, preon models have their problems, but so does string theory!
No, you certainly cannot compare them.
> Anyway, my point is not to
> advocate these models so much as to remind people of their existence.
> They are not popular these days, but they do have their charms.
Could you please write more details about the charms that they are
supposed to have? Your text seems as another attempt to spread the
illusion that string theory is not the unique path to unification -
without having any evidence whatsoever. But string theory probably *is*
the unique path. Preons are something close to technicolor and they share
similar problems; the absence of realistic models is an important example.
String theory certainly do not suffer from a similar kind of troubles.
Toby Bartels
>What was I thinking? Gellman said things are made of quarks, electrons, and
>photons. I guess he must have meant there were structured out of quarks,
>electrons and photons, huh?
>Oops, what are the neutrino things then, debris that's caught in
>back-eddies?
2 possibilities:
* Gell-Mann was being elliptical,
listing only *examples* of the items that things are made of.
Besides quarks, electrons, photons, and neutrinos, the list includes
muons, tauons, gluons, and W, Z, and Higgs bosons,
as well as presumably something along the lines of gravitons.
So far, it appears that none of these have substructure.
* Gell-Mann was talking only about ordinary things.
To a high level of precision, the number of
neutrinos, muons, tauons, and W, Z, and Higgs bosons
in ordinary matter is 0.
Even among quarks, only 2 of the 6 flavours show up significantly.
He could easily have left out gravitons as too speculative.
However, this possibility doesn't explain his omission of gluons,
which are quite common in ordinary stuff.
-- Toby
to...@math.ucr.edu
Lubos Motl
> Er, don't some HEP tests smash electrons into pieces?
HEP experiments can smash one positron and a single electron (with a very
huge energy) and produce 25 protons, 20 antiprotons, some neutrons,
neutrinos, pions etc. If this event does not violate the universal laws
(conservation of momentum, angular momentum, energy and the electric
charge), essentially anything is possible. But this fact does not imply
that electrons are made of 25 protons etc. If we want to say that a
particle is made of some constituents, there should be a way to see them.
For example the deep inelastic scattering experiments "proved" quarks
inside nucleons.
Ralph E. Frost
Lubos Motl <mo...@physics.rutgers.edu> wrote in message
news:Pine.SOL.4.10.101082...@strings.rutgers.edu...
> John Baez:
> > I consider preon models to be almost as reasonable as string
> > theory, and in these models, quarks and leptons are bound states of
> > "preons", with compositenss becoming manifest at length scales
> > far exceeding the Planck length.
> Preon models are simple quantum field theories based on a simple idea that
> leptons, quarks and even gauge bosons (!!) can be composite particles. All
> of them should compose of spin-1/2 preons. There is nothing such as "preon
> theory". This class of models does not contain gravity; they look less
> natural than the Standard Model itself. The models not solve a single
> serious problem of physics today - with a possible exception of the chance
> to explain some hierarchies in QFT. As far as I know, they essentially do
> not offer anything that the Standard Model cannot. In my opinion, it
> sounds funny to compare the preon proposal with string theory. To see how
> unrealistic and unorthodox the models are, see
How come the same can't be said for the standard model of, um, a couple
months ago before it began to SNO? HOW did it describe neutrinos??
I think, given the massive intellectual deposits into the string theory
account, that if someone was going to pull the rabbit out of that hat,
they would have done it by now. It's been several dog-years since Gellman
suggested it was the last great hope for the traditionalists.
Also, I am not too sure that striving to maintain agreement with the
standard model is a wise objective function. Or, did string theory predict
the neutrino "oscillation"/massness BEFORE it was measured?
More likely, given that all the less unified models (aka the traditional
imagery) do not BEGIN with a primary overt tenet that says, "things are
unified", there is rough sledding ahead for SM version xx++ die-hards.
The one world, many descriptions model image sort of guarantees that string
theory must be, or have been useful in the overall transition, but to make
more of it seems presumptuous when staring at such a dearth of, you know,
things that jibe with experiment.
Oops, I guess the same can be said about the prior version of the standard
model (again) (and again.) (..).
Let me guess. You disagree.
> http://arXiv.org/abs/hep-ph/9909569
> > Sure, preon models have their problems, but so does string theory!
> No, you certainly cannot compare them.
> > Anyway, my point is not to
> > advocate these models so much as to remind people of their existence.
> > They are not popular these days, but they do have their charms.
> Could you please write more details about the charms that they are
> supposed to have? Your text seems as another attempt to spread the
> illusion that string theory is not the unique path to unification -
> without having any evidence whatsoever. But string theory probably *is*
> the unique path. Preons are something close to technicolor and they share
> similar problems; the absence of realistic models is an important example.
> String theory certainly do not suffer from a similar kind of troubles.
Life is hard. We all got our problems, don't we?
Do you ever think about synthesizing? I happen to think that's where the
useful trial is. As for there being a "unique trail", I ain't no
mathematician, but even I know there isn't only one unique trail. There is
the <first> trail. There is the <first> really helpful, popular trail. But
there is not just the singular trail.
I feel certain you are aware of that.
John Baez
Lubos Motl <mo...@physics.rutgers.edu> wrote:
>John Baez:
>> I consider preon models to be almost as reasonable as string
>> theory, and in these models, quarks and leptons are bound states of
>> "preons", with compositeness becoming manifest at length scales
>> far exceeding the Planck length.
>In my opinion, it sounds funny to compare the preon proposal with
>string theory.
Of course I said this mainly to see how you'd respond...
but I also had some other reasons, too.
>To see how unrealistic and unorthodox the models are, see
>
> http://arXiv.org/abs/hep-ph/9909569
I'm not sure why you picked this particular model to talk about -
as far as I know, it's not one of the most popular ones. Did you
pick it just because it seems weird? That wouldn't be very fair...
Anyway:
To me, being "unorthodox" is fine - we'll never figure out
the fundamental laws of physics by trying to be "orthodox".
On the other hand, being "unrealistic" is not good. You'll have
to explain to me why the above preon model is unrealistic: I've
never seen this one before, so it would take me a while to see
what physical predictions it gets wrong.
(I assume by saying that a theory is "unrealistic" you mean
that it makes wrong predictions. If you mean something else,
please explain what you mean.)
>> Sure, preon models have their problems, but so does string theory!
>No, you certainly cannot compare them.
Of course the two are very different. String theory is much more
ambitious: it's trying to explain gravity along with the forces
and particles in the Standard Model, and it's trying to be a
"theory of everything", good to arbitrarily high energy scales -
or the string energy scale, whichever comes first. To live up
to what's claimed for string theory, it needs to be pretty much
perfect. Preon models are only trying to serve as a next step
after the Standard model, and they're only trying to handle
physics up to energies of roughly 100 TeV or so. They're not
supposed to be the last word in physics. So, the demands we're
entitled to make on string theory are much higher.
But my point was that as theories of "what happens in particle
physics after the Standard Model", both preon models and string
theory have their problems. The problems of string theory are
well-known. For example:
1) Despite decades of work and over ten thousand papers on the
subject, string theory has not made a single experimentally
verified prediction. One reason is that:
2) There are zillions of different perturbative superstring vacua,
giving zillions of different theories of real-world particle physics.
Nobody knows which one is right, so we cannot use string theory to
make specific predictions about particle physics at low energies.
All we get for sure are very general results such as: there are
forces described by gauge fields, fermions have spin 3/2 or less...
and the following more surprising thing:
3) String theory predicts that every boson has a corresponding fermion
of the same mass! This is clearly wrong. The only way out is for
supersymmetry to be spontaneously broken. Unfortunately, nobody
understands how this works. For this reason, anyone wishing to use
string theory to make predictions about particle physics must break
supersymmetry "by hand" - that is, by penciling in dozens of "soft
supersymmetry breaking terms" in the field theories that arise as
low-energy limits of string theory.
Preon models also have their problems, and they are certainly far
less pretty than string theory. However, given the above problems of
string theory, it is far too soon to rule out alternatives like preon
models.
>> Anyway, my point is not to
>> advocate these models so much as to remind people of their existence.
>> They are not popular these days, but they do have their charms.
>Could you please write more details about the charms that they are
>supposed to have?
Sure! I'll start with something nontechnical that all the lurking
layfolkd can enjoy, and then mention a couple of more technical things.
First of all, everyone who has ever thought about particle physics
has wondered this:
"Molecules are made of atoms,
atoms are made of electrons and nuclei,
nuclei are made of protons and neutrons,
protons and neutrons are made of quarks and gluons....
what if it keeps on going like this?"
In fact, back when I used to read sci.physics, it seems like I'd
see a post about this every few months! For some reason the
people who post these articles usually jump to the conclusion
that particle physics is futile - a silly conclusion, in my view.
The universe is the way it is, and no matter how it is, we should
try to understand it!
Anyway, preon models are an attempt to study the possibility that
the "elementary" particles we know and love are built from more
basic constituents. I am glad people are looking into this sort
of scenario.
Of course, such a scenario is irritating if you want to jump from
the Standard Model to the theory of everything in one fell swoop!
However, there is no terribly strong reason to think this "one
fell swoop" approach is bound to work. It's an incredible
extrapolation which could easily fall flat on its face. So,
we should hedge our bets and also consider alternatives.
More technically, here is a preon model whose charm should
be visible by any particle physicist. I think this one was
cooked up by Pati, Greenberg and Sucher. (I'm no expert on
this stuff and all I know comes from the books on grand unified
theories by Rabindra Mohapatra and Graham Ross.)
The idea here is to lump all the fermions in a given generation into
a single irrep of SU(4) x SU(2) x SU(2). For example:
(u_R u_G u_B nu_e)
(d_R d_G d_B e )
The SU(4) group acts to mix up the columns of this matrix in the
obvious way. There's an obvious SU(3) subgroup mixing up the
red, green and blue quarks; this is the usual strong force SU(3).
But there are also transformations that mix up the quarks and leptons.
Thus, in this model, the distinction between quarks and leptons
arises from the spontaneous breaking of the symmetry from SU(4)
down to SU(3).
The two copies of SU(2) act to mix up the rows. To see how
this works, we need a more detailed picture of the above matrix,
where we separate out the left-handed and right-handed fermions.
We get a picture like this:
(u_r u_g u_b nu_e) <--
LEFT-HANDED QUARKS AND LEPTONS
(d_r d_g d_b e ) <--
(u_r u_g u_b nu_e) <--
RIGHT-HANDED QUARKS AND LEPTONS
(d_r d_g d_b e ) <---
We have one copy of SU(2) acting on the left-handed guys in
the obvious way, another acting on the left-handed ones.
Thus, in this model, the chiral nature of the weak force
arises from the spontaneous breaking of the symmetry from
SU(2) x SU(2) down to the left-handed copy of SU(2).
Now, I think this SU(2) x SU(2) x SU(4) theory goes back to
Pati and Salam in 1974. The new twist in the preon model is
to build the above fermions as bound states of more fundamental
fermions and bosons. The idea is to have the more fundamental
fermions transform nontrivially only under SU(2) x SU(2), and
the bosons under SU(4). The fermions look like this:
F_u <--- LEFT-HANDED "UP" FERMION
F_d <--- LEFT-HANDED "DOWN" FERMION
F_u <--- RIGHT-HANDED "UP" FERMION
F_d <--- RIGHT-HANDED "DOWN" FERMION
That is, they lie in C^2 x C^2 and transform under SU(2) x SU(2)
in the obvious way. The bosons look like this:
(B_r B_g B_b B_l)
and transform under SU(4) in the obvious way. Thus, bound states
consisting of one fermion and one boson will transform under
SU(4) x SU(2) x SU(2) in exactly the way that quarks and leptons do!
Of course, we need something to bind our fundamental fermions
and bosons together. We can do this with an SU(N) gauge field,
analogous to the strong force and usually called "technicolor",
which confines particles together in technicolor-neutral bound
states, just as the strong force binds quarks into hadrons.
To do this, we should make our F and B particles transform under
the fundamental representation of SU(N) and its dual, respectively.
They will then bind together in pairs - one F with one B - a bit
like how a quark and antiquark bind together to form a meson.
In short, besides our F and B particles, we have SU(N) gauge fields
carrying the technicolor force as well as SU(4) x SU(2) x SU(2)
gauge fields carrying the rest of the forces.
There is more to say about how the spontaneous symmetry breaking
goes, but I think I'll stop here.
Now: my point is *not* that I think this model is correct. My
point is just that particle physicists should continue to tinker
with such models, along with many other possibilities - including
string theory.
>Your text seems as another attempt to spread the
>illusion that string theory is not the unique path to unification -
>without having any evidence whatsoever.
String theory is obviously NOT the unique path that people are
taking in the attempt to understand the real world of particle
physics. Whether it's the unique path that succeeds, or whether
it succeeds at all, only time will tell. Once any theory starts
making predictions that are verified by experiments, you can be
sure that everyone will fall in line with that one! But in the
meantime we need people taking all sorts of different paths and
reporting back from time to time on how they're doing. In fact,
there *are* people taking all sorts of different paths, so all
we need to do is read about what they've done. It's not hard to
do, and it's actually fun.
Aaron J. Bergman
>But in the
>meantime we need people taking all sorts of different paths and
>reporting back from time to time on how they're doing. In fact,
>there *are* people taking all sorts of different paths, so all
>we need to do is read about what they've done. It's not hard to
>do, and it's actually fun.
I was bored the other day (there's frightfully little interesting stuff
in strings these days...) and was looking at the first few papers to
show up on lanl. I found this:
hep-th/9109002
The second paragraph of the introduction, in particular. The more things
change....
Ralph E. Frost
Er, pardonne moi, but aren't electrons known and proven to exist as both
particles and waves?
theos ek mechanes
I started...particularly, the final sentence of the second paragraph
of the introduction...
"As I will describe, there are indications that quantum GR provides
a natural cut-off at the Plank scale."
Best
aber...@Princeton.EDU (Aaron J. Bergman) wrote in message news:<slrn9otr7h....@phoenix.Princeton.EDU>...
Charles Francis
<ref...@dcwi.com> writes
No. That is a matter of interpretation. Bohr tried to interpret
electrons as having both a particle and a wave nature, and many
physicists have followed him. But more strictly according to Heisenberg
the Copenhagen interpretation does not include wave-particle duality,
and the apparent wave structure is a reflection of the fact that
particle properties are poorly described in terms of the description of
classical macroscopic apparatus, and states in quantum mechanics
describe our knowledge of the particle, not the particle itself.
Von-Neumann and Dirac both followed this version, without wave-particle
duality. As does Feynman, who in QED seems very clear in his own mind
that we are studying particles, and that wave mechanics is just
something we don't know how to explain at the moment.
Regards
--
Charles Francis
Lubos Motl
> > http://arXiv.org/abs/hep-ph/9909569
> I'm not sure why you picked this particular model to talk about -
> as far as I know, it's not one of the most popular ones. Did you
> pick it just because it seems weird? That wouldn't be very fair...
No, I've picked this paper because I believe that it is one of the most
up-to-date papers about the preon idea.
> To me, being "unorthodox" is fine - we'll never figure out
> the fundamental laws of physics by trying to be "orthodox".
I disagree. In 50% of cases, the puzzles in physics are finally solved by
insisting on a well-established principle; of course, another paradigm
must be abandoned at the same time. Special relativity solved the paradox
of Morley-Michelson's experiments by insisting on the principle of
relativity, as first understood (although in a more classical context) by
Galileo. The black hole entropy has been finally explained microscopically
fully within the framework of orthodox quantum mechanics although many
people were speculating how quantum mechanics could be altered or
generalized because of this problem. And string theory itself is an
extremely orthodox theory that supports essentially everything we knew
before.
Preons are not orthodox in the sense that they organize particles in a
different way than the way that has been established in the Standard Model
(or GUT theories). An economical preon model does not seem to fit
together. The orthodox spectrum of particles, as described by the Standard
Model, is not naturally explained the by the preon models. This contrasts
with the situation of string theory because despite the stringy character,
the particle spectrum predicted from the stringy vibrations coincides -
for a suitable choice of the compactification manifolds etc. - with the
well-known facts.
I wanted to say that the spectrum of bound states of preons is typically
not the same as the spectrum of 3 generations of the Standard Model. In
this sense, preons are not orthodox and it is a bad characteristic: they
smell wrong; they do not unify anything we know and a natural approach is
to cut them off by Occam's razor.
> On the other hand, being "unrealistic" is not good. You'll have
> to explain to me why the above preon model is unrealistic: I've
> never seen this one before, so it would take me a while to see
> what physical predictions it gets wrong.
The prediction of nine quarks, nine leptons and nine heavy vector bosons -
see the paper hep-ph/9909569 - sounds realistic to you? Could you please
show us a preon model with realistic predictions - for instance a model
that contains 3 families of quarks and leptons?
> (I assume by saying that a theory is "unrealistic" you mean
> that it makes wrong predictions. If you mean something else,
> please explain what you mean.)
Yes, by "unrealistic" I meant that it makes wrong predictions, at least if
they are interpreted in the most natural way. The prediction that the
number of generations must be square of an integer - is a wrong
prediction, in my opinion. ;-)
> Preon models are only trying to serve as a next step
> after the Standard model, and they're only trying to handle
> physics up to energies of roughly 100 TeV or so.
The problem is that the claim that everything should be made of spin 1/2
particles is not well-justified. A spin 1 fundamental particle is equally
natural and fine as a spin-1/2 particle (and I would say the same about
the spin 0 Higgs fields, too). Furthermore there are millions of different
possibilities how a new QFT physics beyond a TeV could look like. Preon
models are just an accidental guess which is equally unjustified as the
other unjustified guesses.
In other words, a specific preon model is almost certainly wrong. I don't
understand why physicists should study accidentally chosen theories that
explain nothing new.
> 1) Despite decades of work and over ten thousand papers on the
> subject, string theory has not made a single experimentally
> verified prediction. One reason is that:
It has been explained in detail that this is a problem that all particle
physicists (and their colleagues from related fields) share. It is nothing
specific for string theory: no theory beyond SM could have given us a
verified new prediction simply because experimentalists - mostly because
of the state of the current technology - have not been able to construct a
single experiment that would disagree with the Standard Model (or General
Relativity, in the context of the large distance scales).
>From its philosophy, it is clear that string theory is ultimately able to
predict everything and contains no adjustable parameters etc. Our present
understanding is however not ready to solve the vacuum selection problem.
This is one of the reasons why people should *work* on string theory. The
problem is mainly because we do not have a formulation that is both
nonperturbative and background-independent so that the vacuum selection
could be studied accurately enough.
> 2) There are zillions of different perturbative superstring vacua,
> giving zillions of different theories of real-world particle physics.
> Nobody knows which one is right, so we cannot use string theory to...
Either this point means absolutely the same as 1) - and you were just
trying to sell one cent for two cents - or 1) was wrong. There are of
course general predictions of string theory that do not depend on the
vacuum: for example thermodynamical properties of the black holes. Another
quite general example is your point 3) - which BTW shows that your
paragraphs contradict each other.
> 3) String theory predicts that every boson has a corresponding fermion
> of the same mass! This is clearly wrong. The only way out is for
> supersymmetry to be spontaneously broken. Unfortunately, nobody
> understands how this works. For this reason, anyone wishing to use
If you open the volume II of Joe's book "String Theory" and look for
"supersymmetry breaking" in the index, you will be impressed how many
pages of basic material you have absolutely no idea about. Literature
about SUSY breaking is vast - and I have published a very basic
introduction a few months ago. The problem that we do not know how SUSY is
broken in the real world is a part of the general problem 1) (1=2 in your
conventions). There are also related problems - such as the cosmological
constant problem: why is Lambda so small even after SUSY breaking and does
not acquire something of the order m_{SUSY-breaking}^4? ;-)
> string theory to make predictions about particle physics must break
> supersymmetry "by hand" - that is, by penciling in dozens of "soft
> supersymmetry breaking terms" in the field theories that arise as
> low-energy limits of string theory.
This interpretation is incorrect. In many models, including "ordinary and
simple" quantum field theories, it is well understood that SUSY can be
spontaneously broken - and this breaking can be described from the
fundamental principles. There can be a gaugino condensate (usually in the
hidden sector), for example, and it is as simple as a chiral symmetry
breaking in QCD, for instance: a bilinear expression in gaugino fields
gets a VEV.
Those gauginos etc. have many interactions with the other fields; they are
often indirect, via a mediator (dilaton-mediated, anomaly-mediated,
gravity-mediated SUSY breaking etc.). At low enough energies, the effect
of the broken SUSY in the hidden sector manifests itself by the soft
(relevant) SUSY breaking terms; it is a general rule of QFT to study the
most general theory with the given degrees of freedom and symmetries.
Those are precisely the terms that do not spoil some nice UV properties of
supersymmetry such as the cancellation of the quadratic divergences of the
Higgs self-energy.
But if you know the fundamental theory completely, all those terms are
calculable (at least in principle)! Only because this problem is currently
too difficult (in string theory as well as in simpler models), we must put
all the terms that can be generated with free coefficients. This is why
MSSM has over 100 parameters (compared to 19 parameters of SM) although we
would expect that the freedom should decrease with SUSY (that relates
properties of superpartners).
> Preon models also have their problems, and they are certainly far
> less pretty than string theory. However, given the above problems of
> string theory, it is far too soon to rule out alternatives like preon
> models.
I still do not understand in what sense they are alternatives to each
other. Quantum gravity? Certainly not; preons are not capable to do it.
Physics just beyond the Standard Model? In this respect, they are not
alternatives either. If you had a good enough preon model, you could
almost certainly embed it into string theory, too - for instance, if the
Pati-Salam-like preon model worked, it could be embedded in string theory.
But it does not, especially because of the problem of 3 families.
If I simplify the issue a little bit, the previous sentence is true by
definition because a good idea in physics is defined as something that is
contained in string theory. ;-) Preons of a good enough preon model could
be probably visualized as some vibrations of strings in a new "preonic"
vacuum of string theory. The fact that string theory probably does not
contain any vacuum where gauge bosons are composites of a few spin 1/2
particles (a few strings) can be viewed as a signature that the preon idea
is not so good.
History has taught us that almost every quantum field theory that had some
charms - and no deadly anomalies - was a low energy limit of string
theory. The eleven-dimensional supergravity was a beautiful QFT, for
example. It turned out that it is a low energy description of M-theory,
the only 11-dimensional limit of string theory (in the broad sense).
> Sure! I'll start with something nontechnical that all the lurking
> layfolkd can enjoy, and then mention a couple of more technical things.
>
> First of all, everyone who has ever thought about particle physics
> has wondered this:
>
> "Molecules are made of atoms,
> atoms are made of electrons and nuclei,
> nuclei are made of protons and neutrons,
> protons and neutrons are made of quarks and gluons....
> what if it keeps on going like this?"
Then it's ugly. The whole charm of a useful theory is to stop this
sequence that can be a priori infinite. And the Planck scale is quite
certainly the ultimate cutoff. If de Broglie's wavelength is smaller than
Planck length, the object must be heavier than the Planck mass and
therefore cannot be smaller than the Planckian radius of the Planckian
black hole: distances smaller than Planck length don't exist.
You know, the idea that the hierarchy keeps going is due to V.I.Lenin and
probably even someone older. The name of the author is not why the reason
why I think that the idea is anti-scientific.
Furthermore, some particles have been known to be elementary for more than
a century - namely electrons and photons. The process of "deconstruction"
was successful in the case of strongly interacting particles because there
were so many (hundreds) of them. But there is only one photon and one
electron - or three of them, if we count muon and tau - and this fact does
not offer much freedom for some more elementary constituents. If something
had many constituents of many kinds, there would be many different "bound
states" that you can construct. But two electrons are known for sure to be
absolutely identical - for example because of the cross channels
contributing to the electron-electron scattering.
