Crisis in Fundamental Theoretical Physics
Michael Maroun
I am a young graduate student and I am deeply concerned with the
so-called Bogdanov hoax. I first learned of this business when I
received an email (circulated to the entire department) of the Richard
Monastersky article. I then continued to look into this subject reading
through many threads of the newsgroup. I happened upon actual excerpts
of Bogdanov's work and was amused. I was amused because I am not even an
expert and I could tell that the statements were total bunk. I bring
this up because it touches on the more general subject I am concerned
with, namely the quality of modern theoretical physics research.
One reason why the Bogdanov work is bunk (aside from being clearly
vacuous) is because it does not make a simple hypothetical statement and
subsequent test. Think of what we teach to our young children about what
science is all about. One must make a hypothesis and then devise some
test to verify its validity. This is because physics and science in
general revolve around ascertainable and verifiable truths. Now many
theoretical physicists cringe at the idea of experiment (including
myself) especially in the case of fundamental theory where experiment is
not even physically possible in some cases. But hypothesis and
subsequent verification need not involve billion dollar apparati. For
example one may write down a differential equation with some boundary
conditions. The hypothesis is as follow: There exists solutions which
satisfy the boundary conditions and form a set of countably infinite
orthogonal functions. Test: solve the differential equation produce
solutions verify that they are indeed countably infinite and that they
also obey an orthogonality condition and you are done. Now you may be
wondering why I have brought up such a simple and obvious example. The
reason is that the number of published articles that do not have this
format is staggering!
But there are other problems as well. It seems that many researchers
claim to have answers, the problem is that these are answers to
questions which they do not know. Take string theory for example. I am
completely impressed with the mathematics and the subsequently more
complicated theories such as M theory. They are truly ground breaking in
terms of the quantum geometrodynamics of strings. But who says strings
have any correspondence to physical reality. If I understand correctly,
string theory was primarily introduced by Nambu and others to resolve
the issue of the spin-1 particle (QCD, but turned out not to work and
instead better described a spin-2 particle to which everyone jumped and
said ah ha gravity!) but secondarily to resolve the difficulties of
point particles. Now, this seems to be truly arbitrary. One could easily
conceive of an alternative idea to explain point particles, it is
analogous to marbles rolling on a table or rubber sheet. To those
confined to the surface (table/rubber sheet) the intersection of the
marble is a single point (at least in the flat case). You can now see
how this might in principle solve the issue of point particles. (For fun
think about the marble spinning!) But what dynamics do the marbles obey?
Namely, and I believe this problem comes up in actual theories as well,
what are the dynamics in the bulk? Do the marbles obey F= ma? No one
knows and in some cases I suspect that no one will ever be able to know.
The problem with the whole thing is that the idea is not realistically
verifiable. Anyone can write down a complicated mathematical expression
and claim that it is an expression for some physical amplitude. But what
is the amplitude and how is it relevant to answering questions about
physics? Do we even know how to discern intelligent questions about the
physical world?
The problems go on. Journals in Nuclear physics no longer have
articles on nuclear physics. People publish a solution to something,
change one parameter and republish as a completely separate and
independent article. Article names are named to sound like other
articles in attempts to increase citations. Friends cite each others
works over and over again whether the cited sources have anything to do
with the published material at hand. Physics is becoming more like a
high school popularity contest and less like a science.
As a student of physics and hopefully a member of the next
generation of scientists I am seriously troubled be these things. I look
towards the wisdom of the more experienced members of the field and to
my teachers and instructors to help solve a problem I believe all of us
are responsible for. Is there any way these issues can be fixed? Does
the shear number of researchers in the field exclude such repair
possibilities? What role does economics play? How should funding be
granted to reduce these problems? What is the ratio of independent
journals to total number of researchers and how does it affect the
problems we are seeing? Many more questions come to mind and I look
forward to responses on all levels.
Jim Goodman
Publish or perish. New ideas are few to be had. Many researchers in physics
is a problem and a solution. A problem because truly brand new ideas are
hidden in a pile of diligent well thought out articles making one or two new
hypotheses and building the knowledge base slowly and surely. A solution
because with so many bright students of physics trying, something is getting
accomplished.
