Stephen Hawking's Theory Regarding Eleven Dimensions
Ann Marie Aoki
Ann M. Aoki.
Charles Francis
Aoki <marier...@earthlink.net> writes
>How did Mr. Hawking theorize his eleven dimensions? Thank you very much,
>Ann M. Aoki.
>
way Michio Kaku describes it in Hyperspace it appears to be based on his
failure to understand the distinction between a dimension and an
independent variable. That would make it a matter of incompetence.
Regards
--
Charles Francis
Apparatus
> How did Mr. Hawking theorize his eleven dimensions? Thank you very much,
> Ann M. Aoki.
I believe that you are referring to String Theory. From what I
gathered at a introductory lecture to string theory, the eleven
dimensions resulted from complex, convoluted math, somehow. I myself
am interesed in the mathematical proof of this.
- Apparatus
A.J. Tolland
> marier...@earthlink.net (Ann Marie Aoki) wrote:
> > How did Mr. Hawking theorize his eleven dimensions?
> > Thank you very much, Ann M. Aoki.
>
> I believe that you are referring to String Theory. From what I
> gathered at a introductory lecture to string theory, the eleven
> dimensions resulted from complex, convoluted math, somehow. I myself
> am interesed in the mathematical proof of this.
I can think of two different structures which M. Aoki might be
referring to. The first is maximal 11 dimensional supergravity,
discovered in the late seventies by Cremmer, Julia and Scherk. I don't
think that Hawking had anything to do with this. I'm not sure he ever did
anything with supergravity; he's more of a cosmologist. The second is
M-theory, discovered around 94/95 by Witten and various others. 11
dimensional supergravity actually turns out to contained within M-theory.
Again, I don't think Hawking had anything to do with these discoveries.
Sounds like someone's been reading some bad pop science.
It's not too hard to prove that 11 is the largest number of
dimensions a locally supersymmetric field theory (i.e. a supergravity) can
live in. The reason is that SUSY theories must have as many bosonic
degrees of freedom as they have fermionic degrees of freedom. The number
of d.o.f.'s contained in a single fermionic object grows exponentially
with the dimension of spacetime, while the number of d.o.f.'s in a single
bosonic object grows polynomially. Objects with half-integer spin are
fermionic; objects with integer spin are bosons. Supersymmetry relates
the number of objects you have with spin j to the number of objects you
have with spin j +/- 1/2, so you can't just keep tossing in extra low spin
particles until you have sufficiently many bosonic degrees of freedom.
The only thing you can do is add objects with higher and higher spins.
If you are restricted to have only objects with spin less than 5/2, you
can only construct supergravity theories in low dimensions. Simple
counting arguments show that the maximum dimension is eleven. The actual
computation is pretty unenlightening.
The easiest argument I know of that M-theory is 11 dimensional is
that it has one more spatial dimension that the 5 string theories, which
are all 10 dimensional. There was a thread here recently discussing why
perturbative string theories are 10 dimensional. I don't know of any more
intrinsic proofs (anomaly vanishing, etc,...) that M-theory is 11
dimensional.
--A.J.
Aaron J. Bergman
>How did Mr. Hawking theorize his eleven dimensions? Thank you very much,
>Ann M. Aoki.
The short answer is that he didn't. Witten did.
The answer is somewhat technical. Basically, Witten noticed that in a
certain type of string theory which was known to live in 10 dimensions
(for different technical reasons), there possibly existed a set of
states (BPS states) that had masses of the form an integer times some
constant. As the string coupling changed, the distances between the
states changed. It turns out that this sort of spectrum is exactly what
you expect when you have another dimension. The radius of this extra
dimension is related to the coupling constant of string theory.
This is really quite amazing when you think about it. People had been
working with string theory in ten dimensions for years and, somehow, an
extra dimension that no one put in appeared in the theory.
Aaron
--
Aaron Bergman
<http://www.princeton.edu/~abergman/>
Demian H.J. Cho
> How did Mr. Hawking theorize his eleven dimensions?
Hi,
Since no experts seems to answering your question let me try.
First of all, it wasn't Stephen Hawking who theorize 11 dimension.