You can also suggest the idea that muon and tau are excited states of an
electron. Good but the question is whether you can construct an
interesting theory of this kind. Such a theory should be able to compute
the ratio of muon and electron masses, for example. Of course, none has
done anything like that. Muon and tau seem to be independent from
electron. In string theory, three different generations come from the
multidimensional "holes" of the hidden dimensions.
> The universe is the way it is, and no matter how it is, we should
> try to understand it!
But you should also understand the other side of this sentence: the
Universe is not the way it is not :-), and no matter how it is not, we
should not waste most of our time to understand how it is not done! :-)
> Anyway, preon models are an attempt to study the possibility that
> the "elementary" particles we know and love are built from more
> basic constituents.
Nope. Preon models constitute a much narrower class of models that assume
that all the particles must be made of fundamental spin 1/2 particles and
no known particle is allowed to be elementary (it would be probably too
boring for the authors). ;-)
> I am glad people are looking into this sort of scenario.
No problem. Someone likes chaos, someone does not like it too much. There
are many stories about possible physics smaller than electron, including a
civilization of little green men (with their techni-preon-DNA code) inside
electrons. I am personally not glad when physics is becoming an unlimited
arena of thousands speculations contradicting to each other. It is fine
that those ideas have been tried - but one should be able to admit a
failure at the right moment. Technicolor and preons can be a priori
interesting ideas but their technical realization does not seem to bring
both realistic and interesting results; preons generally predict wrong
(dis)organization of particles into non-3 families. We should be ready
that sometimes we will be forced to return to something similar - but I
think it is completely fair if a physicist thinks about those models
tentatively as about models that have been ruled out.
String theory is just the other way around. The starting point can sound
relatively uninteresting, but if you sit and try to calculate, you
discover all those miracles. This is why string theory is interesting. It
gives us more than we put in. In the case of preon models, the first idea
- summarized in a short sentence - is the biggest treasure. If you start
to calculate something technically, the successes slowly disappear. This
is why it probably is a wrong track, just like many others.
> Of course, such a scenario is irritating if you want to jump from
> the Standard Model to the theory of everything in one fell swoop!
> However, there is no terribly strong reason to think this "one
> fell swoop" approach is bound to work.
There is also no terribly strong reason to think that this approach won't
work. We simply do not know how much new physics is there between the
Standard Model and the Planck scale (and maybe beyond?). In the context of
string theory itself, there have been many "big desert" scenarios as well
as scenarios with dozens of new scales.
This question is very personal and philosophical. If the world works
"economically", photons, electrons and two quarks would be enough for
life. Maybe life needs a parity violation and something like the weak
interactions are necessary; many other particles are then required by
anomaly cancellations. And there might be three generations because the
CP-violating phase in the CKM matrix may be important etc. But what a
composite electron would be good for?
We do not know how much new physics there is. But I think that we know one
thing: a randomly chosen "next step" is most likely wrong because there
are so many of them. Without a deeper motivation - such as the impressing
properties of string theory - you get lost immediately. String theory is a
search for the ultimate theory in the darkness of experiments giving no
results beyond the SM, which is however directed by the strict rules of
the theory. But the alternatives seem to be random walks in theoretical
darkness, trying to get some entertainment in the experimental darkness.
> It's an incredible extrapolation which could easily fall flat on its
> face. So, we should hedge our bets and also consider alternatives.
I think that this philosophy about the "incredible extrapolation" has
turned out to be wrong and counter-productive too many times in the
history. At hep-th/9411233 you find a Gross' review of the last conference
before the World War II. The idea is that all the participants including
the leaders such as Heisenberg etc. were silly - except for the hero,
Oscar Klein who already almost had the Standard Model.
Heisenberg, as well as others, speculated that Quantum Mechanics should
break down at the Compton wavelength of the electron. They were ready to
throw out everything they knew. Recall how much is this distance scale.
Today we know that their approach was not reasonable; it was wrong by many
orders of magnitude. The rules of Quantum Field Theory certainly work at
the scale 100 GeV and maybe higher. Is it six orders above the scale where
QM was supposed to be broken?
There are not too many fundamental length scales in physics we know.
Although there is a lot of interesting hierarchy in the Universe and the
observable Universe is as large as 10^{25} meters or so, everything we
know seems to suggest that there is no fundamental scales between say
10^{25} meters and 10^{-15} meters (I chose the QCD scale; it depends what
you call "fundamental" but even if you choose something else - e.g. the
size of the atom -, you get similar results). In other words, the Universe
contains objects at 40 orders of magnitudes which contain absolutely no
new fundamental physics. The extrapolation of the (MS)SM to the Planck
scale is then nothing special. Newton's laws were also extrapolated by
many and many orders of magnitude before the imperfections were found.
> More technically, here is a preon model whose charm should
> be visible by any particle physicist. I think this one was
> cooked up by Pati, Greenberg and Sucher.
Greenberg has been recently working on quons - generalization of
bosons/fermions with +-1 replaced by some general "q". One can see the
evolution by the distribution of the citations: 40 of 230 citations of the
paper from 1981 is from the 1990s (although one would expect about 1/2).
Your explanation of the Pati-Salam model was nice. The preonization
sounded interesting but there would be many questions: for example, what
happens with the F-anti-F and B-anti-B bound states (and maybe many others
that you would like to hide)? In the case of quarks, these particles give
you well-known mesons etc. Where are the preonic mesons? You seem to start
with a flexible enough structure and choose only a very small fraction of
composite particles that you like.
And there is one more general reason why I think that all those models are
wrong. Your Pati-Salam-like preons described one generation of quarks and
leptons only. But now we know there are three (at least). The preons must
then have three flavours, too, and you then get 9 quarks, 9 leptons etc.
and you are back to the model I mentioned. Such a result is completely
unrealistic - and because preons were assumed to explain the spectrum of
quarks and leptons (just like quarks explain the spectrum of hadrons), I
call this flavor problem of preons a total failure.
> Now: my point is *not* that I think this model is correct. My
> point is just that particle physicists should continue to tinker
> with such models, along with many other possibilities - including
> string theory.
One important fact that you do not seem to appreciate is that string
theory is not "one of many preon-like possibilities". String theory is -
according to essentially all the experience we have - actually *the* only
meaningful possibility. String theory is not an accidental tinkered model
where you can add whatever you wish and modify it in any way you want - so
that you can order any results and the technical calculations must always
work in some way.
String theory is a single and unique structure and people were forced to
learn its properties. As soon as we are able to calculate/deduce something
of it well enough, we always learn that the results are clear and
consistent and there is no way to get different results.
> >Your text seems as another attempt to spread the
> >illusion that string theory is not the unique path to unification -
> >without having any evidence whatsoever.
>
> String theory is obviously NOT the unique path that people are
> taking in the attempt to understand the real world of particle
> physics. Whether it's the unique path that succeeds, or whether
> it succeeds at all, only time will tell.
I did not write that all the people work on string theory. ;-) I wrote
that according to all the available data we have, string theory is the
unique path to unification that can explain all the forces from a more
fundamental starting point. Time has already told us so. You know, now we
already live in the 21st century. Two years ago, string theory just
accidentally fell into that century - and we could still open the old and
answered questions. Today it sounds relatively archaic.
> Once any theory starts
> making predictions that are verified by experiments, you can be
> sure that everyone will fall in line with that one!
I disagree with this radical approach. Experimentalists are also people
and they can be wrong. For example, the fact that the weak interactions
were V-A was clear to Feynman and Gell-Mann much before it was clear to
experimentalists. And it was also clear to these two theoretical
physicists when those renowned experimentalists measured an experiment
that "showed" that the weak interactions were S-T.
Note that your prescription how physics should be done would lead to
disastrous consequences in this case - as well as in many others.
Initially, you would order Feynman and Gell-Mann to spend half of their
time on incorrect S-T theories although they knew very well that the weak
interactions should be V-A. Why did they know it well? Generally speaking,
they had a lot of theoretical reasons. What is a theoretical reason? It is
an argument whose basic assumptions are derived from the experience but
which also uses a lot of brain capacity and knowledge of seemingly
unrelated things to derive the consequences.
When the experimentalists published their measurement that the weak
interactions were S-T, you would even order *all* physicists to work on
S-T only because it was "experimentally proven". History worked much
better: bad physicists worked on S-T and some of them believed S-T even
much later. But it was much more important what Feynman and Gell-Mann were
working on. They knew very well what was going on. And today, good
physicists have similar theoretical reasons why quantum gravity must work
as dictated by the rules of string theory. What do they need for similar
conclusions? They must need basic experimental data (such as the tests
leading to the Standard Model, as well as the falling Newton's apple) and
a lot of abilities to think about many interconnected phenomena.
What I want to say is that in the 20th century, theoretical considerations
were at least as important for new developments in theoretical physics as
experimental input. And good physicists usually studied right directions;
in fact, this defines a good intuition of a physicist. But there is
something more than tautology here: the question whether a physicist jumps
in a right direction is not a random process; physics is not a lottery
where physicists randomly speculate and an experiment chooses the winner.
The success is correlated with many characteristics. A physicist can
simply calculate many new effects from the old ones although a layman
could find such a prediction impossible. But this is precisely the reason
why physics is more than just a way of collecting chaotic experimental
data.
> But in the meantime we need people taking all sorts of different paths
> and reporting back from time to time on how they're doing.
If physics should remain physics, people should have also opinion about
their work as well as the work of their colleagues.
> In fact, there *are* people taking all sorts of different paths, so
> all we need to do is read about what they've done.
I strongly disagree. Reading what all the people at different paths have
done is "all we need" to do physics? I think that there are much more
important things we need to do physics. And I would say that we even don't
need to read papers by all those papers. I am sure that even you do not
take seriously papers why Einstein was wrong etc. But you should accept a
simple observation that some people want the authors of the papers that
should be read seriously to know not only physics found in the beginning
of the 20th century, but also in the 70s and the 80s, for example.
> It's not hard to do, and it's actually fun.
Yes ;-), it's fun. But fun is not necessarily the same thing as good physics.
Lubos Motl
> Er, pardonne moi, but aren't electrons known and proven to exist as both
> particles and waves?
Yes, but this "wave" character of particles is already built in. You can
formulate quantum mechanics using Feynman's sum over trajectories, for
example. There you sum over the trajectories of strictly point-like
electrons and you get all those interference patterns and waves out of it.
This approach is equivalent to the canonical quantization etc. and it is
what we mean by "point-like particles without an internal structure". If
they had a structure, the histories would have to be replaced by something
else: for example trajectories of 3 subquarks or a worldtube of a string,
as in string theory. ;-)
Best wishes
Lubos
zirkus
> I disagree with this radical approach. Experimentalists are also people
> and they can be wrong.
S. Coleman gave a speech in which he reminded the audience that, at 3
seperate times during the 1970s, experiments indicated that the SM was
wrong but then these experiments were shown to have been in error.
I agree with Lubos that string theory feels more like it has been
discovered than contrived. There have been quite a few suprises in the
theoretical development of string theory, and also there has been a
fertile relationship with profound mathematics. If string theory is
nothing more than a fancy mathematical game then how could it have
these two properties? It seems to me that only "God" or Nature could
be ingenious enough to contrive such a game.
Also, I don't know if I would agree with Aaron that not much
interesting is happening in string theory these days. Perhaps Aaron is
correct, but recently e.g. I heard about a categorical approach to
D-branes which might eventually provide new insights into N=1 susy
models that might be relevant for tests at LHC, Fermilab etc. so maybe
there's something to this.
Stephen Speicher
> In article <topijo...@corp.supernews.com>, Ralph E. Frost
> <ref...@dcwi.com> writes
> >Er, pardonne moi, but aren't electrons known and proven to
> >exist as both particles and waves?
> No. That is a matter of interpretation. Bohr tried to interpret
> electrons as having both a particle and a wave nature, and many
> physicists have followed him. But more strictly according to
> Heisenberg the Copenhagen interpretation does not include
> wave-particle duality...
Heisenberg was somewhat conflicted in his views, and over the
course of a lifetime he advocated perspectives which at times
were contradictory. However, if one were to emphasize Charles'
"strictly according to Heisenberg" comment, then Charles' final
statement regarding Heisenberg's view of the Copenhagen
interpretation on wave-particle duality, is mistaken.
There is no question that at times in Heisenberg's earlier years
he did not embrace Bohr's view on wave-particle duality, and in
fact he thought that the very need for duality was itself an
indication that some very essential element was missing from the
theory ("Quantenmechanik", _Naturwissenschaften_, 1926,
14:989-94).
However, one year later, in Heisenberg's uncertainty paper ("Uber
den anschaulichen Inhalt der quantentheoretischen Kinematik und
Mechanik," _Zeitschrift fur Physik_, 1927, 43:172-98.{which
paper, incidentally, is one of many papers of historical interest
reproduced in Wheeler and Zurek's marvelous book, _Quantum Theory
and Measurement.}) Heisenberg relented to pressure by Bohr and
included his now famous remarks (in the "Addition in Proof")
which, in effect, acknowledged in a rather subordinate manner,
the importance and relevance of Bohr's duality. [Note that
Heisenberg was so emotional in regard to the pressure exerted by
Bohr that he occasionally burst into tears.]
Yet later that same year, in a letter to Pauli (Hermann et al.,
_Wolfgang Pauli, Scientific Correspondence with Bohr, Einstein,
Heisenberg, 1979), Heisenberg clearly expressed his disagreement
with the Bohrian philosophy, pointing out essential differences.
These changes all ocurred in the space of little more than one
year!
Fortunately though, Heisenberg's _Physics and Philosophy_ (1958)
is generally considered his single most authoritative work, and
the chapter on the Copenhagen interpretation is generally
considered the most authoritative first-hand presentation of the
theory. I believe in the past that Charles has also stated that
he considered _Physics and Philosophy_ to be the most
athoritative explication of the Copenhagen interpretation.
With that in mind, I offer the following quoted material as
evidence against Charles' assertion that "more strictly according
to Heisenberg the Copenhagen interpretation does not include
wave-particle duality." The quotes are from Heisenberg's _Physics
and Philosophy_, specifically from the chapter titled "The
Copenhagen Interpretation of Quantum Theory."
"Actually, we need not speak of particles at all. For
many experiments it is more convenient to speak of
matter waves; for instance, of stationary matter waves
around the atomic nucleus. Such a description would
directly contradict the other description if one does
not pay attention to the limitations givn by the
uncertainty relations. Through the limitations the
contradiction is avoided...The two pictures are of
course mutually exclusive, because a certain thing
cannot at the same time be a particle (i.e., a
substance confined to a very small volume) and a wave
(i.e., a field spread out over a large space), but the
two complement each other. By playing with both
pictures, by going from the one picture to the other
and back again, we finally get the right impression of
the strange kind of reality behind our quantum
experiments."
...
"The dualism between the two complementary pictures --
waves and particles -- is also clearly brought out in
the flexibility of the mathematical scheme...Therefore,
this possibility of playing with different
complementary pictures has its analogy in the different
transformations of the mathematical scheme; it does not
lead to any difficulties in the Copenhagen
interpretation of quantum theory."
These words clearly embrace Bohr's wave-particle duality into the
folds of the Copenhagen interpretation. It is true that
Heisenberg goes further than this; he questions the ability to be
able to really describe what happens between acts of observation,
none of which takes away from the Copenhagen interpretation
embracing wave-particle duality.
Stephen
s...@compbio.caltech.edu
Welcome to California. Bring your own batteries.
Printed using 100% recycled electrons.
--------------------------------------------------------
Jim Carr
|
>[snip]
|
| It includes the fact that the energy and momentum transfer
| dependence of scattering data agree (to within experimental
| uncertainties) with the predictions of QED without any need
| for a size correction (called a form factor). This is much
| more than the qualitative statement you gave, and places
| a quantitative limit around 10^{-18} m for substructure.
|
| It also inlcudes plausible models (some named in other replies),
| but you do not need a model to measure a model-independent
| quantity like a form factor.
In article <3B816D56...@mitre.org>
Frederick Seelig <fse...@mitre.org> writes:
>
>Current experimental evidence aside, would you care to speculate
>on what physicists in 10 or 50 years will see?
10 years probably limits us to another order of magnitude or so.
Whether (and how far) we push on beyond that depends on money
and interest. If the higgs is found and (say) Lubos manages
to predict that some plausible string-theoretic model has
substructure within another order of magnitude, it might be
easier to get funding than if the LHC comes up dry and some
model that is consistent with those results says substructure
is 10 orders of magnitude away.
>In 2050, will we
>be taught that electrons are still point particles? Or will they
>have substructure? What do you guess?
Tough call. My guess is that quarks will be the first to be
sorted out, if that is the case. I think it possible, but not
likely, that (a) some model for the generations and their mass
pattern looks so reasonable that it is taught even if that
substructure cannot be probed directly, with (b) that experiment
sees substructure being less likely. I think there is some
substructure behind the pattern, I'm just doubtful that nature
has to continue to cooperate as it has in the past 50 years or
that either theory or experiment will necessarily progress on
a DayTimer (R) schedule.
Remember where we came from: It was almost a half-century ago
(1957) that the charge form factor of nuclei and nucleons was
being measured to < 10^{-15}m -- implying non-trivial substructure.
Even with that hint, experiment drove the parton/quark ideas
(which came along in the next decade). It will be harder to
go three orders of magnitude from where we are than it was to
do so from where we were in 1950 due only to space constraints,
and even then there are no guarantees.
Charles Francis
tech.edu>, Stephen Speicher <s...@compbio.caltech.edu> writes
>On Sun, 2 Sep 2001, Charles Francis wrote:
>Heisenberg was somewhat conflicted in his views, and over the
>course of a lifetime he advocated perspectives which at times
>were contradictory. However, if one were to emphasize Charles'
>"strictly according to Heisenberg" comment, then Charles' final
>statement regarding Heisenberg's view of the Copenhagen
>interpretation on wave-particle duality, is mistaken.
<snip account of Heisenberg's apparent changing view>
I don't think that describes a change in Heisenberg's view at all. He
did not accept complementarity, except when pressured to make a
statement so much against his will that he broke down and cried.
>Fortunately though, Heisenberg's _Physics and Philosophy_ (1958)
>is generally considered his single most authoritative work, and
>the chapter on the Copenhagen interpretation is generally
>considered the most authoritative first-hand presentation of the
>theory. I believe in the past that Charles has also stated that
>he considered _Physics and Philosophy_ to be the most
>athoritative explication of the Copenhagen interpretation.
Agreed.
>With that in mind, I offer the following quoted material as
>evidence against Charles' assertion that "more strictly according
>to Heisenberg the Copenhagen interpretation does not include
>wave-particle duality." The quotes are from Heisenberg's _Physics
>and Philosophy_, specifically from the chapter titled "The
>Copenhagen Interpretation of Quantum Theory."
<snip quotes - like the other snip I would have preferred to leave your
text intact, but I must spare the moderator>
>These words clearly embrace Bohr's wave-particle duality into the
>folds of the Copenhagen interpretation. It is true that
>Heisenberg goes further than this; he questions the ability to be
>able to really describe what happens between acts of observation,
>none of which takes away from the Copenhagen interpretation
>embracing wave-particle duality.
Heisenberg's interpretation of the Copenhagen interpretation appears to
be open to interpretation. At the outset of this chapter Heisenberg
says:
"Any experiment in physics, whether it refers to the phenomena of daily
life or to atomic events, is to be described in the terms of classical
physics. The concepts of classical physics form the language by which we
describe the arrangement of our experiments and state the results....
Still the application of these concepts is limited by the relations of
uncertainty. We must *keep in mind* (my emphasis) this limited range of
applicability of the classical concepts while using them..."
It appears to me, in this quote as well as others, that Heisenberg is
saying the limitations of language are such that we do not really mean
what we say. He has found a form of words which enables him to pay lip
service to Bohr, using the language of complementarity while not
agreeing with it, by having said that it is necessary to keep in mind
that such language does not really apply.
Such levels of diplomacy are perhaps more usually the ground of an
ambassador than a physicist, but I found nothing in Physics and
Philosophy to suggest that Heisenberg accepted Bohr's position, rather a
range of subtle statements to the effect that he did not.
On the next page he makes a far clearer statement.
"This probability function represents a mixture of two things, partly a
fact and partly our knowledge of a fact.... The error in the experiment
does - at least to some extent - not represent a property of the
electron but a deficiency in our knowledge of the electron. Also this
deficiency of knowledge is expressed in the probability function."
This statement is absolutely in line with the Dirac-Von Neumann
position, and the more recent information theoretic interpretations. And
it seems to me to summarise Heisenberg's position.
In the chapter on Copenhagen Heisenberg is always keen to ascribe to
Bohr, that which is Bohr's, namely complementarity. One can read that as
giving credit, or one can read it as expressing a view that one does not
entirely go along with. But it seems to me that Heisenberg is saying
that it is legitimate to use the language of complementarity provided
one is aware that the language does not encapsulate reality, and that it
is legitimate to think in terms of waves provided one is only interested
in solving a problem, and not mistaking matter waves for being real.
Regards
- --
Charles Francis
Aaron J. Bergman
zir...@my-deja.com (zirkus) wrote:
> Also, I don't know if I would agree with Aaron that not much
> interesting is happening in string theory these days. Perhaps Aaron is
> correct, but recently e.g. I heard about a categorical approach to
> D-branes
Old news. (ie, almost a year now.)
Actually, the original idea that derived categories might be relevant
goes back Kontsevich's ideas about mirror symmetry and, later, the fact
that the Fourier-Mukai transform seems to implement T-duality, but
instead of acting on the sheaves themselves, it instead acts on the
derived category of coherent sheaves. (I say the words....)
> which might eventually provide new insights into N=1 susy
> models that might be relevant for tests at LHC, Fermilab etc. so maybe
> there's something to this.
Er, well, maybe, I guess. My current understanding (and I find Douglas's
papers so far to be inpenetrable, so this is really just my
understanding) is that the idea itself really isn't terribly deep. It
sort of goes in a few steps.
Once, in the days of yore, we believed that D-branes carried on them a
vector bundle, the Chan-Paton bundle. This idea proved to be too simple
and there were indications (eg, Harvey and Moore, "On the Algebra of BPS
States") that the proper things to look at were coherent sheaves, a
slight generalization of a vector bundle where, for example, the
dimension of the fiber can change. A simple example is that a D0-brane
is basically just a skyscraper sheaf (we're sticking time over there,
not here).
Parallel to this, there were ideas about how to classify D-branes. The
simplest thing is to look at the homology class of the brane, or the
cohomology class of the generated RR fields. Following some ideas of Sen
and also Minasian and Moore, Witten realized that instead of looking at
D-branes, it was better to look at stacks (no, not that kind of stack)
of D-branes and anti-D-branes and let the tachyon field between them
condense. In other words, we have an complex of vector bundles (or,
slightly more generally spin^c bundles)
0 --> E --> F --> 0
to which we associate the K-theory class [E] - [F] which classifies the
D-brane charge. The Chern character gets us back to our nice original
cohomological description. The only thing that's different is torsion.
It's straightforward to consider longer sequences, say,
0 --> A --> B --> C --> D --> 0
to which we associate the Euler character in K-theory
[A] - [B] + [C] - [D]
and so on and so forth.
A brief digression is to note that we really started with a homology
classification and K-theory is a cohomology theory. Shouldn't we find
ourself a K-homology description? There are some ideas in this
direction. What seems more likely to me is that there will actually be a
set of 10 equivalent descriptions in terms of various KK groups starting
with KK(C,X) and ending with KK(X,C). See, for example, hep-th/0108085
for a nice "wouldn't it be nice if..." paper.
Anyways, back to the main line. The question now is to try to combine
these two descriptions. The obvious thing to do is to replace all the
letters representing vector bundles above with letters representing
coherent sheaves. This gives us something called the Grothendieck group
of coherent sheaves. So, now we have a more general classification.