I applaud you for citing the scientific method as the way to scientific
truth and your reliance on athority to solve the problems you have stated.
New ideas must be tested by many competent researchers. Unfortunately if the
idea fails, no new knowledge is gained. In other words the negative of the
hypothesis is not necessarily true. More ideas are published than can
economically be tested and some ideas cannot be tested economically. This
allows for theoretical arguements against the idea to be considered valid.
More papers.
My suggestion to you is if you wish to publish in theorectical physics,
follow your own rules and you may find a new idea that is true and become
famous.
Best of luck.
--
Jim Goodman
sa...@comcast.net
mywebpages.comcast.net/sawf/
"Michael Maroun" <mar...@phys.ufl.edu> wrote in message
news:3DCBFCA4...@phys.ufl.edu...
>
> I am a young graduate student and I am deeply concerned with the
> so-called Bogdanov hoax.
One must make a hypothesis and then devise some
> test to verify its validity. This is because physics and science in
> general revolve around ascertainable and verifiable truths. Now many
> theoretical physicists cringe at the idea of experiment (including
> myself) especially in the case of fundamental theory where experiment is
> not even physically possible in some cases.
I look
Uncle Al
[snip]
> One reason why the Bogdanov work is bunk (aside from being
> clearly vacuous) is because it does not make a simple hypothetical
> statement an d subsequent test.
[snip]
M-theory.
Predict the crystal structure of a molecule. Explain the persistence
of spiral galaxies over a few billion years of observation. These are
two simple questions without any good answers (re the predicted vs.
observed crystal structure of octanitrocubane).
> One must make a hypothesis and then devise some
> test to verify its validity. This is because physics and science in
> general revolve around ascertainable and verifiable truths.
Not really, no. The hard sciences are mathematical modeling
constrained by empirical falsification. Nothing can validate the hard
sciences; one can only disprove or demonstrate incompleteness. As no
extant physical theory allows for c=c, h=h, and G=G
simultaneously, we can say with definitive assurance that all of
physics is limited by boundary conditions. None of it is universally
true.
Maxwell is only four equations. If you think Maxwell is
straightforwardly "ascertainable and verifiable," read "Method of Edge
Waves in the Physical Theory of Diffraction" by Pyotr Ufimtsev. The
USSR released all 242 pages in 1962 without a second thought. When
Operation Desert Storm introduced the world to stealth technology in
1991, emigree Dr. Ufimtsev (by then at Caltech) was shocked
speechless. "Metod Kraevykh Voln v Fizicheskoî Teorii Difraktsii" was
the cookbook. Uber-nerd Denys Overholser at Lockheed's Skunk Works
was the second man in five billion who could embrace it. What were
the chances?
> Now many
> theoretical physicists cringe at the idea of experiment (including
> myself)
http://www.mazepath.com/uncleal/eotvos.pdf
It's the last place remaining to look. It's computable. It's
executable in existing apparatus at no remarkable cost. Why won't
somebody look?
> especially in the case of fundamental theory where experiment is
> not even physically possible in some cases.
Raymond Chiao (UC Berkeley) is credible even if fantastical,
Podkletnov (Tampere University) is not credible. M-theory is a
beautiful skyscraper albeit starting at the third floor.
> But hypothesis and
> subsequent verification need not involve billion dollar apparati. For
> example one may write down a differential equation with some boundary
> conditions. The hypothesis is as follow: There exists solutions which
> satisfy the boundary conditions and form a set of countably infinite
> orthogonal functions. Test: solve the differential equation produce
> solutions verify that they are indeed countably infinite and that they
> also obey an orthogonality condition and you are done. Now you may be
> wondering why I have brought up such a simple and obvious example. The
> reason is that the number of published articles that do not have this
> format is staggering!
[snip]
Publish an article. Physics/science is not static dogma. It learns
and improves.
> The problems go on. Journals in Nuclear physics no longer have
> articles on nuclear physics. People publish a solution to something,
> change one parameter and republish as a completely separate and
> independent article.