There is still something interesting to think about, however. By taking
the Euler character above, or even by taking the cohomology of the
sequence, we lose a lot of information. Instead of dealing with this
coarse information, why not just work with the complexes themselves.
That's all a derived category does. If my understanding is correct (and
I may be missing a ton of subtleties here), it's remarkably less
imposing than it sounds. What I think Douglas is doing is to actually
derive the fact that this works. In other words, we don't know that
string theory needs all this information; one actually has to show that
it does.
For an understandable intro to derived categories, see math.AG/0001045.
I think the original expression of what I'm trying to say here was by
Eric Sharpe in hep-th/9902116.
On a random note, Eric Sharpe seems to enjoy throwing a bunch of
algebraic geometry into string theory. He's also suggested that D-branes
ought to be described as schemes, or even more frighteningly, stacks.
The sum total of my knowledge of stacks comes from a mathematician here:
orbifold:manifold::stack:scheme
Ah well. Time to go back to Hartshorne to understand the last element in
that analogy.
Apologies if I screwed any of this up; again, I don't claim to
understand the ideas in any depth.
John Gonsowski
John Baez wrote:
> The fermions look like this:
>
> F_u <--- LEFT-HANDED "UP" FERMION
>
> F_d <--- LEFT-HANDED "DOWN" FERMION
>
> F_u <--- RIGHT-HANDED "UP" FERMION
>
> F_d <--- RIGHT-HANDED "DOWN" FERMION
>
> That is, they lie in C^2 x C^2 and transform under SU(2) x SU(2)
> in the obvious way. The bosons look like this:
>
> (B_r B_g B_b B_l)
>
> and transform under SU(4) in the obvious way. Thus, bound states
> consisting of one fermion and one boson will transform under
> SU(4) x SU(2) x SU(2) in exactly the way that quarks and leptons do!
Is this kind of like a more "physical" version of a fermion
configuration space?
John
John Baez
zirkus <zir...@my-deja.com> wrote:
>I agree with Lubos that string theory feels more like it has been
>discovered than contrived.
As I've said before, this is a universal characteristic of good
mathematics. It doesn't imply that the mathematics in question
describes the physical world. For a good comparison, you might
try the theory of completely integrable classical systems: roughly
speaking, classical mechanics problems that you can solve exactly -
like the harmonic oscillator, or simple pendulum, or Lagrange top,
or Kowalevsky top, or the Korteweg-deVries equations, or KP hierarchy,
or Toda lattice, or self-dual Yang-Mills equations.
At first glance there is an appalling diversity of such systems,
but after years of study it turned out they are all tied together
by an enormous web of relationships - very much like the different
string theories. For example, some completely integrable systems
can be obtained as limiting cases of others as we tune a parameter
to zero or infinity, and so on. It is now clear that "completely
integrable systems" is a single mathematical subject - although I
would not say it is a single physical theory!
Now, here's the point: workers in completely integrable systems have
the feeling that they are discovering rather than inventing this
subject. They feel the complex web of relationships is in some sense
"already there", and they are just noticing it, rather than making it
up in some ad hoc way as they go along. But they do not thereby conclude
that the universe is a completely integrable classical system!
>There have been quite a few suprises in the
>theoretical development of string theory, and also there has been a
>fertile relationship with profound mathematics.
This is also true of completely integrable classical systems.
>If string theory is
>nothing more than a fancy mathematical game then how could it have
>these two properties? It seems to me that only "God" or Nature could
>be ingenious enough to contrive such a game.
I don't understand the perjorative significance of "just a fancy
mathematical game", and precisely how that's supposed to be different
from "profound mathematics". All I know is that good mathematics
always involves surprising new connections and gives one the feeling
that one is discovering it rather than making it up. This is true
of everything from homotopy theory to number theory to... string theory!
I hope and trust that the laws of physics will involve good mathematics,
but I don't dare turn this around and say that any piece of sufficiently
good mathematics is necessarily bound to describe our universe, because
there are simply too many counterexamples, even among branches of math
with a "physics flavor" - as my example above indicates.
A.J. Tolland
> Also, I don't know if I would agree with Aaron that not much
> interesting is happening in string theory these days. Perhaps Aaron is
> correct, but recently e.g. I heard about a categorical approach to
> D-branes which might eventually provide new insights into N=1 susy
> models that might be relevant for tests at LHC, Fermilab etc. so maybe
> there's something to this.
When I met Douglas last spring, he said that he thought he was
finished with D-geometry for a time, and was trying to think about general
methods for constructing/studying N=1 models. He didn't say that he
thought there was any link between the two subjects. Can you elaborate on
this please.
I tend to agree with Aaron myself. Hep-th is quieter than it was
a few years ago. On the other hand, it's not dead. For instance, there's
some neat work being done in novel M-theory compactifications. Check out
the infamous "Paper with Seven Authors" (hep-th/0103170), Atiyah &
Witten's work on G2 holonomy, and Gukov & Spark's spankin-new "M-theory on
Spin(7) Manifolds: I" (hep-th/0109025).
--A.J.
Ralph E. Frost
news:4t5dfdA$0Nl7...@clef.demon.co.uk...
> In article <Pine.LNX.4.10.101090...@photon.compbio.cal
> tech.edu>, Stephen Speicher <s...@compbio.caltech.edu> writes
>
> >On Sun, 2 Sep 2001, Charles Francis wrote:
>
> >Heisenberg was somewhat conflicted in his views, and over the
> >course of a lifetime he advocated perspectives which at
>
> In the chapter on Copenhagen Heisenberg is always keen to ascribe to
> Bohr, that which is Bohr's, namely complementarity. One can read that as
> giving credit, or one can read it as expressing a view that one does not
> entirely go along with. But it seems to me that Heisenberg is saying
> that it is legitimate to use the language of complementarity provided
> one is aware that the language does not encapsulate reality, and that it
> is legitimate to think in terms of waves provided one is only interested
> in solving a problem, and not mistaking matter waves for being real.
In modern linguistic expressions, aren't matter waves just plain old
everyday gravitational waves?
Just thought.
[Moderator's note: No, the class of matter waves includes many other
types of wave. -MM]
John Baez
Lubos Motl <mo...@physics.rutgers.edu> wrote:
>On Thu, 30 Aug 2001, John Baez wrote:
>> > http://arXiv.org/abs/hep-ph/9909569
>> I'm not sure why you picked this particular model to talk about -
>> as far as I know, it's not one of the most popular ones. Did you
>> pick it just because it seems weird? That wouldn't be very fair...
>No, I've picked this paper because I believe that it is one of the most
>up-to-date papers about the preon idea.
It's new paper, but if your description of it is correct, it's
too silly to be worth discussing.
>The prediction of nine quarks, nine leptons and nine heavy vector bosons -
>see the paper hep-ph/9909569 - sounds realistic to you?
No, this is silly. It's also not representative of good work on preon
models. Picking this paper to talk about is like deliberately picking
a really silly paper on string theory and claiming the whole subject
is like that.
>Could you please
>show us a preon model with realistic predictions - for instance a model
>that contains 3 families of quarks and leptons?
The model I described in my previous post allows for 3 families
if you take N = 12 in the SU(N) technicolor gauge group. (The
anomalies cancel in this case.) Just as in string theory, you
can get pretty much whatever number of families you want in preon
models - though of course having too many families will ruin
asymptotic freedom.
You can probably learn about preon models to your heart's content
in this review article:
Technicolor
Edward Farhi and Leonard Susskind
Published in Phys. Rept. 74:277, 1981
>> 1) Despite decades of work and over ten thousand papers on the
>> subject, string theory has not made a single experimentally
>> verified prediction. One reason is that:
>It has been explained in detail that this is a problem that all particle
>physicists (and their colleagues from related fields) share. It is nothing
>specific for string theory: no theory beyond SM could have given us a
>verified new prediction simply because experimentalists - mostly because
>of the state of the current technology - have not been able to construct a
>single experiment that would disagree with the Standard Model (or General
>Relativity, in the context of the large distance scales).
That's not true. This is a myth propounded by theorists.
Here are 3 examples of experiments that go beyond the Standard Model,
which a really good theory would have made predictions about:
1) Neutrino oscillations. The discovery of neutrino oscillations went
beyond the original Standard Model, which had only left-handed neutrinos
and did not allow for oscillations. After this discovery, the Standard
Model was modified to allow for neutrino oscillations. It now includes
right-handed neutrinos. However, a really good theory of particle physics
would have predicted all this ahead of time.
2) Dark matter. It now seems that the dominant contribution to the
energy of the universe is a poorly understood invisible form of matter
which does not fit into the Standard Model. A good theory of particle
physics would have predicted this ahead of time and said something about
its properties.
3) Cosmological constant. It now seems that the universe's expansion
is accelerating due to a nonzero cosmological constant - that is,
a nonzero vacuum energy density, or something with similar effects.
Again, this does not fit into the Standard Model. Again, a good theory
of particle physics would have predicted this effect before it was
observed. Instead, most theorists were busy trying to explain why
the cosmological constant was zero!
In all 3 cases string theory is sufficiently flexible to retroactively
accomodate the new developments. But in no case did it give a robust
prediction of these experimental developments *before* they happened.
In all 3 cases it is not too late for a good theorist to make predictions
*now*. There is still a lot unknown about neutrino oscilations,
dark matter and the cosmological constant!
Not surprisingly, many physicists are leaping to the challenge. However,
many of the top string theorists are busy chasing "M-theory", leaving
the job of actually making physical predictions to the more lowly
"phenomenologists". The quest for M-theory is a largely mathematical
enterprise, relatively unaffected by experimental results.
>From its philosophy, it is clear that string theory is ultimately able to
>predict everything and contains no adjustable parameters etc.
That's very nice, but being "ultimately able to predict everything" is
a rather dangeorous substitute for being "currently able to predict
something".
You seem here almost to be claiming that ultimately string theorists will
find a unique nonperturbative vacuum and that this will allow them
to derive the Standard Model gauge group and all the coupling constants
from first principles, together with all the new phenomena not included
in the Standard Model. That's what I would call "ultimately predicting
everything", and it would be an incredible triumph - but there is really
no evidence that anything like this will happen.
Of course, you may not really mean that there is a unique nonperturbative
vacuum. Maybe you mean that there are a bunch and that string theorists
will eventually understand them. If they found, say, 5, and one matched
the Standard Model pretty well, but also made new testable predictions
that turned out to be true, this would again be a triumph. If they found
a trillion, and of these several thousand matched the Standard Model pretty
well, that would be less of a triumph, but still interesting.
But my main point is that all these scenarios are just hopes and dreams.
Currently string theory offers far less: there are zillions of perturbative
string theories, we must introduce lots of new parameters by hand when we
break supersymmetry to make them physically realistic, and as a result,
string theory can fit pretty much any data that experimentalists are
presently able to come up with... but never make any solid predictions
ahead of time. The inverse square law for gravity might break down at
submillimeter distances... or it might not. The next generation of
particle accelerators might see the superpartners of known particles...
or it might not. Etcetera.
This is why there is still a need for theories like preon models which
make definite predictions that we have a chance of testing.
(By the way, I'm not a big fan of preon models: I'm just enjoying
defending this very unfashionable dark horse against the fashionable
juggernaut of string theory!)
>> 3) String theory predicts that every boson has a corresponding fermion
>> of the same mass! This is clearly wrong. The only way out is for
>> supersymmetry to be spontaneously broken. Unfortunately, nobody
>> understands how this works.
>If you open the volume II of Joe's book "String Theory" and look for
>"supersymmetry breaking" in the index, you will be impressed how many
>pages of basic material you have absolutely no idea about. Literature
>about SUSY breaking is vast - and I have published a very basic
>introduction a few months ago.
I'll have to read this paper, because I consider this to be the
most urgent problem in string theory, and I'd really like to
understand the state of the art. I'm glad you at least agree with
my most basic claim: we don't know how supersymmetry is broken.
>The problem that we do not know how SUSY is
>broken in the real world is a part of the general problem 1) [...]
Right.
>There are also related problems - such as the cosmological
>constant problem: why is Lambda so small even after SUSY breaking and does
>not acquire something of the order m_{SUSY-breaking}^4? ;-)
Yes, this is related to experiment 3) in my list above.
>> string theory to make predictions about particle physics must break
>> supersymmetry "by hand" - that is, by penciling in dozens of "soft
>> supersymmetry breaking terms" in the field theories that arise as
>> low-energy limits of string theory.
>This interpretation is incorrect.
I am extremely relieved to hear that, and I will be even more
relieved when I am convinced it is true. I'll read your paper.
>In many models, including "ordinary and
>simple" quantum field theories, it is well understood that SUSY can be
>spontaneously broken - and this breaking can be described from the
>fundamental principles. There can be a gaugino condensate (usually in the
>hidden sector), for example, and it is as simple as a chiral symmetry
>breaking in QCD, for instance: a bilinear expression in gaugino fields
>gets a VEV.
I guess to be convinced I will have to see how this works in a toy
model, and assure myself that no funny tricks are being played, and
(the hard part) come to believe that the same mechanisms can work in
more realistic models.
>Those gauginos etc. have many interactions with the other fields; they are
>often indirect, via a mediator (dilaton-mediated, anomaly-mediated,
>gravity-mediated SUSY breaking etc.). At low enough energies, the effect
>of the broken SUSY in the hidden sector manifests itself by the soft
>(relevant) SUSY breaking terms; it is a general rule of QFT to study the
>most general theory with the given degrees of freedom and symmetries.
>Those are precisely the terms that do not spoil some nice UV properties of
>supersymmetry such as the cancellation of the quadratic divergences of the
>Higgs self-energy.
>
>But if you know the fundamental theory completely, all those terms are
>calculable (at least in principle)! Only because this problem is currently
>too difficult (in string theory as well as in simpler models), we must put
>all the terms that can be generated with free coefficients. This is why
>MSSM has over 100 parameters (compared to 19 parameters of SM) although we
>would expect that the freedom should decrease with SUSY (that relates
>properties of superpartners).
Well, I sure hope that people can translate "in principle" to
"in practice". Everything that can be done in principle can
eventually be done in practice... in principle. But in practice,
it's another matter. :-)
>> Preon models also have their problems, and they are certainly far
>> less pretty than string theory. However, given the above problems of
>> string theory, it is far too soon to rule out alternatives like preon
>> models.
>I still do not understand in what sense they are alternatives to each
>other.
They both give descriptions of what we might see in the next generation
of particle accelerators.
>Quantum gravity? Certainly not; preons are not capable to do it.
I already said I wasn't talking about quantum gravity here.
>Physics just beyond the Standard Model? In this respect, they are not
>alternatives either. If you had a good enough preon model, you could
>almost certainly embed it into string theory, too - for instance, if the
>Pati-Salam-like preon model worked, it could be embedded in string theory.
Yes, I realize that the octopus-like flexibility of string theory allows
even preon models to be considered as special cases of this theory. But
as far as I'm concerned, this is just another sign of string theory's
lack of predictive power. A theory which can fit anything predicts nothing.
(As usual, when I talk about string theory's lack of predictive power,
I refer to the theory as it currently exists, not as you dream it will
someday be.)
>If I simplify the issue a little bit, the previous sentence is true by
>definition because a good idea in physics is defined as something that is
>contained in string theory. ;-)
Right - this is exactly what we'd expect of a theory with zero
predictive power.
Ralph E. Frost
> I don't understand the perjorative significance of "just a fancy
> mathematical game", and precisely how that's supposed to be different
> from "profound mathematics". All I know is that good mathematics
> always involves surprising new connections and gives one the feeling
> that one is discovering it rather than making it up. This is true
> of everything from homotopy theory to number theory to... string theory!
Er, but can't you go back further to early pre-Cromagnon days and say that
this neat, mostly one-to-one mapping got programmed in when folks used the
counting numbers? One spear, two spears, three spears......four
spears....five spear..... six spears, all stacked together in different
ways?
>
> I hope and trust that the laws of physics will involve good mathematics,
> but I don't dare turn this around and say that any piece of sufficiently
> good mathematics is necessarily bound to describe our universe, because
> there are simply too many counterexamples, even among branches of math
> with a "physics flavor" - as my example above indicates.
It's the initial question and the resulting new symbols that spark this
"repeatable discovery", process isn't it? I mean I'm guessing that at the
root of string theory some person said, "okay, let's say we say that all
this spinning wiggly stuff can be represented by vibrating strings?"
Then he initiated the _new_ symbolic linkage, and it is that initial
procedural choice that allowed the re-translation of all the other prior
math/physical imagery to "be discovered" in the new symbolic
representation. Something old, something new mixed together, resonanting
out of essentially the same structures in carbon-based consciousness....
You notice though, that when it comes to carving out the HEP versions of
those equations out of stone, magnetics and current drain that there are NOT
a gazillion ways to configure those babies. In that manner those analog
expressions sure do look like they all have much higher information
compression ratios that the abstract math versions.
Yes?
--
Best regards,
Ralph E. Frost
Imagine you are on the team introducing quantum gravity to a student body of
several billion people. Quick! What science education tool are you using?
http://flep.refrost.com --> Frost Low Energy Physics
"...Love one another..." John 15:12
Lubos Motl
> > zirkus: I agree with Lubos that string theory feels more like it has been
> > discovered than contrived.
>
> As I've said before, this is a universal characteristic of good
> mathematics. It doesn't imply that the mathematics in question
> describes the physical world.
But string theory apparently has all the necessary features to describe
the real world. I am convinced - with Dirac, Einstein and others - that
among the candidate theories that are capable to describe the real world,
the mathematically more elegant one is more likely. "Physical laws should
have mathematical beauty," Dirac wrote in Moscow. And I believe that with
increasing time, this is increasingly true.
> For a good comparison, you might try the theory of completely
> integrable classical systems: roughly speaking, classical mechanics
> problems that you can solve exactly - like the harmonic oscillator, or
> simple pendulum, or Lagrange top, or Kowalevsky top, or the
> Korteweg-deVries equations, or KP hierarchy, or Toda lattice, or
> self-dual Yang-Mills equations.
You know, the harmonic oscillator is not sufficient to describe the real
world. I can prove it easily. String theory, on the contrary, *is* enough.
Or at least none has found evidence for the opposite claim.
> At first glance there is an appalling diversity of such systems,
> but after years of study it turned out they are all tied together
> by an enormous web of relationships - very much like the different
> string theories.
It's certainly not "very much like". It is not even "much like". You
misunderstand and underestimate the nontrivial character of dualities in
string theory. A duality between two string theories is not just some kind
of relation or similarity: it is a full equivalence. An equivalence that
is not manifest. Type IIA string theory and type IIB string theory always
had some similarities; in fact, they differed by a sign of the GSO
projection only. Although this difference can look tiny, it is extremely
serious and makes the theory different. You can say "similar" but with a
technical precision that string theorists (as well as all honest exact
scientists) must have, the theories are different just like Monaco is
different from Mexico although they sound similar. However T-duality shows
that they are *exactly* equivalent if you compactify them on corresponding
circles. The relation is not superficial and completely trivial to derive;
however, it's exact. This is how a deep and profound duality looks like.
> For example, some completely integrable systems can be obtained as
> limiting cases of others as we tune a parameter to zero or infinity,
> and so on.
In this case, the more general model containing the parameters is the more
general model and the limit is just a limit. If you understood the more
general theory completely, you would understand the limit, too. But a
duality in string theory is something different. You have two equally good
theories; the first one gives you the second one and the second one gives
you the first one if you set the parameters properly. No limits are
involved. Furthermore dualities are not just some interpolations between
two theories that you could find in your simple examples. If two theories
are dual to each other, all the possible deformations of the first theory
must be also found in the other theory. All the other deformations you
could imagine are necessarily inconsistent. You know, once you work with
string theory, the space of all possible physical deformations is
constrained a lot. There is space for the correct relations only and they
are extremely nontrivial. The only consistent theory containing gravity in
more than 3 dimensions is string theory; this term defines all the
plausible deformations. And if you look at particular perturbative string
expansions from the 1980s, you find the dualities between them extremely
shocking.
Your examples cannot be compared with the situation in string theory. In
those examples, you never have 2 differently-looking theoretical
frameworks with well-defined rules that finally turn out to be equivalent.
You have either two frameworks which are equivalent obviously, or you
don't have well-defined rules (constraining requirements such as the
requirement of quantum gravity inside) so that you can do essentially any
deformations and interpolate between two theories - or the relations
between the theories are just some vague similarities but not a full
equivalence. Only if you obey all three rules, you deal with something
at least remotely similar to dualities in string theory. And only if you
understand why all three requirements are essential to get those shocking
results, you can learn what the magic of dualities is all about.
> It is now clear that "completely integrable systems" is a single
> mathematical subject - although I would not say it is a single
> physical theory!
Right, exactly; this is the difference. String theory, on the contrary,
*is* a single physical theory and therefore your analogy is incorrect. It
has a single Hilbert space, so to say. Even if you consider its
superselection sector connected with one set of asymptotic conditions, you
find states of the Hilbert space that physically look just like the states
in other sectors, at least locally. This is a physical way to see that the
direct sum is not artificial but essential.
> Now, here's the point: workers in completely integrable systems have
> the feeling that they are discovering rather than inventing this
> subject.
Sure, many integrable systems are important tools to describe
(approximately) many interesting physical situations. They are limits of
M-theory and therefore the researchers are often correct that they are
discovering the subject.
> They feel the complex web of relationships is in some sense "already
> there", and they are just noticing it, rather than making it up in
> some ad hoc way as they go along.
In this sentence, you seem to say that you like the Platonic viewpoint
that the mathematical ideas already exist "somewhere" independently of
physical reality. Sure, I also share this philosophy. But the claim that
string theory is being discovered rather than invented is more profound
than the Platonic philosophy. This claim is about string theory's
uniqueness. If you are inventing or constructing something, you can do it
in very many ways. If you are discovering a continent, the resulting
discovery can have 6 faces only. You can call them Europe, Asia, America,
Africa, Australia, Antarctis - or perhaps I, IIA, IIB, HE, HO, M11. The
claim about "discovering" means that the "planet" of string theory is
essentially unique.
> But they do not thereby conclude that the universe is a completely
> integrable classical system!
That's correct because one can easily prove that the Universe is *not* a
completely integrable classical system. On the contrary, the Universe *is*
probably described by string theory. This statement is not derived from
the mere fact that the pieces of string theory are connected by some
ideas. It is derived from the generally believed conjecture that string
theory is the only consistent theory containing the well-known features of
the world, such as the gauge theories, families of particles, quantum
mechanics and gravity. And if Universe obeys a theory - and everything
suggests that it does - string theory is most likely the only choice.
> >There have been quite a few suprises in the
> >theoretical development of string theory, and also there has been a
> >fertile relationship with profound mathematics.
>
> This is also true of completely integrable classical systems.
Could you remind us which surprises you really mean, just to be sure?
Otherwise, completely integrable physical systems are mostly part of
mathematics and therefore the second sentence about their interactions
with mathematics is a tautological consequence of reflexivity of the
relations. ;-)
> >If string theory is
> >nothing more than a fancy mathematical game then how could it have
> >these two properties? It seems to me that only "God" or Nature could
> >be ingenious enough to contrive such a game.
>
> I don't understand the perjorative significance of "just a fancy
> mathematical game", and precisely how that's supposed to be different
> from "profound mathematics".
The reason why you don't understand it is probably because you are a
mathematician, not a physicist. If you say that a framework of physical
ideas is just a "fancy mathematical game", it is a very pejorative
statement because physicists should work on something which is more than
just a puzzle of recreational mathematics for the weekend: the ideas
should describe the real world. The real world that contains trillions of
stars, life, love, trillions of dollars, beautiful things, girls and
scientists who are able to study the world itself.
I am extremely disappointed if you don't see any difference between
"profound mathematics" and "fancy mathematical game". It sounds a little
bit like if you say that you believe that there can exist no intuition for
good ideas in physics.