[snip]
MBA-based grant funding demands zero risk, assured results, a PERT
chart (i.e., a business plan); degree conferral and publication
therefrom. Discovery does not fit into a spreadsheet. The increasing
result is Lucent Technologies' takeover of Bell Labs - that wasn't
blatant fraud, that was a researcher learning how to act like
management.
Look at published NSF funding statistics. Almost no budget (<7%) is
allocated to young faculty. We are funding a future we loathe. This
is the model for social engineering, too - unlimited funding for the
dregs, overt discouragement of the Gifted.
Why are we surprised when we bountifully receive what we have
purchased at dear price? Caltech was recently excoriated for not
admitting unqualified Blacks. Welcome to the future.
> As a student of physics and hopefully a member of the next
> generation of scientists I am seriously troubled be these things. I
> look towards the wisdom of the more experienced members of the
> field and to my teachers and instructors to help solve a problem I
> believe all of us are responsible for.
> Is there any way these issues can be fixed?
Find a hotbed of social activists, go postal. Vote "no" by not
reproducing. Run for political office and get elected while not being
purchased. Discover something to reroute all of physics (and
requisition a soapbox out of capital budget). To criticize is to
volunteer.
> Does the shear number of researchers in the field exclude such
> repair possibilities?
Mediocrity is a vice of the doomed. We look at a bright, bright
future in which every child is above average - and we will continue to
drop the average until that lofty goal is achieved.
> What role does economics play? How should funding be
> granted to reduce these problems? What is the ratio of independent
> journals to total number of researchers and how does it affect the
> problems we are seeing? Many more questions come to mind and I look
> forward to responses on all levels.
Start by funding a cadre of credible wild mentalities to see if
looking for a needle in a haystack turns up the farmer's daughter (who
isn't prone to argue). It ain't gonna happen. Start by firing the
bottom third of the heap - the worst undergrads, the worst grads, the
worst post-docs, the worst professors, the worst industrial folks; the
worst administrators, the worst managment. It ain't gonna happen.
At the very least, be personally disaffected and achieve great
things. One cannot enslave a free man, one can only kill him.
--
Uncle Al
http://www.mazepath.com/uncleal/eotvos.htm
(Do something naughty to physics)
Danny Ross Lunsford
....a heartfelt message...
There is nothing to say to you. You will either go forward or you will
not. If you have real ideas, they will develop a life of their
own. If not, then what has really been lost? The *truly* sad thing is
that *teaching in itself* is no more honorable or desired in higher
education than it is in elementary education. Other than that real
loss, one can do physics without having the impediments of a moribund
and decrepit academic environment to impede you. You can get a day
job. I would point to Wallace Stevens and Edward Hopper - they were
insurance men.
As for my personal feeling about these things, if that is worth
stating - I feel only lucky to have escaped the sordid world you are
entering with more or less an entire skin.
I will give you some comfort - yes, things are just as bad as they
seem, if not worse. Your judgment is still sound. That means you can
still hope.
-drl
Urs Schreiber
the assumption that point particles are limits of strings...
> seems to be truly arbitrary. One could easily
> conceive of an alternative idea to explain point particles,
...namely, for instance, one could consider a model consisting
of...
> marbles rolling on a table or rubber sheet. To those
> confined to the surface (table/rubber sheet) the intersection of the
> marble is a single point (at least in the flat case).
I find this an interesting question, in general: It is
frequently argued that string theory has only one single
assumption from which all the rest follows by imposing
consistency conditions. This single assumption is that the
fundamental perturbative degrees of freedom are subject to the
Nambu-Goto action. But from what pool of possibilities does
one choose when picking that?
The most obvious part of the answer is that there are NG
actions for any dimension p+1 of the worldvolume and a priori
none of them might be preferred. But modern string theory now
knows a lot about all these brane actions and that they are
not independent of each other. Hence this is a whole family of
potential candidates for action principles which are already
dealt with. What else could one try?
Can one imagine a sensible action principle for the "marble
theory" that was proposed above? I know that this was just
supposed to be a simple example and that nobody is seriously
inventing a "marble theory". But suppose we were keen on doing
just that, or something similar. Do we have much of a choice?