Consider two things: chess and General Relativity (on Calabi-Yau
manifolds, to make it more explicit). Both require some skills if we want
to understand them or solve them. Intelligent people can be very busy with
both of them. However, while General Relativity and geometry (and
topology) of Calabi-Yau manifolds involve profound mathematics, looking
for winning strategies in chess is just a fancy mathematical game.
What is the difference? Again, it is related to the uniqueness of profound
mathematical ideas. Knowing things about geometry is absolutely inevitable
to understand behavior of almost anything in the worlds similar to ours;
and they are certainly an important category of the worlds. ;-) God (or
Nature) had to know all those things before our Universe was designed.
>From another point of view, chess is just one of millions of comparably
complicated games and our civilization can spend millions of weekends by
playing them and studying them.
Profound mathematics is essential and inevitable for understanding or
construction of wide classes of things in the world of ideas (and the
physical worlds themselves) while fancy mathematical games are not
essential. Once again, I would like to believe that it was just your typo
saying that you didn't see the difference - because otherwise I call this
direction of thinking "mathematical atheism". According to mathematical
atheists, no mathematical ideas are deeper than others. They think that
the only difference is how much effort we must spend to solve them.
> All I know is that good mathematics always involves surprising new
> connections and gives one the feeling that one is discovering it
> rather than making it up. This is true of everything from homotopy
> theory to number theory to... string theory!
You still don't see the essential difference. If you play chess, you see
also many surprising connections that "objectively exist". Yet, strategies
in chess are not examples of profound mathematics; chess is a fancy
(mathematical) game. It's because chess is not unique; consequently it is
not important for the structure of the universes; God did not have to play
chess well but He certainly had to understand operators on Hilbert spaces;
aliens from other planets most likely don't play chess as we know it.
Without geometry, God could not have created our Universe, so to say.
Once again, I agree that homotopy theory and number theory are also being
discovered, much like string theory. The difference here is that number
theory is obviously *not* a physical theory capable to describe the real
world and the mere homotopy theory is *not* a physical theory either.
However, string theory *is* a physical theory capable to describe the real
world. And this fact makes a huge difference.
> I hope and trust that the laws of physics will involve good mathematics,
> but I don't dare turn this around and say that any piece of sufficiently
> good mathematics is necessarily bound to describe our universe, because
> there are simply too many counterexamples, even among branches of math
> with a "physics flavor" - as my example above indicates.
While I agree that something that we find cute in mathematics is not
necessarily deep and important for the essence of the cosmos, I disagree
with the interpretation of your examples. The classical integrable systems
can be relatively interesting from the mathematical point of view - but
they can also approximately describe phenomena in the real world. However
they are not *enough* mathematically beautiful and deep. And this fact is
related to the observation that they don't describe the theory of
everything. If one wants to judge whether a mathematically beautiful
theory XY is the right one to describe a class of phenomena, it should
have first of all at least some chance. ;-) But if it does have a chance,
I think that history has taught us that the mathematically nicer theory
(and sometimes we need time to learn which one is really nice) is usually
the more relevant one. I don't think that you have found any
counterexamples against this statement.
Of course, if we define "a beautiful theory" as "the theory that finally
wins", such a claim becomes a tautology; aesthetics of the winner (and
leading physicists) determines the "correct" taste. But anyway I think
that it is essentially true - and if you think that chess or calculation
of trajectories in some potential is equally mathematically beautiful and
profound as some aspects of string theory, you are just wrong.
Paul Arendt
Aaron Bergman <aber...@Princeton.EDU> wrote:
>Technicolor is a composite Higgs theory as I remember it...
This seems like a good lead-in to ask something that's been
bugging me for a while. I've seen statements here on s.p.r. in
the past that some folks find the concept of an elementary
(non-composite) spin-0 Higgs field disturbing.
I can think of an aesthetic-ish reason for this. When we
quantize a field which has spin 1/2 or greater, there are
at least two spin components around. For a specified normal
mode of the field, these different components become canonically
conjugate variables of the mode, related by some differential
equation which is first order in time.
For instance, free photons have their E and B fields as conjugate
variables (in a chosen gauge), related by Maxwell's equations.
Free electrons have (unobservable) different components of their
two-component spinor as conjugate variables, related by the
Dirac equation.
(An aside: this seems to be another way of interpreting the question
"Does an electron have substructure?" For although the spinor
components cannot be observable, they really do limit how "pointlike"
an electron can be. The canonical conjugacy between the different
components limits a single electron's size to the Compton wavelength
before weird things start happening.)
Anyway, for the process of quantization in general, we complexify
the classical degrees of freedom (generalizing "classical" to
describe a non-quantized Dirac field, even though there are none),
giving us a space that's twice as large in some sense. But we
also throw out one of the variables, trimming the space back down
to its original size (I'm talking about "polarization" in geometric
quantization, for those who know what that is). This is necessary
since describing a space by both variables of a conjugate pair
(like p and q) is forbidden by the uncertainty principle.
Anyway, the information about the thrown-away variable is retained
in some sense in the complexification of the variable that was kept.
But for a non-composite scalar Higgs field, there IS no other
component to be canonically conjugate! The Klein-Gordon equation,
second-order in time, is all that's around to describe the poor
scalar Higgs. Quantizing the Higgs field sort of requires the
complexification to encode information about the time derivative
of the field, but that's not a field in itself like it is for
the higher-spin fields.
Of course, this is just an argument against non-composite spin-0
fields in general, so there's nothing specific to the scalar Higgs about
it other than that's the only spin-0 field that the Standard Model
thinks is around. So I suspect that there may be arguments against
non-composite Higgses which actually have to do with the Higgs
mechanism. Can anybody enlighten me here?
Jim Carr
news:Pine.SOL.4.10.101082...@strings.rutgers.edu...
}
}
} As far as I know, they [preon models] essentially do
} not offer anything that the Standard Model cannot. In my opinion, it
} sounds funny to compare the preon proposal with string theory. To see how
In article <tom4e8c...@corp.supernews.com>
"Ralph E. Frost" <ref...@dcwi.com> writes:
>
>How come the same can't be said for the standard model of, um, a couple
>months ago before it began to SNO? HOW did it describe neutrinos??
The Revised Standard Version of the SM was confirmed by SNO, so
your comment seems to be based on a misconception. Neutrino
mixing had to be added to the SM because of the Super-K results,
although it had been becoming increasingly clear that mixing
had to exist before those Super-K atmospheric neutrino results.
What SNO did was show that the SSM (standard solar model) value
for neutrinos from mass-8 reactions was correct, a related but
quite different result.
<... snip assault on string theory ...>
zirkus
>As I've said before, this is a universal characteristic of good
>mathematics.
Yes, but IMO the historical origin of string theory is somewhat ad hoc [1]
and not very axiomatic or rigorous yet, despite this, string theory has
(surprisingly) derived all kinds of things that seem consistent and do
not seem too contrived nor ad hoc (such as GTR).
[1] By saying that string theory has an origin which feels kind of ad hoc,
I mean that one day Veneziano pulled out of his hat a crossing symmetric
S-matrix related to the mathematical properties of Gamma functions and
not according to a natural classification of physical realizations of
crossing (i.e. Veneziano did not really answer the original problem of
what kind of operator theory produces this S-matrix via its LSZ scattering
theory - the string theory interpretation is not based on localization
but instead on features of the momentum space spectral properties.)
>It is now clear that "completely
>integrable systems" is a single mathematical subject - although I
>would not say it is a single physical theory!
But string theory may be a single physical theory.
>I don't understand the perjorative significance of "just a fancy
>mathematical game", and precisely how that's supposed to be different
>from "profound mathematics".
One difference might be that a "fancy mathematical game" such as go,
bridge or some tiling game or whatever might only influence a fairly
narrow area of math whereas profound math such as NCG could influence
multiple different areas of physics or math. For instance, this
physicist in France just released a preprint about quaternions,
Hopf maps and qubits in quantum information theory. I emailed
him to say that something similar could be done with the octonions
but he told me that he already has a manuscript in preperation
which does just that.
>I hope and trust that the laws of physics will involve good mathematics
Please take 30 seconds to read the abstract below because it sounds kind
of provocative, and because perhaps the laws of physics might not involve
"good math" as much as computation or complexity (I'm still waiting for
that Wolfram book).
[1] http://arxiv.org/abs/math.HO/9911150
Aaron J. Bergman
>In article <Pine.SOL.4.10.101083...@strings.rutgers.edu>,
>Lubos Motl <mo...@physics.rutgers.edu> wrote:
>>In many models, including "ordinary and
>>simple" quantum field theories, it is well understood that SUSY can be
>>spontaneously broken - and this breaking can be described from the
>>fundamental principles. There can be a gaugino condensate (usually in the
>>hidden sector), for example, and it is as simple as a chiral symmetry
>>breaking in QCD, for instance: a bilinear expression in gaugino fields
>>gets a VEV.
>I guess to be convinced I will have to see how this works in a toy
>model, and assure myself that no funny tricks are being played, and
>(the hard part) come to believe that the same mechanisms can work in
>more realistic models.
I'll back Lubos on this idea. Measuring the soft SUSY breaking
parameters may be the best probe we're going to get of higher energy
physics. The soft SUSY breaking lagrangian is essentially
phenomenological, after all. Relations between the oft-mentioned 109
parameters should tell us just how SUSY really is broken.
zirkus
Tolland says...
> When I met Douglas last spring, he said that he thought he was
>finished with D-geometry for a time, and was trying to think about general
>methods for constructing/studying N=1 models. He didn't say that he
>thought there was any link between the two subjects. Can you elaborate on
>this please.
The best intro appears to be a paper by Douglas called "D-branes and
N=1 supersymmetry" hep-th/0105014. If you have any questions then
even if I can't answer them, Aaron might be able to since he seems
to know about D-branes and categories (an approach which perhaps
could be important for susy gauge theory).
James Gibbons
> John Baez wrote:
> > They feel the complex web of relationships is in some sense "already
> > there", and they are just noticing it, rather than making it up in
> > some ad hoc way as they go along.
> In this sentence, you seem to say that you like the Platonic viewpoint
> that the mathematical ideas already exist "somewhere" independently of
> physical reality. Sure, I also share this philosophy. But the claim that
> string theory is being discovered rather than invented is more profound
> than the Platonic philosophy. This claim is about string theory's
> uniqueness...
To a mathematician looking in, string theory is really just messing
around in the categories: Top, Diff, Scheme, Tannk, ect.
These categories already exist platonically, we are just discovering
their properties.
cheers,
Jim Gibbons
John Baez
ludicrously irrelevant to what we're talking about now.
Thanks for a cool post, Aaron!
In article <slrn9p8lcr....@phoenix.Princeton.EDU>,
Aaron J. Bergman <aber...@Princeton.EDU> wrote:
>Once, in the days of yore, we believed that D-branes carried on them a
>vector bundle, the Chan-Paton bundle.
Ah, the innocence of youth. :-)
>This idea proved to be too simple
>and there were indications (eg, Harvey and Moore, "On the Algebra of BPS
>States") that the proper things to look at were coherent sheaves, a
>slight generalization of a vector bundle where, for example, the
>dimension of the fiber can change. A simple example is that a D0-brane
>is basically just a skyscraper sheaf (we're sticking time over there,
>not here).
Now I forget the definition of a coherent sheaf, so I'm wondering
just how big of a generalization we're talking about here.
Let me pull out Hartshorne's book.... [blows dust off cover].
Hmm, he defines coherent sheaves only over schemes, which makes me
wonder if this whole business requires us to work in a context
where we can use algebraic geometry to describe space, or spacetime.
For example, what if I wanted to work over a smooth manifold?
Wait a minute - there isn't any way to think of a smooth manifold
as a special sort of scheme, is there? Can we just start with
the ring of smooth functions on a manifold and use that to build
an affine scheme?? Is this scheme stuff supposed to generalize
differential topology as well as algebraic geometry? If so, how
come nobody ever told me? If not, what DOES generalize both these
subjects?
Anyway:
Definition - Let (X, O(X)) be a scheme. A sheaf F of O(X)-modules
is *quasi-coherent* if X can be covered by open affine subsets
U_i = Spec(A_i) such that for each i there is an A_i-module M_i
with F|U_i = tilde(M_i). We say that F is *coherent* if moreoever
each M_i can be taken to be a finitely generated A_i-module.
Hmmmm. tilde(M_i) is the sheaf over U_i that's more or less
obviously associated to the module A_i... and I think I understand
the rest of this jargon. Okay, so a sheaf is coherent if it's
really just another way of talking about a bunch of finitely
generated modules over the rings A_i whose spectra are the open
sets covering your scheme. If these modules were projective or
free, we'd be a lot closer to having a vector bundle - I forget
the algebraic geometry theorem about this, but the differential
topology result is Swan's theorem: finitely generated *projective*
modules over the ring of smooth functions are really the same as
vector bundles over your compact smooth manifold.
>Parallel to this, there were ideas about how to classify D-branes. The
>simplest thing is to look at the homology class of the brane, or the
>cohomology class of the generated RR fields. Following some ideas of Sen
>and also Minasian and Moore, Witten realized that instead of looking at
>D-branes, it was better to look at stacks (no, not that kind of stack)
>of D-branes and anti-D-branes and let the tachyon field between them
>condense. In other words, we have an complex of vector bundles (or,
>slightly more generally spin^c bundles)
>
>0 --> E --> F --> 0
>
>to which we associate the K-theory class [E] - [F] which classifies the
>D-brane charge.
Cool! So the map E -> F is somehow "tachyon condensation"?
Physicists always make math sound so science-fictiony. :-)
>The Chern character gets us back to our nice original
>cohomological description. The only thing that's different is torsion.
>It's straightforward to consider longer sequences, say,
>
>0 --> A --> B --> C --> D --> 0
Right, and now you're almost in the derived category of
vector bundles: chain complexes of vector bundles are the
objects... so just take the chain complex maps and formally
invert those which give isomorphisms on (co)homology and
you've got the derived category!
>Anyways, back to the main line. The question now is to try to combine
>these two descriptions. The obvious thing to do is to replace all the
>letters representing vector bundles above with letters representing
>coherent sheaves. This gives us something called the Grothendieck group
>of coherent sheaves. So, now we have a more general classification.
Righto.
>There is still something interesting to think about, however. By taking
>the Euler character above, or even by taking the cohomology of the
>sequence, we lose a lot of information.
Yeah - taking the Euler character of a complex is a form of
"decategorification", like taking the dimension of a vector
space.
>Instead of dealing with this
>coarse information, why not just work with the complexes themselves.
>That's all a derived category does.
Well, there's the stuff about inverting the maps that give
isomorphisms on cohomology - the so-called "quasiisomorphisms".
But yeah, you're right to want to demystify this derived category
business.
>If my understanding is correct (and
>I may be missing a ton of subtleties here), it's remarkably less
>imposing than it sounds.
Yes! It's like a piece of 20th-century mathematics which somehow
accidentally fell into the 21st century.
>On a random note, Eric Sharpe seems to enjoy throwing a bunch of
>algebraic geometry into string theory. He's also suggested that D-branes
>ought to be described as schemes, or even more frighteningly, stacks.
>The sum total of my knowledge of stacks comes from a mathematician here:
>
>orbifold:manifold::stack:scheme
Stacks are cool!!! Here's another equally valid analogy:
sheaf: set :: gerbe : groupoid :: stack : category
A sheaf has a set of sections over any open set,
a gerbe has a groupoid of sections over any open set,
a stack has a category of sections over any open set!
The thing that used to get me confused is how one uses
stacks to describe orbifold-ish spaces. Then my pal
Minhyong Kim demystified that a bit for me. When you
have a group acting on some sort of space you are naively
tempted to mod out and get a quotient space. This can
give nasty singularities and you run the danger of losing
track of whatever smoothness the situation had - say a
Lie group acting smoothly on a smooth manifold or algebraic
group acting algebraically on a smooth variety...
... so, instead, consider the original space sitting over
the quotient space, projecting down to it. But don't just
think about the *set* of points in the original space that
map to any given point in the quotient space; think about
the *groupoid* having these points as objects and morphisms
coming from the tranformations in your group.
So you get a gerbe!
(I don't know why you'd need stacks that aren't gerbes,
in these orbifold-ish examples.)
>Ah well. Time to go back to Hartshorne to understand the last element in
>that analogy.
Hartshorne. :-( Will I ever penetrate all the way through that
book before I die?
Robert C. Helling
Aaron J. Bergman <aber...@Princeton.EDU> wrote:
> Er, well, maybe, I guess. My current understanding (and I find Douglas's
> papers so far to be inpenetrable, so this is really just my
> understanding) is that the idea itself really isn't terribly deep. It
> sort of goes in a few steps.
From what I understood from people trying to explain me the main line of
Douglas' papers is the following:
The object to study is type II strings on a Calabi-Yau (CY) manifold. As you
know (just for reference) a CY can be deformed in certain ways that leave
the CY properties intact. The space of those deformations is the moduli
space of the CY. It turns out that this moduli space is a cartesian product
of two spaces, the Kaehler and the complex structure moduli spaces (the
deformations are induced by elements of different cohomology classes).
For a visualization think of the toy example of a CY, the torus: It is
obtained as C / (a Z + b Z) where a and b are complex numbers that are real
linear independent. For the complex structure (i.e. as a complex manifold)
only the quotient a/b matters, this is the complex structure modulus. But
there is also a Kaehler modulus: It is the volume of the torus (actually
this is the imaginary part and some B field flux thru the torus is the real
part).
The same is true for true CYs: Among the Kaehler moduli there is one that
determines the volume. In the limit of infinite volume, the CY is large
compared to the strings that live on it. It is a valid approximation that
the strings behave just as point particles on the CY. In this large volume
limit, ordinary geometry is valid (the geometry of points rather than some
stringy geometry). It is this limit in which we know for example that D3
branes are special Lagrangian submanifolds (some submanifolds of minimal
volume defined by requiring that certain forms that come with the CY vanish
when pulled back).
Once you move away from this large volume point in Kaehler moduli space, not
much is known exept for a few things: There is another point called the
Gepner point where the CY can be described exactly by some abstract
conformal field theory (a Gepner model). There is also a definition of
D-branes in the language of CFTs but it turns out the spectra differ between
the two points. There might be some more points like "orbifold points" where
there is information accessible about the D-brane spectra, but generically
the situation is unclear.
This was the background, now comes Douglas. One observation is that there is
a "topological string theory" (where amplitudes only depend on the topology
of the world sheet and not on the complex structure of the world sheet, yet
another complex structure!). It turns out, amplitudes in this string theory
are independent of the Kaehler moduli.
Second observation: There are D-branes in the topological theory and it
turns out that all D-branes in the true string theory are also D-branes in
the topological theory but not vice versa. So the problem of finding the
spectrum of D-branes at some point in Kaehler moduli space is translated
into the problem selecting those topological branes (out of those calculated
in the large volume limit) that are true branes at that specific point in
moduli space.
Third observation: The construction of the topological branes exacly
parallels the construction of the derived category. In fact, the topological
branes can be tought of as objects of that category, the tachyon field
somehow representing the morphisms.
As you wrote, the derived category is made out of some category of chain
complexes that should be thought of cohomology classes. But it is also in
some sense coarse grained: At each level it kind of knows what the next level
(and the previous) level is but there is no distinct level 0. In fact, it can
be chosen. And it is this choice that corresponds to selecting the physical
branes from the topological ones.
Those are the rumors that I heard about Douglas' papers. Please correct me!
Robert
--
.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oOo.oO
Robert C. Helling Institut fuer Physik
Humboldt-Universitaet zu Berlin
print "Just another Fon +49 30 2093 7964
stupid .sig\n"; http://www.aei-potsdam.mpg.de/~helling
Aaron J. Bergman
>In article <slrn9p8lcr....@phoenix.Princeton.EDU>,
>Aaron J. Bergman <aber...@Princeton.EDU> wrote:
>>This idea proved to be too simple
>>and there were indications (eg, Harvey and Moore, "On the Algebra of BPS
>>States") that the proper things to look at were coherent sheaves, a
>>slight generalization of a vector bundle where, for example, the
>>dimension of the fiber can change. A simple example is that a D0-brane
>>is basically just a skyscraper sheaf (we're sticking time over there,
>>not here).
>Now I forget the definition of a coherent sheaf, so I'm wondering
>just how big of a generalization we're talking about here.
There is some sense, I think, where coherent sheaves can be considered
as an obvious generalization of vector bundles, but I can't remember the
big words the person in the math department told me.
>Let me pull out Hartshorne's book.... [blows dust off cover].
Eek.
>Hmm, he defines coherent sheaves only over schemes, which makes me
>wonder if this whole business requires us to work in a context
>where we can use algebraic geometry to describe space, or spacetime.
>For example, what if I wanted to work over a smooth manifold?
You could just pull out Griffiths and Harris. There are a bunch of
equivalent definitions. I confess to a lack of intuition for the things,
but the best I can come up with is that a coherent sheaf is something
that looks locally like a quotient of vector bundles. Either that, or
something that looks like a free module with a couple relations and a
few finiteness conditions.
>Wait a minute - there isn't any way to think of a smooth manifold
>as a special sort of scheme, is there?
There is a map from the category of varieties into the category of
schemes. Hartschorne II 2.6, although I still don't understand one or
two details about that.
>>Parallel to this, there were ideas about how to classify D-branes. The
>>simplest thing is to look at the homology class of the brane, or the
>>cohomology class of the generated RR fields. Following some ideas of Sen
>>and also Minasian and Moore, Witten realized that instead of looking at
>>D-branes, it was better to look at stacks (no, not that kind of stack)
>>of D-branes and anti-D-branes and let the tachyon field between them
>>condense. In other words, we have an complex of vector bundles (or,
>>slightly more generally spin^c bundles)
>>
>>0 --> E --> F --> 0
>>
>>to which we associate the K-theory class [E] - [F] which classifies the
>>D-brane charge.
>Cool! So the map E -> F is somehow "tachyon condensation"?
>Physicists always make math sound so science-fictiony. :-)
In fact, the map is exactly the tachyon that you get from a string
connecting a D-brane to an anti-D-brane. Really, Witten's work is a
synthesis of the ideas of Sen, and Moore and Minasian.
The relevant part of the Sen conjectures basically go like this. To save
space, I'm only going to discuss the superstring case, but one of the more
amazing things to have been discovered in recent years is that
nonperturbative calculations can be done to verify this and all the
following conjectures have strong evidence fromt hese calculations.
So, in IIA/IIB string theory, there are only stable (BPS) D-branes in
even/odd (spatial) dimensions, ie, in IIA there is a D0-brane which is
0+1 dimensional. In the opposite dimensions there are unstable D-branes.
On an unstable D-brane there is a tachyon that should look roughly
quartic with two minima and a maximum in the middle. Now, we can imagine
a kink tachyon solution which is solitonic and which is localized in one
less dimenson. Sen conjectured that when the tachyon condenses in this
configuration, a stable (D-1)-brane is left behind. More relevant to our
case, we can look at the situation with a D-brane and an anti-D-brane on
top of each other. The tachyon in this system is complex and looks
basically like a Mexican hat potential. Now, a kink solution still
exists, but is unstable because pi_0 of the vacuum is trivial. However,
we can look at a whorl solution taking advantage of the nontrivial pi_1
of the solution. This gives a stable (D-2)-brane after tachyon
condensation. One can go further, with lots of D- and anti-D-branes, and
construct all the stable lower dimensional branes via the
Atiyah-Bott-Shapiro construction.
But I haven't talked about K-theory yet. So, let's look at IIB string
theory with stable spacetime filling D9-branes. We have just seen that
any configuration of lower dimensional branes is conjectured to be
realizable as some configuration of the tachyon (and, hence, the gauge
bundle) on those sets of branes. Thus, we want to say that the
configuration of D-branes is given by a pair (E,F) where E is the vector
bundle on the D-branes and F is the vector bundle on the anti-D-branes.
Of course, because of tachyon condensation, we have to identify the
following pairs (E,F) ~ (E+H,F+H). Et voila! K-theory. This argument is
essentially what Witten gave in his original paper.
John Baez
Aaron J. Bergman <aber...@Princeton.EDU> wrote:
>There is some sense, I think, where coherent sheaves can be considered
>as an obvious generalization of vector bundles, but I can't remember the
>big words the person in the math department told me.
Maybe if we publicly flounder around long enough, some algebraic
geometer will pull a deus ex machina and explain some of this stuff.
>>For example, what if I wanted to work over a smooth manifold?
>You could just pull out Griffiths and Harris.
Oh, wow - much easier to read.
>I confess to a lack of intuition for the things,
>but the best I can come up with is that a coherent sheaf is something
>that looks locally like a quotient of vector bundles. Either that, or
>something that looks like a free module with a couple relations and a
>few finiteness conditions.
Those both sound right to me - and in nice situations they may
be two ways of talking about the same thing. Maybe it's something
like this: given some reasonable hypotheses, algebraic vector bundles
on a variety correspond to "locally free" coherent sheaves (where
the associated module of sections over any small enough neighborhood
is a free module), while coherent sheaves should be the more general
notion you're forced into when you want an abelian category that
contains the locally free coherent sheaves. An abelian category has
kernels and cokernels, so this is just a fancy way of restating your
remarks about "locally like a quotient of vector bundles". We
definitely want an abelian category because that's the sort of thing
people form derived categories from - in other words, all the usual
stuff about chain complexes and co/homology works in any abelian
category.
>>Wait a minute - there isn't any way to think of a smooth manifold
>>as a special sort of scheme, is there?
>There is a map from the category of varieties into the category of
>schemes. Hartschorne II 2.6, although I still don't understand one or
>two details about that.
Okay, I was dreaming of something that would even work for just *smooth*
manifolds, but that may be too ambitious.
>So, in IIA/IIB string theory, there are only stable (BPS) D-branes in
>even/odd (spatial) dimensions, ie, in IIA there is a D0-brane which is
>0+1 dimensional. In the opposite dimensions there are unstable D-branes.
>On an unstable D-brane there is a tachyon that should look roughly
>quartic with two minima and a maximum in the middle.
I don't understand this stuff. Can you stand explaining it?
What does it mean to say there's a tachyon on the D-brane?
My vague guess is something like this: D-branes can serve as
boundary conditions for strings, but somehow (I forget - how?)
they are dynamical too, and (perhaps in some limit?) their degrees
of freedom are described by a quantum field theory (what's this
theory like?), and you're saying that in certain situations this
theory has tachyons.
That's probably enough questions for now! I'm basically asking
you to take pity on me and tell me some basic stuff about D-branes.
Sheaves, schemes, stacks, derived categories... those are not so
scary for me. But D-branes... that's another matter!
Aaron J. Bergman
>In article <slrn9q2une....@yuma.Princeton.EDU>,
>Aaron J. Bergman <aber...@Princeton.EDU> wrote:
>>There is some sense, I think, where coherent sheaves can be considered
>>as an obvious generalization of vector bundles, but I can't remember the
>>big words the person in the math department told me.
>Maybe if we publicly flounder around long enough, some algebraic
>geometer will pull a deus ex machina and explain some of this stuff.
Somehow, I think adding in coherent sheaves makes the moduli space of
vector bundles prettier.
>>So, in IIA/IIB string theory, there are only stable (BPS) D-branes in
>>even/odd (spatial) dimensions, ie, in IIA there is a D0-brane which is
>>0+1 dimensional. In the opposite dimensions there are unstable D-branes.
>>On an unstable D-brane there is a tachyon that should look roughly
>>quartic with two minima and a maximum in the middle.
>I don't understand this stuff. Can you stand explaining it?
>What does it mean to say there's a tachyon on the D-brane?
>
>My vague guess is something like this: D-branes can serve as
>boundary conditions for strings, but somehow (I forget - how?)
>they are dynamical too, and (perhaps in some limit?) their degrees
>of freedom are described by a quantum field theory (what's this
>theory like?), and you're saying that in certain situations this
>theory has tachyons.
Well, you remember that there's this strange duality between the
worldsheet and spacetime in string theory. Just as we quantize the
fields on the worldsheet and think of these as fields in spacetime, we
can look at the CFT on the worldsheet of an open string with not just
Neumann boundary conditions, but also Dirichlet boundary conditions in
some direction. When you look at this, you find that, in the "wrong"
dimension for the superstring, there is a tachyon in the spectrum. There
is also a massless gauge field in the spectrum and, as usual, an
infinite hieracrhy of massive fields. As before, we want to interpret
these fields in spacetime. Because the strings are confined to a
submanifold, we have an action on that submanifold that gives eoms for
the various fields you get from quantizing the open string. There are
actually ways of obtaining the nonperturbative form of the action by
looking at RG flows on the worldsheet and the conditions for conformal
invariance. When I said, "the tachyon should look" above, I misspoke. I
meant that "the tachyon potential should look...".
Andy Neitzke
> Hmm, he defines coherent sheaves only over schemes, which makes me
> wonder if this whole business requires us to work in a context
> where we can use algebraic geometry to describe space, or spacetime.
> For example, what if I wanted to work over a smooth manifold?
In most (all?) of the work so far on derived categories in string theory
one considers the case of strings propagating on a Calabi-Yau manifold
times four-dimensional Minkowski space. The arguments of Douglas seem to
depend heavily on the properties of superconformal field theories as
opposed to ones which are merely conformal; e.g. given a particular string
boundary condition, one decides whether it is a "brane" or "anti-brane" or
something inbetween by asking which combination of world-sheet supercharges
it preserves.
-Andy
Aaron J. Bergman
par...@black.nmt.edu (Paul Arendt) wrote:
> In article <abergman-5142DA...@cnn.princeton.edu>,
> Aaron Bergman <aber...@Princeton.EDU> wrote:
>
> >Technicolor is a composite Higgs theory as I remember it...
>
> This seems like a good lead-in to ask something that's been
> bugging me for a while. I've seen statements here on s.p.r. in
> the past that some folks find the concept of an elementary
> (non-composite) spin-0 Higgs field disturbing.
Generally this is because of naturalness issues. In other words, it's
difficult to stop the Higgs mass from blowing up to your cutoff scale
from loop corrections.
There are some other weirdnesses with scalar fields, though. I know
Hawking had some idea that they might not be observable due to QG
effects, but I've never actually looked at the paper. There's also the
word of Barcelo and Visser showing that conformally coupled scalar
fields violate pretty much every energy condition you can think of.
Stephen Speicher
>
> In the chapter on Copenhagen Heisenberg is always keen to
> ascribe to Bohr, that which is Bohr's, namely complementarity.
> One can read that as giving credit, or one can read it as
> expressing a view that one does not entirely go along with. But
> it seems to me that Heisenberg is saying that it is legitimate
> to use the language of complementarity provided one is aware
> that the language does not encapsulate reality, and that it is
> legitimate to think in terms of waves provided one is only
> interested in solving a problem, and not mistaking matter waves
> for being real.
>
I've pared Charles' response down to his final statement above,
which sums up the essence of his argument. Permit me to remind
Charles what is in question here, namely Charles' assertion that:
"But more strictly according to Heisenberg the
Copenhagen interpretation does not include
wave-particle duality..."
I agree that Heisenberg goes further than Bohr in regard to his
view of quantum reality -- I said so myself in my initial
response. But that is not the issue here; the issue is whether or
not wave-particle duality is a part of the standard Copenhagen
interpretation. The quotes I provided were from Heisenberg's book
in the chapter titled "The Copenhagen Interpretation of Quantum
Theory." Any appeal to other sections of the book -- as Charles
has done -- is helpful in gaining a full appreciation of the
depth and scope of Heisenberg's thoughts, but such goes beyond
the immediacy of the issue, i.e., wave-particle duality in the
Copenhagen interpretation.
I will repeat one short quote from the section on the Copenhagen
interpretation. That Heisenberg chooses to make these comments
_while discussing what the Copenhagen interpretation is_, should
be sufficient evidence to realize that Heisenberg includes
wave-particle duality as part of the Copenhagen interpretation.
"The dualism between the two complementary pictures --
waves and particles -- is also clearly brought out in
the flexibility of the mathematical scheme...Therefore,
this possibility of playing with different
complementary pictures has its analogy in the different
transformations of the mathematical scheme; it does not
lead to any difficulties in the Copenhagen
interpretation of quantum theory."
Note the final sentence -- a clear statement of inclusion of
wave-particle duality in the Copenhagen interpretation, as stated
by Heisenberg. That Heisenberg had additional thoughts, thoughts
which put various quantum issues into a different context, is
quite interesting and worthy of separate discussion, but not
directly relevant to the issue here.
Lubos Motl
> The model I described in my previous post allows for 3 families
> if you take N = 12 in the SU(N) technicolor gauge group.
Could you please say or repeat the reference where one can read about such
a SU(12) preon model with 3 families?
> You can probably learn about preon models to your heart's content
> in this review article:
>
> Technicolor
> Edward Farhi and Leonard Susskind
> Published in Phys. Rept. 74:277, 1981
Once I asked Lenny a stupid question, something like "Could you please
tell me a few words about the way how you (co)discovered technicolor?"
Lenny got a slightly upset and he said "I would prefer to tell you how I
discovered string theory." And it was an exciting story although David
Gross calls these contributions that identified the one-dimensional string
with its tower of harmonic oscillators waiting behind the Veneziano
amplitude a "poetry". :-)
I want to say that technicolor is not necessarily the thing that Lenny
(and others) are most proud about.
> That's not true. This is a myth propounded by theorists.
>
> Here are 3 examples of experiments that go beyond the Standard Model,
> which a really good theory would have made predictions about:
>
> 1) Neutrino oscillations. The discovery of neutrino oscillations went
> beyond the original Standard Model, which had only left-handed neutrinos
> and did not allow for oscillations.
By the "Standard Model" I meant the "generalized" Standard Model with the
full Dirac neutrinos.
> After this discovery, the Standard Model was modified to allow for
> neutrino oscillations. It now includes right-handed neutrinos.
> However, a really good theory of particle physics would have predicted
> all this ahead of time.
Well, I completely agree. As Jacques Distler said, even to us who know and
love Her, the Standard Model is an ugly monster. :-) But anyway, it works.
It has a lot of input that you must put it, but the predictions made
afterwards agree with the experience.
The Standard Model cannot explain the value of its 19 parameters, the
number of families, the precise representations and gauge groups, no
details of its construction. Well, this is one of the basic reasons why
people study string theory that has the capacity to explain those things.
However, you certainly cannot say that the Standard Model disagrees with
reality just because you do not like the way how it was created. Neutrino
masses are too small and it is not surprising that people did not see
them. Therefore they created a simplified Standard Model without the
right-handed neutrinos just like they invented nonrelativistic theories
because "c" is so huge. Later, the effects resulting from a finite "c" or
finite neutrino masses were found and physical theories were "improved".
This is an ashaming way to do research but the results do agree. You
cannot say that special relativity is not a good theory because it
predicted Morley-Michelson experiment only after it was actually measured. ;-)
> 2) Dark matter. It now seems that the dominant contribution to the
> energy of the universe is a poorly understood invisible form of matter
> which does not fit into the Standard Model. A good theory of particle
> physics would have predicted this ahead of time and said something about
> its properties.
Once again, the Standard Model is not "so" great theory of particles.
However I disagree with the word "good". You cannot say that a theory is
"not good" because it did not predict something long time ago.
Furthermore, dark matter has probably components consisting of particles
beyond the Standard Model (and there are very many candidates today).
Therefore I am absolutely confused why you blame the Standard Model for
ignoring it.
> 3) Cosmological constant. It now seems that the universe's expansion
> is accelerating due to a nonzero cosmological constant - that is,
> a nonzero vacuum energy density, or something with similar effects.
> Again, this does not fit into the Standard Model.
Not only cosmological constant. Gravity itself - including the falling
Newton's apple - contradicts the Standard Model as well as any local
quantum field theory. This is the second major reason why we study string
theory. It is not reasonable to think about the resolution of the
cosmological constant puzzle before you can actually talk about gravity.
And in the Standard Model, you cannot talk about gravity consistently.
> Again, a good theory of particle physics would have predicted this
> effect before it was observed. Instead, most theorists were busy
> trying to explain why the cosmological constant was zero!
I think that you completely misunderstand the way how our knowledge of
physics is getting improved. "The good theory" i.e. the final theory of
everything i.e. string/M-theory in its final form will be perhaps able to
calculate and predict everything. Unfortunately (or fortunately), it will
be found much later than most of the effects you mentioned are known to
the experimentalists.
If physics experiments were banned and only theoreticians were allowed to
think, maybe - if they had enough imagination - after a couple of
thousands of years they could find the theory of everything. Actually I
doubt that something like that is possible although some old Greeks
believed that it was possible. Many experiments were extremely important
for our understanding of the Universe and we also needed to improve
technology etc. to be able to do new experiments. Without seeing many
effects, we would be constrained to various prejudices: the
non-relativistic prejudice, the non-quantum prejudice, the non-stringy
prejudice, the flat Euclidean geometry prejudice, the 3-dimensional
prejudice etc.
But it is clear that the final theory of everything admits many layers of
approximations and we were learning all the things step by step. You could
also blame Newton that he did not predict the spectrum of Hydrogen: his
theories were not good. Well, yes, they were not good enough but they
constituted a tremendous progress just like the Standard Model constitutes
a quantum leap. One day, maybe, we will do more than just "another step":
a final step. But it is not reasonable to think that we may do all the
steps at the same moment.
And once again, you cannot say that a theory is not good or it is partly
wrong just because it was constructed or completed after some of its
consequences were known experimentally. We should agree about those words:
the Standard Model is not fully satisfactory - this is one reason why we
go beyond it - but it *is* a *good* theory explaining the known facts.
> In all 3 cases string theory is sufficiently flexible to retroactively
> accomodate the new developments. But in no case did it give a robust
> prediction of these experimental developments *before* they happened.
Once again, it certainly does not mean that the theory is bad it any way,
especially if there are no competitors that would be able to achieve the
goal you mentioned. It is also a consequence of our limited human
abilities that we cannot figure everything out before we see anything. If
you think that you are better than human beings, try it. However I do not
think that you have much chance to achieve what only God can. :-)
> In all 3 cases it is not too late for a good theorist to make predictions
> *now*. There is still a lot unknown about neutrino oscilations,
> dark matter and the cosmological constant!
Right. So answer those questions if you think that your colleagues are
doing a bad job! :-) If you worked in NASA, would you blame them that they
cannot send missions to other galaxies right away?
> Not surprisingly, many physicists are leaping to the challenge. However,
> many of the top string theorists are busy chasing "M-theory", leaving
> the job of actually making physical predictions to the more lowly
> "phenomenologists". The quest for M-theory is a largely mathematical
> enterprise, relatively unaffected by experimental results.
I think that this approach is the most reasonable one. We are clearly
missing some links in the basic properties of string theory that are
obviously inevitable to answer *all* the questions you mentioned as well
as many others. This is why many reasonable people focus on the properties
of M-theory. There are other people who would prefer to answer simple
questions (like yours) tonight and get a Nobel prize next month (I don't
claim that this is the main motivation for all of them). Well, I do not
think that they have too much chance. It is good that people do different
things but it is very unlikely to obtain the final answers to your
questions before the relevant conceptual properties of M-theory are
revealed.
To give you experimental evidence for my claim, note that although many
people tried to solve all your problems for years "directly", none has
succeeded. On the other hand, (other - or sometimes the same) people have
made a tremendous progress in understanding the theoretical framework of
M-theory. Well, I think that the direct attempts to attack phenomenology
do *not* constitute the highest quality research that is going on and I
also think that its results are far less convincing than the results of
the purely theoretical investigations. The pure theoreticians have much
more patience. I think you should learn to be patient, too: when
everything will be explain, we will have nothing to study in fundamental
physics!
> >From its philosophy, it is clear that string theory is ultimately able to
> >predict everything and contains no adjustable parameters etc.
>
> That's very nice, but being "ultimately able to predict everything" is
> a rather dangeorous substitute for being "currently able to predict
> something".
It is not a substitute, it is a different thing. String theory will be
probably ultimately able to predict everything but it is also currently
able to predict something (thermodynamical properties of black holes, for
example) although very relatively things like that are specific for string
theory; however string theory is the only framework that can combine all
of them together. Anyway if we are close to a perturbative limit of string
theory, the experimental signs would be very distinctive at high enough
energies.
> You seem here almost to be claiming that ultimately string theorists will
> find a unique nonperturbative vacuum and that this will allow them
> to derive the Standard Model gauge group and all the coupling constants
> from first principles, together with all the new phenomena not included
> in the Standard Model.
Sure, this is the goal, of course. Is it the first time that you hear that
this is the goal of string theory?
> That's what I would call "ultimately predicting everything", and it
> would be an incredible triumph - but there is really no evidence that
> anything like this will happen.
I don't think that there is no evidence. String theory predicts gravity,
gauge fields and matter as qualitatively seen in the Standard Model and
everything in it is completely dynamical as we know very well; once we are
able to calculate the potential etc. properly and nonperturbatively (and
we have learned many pieces of this task although not completely), the
structure of the ground states etc. will be clear and we will be able to
derive the consequences of string theory, indeed. Maybe there are millions
of ground states and we will have to pick one by guessing. Maybe there is
only one ground state after SUSY is broken. But anyway, this will give us
a full key to decide whether string theory describes the real world or
not. Of course, I do not think that history will go in this "exact" way.
We will learn pieces by pieces, just like we always did in physics!
> Of course, you may not really mean that there is a unique
> nonperturbative vacuum.
I don't know whether there is one, two or a billion. I know that there are
infinitely many vacua with large unbroken supersymmetry that will have to
be accepted as "existent somewhere". We must apply the anthropic principle
or something like that to explain why we don't live in a world with 16
supercharges, for example. But among the phenomenologically plausible
vacua with N=0/1 SUSY in 4 dimensions, it is still possible that there is
a unique nonperturbative vacuum. It is certainly the possibility that
physicists would prefer aesthetically but we don't know. If there are 26
of them, how can you complain about that? :-)
> Maybe you mean that there are a bunch and that string theorists will
> eventually understand them. If they found, say, 5, and one matched
> the Standard Model pretty well, but also made new testable predictions
> that turned out to be true, this would again be a triumph. If they
> found a trillion, and of these several thousand matched the Standard
> Model pretty well, that would be less of a triumph, but still
> interesting.
Right.
> But my main point is that all these scenarios are just hopes and dreams.
No, they are not. They are more than dreams; they have been partially
realized. In the 80s people thought that there were 5 string theories.
Today we know that there is one string theory only. You could have
compactified string theory on thousands of different Calabi-Yau spaces.
Today we know that there are critical transitions that can change topology
and connect all those vacua to a simple structure, too. People dreamed to
find a nonperturbative formulation of string theory. Now we have couple of
them for certain backgrounds. In the past, people did not understand the
meaning of the coupling constants. Later it has been found that they are
scalar fields in string theory whose values are determined dynamically.
People knew from 1974 that string theory should contain quantum gravity
and they knew that it should also predict the correct entropy of black
holes. When Strominger and Vafa tried it for the first time, it precisely
agreed. Before 1985 people did not know how can string theory predict the
number of families. It was realized how they are related to the Euler
character of the Calabi-Yau space. In the early 70s it was not known that
string theory contains gravity. It was found out that it does contain
gravity with everything we want. It was not known whether it can give us
realistic SM-like models. It was found in 1985 that it can give us
everything we need. Well, there are many more important examples from the
past. There are also many examples from the future; unfortunately, I don't
know them. :-) But it is neither reasonable nor fair to criticize string
theory (or anything or anyone else) because we don't live in the future.
Our state of knowledge is where it is and is continuously improving. Even
the current state of string theory makes it much more attractive than any
non-stringy competitor; this is why most papers about high-energy theory
are related to strings.
> Currently string theory offers far less: there are zillions of perturbative
> string theories, we must introduce lots of new parameters by hand when we
> break supersymmetry to make them physically realistic, and as a result,
> string theory can fit pretty much any data that experimentalists are
> presently able to come up with... but never make any solid predictions
> ahead of time.
You say several sentences but you still talk about the only single
problem. We know that the perturbative string theories are mostly
connected into one; that there is a potential on the full configuration
space that chooses not only the local minima in "one perturbative string
theory" but chooses them globally in all the components (and the minimum
can be unique). The problem is that we cannot yet fully describe "what is
the full configuration space" (this formulation is clearly misleading in
the full stringy context) and what is precisely the potential (that can be
calculated only partly); we know partial and approximate answers to this
question. Once you know the potential, you can calculate all the
parameters - the old ones as well as those from SUSY breaking - without
knowing anything from the experiments, at least if you are powerful
enough. Therefore you still talk about the same single incompleteness of
our understanding that can be solved in 50 years but also this year.
> The inverse square law for gravity might break down at
> submillimeter distances... or it might not. The next generation of
> particle accelerators might see the superpartners of known particles...
> or it might not. Etcetera.
Right. We don't know. If you do, I will be more than happy to learn the
answer.
> This is why there is still a need for theories like preon models which
> make definite predictions that we have a chance of testing.
I completely disagree. While string theory predicts the inverse square law
in 4D at long distances, the preon model does not. Therefore string theory
is not ruled out as the ultimate theory while the preon models are. I
completely disagree that we should play with some accidental theories just
because we should have something that can be tested. There are thousands
of different preon models and trillions of other models of comparable
qualities - and neither of them can be the ultimate theory. I find it
useless to work on such theories because they cannot give us more
information than the immediate data from the experiments.
>From thousands of preon models, a few can agree with the new experimental
data that will eventually show something beyond the SM. OK, you choose
them. Then you will desire to go further. So you create million extensions
of the successful preon models. A new wave of experiments picks a few
hundred of them. I don't think that the preon models would give you more
than the experiments themselves; they represent guessing, nothing more.
There are millions of them. They are completely disconnected. And even the
more successful ones are guaranteed not to be the ultimate theory, just
like the Standard Model is not: they have parameters; their details are
unexplainable; they do not explain gravity; they share all the problems of
the Standard Model. So what are they good for? They are just funny games
trying to interpret the known phenomenological data using a new composite
structure. They are not "true" in any deep way.
> (By the way, I'm not a big fan of preon models: I'm just enjoying
> defending this very unfashionable dark horse against the fashionable
> juggernaut of string theory!)
I don't think so: at this newsgroups, string theory is an outsider that
enjoys say 40% of favorable votes. You represent the cruel majority that
wants to prosecute the string theory minority. ;-)
> I'll have to read this paper, because I consider this to be the
> most urgent problem in string theory, and I'd really like to
Sorry, I did not mean paper. I meant a post at this newsgroups. Sorry for
the confusion. ;-) Look at Joe's book first and then try to look at
various papers.
> understand the state of the art. I'm glad you at least agree with
> my most basic claim: we don't know how supersymmetry is broken.
Yes, we don't know how it is broken but we (or at least some colleagues
who are very good at it) know many things about how it can be broken.
> I guess to be convinced I will have to see how this works in a toy
> model, and assure myself that no funny tricks are being played, and
> (the hard part) come to believe that the same mechanisms can work in
> more realistic models.
Yes, a good strategy to understand something.
> Well, I sure hope that people can translate "in principle" to
> "in practice".
Yes, after some time, they can. But in string theory the situation is
harder because so far we are not able to calculate all the necessary terms
nonperturbatively exactly, even in principle.
> Everything that can be done in principle can eventually be done in
> practice... in principle. But in practice, it's another matter. :-)
:-)
> They both give descriptions of what we might see in the next generation
> of particle accelerators.