Whatever we do, we'd very probably want to have an integral of
some geometrical invariant over the world volume of the
fundamental objects of our would-be theory. Thereby the
Nambu-Goto action is already singled out as the simplest
choice compatible with this requirement.
Next we may consider inserting any scalar funtion of the
world-volume coordinates into the integral. But this is just
the dilaton coupling of a brane and hence already out.
Similarly couplings to p+1-forms are already dealt with by
string theory. What aboout writing the curvature scalar into
the integral? For p=1 this gives another description of
dilaton coupling, for p>1 we are merely reinventing gravity.
That's probably not what we want.
So what else could we try? Are there serious alternatives?
> You can now see
> how this might in principle solve the issue of point particles. (For fun
> think about the marble spinning!) But what dynamics do the marbles obey?
> Namely, and I believe this problem comes up in actual theories as well,
> what are the dynamics in the bulk? Do the marbles obey F= ma? No one
> knows and in some cases I suspect that no one will ever be able to know.
> The problem with the whole thing is that the idea is not realistically
> verifiable.
If you write down any theory that looks remotely like that
marble idea described above there would surely be a host of
phenomena where this model deviates from point particle models
on small enough scales. For instance the marbles would collide
in the higher dimensions before their point shadows come very
close to each other.
> Anyone can write down a complicated mathematical expression
> and claim that it is an expression for some physical amplitude.
If you are still talking about string theory here this looks
like a somewhat odd statement: Historically the "expression
for some physical amplitude" was there first.
Aaron Bergman
Urs Schreiber <Urs.Sc...@uni-essen.de> wrote:
> Michael Maroun wrote that
>
> the assumption that point particles are limits of strings...
>
> > seems to be truly arbitrary.
Of course, this came later. The fact that "string theory" is a theory of
strings was derived, not postulated.
> > One could easily
> > conceive of an alternative idea to explain point particles,
>
> ...namely, for instance, one could consider a model consisting
> of...
>
> > marbles rolling on a table or rubber sheet. To those
> > confined to the surface (table/rubber sheet) the intersection of the
> > marble is a single point (at least in the flat case).
>
> I find this an interesting question, in general: It is
> frequently argued that string theory has only one single
> assumption from which all the rest follows by imposing
> consistency conditions. This single assumption is that the
> fundamental perturbative degrees of freedom are subject to the
> Nambu-Goto action. But from what pool of possibilities does
> one choose when picking that?
>
> The most obvious part of the answer is that there are NG
> actions for any dimension p+1 of the worldvolume and a priori
> none of them might be preferred.
The string is preferred for the simple reason that we know how to
quantize it. A sort of lightcone thing can be done in 2+1 dims, but
after that, I think we're pretty much clueless.
Aaron
--
Aaron Bergman
<http://www.princeton.edu/~abergman/>
John Baez
In article <3DCBFCA4...@phys.ufl.edu>,
Michael Maroun <mar...@phys.ufl.edu> wrote:
>One reason why the Bogdanov work is bunk (aside from being clearly
>vacuous) is because it does not make a simple hypothetical statement and
>subsequent test.
I'm afraid this is neither a necessary or sufficient condition
for a paper to be okay. It's not necessary, because physics
is a difficult enterprise that does not proceed one paper
at a time. It can take quite a bit of floundering around for
theorists to develop ideas to the point where they can make a
testable experimental prediction... and they need to be able to
publish papers *while* floundering around, because this is
actually how progress happens.
On the other hand, it's not sufficient, because it's easy
to write papers that are bunk yet still make a simple
hypothetical statement and subsequent test: e.g., "if
we fly to Pluto and dig 50 feet, we'll hit a stratum of Roquefort".
The problems with the Bogdanov's papers are actually a
bit trickier to spot, since it requires expertise in a
subject to gauge whether a statement about that subject
is meaningful, and sometimes it can take quite a long time
to do this.
Kevin A. Scaldeferri
Aaron Bergman <aber...@princeton.edu> wrote:
>Of course, this came later. The fact that "string theory" is a theory of
>strings was derived, not postulated.
This statement has me a bit confused. Could you explain what you mean
by it?
No presentation I've seen in an introductory text or article on string
theory supports this, nor does my knowledge of the early history of
string theory.
I suppose that there is some sense in which this may be true, akin to
the way that one could prove that normal QFT is a theory of point
particles, but it is the sort of purely mathematical exercise that
doesn't surprise anyone and is really a sanity check more than
anything else.
--
======================================================================
Kevin Scaldeferri Calif. Institute of Technology
The INTJ's Prayer:
Lord keep me open to others' ideas, WRONG though they may be.
Aaron Bergman
In article <aqp71e$ph7$1...@sue.its.caltech.edu>,
ke...@sue.its.caltech.edu (Kevin A. Scaldeferri) wrote:
> In article <abergman-465BC4.12180611112002@localhost>,
> Aaron Bergman <aber...@princeton.edu> wrote:
>
> >Of course, this came later. The fact that "string theory" is a theory of
> >strings was derived, not postulated.
>
> This statement has me a bit confused. Could you explain what you mean
> by it?
>
> No presentation I've seen in an introductory text or article on string
> theory supports this, nor does my knowledge of the early history of
> string theory.
Check out chapter one of GSW. Virasoro wrote down his amplitude as
something that would obey a nice duality of poles in the, er, s and t
channels, I think. Hence the term "dual models". It was later discovered
(by Susskind, I think) that the Virasoro amplitude could be derived from
a theory of oscillating strings.
Arkadiusz Jadczyk
Baez) wrote:
>The problems with the Bogdanov's papers are actually a
>bit trickier to spot, since it requires expertise in a
>subject to gauge whether a statement about that subject
>is meaningful, and sometimes it can take quite a long time
>to do this.
I agree. But the case is even more than that.
We know that there were papers that were written by authors who were not
able to express their ideas using high standards that should become
normal in publications in mathematical physics. Some of these papers
required work of someone else to convert them into new, original,
and understandable contribution.
The case of Tomita and Takesaki is one such case.
Probably many experts in the fields were shown Tomita's notes
and conference talk, but it is only Takesaki who was able to
"see the light in the mud." The result is an increadible, beautiful
and powerful theory. It is called Tomita-Takesaki. All the idea is due
to Tomita. All the "real hard work of making sense" is due to Takesaki.
In fact, I ma not even sure if what today know as Tomita-Takesaki is
ALL that could have been extracted from Tomita notes. In fact this is
something not untypical in Japaneese mathematics. There are quite
a lot of papers by Japaneese authors which somewhat do not fit to
the western standards. Either by lack of precision, or by following very
strange patterns of ideas that are not quite congruent for other
mathematicians. Finsler spaces, for instance, are mostly considered
as a curiosity in the western world and it is only the monograph by Bao
and Chern that perhaps will change it in the future.
ark
--
Arkadiusz Jadczyk
http://www.cassiopaea.org/quantum_future/homepage.htm
--
Anonymous Coward
> In article <abergman-465BC4.12180611112002@localhost>,
> Aaron Bergman <aber...@princeton.edu> wrote:
>
> >Of course, this came later. The fact that "string theory" is a theory of
> >strings was derived, not postulated.
>
> This statement has me a bit confused. Could you explain what you mean
> by it?
>
> No presentation I've seen in an introductory text or article on string
> theory supports this, nor does my knowledge of the early history of
See the first chapter of GSW in particular section 1.1. Also for the
original reference on this see..
Veneziano, G. (1968) "Construction of a crossing symmetric, Regge-behaved
amplitude for linearly rising trajectories," Nuovo Cim. 57A, 190
Equation 1.1.5 of GSW was first guessed, then only later was it understood
as arising from a string, see section 1.1.3 of GSW.
Dark Fruitbasket
> I find this an interesting question, in general: It is
> frequently argued that string theory has only one single
> assumption from which all the rest follows by imposing
> consistency conditions. This single assumption is that the
> fundamental perturbative degrees of freedom are subject to the
> Nambu-Goto action. But from what pool of possibilities does
> one choose when picking that?