Yes, that's correct. If you want to bet that LHC will see 3 or 12
constituents of the electron, I will be more than happy to make the bet
with you! :-) I am ready to give you 5 times more if you win.
> Yes, I realize that the octopus-like flexibility of string theory allows
> even preon models to be considered as special cases of this theory. But
> as far as I'm concerned, this is just another sign of string theory's
> lack of predictive power. A theory which can fit anything predicts nothing.
I did not say that string theory can embed all the preon models. In fact I
believe that no preon model can be embedded in string theory. I just said
that string theory would be able to include a good preon model. ;-)
Because it probably cannot, it is an example of the string theory's
predictive power that we see even before all the strength of string theory
is revealed. :-) Sometimes you complain that string theory is too
flexible. But you know that it is not. It has pretty clear properties that
show that it cannot be equivalent to Loop Quantum Gravity (and probably
also to preon models). If a progress is done in the full stringy dynamics,
it will be able to rule essentially any wrong model out.
> (As usual, when I talk about string theory's lack of predictive power,
> I refer to the theory as it currently exists, not as you dream it will
> someday be.)
But it is only because we talk about pretty complicated 4D low-SUSY vacua
that are harder to study. If we talked about the vacua with 16
supercharges in SUSY (in higher dimensions), we could derive anything and
rule anything else out; the predictive power would be almost absolute
already now. You are just abusing that string theory is in the process of
construction.
> >If I simplify the issue a little bit, the previous sentence is true by
> >definition because a good idea in physics is defined as something that is
> >contained in string theory. ;-)
>
> Right - this is exactly what we'd expect of a theory with zero
> predictive power.
Nope. A theory with zero predictive power contains *every* idea or *no*
idea. String theory contains *every good* idea only. ;-)
Alfred Einstead
> the real world.
Except the most important one, the one that counts: actually doing so.
Here's a simple exercise for you. Derive the value of g for the electron
from string theory, directly, without any handwaving arguments or
appeals to things "we're on the verge of proving but the correct
theory/definition/equation/concept/(fill in blank) is not yet available".
I expect a written report on my desk by next week.
J. Michael Niczyporuk
> In article <abergman-5142DA...@cnn.princeton.edu>,
> Aaron Bergman <aber...@Princeton.EDU> wrote:
>
> >Technicolor is a composite Higgs theory as I remember it...
>
Be careful with terminology here. The Higgs mechanism is the
spontaneous breaking of a (local) gauge symmetry, that is, a means
of writing down gauge-boson mass terms in a gauge-invariant fashion.
Since mass terms are relevant deformations (in the Wilsonian sense),
they do not affect the nice UV properties of gauge theories.
To the extent that the Standard Model is a gauge theory,
valid to at least around 1 TeV, the Higgs mechanism exists.
However, whether or not a (physical) Higgs boson exists is another
matter. For the Higgs mechanism to take place, one only really needs
three would-be Goldstone modes of some symmetry-breaking sector,
which become the longitudinal degrees of freedom of the W and Z.
If you demand that this symmetry-breaking sector be perturbative
(weakly coupled) and renormalizable, then there must be a
light (say, less than around 600 GeV) Higgs boson. In general,
one need not have a Higgs boson. In particular, there is no
Higgs boson in generic technicolor theories. There is nothing wrong,
a priori, with strongly-coupled symmetry-breaking sectors,
although one has to work much harder to be consistent with
existing precision phenomenology.
In general, to have a (light) Higgs boson, one needs to fine tune
the parameters of theory. And it is the necessity of such fine tuning
that makes Higgs bosons, whether they be fundamental or composite,
theoretically unattractive. [Actually, since interacting scalar field
theories
don't make sense to arbitrarily large energies, there is no such
thing as a truly "fundamental" Higgs boson.]
> So I suspect that there may be arguments against
> non-composite Higgses which actually have to do with the Higgs
> mechanism. Can anybody enlighten me here?
The basic point is that, in a theory with some ultraviolet cutoff M
(which could be the GUT or Planck scale, for example), the mass
of any interacting scalar field, such as a Higgs boson, is naturally
of order M. Even if you set it to be light at tree-level, radiative
corrections will shift it to the cutoff scale M. This is the gauge
hierarchy problem. It is really a naturalness problem: why is
the mass of the Higgs (few 100 GeV) so much smaller than
typical contributions to it, which are order M?
It really comes down to symmetry, or lack thereof. We know how
to ensure light spin-1 particles, by using gauge symmetry. We know
how to ensure light spin-1/2 particles, by using chiral symmetry.
But there is no symmetry that ensures a light, interacting scalar field.
(Goldstone bosons are naturally light, but they also cannot have
non-derivative interactions.) This is why supersymmetry solves
the hierarchy problem. It requires a Higgsino, the spin-1/2, degenerate
partner of the Higgs. Since chiral symmetry ensures a light Higgsino,
supersymmetry requires that the Higgs be likewise light! Radiative
corrections no longer destabilize the hierarchy between the Higgs mass
and some UV cutoff M.
The other way to solve the hierarchy problem is to get rid of the hierarchy,
i.e., lower M to the TeV scale! This is the idea behind large extra
dimensions, for example...
Michael
Robert C. Helling
>I have changed the title away from "Preon models", which is
>ludicrously irrelevant to what we're talking about now.
You should have done this earlier! I deleted those posts without looking at
them (shame on me, I have to go back to the archive).
>Now I forget the definition of a coherent sheaf, so I'm wondering
>just how big of a generalization we're talking about here.
I am not really sure, but my little private interpretation of what I think
of when I hear people talk about coherent sheaves is the following: For maps
of vectorspaces f : V -> W we all know and love the notion of "kernel" (for
example we need it in exact sequences etc). But now think of V and W not as
vectorspaces but of vectorbundles over some spaces X. Maps between those
(let's say: base point preserving) do in general not have kernels: Of course
you can form kernels fiberwise but you cannot glue them together to get a
new vectorbundle:
For example take X= C (the complex numbers) and V and W line bundles. Define
f:V->W fiberwise by
f_x(v) = xv for x in C and v in the fiber at x.
Obviously, the "kernel" is 0 everywhere except for the origin of the base
where it is C. This is not a vectorbundle as the rank is not locally
constant. To my understanding, this is the archetypical example of a
coherent sheaf that is not a vectorbundle. So my working physicist's
definition of a coherent sheaf is "a vectorbundle where the dimension can
jump". It might be the case that the location of the jump must be a
codimension 1 submanifod of X, but for this I am even less sure.
Andy Neitzke
>In most (all?) of the work so far on derived categories in string theory
>one considers the case of strings propagating on a Calabi-Yau manifold
but managed to omit the reason why the supersymmetry is really
essential: the papers I've seen work not with the physical open
string superconformal field theory, but rather with a "twisted"
version of that theory, which has the advantage of being topological
and hence in some sense more tractable. Now the way it gets to be
topological is that it contains a scalar "BRST-like" operator Q, which
is the twisted analog of the fermionic supersymmetry operator, and
then one works just on the cohomology of Q. So for this construction
to make any sense we have to start with a supersymmetric theory.
(Of course there then remains the difficult question of understanding
the relation between boundary conditions in the topological theory and
in the physical theory -- in particular, one wants to understand which
objects in the derived category of coherent sheaves are actually
stable in the physical theory.)
-Andy
Gordon D. Pusch
> In article <9n8n98$10hv$1...@newshost.nmt.edu>,
> par...@black.nmt.edu (Paul Arendt) wrote:
[...]
>> This seems like a good lead-in to ask something that's been
>> bugging me for a while. I've seen statements here on s.p.r. in
>> the past that some folks find the concept of an elementary
>> (non-composite) spin-0 Higgs field disturbing.
>
> Generally this is because of naturalness issues. In other words, it's
> difficult to stop the Higgs mass from blowing up to your cutoff scale
> from loop corrections.
>
> There are some other weirdnesses with scalar fields, though. I know
> Hawking had some idea that they might not be observable due to QG
> effects, but I've never actually looked at the paper.
The gist of Hawking's argument is that for particles interacting with
``gravitational instantons,'' there is a spin-dependent phenomenon
analogous to an ``angular momentum barrier'' that keeps anything but
an elementary scalar from actually ``feeling'' the planck-scale core
of the instanton, so that elementary scalars are the only particles
that will be strongly influenced by gravitational instanton effects.
He then classifies gravitational instantons topologically, and argues that
in the ``dilute iunstanton gas'' approximation, one class of instantons
destabilizes the propagation of an elementary scalar, driving it to become
a planck-mass tachyon. He therefore argues that elementary scalars probably
do not make sense in the quantized version of any metric theory gravity.
> There's also the word of Barcelo and Visser showing that conformally
> coupled scalar fields violate pretty much every energy condition you
> can think of.
However, it's not clear that conformally coupled scalars make sense
_anyway_, so that may perhaps not be a strong objection to scalars...
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
ba...@galaxy.ucr.edu
Lubos Motl <mo...@physics.rutgers.edu> wrote:
>John Baez wrote:
>> They feel the complex web of relationships is in some sense "already
>> there", and they are just noticing it, rather than making it up in
>> some ad hoc way as they go along.
>In this sentence, you seem to say that you like the Platonic viewpoint
>that the mathematical ideas already exist "somewhere" independently of
>physical reality.
Actually I was carefully trying to avoid stating my own view on
these matters: I was just saying that researchers in completely
integrable systems *feel* that they're discovering something that
is already there.
However, if you really want to know my opinion, I'll admit it:
I think they are right.
>> Zirkus wrote:
>> >There have been quite a few surprises in the
>> >theoretical development of string theory, and also there has been a
>> >fertile relationship with profound mathematics.
>> This is also true of completely integrable classical systems.
>Could you remind us which surprises you really mean, just to be sure?
Well, for example, the fact that you get an infinite set of
conserved quantities for the KdV equations by using the solution
(at any given moment in time) as the potential for a Schrodinger-type
Hamiltonian and using the eigenvalues of this Hamiltonian as the
conserved quantities. In other words, the Lax pair idea. By now
this is old news, but if you remember that the KdV equation started
out as a description of waves in shallow water, you'll understand how
surprised people were to find quantum mechanics sneaking into the game!
It was then surprising how the Lax pair idea wound up being generalized
to cover vast classes of integrable systems, and how it wound up being
related to the Yang-Baxter equations, quantum groups, and ultimately knot
theory.
>From shallow water waves to knots - quite a journey! But this is just
a small fragment of the whole story.
>Otherwise, completely integrable physical systems are mostly part of
>mathematics and therefore the second sentence about their interactions
>with mathematics is a tautological consequence of reflexivity of the
>relations. ;-)
Completely integrable systems are indeed mostly part of mathematics;
the same is true of string theory so far, which is why I made the
analogy. My point was nontautologous: it was that like string theory,
the study of completely integrable systems leads one into *profound*
mathematics. One might not at first expect that Lagrange and
Kowalewski fiddling around with exactly solvable problems involving
tops would have led into such deep waters.
>I am extremely disappointed if you don't see any difference between
>"profound mathematics" and "fancy mathematical game".
Eh? I see a huge difference!
>It sounds a little bit like if you say that you believe that there
>can exist no intuition for good ideas in physics.
Eh? I certainly DO believe there is such an intuition.
>> All I know is that good mathematics always involves surprising new
>> connections and gives one the feeling that one is discovering it
>> rather than making it up. This is true of everything from homotopy
>> theory to number theory to... string theory!
>You still don't see the essential difference. If you play chess, you see
>also many surprising connections that "objectively exist". Yet, strategies
>in chess are not examples of profound mathematics; chess is a fancy
>(mathematical) game.
Eh? It sounds like you're arguing against someone other than me!
We agree that the rules of chess are arbitrary human inventions, and
that a new chess strategy is not a very profound discovery, because it
won't help you understand a broad range of phenomena. Deep mathematics
is very different - it helps you understand all sorts of superficially
unrelated things.
Here was my point again: when people say that string theory is
good physics because they feel it is being discovered rather than
invented, they neglect the fact that everyone coming upon deep
mathematics has this feeling. This feeling is not a sign of
good physics; it's a sign of good mathematics. To be good physics,
a theory must actually make predictions that are verified by experiment.
Squark
<slrn9q3nce....@qft102.physik.hu-berlin.de>):
>So my working physicist's definition of a coherent sheaf is "a vectorbundle
>where the dimension can jump".
This intuition is not always right. For example, consider the scheme X =
Spec C[x] (I am using the field of complex numbers C for simplicity,
though any other field would for just as well), and two coherent sheaves
over it: O_X/(x) and O_X/(x^2). In both cases, the dimension of the
fibers over all points is zero, except the point 0, where the dimension
is 1. Nevertheless, the two sheaves (or O-modules: I prefer to call them
that way) are different. This may be intuitively imagined as another
non-zero fiber in the O_X/(x^2) case, over a point infinitesimally close
to zero. The naive "dimension jumping" picture is thus incorrect, but
can give the right intuition when treated with care.
Best regards,
Squark.
----------------------------------------------------------------------------
Write to me at:
[Note: the fourth letter of the English alphabet is used in the following
exclusively as anti-spam]
dSdqudarkd_...@excite.com
Lubos Motl
> However, if you really want to know my opinion, I'll admit it:
> I think they are right.
Good.
> Well, for example, the fact that you get an infinite set of
> conserved quantities for the KdV equations by using the solution...
Yes, it must be nice. I also know other interesting topics in math which
are unrelated to fundamental physics.
> Completely integrable systems are indeed mostly part of mathematics;
> the same is true of string theory so far, which is why I made the
> analogy.
Nope. I don't understand the sense in which string theory is a "part of
mathematics" instead of a "mathematically deep physical theory". String
theory is mostly done in physics departments by physicists who have
degrees in physics and publish their papers mostly in physics journals.
They understand physics, they use the intuition and the level of rigor as
physicists do and their motivations is clearly physical. And string theory
is also a very physical theory that contains objects and phenomena very
closely related to those that we know from the real world; in fact all of
them.
I also do not understand the words "so far". String theory can be a
physical theory that has not been fully confirmed experimentally and
accepted by the whole scientific community. But it is a *physical theory*
and this question cannot change in time. Whether something is a physical
theory or not, does not depend on immediate subjective feelings of Prof.
Baez.
Laymen think that the word "theory" means just a "conjecture" or
"speculation". But a theory is much more: it must be a consistent
collection of laws and rules intended to describe a broad enough class of
observations. In fact I think that there are very good reasons why string
theory or M-theory is called "theory" (just like the theories of
relativity or quantum field theory) while Loop Quantum Gravity, for
example, is not.
> My point was nontautologous: it was that like string theory,
> the study of completely integrable systems leads one into *profound*
> mathematics. One might not at first expect that Lagrange and
> Kowalewski fiddling around with exactly solvable problems involving
> tops would have led into such deep waters.
Let us not argue whether the depth is equal; I would probably disagree.
But there is one clear difference: the integrable systems as you describe
them are not a theory that can describe the whole fundamental physics of
this Universe - and none tries to claim this I hope - while string theory
is one. Therefore the integrable systems are not - in any reasonable sense
- competitors of string theory in particle physics.
> >I am extremely disappointed if you don't see any difference between
> >"profound mathematics" and "fancy mathematical game".
> Eh? I see a huge difference!
I thought that you wrote the following sentences.
> I don't understand the perjorative significance of "just a fancy
> mathematical game", and precisely how that's supposed to be different
> from "profound mathematics".
Please let me know whether you wrote them and if you did, what you meant
different than I thought.
> We agree that the rules of chess are arbitrary human inventions, and
> that a new chess strategy is not a very profound discovery, because it
> won't help you understand a broad range of phenomena. Deep mathematics
> is very different - it helps you understand all sorts of superficially
> unrelated things.
Good! Agreement.
> Here was my point again: when people say that string theory is
> good physics because they feel it is being discovered rather than
> invented, they neglect the fact that everyone coming upon deep
> mathematics has this feeling.
Everyone can have this feeling but only string theory can be claimed to
describe the fundamental physics. What I say is no speculation: I don't
believe that anyone argues that the integrable systems as studied by the
experts describe the whole world of particle physics; you can show quite
clearly what is missing (essentially everything). On the contrary, string
theory has no known reasons not to describe fundamental physics. Or do you
know a reason? Or you can perhaps use those integrable models to construct
a TOE? Or do you think that this difference - whether something has a
capacity to be a TOE or not - is unimportant for fundamental physics?
> This feeling is not a sign of good physics; it's a sign of good
> mathematics. To be good physics, a theory must actually make
> predictions that are verified by experiment.
I do not agree completely with your choice of the words. If you have a
physical theory that agrees with an experiment or two, it does not mean
that it is a good physical theory. On the contrary, if a theory disagrees
with a single carefully and properly done experiment, it means that the
theory is wrong. But even if you have a working physical theory, it does
not mean that it is nice or satisfactory. We must use theoretical (or
"mathematical") criteria to decide about that. The experience has
certainly told us that among several candidate theories that looked
remotely plausible and had about the same power, the more symmetric and
more mathematically beautiful one turned out to be the correct one. I
don't claim that this must be the universal rule - especially because our
sense for beauty must improve. But the intuition telling us whether a
theory is mathematically nice is important for physics, maybe even more
important for physics than for mathematics. And I believe that if you
think that the mathematical beauty should not count as an argument in our
search for the ultimate theory of physics, you are completely wrong.
Best wishes
Lubos
______________________________________________________________________________
E-mail: lu...@matfyz.cz Web: http://www.matfyz.cz/lumo tel.+1-617/496-8199
Lubos Motl
> >>There is some sense, I think, where coherent sheaves can be considered
> >>as an obvious generalization of vector bundles, but I can't remember the
> >>big words the person in the math department told me.
My feeling has always been the a coherent sheaf is a generalized vector
bundle whose fiber can jump and have a different character - or even
dimension - in different regions of the base space.
> >J.Baez: I don't understand this stuff. Can you stand explaining it?
> >What does it mean to say there's a tachyon on the D-brane?
> >My vague guess is something like this: D-branes can serve as
> >boundary conditions for strings, but somehow (I forget - how?)
> >they are dynamical too, and (perhaps in some limit?) their degrees
> >of freedom are described by a quantum field theory (what's this
> >theory like?), and you're saying that in certain situations this
> >theory has tachyons.
The effective field theory describing the dynamics of D-branes looks like
the Born-Dirac-Infeld action - integral of sqrt(det g_{mn} + F_{mn} +
B_{mn}) at low energies - the total invariant worldvolune corrected by the
electromagnetic field and the B-field - and also some scalar fields should
be added; this is the bosonic part of the simplest case. At higher
energies, you find an infinite tower of massive fields, too. Why is the
D-brane dynamical? D-brane is defined as the submanifold where the
fundamental strings are allow to terminate. The resulting open strings
then have Neumann boundary conditions in the directions parallel to the
worldvolume of the brane - and Dirichlet boundary conditions in the
transverse directions (such as x=0, so that they end where they should
end).
The old open strings always had Neumann boundary conditions only. It means
that they describe a spacetime-filling brane. The strings can terminate
anywhere. People such as Petr Horava and Joe Polchinski studied in 1989
what happens with the open strings under T-duality. They realized that the
Neumann conditions change to Dirichlet ones: the D-brane changes its
dimension by one!
But if you study the states of a single open string with such boundary
conditions, you find a suprise. Sometimes there is a tachyonic ground
state - much like the closed string tachyon of the closed bosonic string;
a ground state corresponding to a particle with m^2 < 0 in spacetime. For
the BPS-branes there is no tachyon. But the first excited state also
contains a (massless) U(1) gauge field and (massless) scalar fields
corresponding to the transverse fluctuations of the brane.
In fact, by a direct quantization of the open string you find the
particles - the quanta of those fields - only. But if you compute the
scattering of all those particles, you realize that the dynamics precisely
corresponds to the scattering amplitudes derived from a
Born-Dirac-Infeld-like field theory with the spin-1 Yang-Mills field and
with some spin-0 scalars, coupled to gravity (a closed string background).
Therefore you know that the transverse scalar can acquire an expectation
value and the brane can bend.
This phenomenon is very similar to the case of the closed string. In that
case you could also see that there is a spin-2 excitation of a closed
string. Dynamics computed for such particles precisely agrees with
Einstein's gravity at low energies. In fact, you can derive Einstein's
equations from the conformal invariance - a consistency condition for the
background - too. This procedure is possible for the open strings, too.
You can postulate some more general boundary conditions for the open
string. The string can be constrained to end on a brane which has a
nontrivial shape and some values of the gauge field etc. You can however
prove that the resulting boundary conformal field theory (CFT with a
bonudary on the worldsheet) is only consistent if the background satisfies
the equations of motion resulting from the appropriate
Born-Dirac-Infeld-like action.
You see that in perturbative string theory, any field that you know
classically, either stuck to the brane (open string) or free to move in
the spacetime (closed string: gravity etc.) results from a proper
quantization of a string with correct boundary conditions on it. The
dynamics is not put by hand: the dynamics of all the scalars, gauge
fields, gravity, as well as the infinite towers of states above them, can
be uniquely derived from string theory - actually in many ways.
> ... some direction. When you look at this, you find that, in the "wrong"
> dimension for the superstring, there is a tachyon in the spectrum. There
Aaron, I think that this comment is extremely misleading. The CFT of an
open string has always the correct central charge and it lives in the
spacetime of a correct dimensionality (10 in the superstring case): the
transverse scalars are still allowed to fluctuate. Only the zero modes are
quantized differently if some coordinates have Dirichlet boundary
conditions. And furthermore, the appearance of the tachyon has nothing to
do with a "wrong dimensionality". Some D-branes have tachyons, others -
with the same possible dimensions - don't. A noncritical string would lead
to ghosts in the physical spectrum (negative norm states). For any
D-brane, you should still say that the (boundary) conformal field theory
lives in 10 dimensions; only the endpoints of the strings (and
consequently also the effective point-like particles describing physics)
are confined to the brane. I am sure that you know all of this and it was
just a difference in terminology.
-------------
Finally, the physical meaning of the scalar and gauge-field excitations of
the open string is clear - BTW the endpoints of a string themselves carry
a charge under this U(1) and for many coincident branes, U(1) is extended
to U(N) and the fields are promoted to matrices. But what does the tachyon
T mean? The negative mass tell us that locally, around T=0, the potential
energy for it has a local maximum. Nonperturbatively, it has been
conjectured by Ashoke Sen that the tachyon potential has a minimum, too.
In the superstring case, V(T) is even and therefore you have two more or
less equivalent minima. But the punchline of the conjecture is that V(T)
for T=T* (the minimum) is negative and precisely cancels the tension
(energy per unit worldvolume) of the brane(s) we started with. In this
point of the configuration space, all the dynamics - as well as the branes
themselves - should disappear: we initially expand around the maximum of
the potential - it signals an instability and the instability is with
respect to the total destruction of the brane which we see if we let the
tachyon roll down to the minimum. This gives us a clear prediction for
the value of V(T) as well as many coupling constants that guarantee that
everything decouples. This conjecture has been recently tested by
numerical calculations in the cubic string field theory, as well as some
exact analyses in the boundary string field theory - and it has passed all
the tests beautifully.
Today, there are no serious doubts that the fate of the open string
tachyons has been understood. The physical meaning (and condensation) of
various closed string tachyons (in nonsupersymmetric theories) has been
investigated, too. And especially in the case of tachyons found in twisted
sectors, a lot of progress has been done, too. We are not at the end yet.
The tachyon of the bosonic string in 26 dimensions is probably the
toughest one to understand. We still do not think whether we should say
that the bosonic string belongs to the consistent physics of
string/M-theory and whether the tachyon can be stabilized in some way.
Charles Francis
Lubos Motl <mo...@physics.rutgers.edu> writes
>Nope. I don't understand the sense in which string theory is a "part of
>mathematics" instead of a "mathematically deep physical theory". String
>theory is mostly done in physics departments by physicists who have
>degrees in physics and publish their papers mostly in physics journals.