<snip>
> Whatever we do, we'd very probably want to have an integral of
> some geometrical invariant over the world volume of the
> fundamental objects of our would-be theory. Thereby the
> Nambu-Goto action is already singled out as the simplest
> choice compatible with this requirement.
<snip>
> So what else could we try? Are there serious alternatives?
How about the Polyakov action? Or one of a godzillion other
actions that give rise to the same classical equations (For
a set of silly examples, write the classical equations on a
first order homogenous form, i.e. E=0, where E contains
no second order differentials or higher. Set X=E^2. Any
polynomial P(X) is invariant under variations around the
classical solution) (And if you're craving for more, you
can also multiply any non-constant term by anything that
isn't singular at the classical solution, say another
lagrangian density)
Them string-theorists have ways to pick. But, to flaunt my
flamboyant ignorance, I must admit that I was under the
impression that they *didn't* pick the Nambu-Goto action,
but the Polyakov action.
Urs Schreiber
Aaron Bergman wrote:
[..]
> The string is preferred for the simple reason that we know how to
> quantize it. A sort of lightcone thing can be done in 2+1 dims, but
> after that, I think we're pretty much clueless.
My point is that all branes for arbitrary p < 10 are related. We would not
expect that quantizing the p=3 brane gives something completey outside the
scope of string/M theory. In fact, the quantization of the supermembrane
(p=2) shows that one finds new interesting stuff, but it is still string
theory. The string is preferred because it is the simplest and most
tractable case, but still we know that the string implies branes of all
sorts. In fact branes can be sort of quantized by looking at open strings
with one end attached to the brane.
Therefore, in order to find an action for a fundamental extended object that
is _not_ part of string theory one has to look for something other than
brane actions, I'd say. I am not aware of any sensible canidates. Are you?
Urs Schreiber
> Urs Schreiber <Urs.Sc...@uni-essen.de> wrote:
[...]
>> So what else could we try? Are there serious alternatives?
>
> How about the Polyakov action? Or one of a godzillion other
> actions that give rise to the same classical equations
Sure, you can pick equivalent actions for the string. They'll all describe
the string. That's not what I was getting at. Whether Polyakov or NG
actions, they all describe objects whose energy is (roughly) proportional
to their proper volume, i.e branes. My thought was: What other fundamental
extended objects except for branes can one imagine that have a sensible
world-volume theory. Are "marbles" among these objects?
The original poster was pointing out that there is a lot of arbitrariness
in postulating that the world consists of string/brane. He imagined, if I
got him right, that there should be many more possibilities for
postulating extended fundamental objects. I was wondering if this is
really true. Can you give a sensible action for an extended fundamental
object that is _not_ equivalent to the string/brane action? That would be
interesting.
> Them string-theorists have ways to pick. But, to flaunt my
> flamboyant ignorance, I must admit that I was under the
> impression that they *didn't* pick the Nambu-Goto action,
> but the Polyakov action.
Sure, mostly one works with the Polyakov action because it is equivalent to
the p=1 NG action and often more convenient. I was referring to the NG
action in my post because it looks more fundamental to me, in some vague
sense, but never mind.
Even if it is not emphasized in most texts, canonically quantizing the NG
action leads readily to the same set of constraints as the Polyakov action
does. But have you ever tried to generalize the Polyakov action to higher
word-volume dimensions, i.e. to branes with p > 1? If you do that you'll
find that it's only for p=1 that the Polyakov action takes the familiar
form, for p>1 one has to insert an appropriate "cosmological constant"
type of term on the worldsheet in order that the action still be
equivalent to the corresponding NG action, which has the same form for all
p. Hence the physical system described by the NG action is what one wants
to have and the Polyakov form is a (sometimes) convenient reformulation.
In fact, when one generalizes the brane action to full Dirac-Born-Infeld
actions I am only aware of the use of the square-root form, corresponding
to the NG form. (Which is not to say that one couldn't use a Polyakov-like
reformulation just as well.)