>
>They understand physics, they use the intuition and the level of rigor as
>physicists do and their motivations is clearly physical. And string theory
>is also a very physical theory that contains objects and phenomena very
>closely related to those that we know from the real world; in fact all of
>them.
>
>I also do not understand the words "so far". String theory can be a
>physical theory that has not been fully confirmed experimentally and
>accepted by the whole scientific community. But it is a *physical theory*
>and this question cannot change in time. Whether something is a physical
>theory or not, does not depend on immediate subjective feelings of Prof.
>Baez.
By the same token, if it does not depend on the immediate subjective
feelings of Prof Baez, or even those of Charles Francis, then why should
it depend on the immediate subjective feeling of a bunch of physicists,
who, by your own admission, are working from intuition and a level of
rigor which as physicists use, which is not regarded by many a
mathematician as adequate.
>Everyone can have this feeling but only string theory can be claimed to
>describe the fundamental physics. What I say is no speculation: I don't
>believe that anyone argues that the integrable systems as studied by the
>experts describe the whole world of particle physics; you can show quite
>clearly what is missing (essentially everything). On the contrary, string
>theory has no known reasons not to describe fundamental physics. Or do you
>know a reason?
I know a number of reasons. Most of these are rooted in fundamentally
flawed assumptions about space-time, and a failure to examine
foundations rigorously. It is not okay to say something is a theory of
physics based only on the immediate subjective feelings of a bunch of
physicists working from intuitions. It is doubtful that the metaphysical
concept of string even makes sense, since it seems to incorporate
without interpretation aspects of quantum behaviour which a TOE would
need to explain. It is based on gauge invariance, which seems like a
nice compelling symmetry when you read it one way, but is actually just
a degree of freedom in a mathematical structure, not corresponding to
any physics at all when you look at it another way. The whole concept of
string appears therefore to be based on a non-physical degree of freedom
in a mathematical structure.
>> This feeling is not a sign of good physics; it's a sign of good
>> mathematics. To be good physics, a theory must actually make
>> predictions that are verified by experiment.
>I do not agree completely with your choice of the words. If you have a
>physical theory that agrees with an experiment or two, it does not mean
>that it is a good physical theory. On the contrary, if a theory disagrees
>with a single carefully and properly done experiment, it means that the
>theory is wrong.
Historically there are numerous examples where it has meant that the
experiment was wrong, and numerous others when the theory was
fundamentally not wrong, but the calculations of the theorists were
either wrong or incomplete. If one wants to base any philosophy on such
examples, one should at least study them historically to see what they
might signify, rather than pick up on a popular "coffee table"
philosophy of science, and assert that scientific progress is subject to
it.
Sorry, but I do not care how many physicists you have working on string
theory from intuitions and accepted standards (among same physicists) of
rigour. If you want to produce a TOE, a fundamental theory of physics,
you will have to study the fundamentals, such as how space and time are
defined and measured, with absolute rigour.
If these string theorists cannot do such a thing, then they are charged
that the intuitions on which they base their model are nothing but
misconceptions. Just because they work in physics departments and have
degrees in physics, and even publish in physics journals, if they are
working from shared misconception (as has happened numerous times in
history) then there is no particular reason even to think that they are
working on physics at all.
Regards
--
Charles Francis
AG
> John Baez wrote:
> > Well, for example, the fact that you get an infinite set of
> > conserved quantities for the KdV equations by using the solution...
> Yes, it must be nice. I also know other interesting topics in math which
> are unrelated to fundamental physics.
When you look at the history of math and physics you'll see that countless
times pure mathematical research which initially looked totally unrelated to
any physics eventually turned out to have fundamental physical relevance.
> > Completely integrable systems are indeed mostly part of mathematics;
> > the same is true of string theory so far, which is why I made the
> > analogy.
>
> Nope. I don't understand the sense in which string theory is a "part of
> mathematics" instead of a "mathematically deep physical theory". String
> theory is mostly done in physics departments by physicists who have
> degrees in physics and publish their papers mostly in physics journals.
"Physics" is a fluid word. Its meaning is in continual flux. What does it
mean today? As far as I know it is a method of investigation of nature. The
fundamental subject of physics is motion. So physics is the study of motion.
The quality of a theory is independent of the department the paychecks of
researchers come from.
What is "a mathematically deep physical theory?" Does it mean that the
theory is thick with cabalistic notation? :)
> Laymen think that the word "theory" means just a "conjecture" or
> "speculation". But a theory is much more: it must be a consistent
> collection of laws and rules intended to describe a broad enough class of
> observations.
This reveals a gross misunderstanding of what a theory is. Let me give you
an example: Kepler's laws is a collection of laws and rules, but it is not a
theory. Newton's universal theory of gravitation is a theory.
"Broad enough?" This a totally subjective notion. A theory can be about a
very narrow set of observations. It does not have to be the Mother of all
theories to be a theory.
John Baez
Lubos Motl <mo...@physics.rutgers.edu> wrote:
>On Mon, 10 Sep 2001, John Baez wrote:
>> The model I described in my previous post allows for 3 families
>> if you take N = 12 in the SU(N) technicolor gauge group.
>Could you please say or repeat the reference where one can read about such
>a SU(12) preon model with 3 families?
I got this from Mohapatra's book "Unification and Supersymmetry",
the 1986 edition, page 181. I'm sure there is much better information
about preon models in here:
>> Technicolor
>> Edward Farhi and Leonard Susskind
>> Published in Phys. Rept. 74:277, 1981
but so far I've been too lazy to read it! Are you gonna force me
to become an expert on preon models, just to keep enjoying the pleasure
of arguing with you? Won't that be going against your ultimate goal
of getting me to learn and love string theory?
>Once I asked Lenny a stupid question, something like "Could you please
>tell me a few words about the way how you (co)discovered technicolor?"
>Lenny got a slightly upset and he said "I would prefer to tell you how I
>discovered string theory."
Heh, yes, I suppose he would.
>I want to say that technicolor is not necessarily the thing that Lenny
>(and others) are most proud about.
I understand! Of course this is only a vague "sociological" argument
against the correctness of technicolor theories. I prefer to talk
about physics per se, rather than comparing notes on what theories
people are "proud" of. But of course gossip is always fun....
>> Lubos Motl wrote:
>>>no theory beyond SM could have given us a
>>>verified new prediction simply because experimentalists - mostly because
>>>of the state of the current technology - have not been able to construct a
>>>single experiment that would disagree with the Standard Model (or General
>>>Relativity, in the context of the large distance scales).
>> That's not true. This is a myth propounded by theorists.
>>
>> Here are 3 examples of experiments that go beyond the Standard Model,
>> which a really good theory would have made predictions about:
>>
>> 1) Neutrino oscillations.
>By the "Standard Model" I meant the "generalized" Standard Model with the
>full Dirac neutrinos.
Okay, fine, as long as everyone remembers that it's only been in the
last decade that this "generalized" model has become the "standard"
one, as really convincing evidence came in. Even before this switch
occurred, lots of theorists were running around saying what you say
now - namely, that experimentalists aren't able come up with any
new evidence that could push us beyond the Standard Model. Then the
experimentalists did just that, and now... the new improved model is
called the Standard Model again! :-)
>> After this discovery, the Standard Model was modified to allow for
>> neutrino oscillations. It now includes right-handed neutrinos.
>> However, a really good theory of particle physics would have predicted
>> all this ahead of time.
>Well, I completely agree. As Jacques Distler said, even to us who know and
>love Her, the Standard Model is an ugly monster. :-) But anyway, it works.
>It has a lot of input that you must put it, but the predictions made
>afterwards agree with the experience.
No, they don't! Even the new "generalized" Standard model appears to be
violated by this result:
>> 2) Dark matter. It now seems that the dominant contribution to the
>> energy of the universe is a poorly understood invisible form of matter
>> which does not fit into the Standard Model. A good theory of particle
>> physics would have predicted this ahead of time and said something about
>> its properties.
Also, the good old "cosmological constant equals zero" version
of general relativity, which used to be the conventional wisdom,
was also killed by experiment:
>> 3) Cosmological constant. It now seems that the universe's expansion
>> is accelerating due to a nonzero cosmological constant - that is,
>> a nonzero vacuum energy density, or something with similar effects.
>> Again, this does not fit into the Standard Model.
But please remember, my point is not to criticize the Standard Model
or general relativity!
My point is to criticize the theorists who should have predicted
the results of experiments 1 - 3 before they happened, but were lulled
into hypnosis by the evil mantra: "experiment cannot tell us anything
interesting right now... we'll just think about our theories."
At the very least, I want theoretical physicists to stop saying
that experimentalists "have not been able to construct a single
experiment that would disagree with the Standard Model (or General
Relativity, in the context of the large distance scales)." They
said this back before the experimentalists discovered right-handed
neutrinos and the nonzero cosmological constant was zero... they
said it afterwards... and they're still saying it now, even
though most of the universe seems to be made of some poorly
understood form of matter which isn't INCLUDED in the Standard Model!
>> In all 3 cases it is not too late for a good theorist to make predictions
>> *now*. There is still a lot unknown about neutrino oscilations,
>> dark matter and the cosmological constant!
>Right. So answer those questions if you think that your colleagues are
>doing a bad job! :-)
I don't mind theorists being unable to come up with theories of
these things. It's probably just hard. What I do mind is them
coming up with bad excuses for not even trying. I wouldn't mind
good excuses, like: "I don't feel like it, and besides, to get
jobs today it helps to work on string theory."
>> You seem here almost to be claiming that ultimately string theorists will
>> find a unique nonperturbative vacuum and that this will allow them
>> to derive the Standard Model gauge group and all the coupling constants
>> from first principles, together with all the new phenomena not included
>> in the Standard Model.
>Sure, this is the goal, of course. Is it the first time that you hear that
>this is the goal of string theory?
No - but for a while, some people retreated to a safer position,
saying that string theory has lots of vacua describing different
low energy physics, and we'll never be able to calculate from
first principles which vacuum ours "must be". I'm interested to
hear you taking the bolder stance!
John Baez
Lubos Motl <mo...@physics.rutgers.edu> wrote:
>John Baez wrote:
>> Well, for example, the fact that you get an infinite set of
>> conserved quantities for the KdV equations by using the solution...
>Yes, it must be nice. I also know other interesting topics in math which
>are unrelated to fundamental physics.
Good. Then you must certainly agree with my point that just because
a mathematical structure is deep and gives researchers the feeling
that it is "more discovered than contrived", is not sufficient for
it to be the correct theory of the physical universe. These
qualities are promising but not *by themselves* anywhere near
sufficient. And thus, if string theory is to be a plausible
candidate for a correct theory of the universe, it must also pass
*other* hurdles, such as:
1) giving a clear resolution of various problems involving gravity
and quantum mechanics,
2) making definite new predictions, not just "in principle" but
in practice,
and so on.
All this seems so uncontroversial to me that I'm amazed we're still
arguing about it! The argument should really come when we discuss
whether string theory passes these other hurdles.
>> Completely integrable systems are indeed mostly part of mathematics;
>> the same is true of string theory so far, which is why I made the
>> analogy.
>Nope. I don't understand the sense in which string theory is a "part of
>mathematics" instead of a "mathematically deep physical theory".
I never said that string theory was not a physical theory.
When I said that string theory is "mostly part of mathematics so
far", I meant that string theory has so far led to a vast number
of new mathematical concepts and theorems, but has not made a
single experimentally verified prediction - nor even many predictions
that *could* be verified by current techniques! This means that
the usual interplay between theorists and experimentalists is missing.
Instead, we have an interplay between theorists and mathematicians.
>String
>theory is mostly done in physics departments by physicists who have
>degrees in physics and publish their papers mostly in physics journals.
That's true - I agree that string theory is *sociologically speaking*
a branch of physics. However, disciplines evolve over time, and
if string theory fails to make verified experimental predictions for
another few decades, people may reclassify it as mathematics. It
will be interesting to see what happens.
>I also do not understand the words "so far". String theory can be a
>physical theory that has not been fully confirmed experimentally and
>accepted by the whole scientific community. But it is a *physical theory*
>and this question cannot change in time.
Again, I never said that string theory was not a physical theory.
>Whether something is a physical
>theory or not, does not depend on immediate subjective feelings of Prof.
>Baez.
Shucks, and just when those delusions of grandeur were getting
really convincing! :-) Seriously, whether something is a physical
theory or not, mainly depends on the definition of "physical theory".
My own definition of this term is somewhat vague, but quite generous,
so I certainly count string theory as a physical theory.
>Laymen think that the word "theory" means just a "conjecture" or
>"speculation". But a theory is much more: it must be a consistent
>collection of laws and rules intended to describe a broad enough class of
>observations.
I don't agree with that "broad enough" business; for example,
I would consider Balmer's formulas for the spectral lines of
hydrogen, or Bohr's model of the hydrogen atom, or Kepler's laws,
or even the Bode-Titus law, a "physical theory". However, it
doesn't really matter to me how anyone defines the concept of
"physical theory", because this definition is not very important
when you are actually doing physics!
>In fact I think that there are very good reasons why string
>theory or M-theory is called "theory" (just like the theories of
>relativity or quantum field theory) while Loop Quantum Gravity, for
>example, is not.
Yes: most importantly, "Loop Quantum Gravity Theory" sounds silly!
It's just too long, like "Standard Model Theory" or "Quantum Mechanics
Theory".
>> My point was nontautologous: it was that like string theory,
>> the study of completely integrable systems leads one into *profound*
>> mathematics. One might not at first expect that Lagrange and
>> Kowalewski fiddling around with exactly solvable problems involving
>> tops would have led into such deep waters.
>Let us not argue whether the depth is equal; I would probably disagree.
>But there is one clear difference: the integrable systems as you describe
>them are not a theory that can describe the whole fundamental physics of
>this Universe - and none tries to claim this I hope - while string theory
>is one. Therefore the integrable systems are not - in any reasonable sense
>- competitors of string theory in particle physics.
Of course not! I hope nobody was so confused as to think anyone
said otherwise. I certainly did not.
>> >I am extremely disappointed if you don't see any difference between
>> >"profound mathematics" and "fancy mathematical game".
>> Eh? I see a huge difference!
>I thought that you wrote the following sentences.
>> I don't understand the perjorative significance of "just a fancy
>> mathematical game", and precisely how that's supposed to be different
>> from "profound mathematics".
>Please let me know whether you wrote them and if you did, what you meant
>different than I thought.
I wrote them in a conversation with Zirkus and they can only be
understood in that context. Briefly, I was trying to coax Zirkus
to tell me what *he* meant by "just a fancy mathematical game" vs.
"profound mathematics". I know what *I* mean by them, but I also
know that one man's "profound mathematics" is often another man's
"game", so I didn't assume he drew his distinctions the way I do.
>What I say is no speculation: I don't
>believe that anyone argues that the integrable systems as studied by the
>experts describe the whole world of particle physics; you can show quite
>clearly what is missing (essentially everything).
Right: nobody argues this, so I'm having trouble understanding why
you're even talking about.
>On the contrary, string
>theory has no known reasons not to describe fundamental physics. Or do you
>know a reason?
Yes - if I didn't, I would work on string theory.
>Or you can perhaps use those integrable models to construct a TOE?
Huh?? Of course not.
>Or do you think that this difference - whether something has a
>capacity to be a TOE or not - is unimportant for fundamental physics?
What?? You seem to keep making up weird ideas and asking me if
I believe them.
>And I believe that if you
>think that the mathematical beauty should not count as an argument in our
>search for the ultimate theory of physics, you are completely wrong.
Zounds! Of course I don't think this. I hope my careful restatement
of my views near the beginning of this article clarifies things.
Charles Francis
tech.edu>, Stephen Speicher <s...@compbio.caltech.edu> writes
>On Tue, 4 Sep 2001, Charles Francis wrote:
>I've pared Charles' response down to his final statement above,
>which sums up the essence of his argument. Permit me to remind
>Charles what is in question here, namely Charles' assertion that:
>
> "But more strictly according to Heisenberg the
> Copenhagen interpretation does not include
> wave-particle duality..."
>
>I agree that Heisenberg goes further than Bohr in regard to his
>view of quantum reality -- I said so myself in my initial
>response. But that is not the issue here; the issue is whether or
>not wave-particle duality is a part of the standard Copenhagen
>interpretation. The quotes I provided were from Heisenberg's book
>in the chapter titled "The Copenhagen Interpretation of Quantum
>Theory." Any appeal to other sections of the book -- as Charles
>has done -- is helpful in gaining a full appreciation of the
>depth and scope of Heisenberg's thoughts, but such goes beyond
>the immediacy of the issue, i.e., wave-particle duality in the
>Copenhagen interpretation.
Upon further contemplation and rereading, I accept what you say, and I
also remark that Heisenberg's thoughts on the issue are deeper and more
complex than most people seem to understand by the Copenhagen
interpretation.
I think the distinction Jeffrey Bub makes between Copenhagen and
Orthodox is helpful in this regard, since the evolved form of Copenhagen
found in Dirac and Von Neumann does not include complementarity, and
this is what Bub calls orthodox. There is a great deal of Heisenberg's
thinking in the orthodox interpretation, but he does seem to have stuck
with complementarity as a physical property of matter, although there is
also much discussion that the real properties are not what is described
by classical language.
Regards
--
Charles Francis
AG
> And once again, you cannot say that a theory is not good or it is partly
> wrong just because it was constructed or completed after some of its
> consequences were known experimentally. We should agree about those words:
> the Standard Model is not fully satisfactory - this is one reason why we
> go beyond it - but it *is* a *good* theory explaining the known facts.
Consider a polynomial fit to some data points. Particles are data points and
"Standard Model" is the "polynomial fit," i.e. a simulation, it is not a
theory. If there is a new observation, the fit is tweaked a little and the
observation is saved. The process is foolproof and it can explain any and
every observation. Therefore a naive observer looking at how successful this
Standard Model "theory" is may even claim that God wrote the world in
Standard Model theory.
> Superstring/M-theory is the language in which God wrote the world.
But of course that would be theology or polemic or propaganda. Any "theory"
which needs to invoke the authority of God must be worthless in terms of
scientific value.
Toby Bartels
[stuff]
I wish that you'd make up your mind!
First you say that the Standard Model is good
because it explains phenomenology very well.
When John seems to complain that the SM is bad
because it doesn't explain every phenomenon
(which I think is a misreading of what he meant,
but we can wait to see what he says about that),
you argue against him, and cogently I think.
But then when John suggests that it's worthwhile
to study phenomena that go beyond the SM,
you argue that this is a useless endeavour
unless you study a theory that explains everything.
Well, which is it? Are phenomenological theories,
like the Standard Model, worthwhile efforts or not?
Personally, I think that your arguments for the SM
can also be applied to successful theories that
explain phenomena beyond the Standard Model --
which we currently know none of, but which it's
worthwhile to look for.
-- Toby
to...@math.ucr.edu
Lubos Motl
> Lubos Motl <mo...@physics.rutgers.edu> wrote in message
> > LM: But string theory apparently has all the necessary features to
> > describe the real world.
>
> Except the most important one, the one that counts: actually doing so.
First of all, it is probably not true that string theory will not describe
the real world completely some day. Second of all, even in the
hypothetical case that it will not, it would not count as a "feature". In
other words, you do not have a single argument against the theory except
for one: that you don't like it.
> Here's a simple exercise for you. Derive the value of g for the electron
> from string theory, directly, without any handwaving arguments or
> appeals to things "we're on the verge of proving but the correct
> theory/definition/equation/concept/(fill in blank) is not yet available".
Well, if you think that this exercise is simple, just try to solve it
using any theory you like. Six billions non-string-theorists can help you
and you can work on it for 20 years if necessary. I will be more than
happy and surprised if you find at least some partial results.
> I expect a written report on my desk by next week.
This is probably not the only extremely unreasonable expectation related
to physics that you have. So you didn't surprise me. ;-)
P.S. I think that there exist many non-stringy papers deriving the value
of the fine structure constant that you will like, for example the
following Czech paper:
http://xxx.lanl.gov/abs/physics/9906023
Best wishes and good luck :-)
Lubos
______________________________________________________________________________
E-mail: lu...@matfyz.cz Web: http://www.matfyz.cz/lumo tel.+1-617/496-8199
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Aaron J. Bergman
Lubos Motl wrote:
I said:
>> ... some direction. When you look at this, you find that, in the "wrong"
>> dimension for the superstring, there is a tachyon in the spectrum. There
>
>Aaron, I think that this comment is extremely misleading. The CFT of an
>open string has always the correct central charge and it lives in the
>spacetime of a correct dimensionality (10 in the superstring case):
By "wrong dimensionality", I meant the dimension of the D-brane, not the
critical dimension for the superstring, of course. Sorry for the
confusion.
Toby Bartels
>When I said that string theory is "mostly part of mathematics so
>far", I meant that string theory has so far led to a vast number
>of new mathematical concepts and theorems, but has not made a
>single experimentally verified prediction - nor even many predictions
>that *could* be verified by current techniques! This means that
>the usual interplay between theorists and experimentalists is missing.
>Instead, we have an interplay between theorists and mathematicians.
This is why I say that string theories and LQG people
are primarily doing applied mathematics, not science --
a statement that you strongly objected to!
>Lubos Motl wrote:
>>String
>>theory is mostly done in physics departments by physicists who have
>>degrees in physics and publish their papers mostly in physics journals.
>That's true - I agree that string theory is *sociologically speaking*
>a branch of physics. However, disciplines evolve over time, and
>if string theory fails to make verified experimental predictions for
>another few decades, people may reclassify it as mathematics. It
>will be interesting to see what happens.
It's possible that the definition of "physics" will change.
-- Toby
to...@math.ucr.edu
Lubos Motl
> By the same token, if it does not depend on the immediate subjective
> feelings of Prof Baez, or even those of Charles Francis, then why should
> it depend on the immediate subjective feeling of a bunch of physicists,
A very good question. The answer is, of course, that the classification
whether string theory is a physical theory or not does not directly depend
on a feeling of the other physicists either. But there can be also a
confusion stemming from terminology. If we want to understand each other,
we should use the word "physical" in a way that is compatible at least in
some basic cases. I am afraid that this is not the case.
> who, by your own admission, are working from intuition and a level of
> rigor which as physicists use, which is not regarded by many a
> mathematician as adequate.
Right. This is both a reason and a consequence of the fact that string
theory is a theory of physics, not pure mathematics.
> I know a number of reasons. Most of these are rooted in fundamentally
> flawed assumptions about space-time, and a failure to examine
> foundations rigorously. It is not okay to say something is a theory of
> physics based only on the immediate subjective feelings of a bunch of
> physicists working from intuitions.
You know, what you call "immediate subjective feelings of a bunch of
physicists working from intuitions" should be probably called "an
overwhelming amount of evidence that has been collected for more than 30
years by some of the brightest and smartest physicists ever in thousands
of their mathematically deep papers".
Sure, from a general point of view, a non-physicist can find the results
of physicists to be just a weird collection of immediate subjective
feelings, just like physicists have a similar opinion about some
statements of non-physicists. However, from a physics point of view, this
Z2 symmetry is broken. :-) From the point of view of physics, the
"opinion" of physicists, supported by physical arguments, is most likely
correct while the non-physicist's opinion is most likely wrong, regardless
of the unfounded self-confidence and arrogance that the non-physicist
might want to apply.
> It is doubtful that the metaphysical concept of string even makes
> sense, since it seems to incorporate without interpretation aspects of
> quantum behaviour which a TOE would need to explain.
In physics, one does not care about "metaphysical concepts". One cares
about theoretical frameworks that are capable to make predictions.
Furthermore the correct interpretation of quantum mechanics has been more
or less understood. String theory does not change anything about the
principles of quantum mechanics. Consequently, the question of the
interpretation of quantum mechanics does not directly affect string
theory; except for a few puzzling things related to the information below
the even horizons, replacement for an S-matrix in de Sitter space etc. But
if you like to do so, you can imagine a "many-worlds" scenario of Quantum
Mechanics even in string theory, for example. Most string theorists don't
do it; in fact most string theorists don't care about this question
because the task for string theory is to explain kinematics and dynamics -
the more complete laws of the Universe that include all the forces - and
not various philosophical interpretations of well-known insights of
physics.
> It is based on gauge invariance, which seems like a nice compelling
> symmetry when you read it one way, but is actually just a degree of
> freedom in a mathematical structure, not corresponding to any physics
> at all when you look at it another way.
Perturbative string theory satisfies conformal invariance; it is a type of
(local) gauge invariance which is necessary to get rid of the physical
ghosts (with a negative squared norm). Other important theories in physics
have the same property: the Standard Model is built on SU(3) x SU(2) x
U(1) gauge invariance and the General Relativity is based on general
covariance.
However in string theory, gauge invariance is a kind of redundance of our
description, just like you say. Your point of view that gauge invariance
is just a freedom in our description that has no physical meaning - and
perhaps even the question which gauge invariance the system should have is
not physically meaningful - is particularly favored by Nati Seiberg. His
papers (together with Ed Witten) show that the same physical system can be
described by many descriptions that have a different gauge invariance but
that are physically equivalent. You can see it if you study S-duality but
you can also observe this phenomenon if you study theories defined on
noncommutative spaces; in fact, the famous equivalence between the systems
with commutative U(1) invariance and a noncommutative U(1) invariance has
been explained in another, more recent paper by Seiberg and Witten.
Once again, string theory is precisely the framework in which the
consequences of gauge invariance hold as exactly as in the approximate
theories; however gauge invariance is just a *derived* concept in string
theory - it is a part of consequences of a deeper theoretical structure -
and the philosophy that gauge invariance is an *unphysical* feature that
cannot be directly defined for a given *physical* system, sounds very
reasonable in the stringy context.
> The whole concept of string appears therefore to be based on a
> non-physical degree of freedom in a mathematical structure.
Because the Standard Model and General Relativity satisfy the assumptions
of your criticism better than String Theory, your paragraph is actually
not a criticism against String Theory but rather an argument why it is
more satisfactory than the previous pictures.
> Historically there are numerous examples where it has meant that the
> experiment was wrong, and numerous others when the theory was
> fundamentally not wrong, but the calculations of the theorists were
> either wrong or incomplete.
I agree, these examples can be found, too.
> If one wants to base any philosophy on such examples, one should at
> least study them historically to see what they might signify, rather
> than pick up on a popular "coffee table" philosophy of science, and
> assert that scientific progress is subject to it.
I agree. Therefore I think that you should reconsider your claims.
> Sorry, but I do not care how many physicists you have working on string
> theory from intuitions and accepted standards (among same physicists) of
> rigour. If you want to produce a TOE, a fundamental theory of physics,
> you will have to study the fundamentals, such as how space and time are
> defined and measured, with absolute rigour.
Nope. Once we will *know* everything about the TOE, we will be able to say
it with absolute rigor. But when a physicist is looking for explanations
and theories, it is never done with absolute rigor; it is done according
to the standard rational criteria that physicists always liked.
> If these string theorists cannot do such a thing, then they are charged
> that the intuitions on which they base their model are nothing but
> misconceptions.
Your comments have nothing to do with string theory. String theory, just
like quantum field theories in the past, for example, were investigated
with the rigor that they deserved and needed. And this approach has been
proved to be very fruitful in both cases. You can charge string theorists
in any way; however your "charges" do not change anything about the
question whether a theory is correct or wrong. Scientists are answering
these questions using methods of science and scientific arguments - and
they don't pay too much attention to superficial charges which are not
based on science at all.
Best
Lubos Motl
> I wish that you'd make up your mind!
> First you say that the Standard Model is good
> because it explains phenomenology very well.
For the practical phenomenology, the Standard Model is great because it
explains virtually everything in particle physics.
> When John seems to complain that the SM is bad
> because it doesn't explain every phenomenon
Right, it does not explain a detail called gravity, for example. It is
also not satisfactory because the details of its construction - as well as
19 parameters - are unexplained. The Standard Model is great if you
compare it to the worse theories; but it is not so great if you compare it
to string theory, for example.
> (which I think is a misreading of what he meant,
> but we can wait to see what he says about that),
> you argue against him, and cogently I think.
> But then when John suggests that it's worthwhile
> to study phenomena that go beyond the SM,
Because I simply do not think that we have a large enough body of
experimental results that go beyond the Standard Model so that it would
make sense to concentrate on them.
> you argue that this is a useless endeavour
> unless you study a theory that explains everything.
It does not have to be a TOE yet. But the nature of the dark matter can
hardly be found before another kind of progress takes place in the theory.
I just think that it is not reasonable to try to directly explain those
small glimpses of physics beyond the SM. Simply because the true path to
the correct explanation will be much more difficult and the experimental
data available today are completely insufficient.
> Well, which is it? Are phenomenological theories,
> like the Standard Model, worthwhile efforts or not?
The Standard Model is not just one of the phenomenological theories. It is
*the* Standard Model, it is *the* theory that explains virtually
everything in particle physics. There is no other existing and confirmed
theory that the SM could be compared with. The Standard Model - despite
its imperfections - is certainly a great achievement of science. However
it is not the case of other theories that you would like to put on equal
footing with the SM. There is no "standard" theory explaining the nature
of the (hot component of the) dark matter, for instance.
And one more comment. The Standard Model has been already found. It
belongs to the past, from this point of view.
> Personally, I think that your arguments for the SM
> can also be applied to successful theories that
> explain phenomena beyond the Standard Model --
> which we currently know none of, but which it's
> worthwhile to look for.
Yes. This is why the people study string theory - in fact the only known
framework of ideas beyond the SM that deserves to be called a "theory".
Best wishes
Lubos
______________________________________________________________________________
E-mail: lu...@matfyz.cz Web: http://www.matfyz.cz/lumo tel.+1-617/496-8199
Charles Francis
writes
>And thus, if string theory is to be a plausible
>candidate for a correct theory of the universe, it must also pass
>*other* hurdles, such as:
>
>1) giving a clear resolution of various problems involving gravity
>and quantum mechanics,
What counts as clear? Differential calculus is absolutely transparent to
you and I, but huge numbers of people find it as clear as mud. And there
is probably nothing much you can do to clarify it for them. Differential
geometry was as clear as mud to everyone but Riemann when he invented
it, and still is as clear as mud to people in large numbers. So when a
new theory is produced, should we not expect to find it as clear as mud
at least until we learn how to think about it?
And how can an individual even tell whether a theory is not clear
because of the theory or the expression of the theory, or whether it is
not clear because of the limitations of his own individual thought?
Would the thousands of mathematicians and physicists who could not
understand Riemann have been correct to assume that because they found
it not clear, he was talking garbage?
>2) making definite new predictions, not just "in principle" but
>in practice,
What counts as new predictions? I would think that a unified theory of
gravity and quantum mechanics should "predict" Einstein's field
equation. But that will only give an equation we have known for nearly a
hundred years. Would that constitute a prediction?
Suppose a theory successfully integrated qed with general relativity.
What experimentally testable predictions might we find? Is there a
single experiment we might expect to do with our current technology
which would give a different result than predictions based on our
existing, disparate theories?
Do theoretical predictions count? Does predicting the non-existence of
the Landau pole constitute a new prediction? Does predicting that it is
meaningless to talk of the inside of an event horizon, and therefore
that there is no singularity in a black hole constitute a prediction?
(not that I am making such a prediction, but it is the sort of thing
that I might expect to find in a theory of quantum gravity, since much
of what I understand of quantum mechanics has to do with not being able
to talk in classical terms)
It seems to me that, in the first instance, a new theory should not have
to make new predictions. If it replicates the experimental predictions
of the old theory then it is at least an equal candidate to the old
theory, and neither more nor less speculative than the old theory. That
does not mean you would start teaching it to undergraduates, or even
graduate students, but it should be accepted as an equal candidate from
the point of view of research. If it also resolves technical,
mathematical, or interpretational problems in the old theory without
introducing similar unresolved problems of its own, then it is probably
an advance on the old theory.
But before any theory is to be considered :-
> a plausible
>candidate for a correct theory of the universe,
one must first show that it has no internal problems or inconsistencies.
And since we cannot say that of the standard quantum field theory, then
we are quite wrong to reject any other theory which may not be a
complete theory of the universe, but has no more faults than standard
quantum field theory, and quite wrong to ask such a theory to jump
hurdles which standard quantum field theory cannot itself jump.
Of course none of this gives us a reason to accept string theory. String
theory does not even talk of foundational principles like the relativity
of space and time measurement, or the effect of measurement and
observation on the thing measured, or the deep philosophical connection
between these principles, one at the heart of relativity and the other
at the heart of quantum mechanics.
If there is to be a unification these are the philosophical issues which
must be addressed. Instead we find that string theorists in general do
not even seem to grasp that there are such issues, and when you try to
explain them, they find them as clear as mud. So is the problem in the
explanation, or is it in the capacity of the string theorist to grasp
the explanation?
Regards
--
Charles Francis
John Baez
Toby Bartels <to...@math.ucr.edu> wrote:
>John Baez wrote in part:
>>When I said that string theory is "mostly part of mathematics so
>>far", I meant that string theory has so far led to a vast number
>>of new mathematical concepts and theorems, but has not made a
>>single experimentally verified prediction - nor even many predictions
>>that *could* be verified by current techniques! This means that
>>the usual interplay between theorists and experimentalists is missing.
>>Instead, we have an interplay between theorists and mathematicians.
>This is why I say that string theories and LQG people
>are primarily doing applied mathematics, not science --
>a statement that you strongly objected to!
The vehemence of my disagreement arose from a strong visceral
dislike of separating "applied mathematics", or indeed "mathematics"
in general, from "science". I can imagine reasons for doing so
(e.g. some sort of distinction between empirical and a priori
knowledge), but I don't find those reasons convincing. So I
don't find it useful to go around saying that string theorists
aren't doing "science"; I prefer to state the facts of the matter
as I did above.
(Of course everything I wrote applies to loop quantum gravity as
well as string theory, but since I was just having fun arguing with
Lubos Motl, I didn't feel the need to point that out.)
Jim Carr
<Pine.LNX.4.10.101090...@photon.compbio.caltech.edu>
Stephen Speicher <s...@compbio.caltech.edu> writes:
>
... regarding wave-particle duality ...
>
>However, one year later, in Heisenberg's uncertainty paper ("Uber
>den anschaulichen Inhalt der quantentheoretischen Kinematik und
>Mechanik," _Zeitschrift fur Physik_, 1927, 43:172-98.{which
>paper, incidentally, is one of many papers of historical interest
>reproduced in Wheeler and Zurek's marvelous book, _Quantum Theory
>and Measurement.})
I will second that, as well as the commentary in Wheeler and
Zurek's book. For the following, see also Pais biography of
Bohr (which has some overlap with Pais' earlier books on the
history of QM) and the bio of Heisenberg by Cassidy.
>Heisenberg relented to pressure by Bohr and
>included his now famous remarks (in the "Addition in Proof")
>which, in effect, acknowledged in a rather subordinate manner,
>the importance and relevance of Bohr's duality. [Note that
>Heisenberg was so emotional in regard to the pressure exerted by
>Bohr that he occasionally burst into tears.]
"Relent" suggests that he had another choice, but given that the
other choice would be retraction of the paper due to the error
he made or having it pointed out by Bohr in a later paper, perhaps
you can see why he might be upset. The other reason is that the
error he made was, apparently, similar to an error he made during
his PhD oral exam when he got a basic optics question on resolving
power wrong -- and possibly because the example that caused all of
the trouble was not even a necessary part of the paper. (If he
had left it out, there would have been no mention of waves needed
since the derivation did not use them. See below.)
The note added in proof was needed because his "gamma-ray microscope"
gedanken was in error. It is not true that the simple classical act
of measuring position by scattering necessarily removes knowledge of
the momentum of the particle being studied, because you can simply
measure the recoil momentum of the scatteree and use that to determine
the new momentum of scatterer. That gedanken only works if you include
the wave-optics effect of the apperture of the microscope, which was
the error Bohr pointed out to Heisenberg.
>Yet later that same year, in a letter to Pauli (Hermann et al.,
>_Wolfgang Pauli, Scientific Correspondence with Bohr, Einstein,
>Heisenberg, 1979), Heisenberg clearly expressed his disagreement
>with the Bohrian philosophy, pointing out essential differences.
>These changes all ocurred in the space of little more than one
>year!
Not inconsistent, since you don't need to use Bohr's philosophy
to get the results from quantum mechanics. After all, the
uncertainty principle was derived entirely from the Dirac-Jordan
formulation of Heisenberg's quantum mechanics with nary a wave
in sight, not from wave mechanics.
<... snip rest about Heisenberg's views ...>
--
James Carr <j...@scri.fsu.edu> http://www.scri.fsu.edu/~jac/
SirCam Warning: read http://www.cert.org/advisories/CA-2001-22.html
e-mail info: new...@fbi.gov pyr...@ftc.gov enfor...@sec.gov
Lubos Motl
> When you look at the history of math and physics you'll see that countless
> times pure mathematical research which initially looked totally unrelated to
> any physics eventually turned out to have fundamental physical relevance.
I completely agree. It is one of the nice and surprising features of the
relation between mathematics and physics.
> "Physics" is a fluid word. Its meaning is in continual flux. What does it
> mean today? As far as I know it is a method of investigation of nature.
I don't think that physics is such a "fluid". Physics is the natural
science that wants to understand those objects and phenomena in the real
world of Nature that can be most accurately described in terms of
mathematics - usually because their essence is not spoiled by too many
complex properties that can make an exact analysis completely impossible.
Aside from this general definition, there is a lot of convention. Physics
can be given a slightly different definition but there is a general
agreement what kind of human activity is called "physics".
> The fundamental subject of physics is motion.
I don't think so. Maybe the word "mechanics" or even "kinematics" would be
enough to describe this limited understanding of physics. A great deal of
physics concerns static configurations; motion can be completely turned
off and physics can be still interesting.
> So physics is the study of motion. The quality of a theory is
> independent of the department the paychecks of researchers come from.
It is a priori an independent thing but it is certainly not an
uncorrelated thing.
> What is "a mathematically deep physical theory?" Does it mean that the
> theory is thick with cabalistic notation? :)
I don't think that such an essential feature of a good physical theory as
the mathematical depth undoubtedly is, deserves humuliation. It is hard to
define it because one either "feels" it or he does not. However I will
try: mathematical depth means that the theory deals with general enough
mathematical concepts that are likely to be found at very many places in
the universe of ideas; mathematical concepts which are inevitable to
understand many phenomena both in mathematics and physics.
> > Laymen think that the word "theory" means just a "conjecture" or
> > "speculation". But a theory is much more: it must be a consistent
> > collection of laws and rules intended to describe a broad enough class of
> > observations.
>
> This reveals a gross misunderstanding of what a theory is. Let me give you
> an example: Kepler's laws is a collection of laws and rules, but it is not a
> theory. Newton's universal theory of gravitation is a theory.
Kepler's laws are often not called a "theory" because they do not explain
the origin of the motion (universal gravity); consequently, their range of
validity is not broad enough because they can explain the motion of 9
planets only. It is not "broad enough" and therefore it is fair not to
call Kepler's laws "a theory" if you don't wish to do so.
> "Broad enough?" This a totally subjective notion. A theory can be about a
> very narrow set of observations. It does not have to be the Mother of all
> theories to be a theory.
I think that exactly your example with Kepler's laws shows why "my"
definition is so good. Newton's theory explains the universal force of
gravity; it can be used to predict the motion of planets, the Moon or the
apple falling from the tree. If a collection of ideas is able to describe
a very limited amount of obserations, it should not be really called "a
theory"; it is just a (slightly organized) collection of observations.
Kepler's laws are in the middle: they are able to describe - with a
plausible degree of accuracy - the motion of nine planets.
Once again, people can have different opinions but the well-educated ones
usually more or less agree what should be called a theory and what should
not. Theoretical breadth is certainly not a "totally" subjective notion as
you say. And a "very narrow set of observations" is not a theory yet as I
have tried to explain. For a collection of ideas to be a theory, it
needs to predict a broader set of observations than those which have been
inserted to it! And finally, while it is true that there are other
theories than just the Mother of all theories, it is still true that the
Mother of all theories deserves to be called a "theory" most of all! ;-)
Lubos Motl
> >> Technicolor
> >> Edward Farhi and Leonard Susskind
> >> Published in Phys. Rept. 74:277, 1981
Kewl, I must look at it sometimes. By the way, Eddie Farhi was giving a
talk here at Harvard about quantum computing - quite a different topic. I
think that he is a great lecturer! Is it the same person?
[Moderator's note: I think so. And, yes, he is a great lecturer. -MM]
> but so far I've been too lazy to read it! Are you gonna force me
> to become an expert on preon models, just to keep enjoying the pleasure
> of arguing with you? Won't that be going against your ultimate goal
> of getting me to learn and love string theory?
Maybe I have already given up you as the possible future lover of string
theory. Maybe the only goal that has some chance to be realized is to make
you frustrated out of all those preon and technicolor models that really
don't work at all. Such a frustration may be a satisfactory substitute for
your love with string theory; who knows. :-)
> I understand! Of course this is only a vague "sociological" argument
> against the correctness of technicolor theories.
Sure, I don't pretend that this one is a scientific argument ruling the
preon models out. Well, I like Lenny - but this observation can hardly be
an argument, indeed. :-)
> I prefer to talk about physics per se, rather than comparing notes on
> what theories people are "proud" of. But of course gossip is always
> fun....
I share your approach.
> Okay, fine, as long as everyone remembers that it's only been in the
> last decade that this "generalized" model has become the "standard"
> one, as really convincing evidence came in.
The "old" Standard Model itself was finished 25 years ago or so. The
difference in the time intervals is not so dramatic.
> Even before this switch occurred, lots of theorists were running
> around saying what you say now - namely, that experimentalists aren't
> able come up with any new evidence that could push us beyond the
> Standard Model. Then the experimentalists did just that, and now...
> the new improved model is called the Standard Model again! :-)
Well, it is funny but I believe that you'll finally agree that adding the
right-handed components of neutrinos with some very tiny masses - concepts
that have been used for other fermions for 60 years (and in fact people
always realized that one can make massive neutrinos, too) - does not
constitute a true revolution in theoretical physics and maybe it is better
to save the words and go on to use the phrase "The Standard Model".
> No, they don't! Even the new "generalized" Standard model appears to be
> violated by this result:
>
> >> 2) Dark matter. It now seems that the dominant contribution to the...
Yes, dark matter is quite likely an example of physics beyond the Standard
Model. Unfortunately it is hard to say more details about it. Anyway, it
is not hard to get new particles for the dark matter in theories going
beyond the SM. So I do not think that the dark matter is a principal
theoretical puzzle. And the available experiments don't allow us to say
too much more than this general paragraph.
> Also, the good old "cosmological constant equals zero" version
> of general relativity, which used to be the conventional wisdom,
> was also killed by experiment:
Yes, this observation is much more serious theoretically. Most string
theorists think that the cosmological constant puzzle is among the most
important ones.
> My point is to criticize the theorists who should have predicted
> the results of experiments 1 - 3 before they happened, but were lulled
> into hypnosis by the evil mantra: "experiment cannot tell us anything
> interesting right now... we'll just think about our theories."
I think that this criticism is completely unrealistic. Even today, we are
not able to explain the size of the neutrino masses. We cannot calculate
masses of any elementary particles at all. I also like to criticize e.g.
supergravity guys in the 80s who were not able to compare the tensions of
the membranes and fivebranes and find out that type IIA string theory was
the 11D supergravity on a circle. But I can partly afford to say this
criticism because today we know the answer and it was pretty easy to
"rediscover it" independently, even for me. However I suppose that you
don't have the answers to your questions either - so I don't understand
how can you criticize other theorists for the same kind of ignorance.
And once again. If a prediction of a theory is found after the phenomenon
is experimentally observed, it may be a less satisfactory situation but it
certainly cannot be used as an argument saying that something is wrong
about the theory itself!
> At the very least, I want theoretical physicists to stop saying
> that experimentalists "have not been able to construct a single
> experiment that would disagree with the Standard Model (or General
> Relativity, in the context of the large distance scales)." They
> said this back before the experimentalists discovered right-handed
> neutrinos and the nonzero cosmological constant was zero...
They said it because it was true. The Standard Model now finally works
with neutrino masses and therefore the neutrino oscillation experiments
are not an example for your claim. And the dark matter is too fuzzy; we
know that a theory beyond the SM is generically able to do something like
that but this is it. The experiments do not give us any clues.
Cosmological constant is a gravitational phenomenon that is - of course -
completely unexplained by the Standard Model, just like everything related
to gravity! A naive calculation of the vacuum energy in the SM gives us a
completely weird result but in fact the SM itself should not be expected
to give answers to such questions.
Therefore I think that you do not know an experiment that goes beyond the
SM plus GR either. OK, we can talk about a small amount of unclear
exceptions.
> they said it afterwards... and they're still saying it now, even
> though most of the universe seems to be made of some poorly understood
> form of matter which isn't INCLUDED in the Standard Model!
I hope that you do not count the importance of an idea in physics by
kilograms. It does not matter whether the dark matter makes 80% of 90% of
the non-cosmological-constant matter. It can be made of one particle
species only and this particle is not more important than electrons! In
fact, I would still say that electrons are much more important for life
than a potential particle making up the dark matter. ;-)
Otherwise, the antistringy prof. Friedwardt Winterberg
<wint...@physics.unr.edu> from Nevada really thinks that the importance
of the things is measured by their percentage in the mass of the Universe
- and he invented a theory of "rotons" that - he says - gives 70% of
something that looks like the cosmological constant. Unfortunately, if 70%
is correct now, it will be certainly wrong in a couple of billion of
years. :-)
> I don't mind theorists being unable to come up with theories of
> these things. It's probably just hard. What I do mind is them
> coming up with bad excuses for not even trying. I wouldn't mind
> good excuses, like: "I don't feel like it, and besides, to get
> jobs today it helps to work on string theory."
But it is really hard. And I think that the experiments just do not give
us enough data and hints to attack those questions directly. I just think
that it is much more reasonable to try to attack different questions. And
the answers to the dark matter problem and other problems will probably
appear as very small indirect consequences of much richer theoretical
framework. A direct attack on the question of the dark matter - which you
seem to suggest - is just not reasonable, I think.
You know, when the first hyperon was observed, we also did not have enough
data to construct QCD. When radioactivity was first observed, people could
not construct Quantum Mechanics yet. I am not sure why you think that you
can create a deeper theory based on the trivial knowledge that there is
some dark matter in the Universe. If you can, write a paper about it! :-)
> No - but for a while, some people retreated to a safer position,
> saying that string theory has lots of vacua describing different
> low energy physics, and we'll never be able to calculate from
> first principles which vacuum ours "must be". I'm interested to
> hear you taking the bolder stance!
String theory can have many vacua like that but it seems almost certain
that this collection is discrete. So if you take say those 7 trillion
vacua, you find out that only 2001 vacua have a SM-like gauge groups at
low energies. The "second most realistic" vacuum has alpha = 1/134 and is
ruled out experimentally. This will finally determine the correct vacuum
uniquely and you should be able to calculate *everything* out of it; all
the constants etc. can be calculated with the highest precision which is
theoretically plausible. Of course, you can still ask "why don't we live
in this 1/134 universe or any other universe (do the anthropic ideas
matter, for instance?)" - but the questions of physics of *this* Universe
should be answered by the correct vacuum.