Kevin A. Scaldeferri
Aaron Bergman <aber...@princeton.edu> wrote:
>
>In article <aqp71e$ph7$1...@sue.its.caltech.edu>,
> ke...@sue.its.caltech.edu (Kevin A. Scaldeferri) wrote:
>
>> In article <abergman-465BC4.12180611112002@localhost>,
>> Aaron Bergman <aber...@princeton.edu> wrote:
>>
>> >Of course, this came later. The fact that "string theory" is a theory of
>> >strings was derived, not postulated.
>>
>> This statement has me a bit confused. Could you explain what you mean
>> by it?
>
>something that would obey a nice duality of poles in the, er, s and t
>channels, I think. Hence the term "dual models". It was later discovered
>(by Susskind, I think) that the Virasoro amplitude could be derived from
>a theory of oscillating strings.
I won't be able to lay hands on my GSW for a couple of days, so I'm
working from fuzzy memory here...
However, even what you say seems more like postulating strings than
deriving them. You say, if you postulate a theory of strings, you can
derive the Virasoro amplitude. Is there a way to go the other
direction?
Perhaps Virasoro did write down his amplitude first, but the standard
lore as I remember it (poorly, at this point) went like:
we observe confinement & a roughly linear binding potential in mesons
we visualize/explain this in terms of flux tubes
inspired by this we try to construct a quantum theory of 1-d objects,
arriving at the Goto-Nambu (and later Polyakov) action
This reproduces the Virasoro amplitude, but also necessarily has
massless spin-2 particles, and requires 26-dimensions for anomaly
cancellation, and ... string theory is (re)born as a TOE.
John Baez
In article <aqu7t8$9jf$1...@sue.its.caltech.edu>,
Kevin A. Scaldeferri <ke...@sue.its.caltech.edu> wrote:
>In article <abergman-0E8B51.18164811112002@localhost>,
>Aaron Bergman <aber...@princeton.edu> wrote:
>>Check out chapter one of GSW. Virasoro wrote down his amplitude as
>>something that would obey a nice duality of poles in the, er, s and t
>>channels, I think. Hence the term "dual models". It was later discovered
>>(by Susskind, I think) that the Virasoro amplitude could be derived from
>>a theory of oscillating strings.
>I won't be able to lay hands on my GSW for a couple of days, so I'm
>working from fuzzy memory here...
>
>However, even what you say seems more like postulating strings than
>deriving them. You say, if you postulate a theory of strings, you can
>derive the Virasoro amplitude.
>Perhaps Virasoro did write down his amplitude first [...]
Right, he did - that's the point! This story is quite remarkable
and often retold, a standard part of string lore. People working
on hadrons were looking for scattering amplitudes that satisfied
something like this:
\ / \ /
-- = |
/ \ / \
presumably because experiments show something like this is roughly
true.
Veneziano went digging around in some books of special functions
and found a function with this property! I think it's built
from Euler's beta function B(p,q), and he just tripped over a
nice identity that makes the above equation true. It's probably
equation 24 on this webpage:
http://mathworld.wolfram.com/BetaFunction.html
although there must be a typo in this equation.
*Later*, somebody realized that this function arose naturally
from string theory - in which the above Feynman diagrams are
revealed to be two ways of drawing the same Riemann surface!
I don't know if the idea of mesons as quarks connected by
pieces of elastic string came after all this, or was developed
independently, or what.
Aaron Bergman
>
> However, even what you say seems more like postulating strings than
> deriving them. You say, if you postulate a theory of strings, you can
> derive the Virasoro amplitude. Is there a way to go the other
> direction?
I'm not really up on the history, but I do know that Susskind
postulated a string to get the previously known Veneziano
amplitude. (too many 'V' people.) The legend I've heard is mostly
what's described in the beginning of GSW. I bet John Schwarz can
tell you for sure.
> This reproduces the Virasoro amplitude, but also necessarily has
> massless spin-2 particles, and requires 26-dimensions for anomaly
> cancellation, and ... string theory is (re)born as a TOE.
I think 26 dimensions was originally derived for unitarity. It
was later reinterpreted as the cancellation of the conformal
anomaly in that approach to strings. The lightcone came first, I'm
fairly sure.
Aaron