Theory based on more than 4 dimensional spacetime was initiated
by Kaluza and Klein about 70 years ago. By assuming we lives in
five dimensional spacetime, where 'extra' spatial dimension looks
like tiny circle we can 'derive' 4 dimensional Einstein gravity and
electromagnetism together from 5 dimensional Einstein gravity.
Because of this aspect it was often called unified field theory, and
Einstein himself spent last years of his life on it without much of success.
Modern incarnation of theory began by many people, including
Freund, Cho (not me), DeWitt (as a homework problem in his
Les Houches summer school), Kerner, and Trautman and many
more. The idea is we can 'unify' not only gravity and
electromagnetism, but also with gauge theory (theory of forces
governing nuclear processes) if we use more than one extradimension.
Also, at the same time people developed theory called Super
Gravity(SUGRA). What is relevant here is;
1. There is a UNIQUE 11 dimensional SUGRA.
2. There is a sort of unique way to choose a vacuum (well,
our universe - I hear screams from many of news group
members.) called Freund-Rubin solution. What is cool about
this solution is it nail down the fact we are living in the
4-dimensional universe. In detail, it is SUSY that makes this
solution works. So in some sense dimension of our universe
- 4 - is nailed down by SUSY.
3. (Most relevant for us) 11 is MAXIMUM dimension for SUGRA.
If we have more dimensions we are going to have a trouble in
our 4-d universe. (In detail, when you reduce D=11, N=1
SUGRA into 4-d SUGRA, you are end up with N=8, which
is maximum consistent SUSY. This is because if N > 8 we
are going to see particles with spin higher than 2, which
believe to lead into inconsistency. - By the way, how tight this
argument? Does anyone has comment?)
It was Ed Witten, who nail down 11 dimension in his classic paper
"Search for a Realistic Kaluza-Klein Theory". Nucl. Phys. B186
412-492 (1983). Here is a rough logic.
We demand that theory contains standard model. (Current theory
of all elementary particles), and be a SUGRA. He showed that to contain
standard model the dimension of extra space must be at
least 7. ( Space of lowest dimension with symmetry G act on it
is always a homogeneous space G/H with H maximal subgroup
of G. In the case of G= SU(3) x SU(2) x U(1), H = SU(2) x U(1)
x U(1). The dimension of G/H in this case is 7).
So, 11 dimension is very unique in a sense that this is a minimum
required dimension to contain standard model, and maximum
allowed dimension for SUGRA. Eventually, however, it was
Witten himself showed that there is a problem to get chiral fermion
from 11 dimension (using Atiyah - Hirzebruch index theorem for
dirac operator). So people eventually give up this 'naive' way of
doing it, and move on to string theory. - the point where my
confidence level begin falling down, so I am not going to talk about
it.
Cheers,
--
Demian H.J. Cho
Center for Gravitation and Cosmology
University of Wisconsin-Milwaukee
Urs Schreiber
news:3B604F7D...@uwm.edu...
> (In detail, when you reduce D=11, N=1
> SUGRA into 4-d SUGRA, you are end up with N=8, which
> is maximum consistent SUSY. This is because if N > 8 we
> are going to see particles with spin higher than 2, which
> believe to lead into inconsistency. - By the way, how tight this
> argument? Does anyone has comment?)
How about this: In susy qm the supercharges are related to the exterior
derivatives. So we have N=1 on real manifolds, N=2 on complex manifolds, N=4
on quaternionic manifolds (?) and N=8 on octonionic manifolds (??) and
that's presumably it since there are no hexadeconions... Maybe there is a
relation?
Lubos Motl
> The short answer is that he didn't. Witten did.
Well, I wanted to write the same, to have some fun. But actually I hope
that both of us realize that Witten certainly was not the first guy who
realized why "11" was important. :-)
Cremmer, Julia and Scherk invented their eleven-dimensional supergravity
in the late 70s. This theory was the most symmetric, most beautiful of all
the supergravity theories. It worked in the highest possible dimension.
Why 11 is the maximum dimension that allows a physical supersymmetric
theory? Because in 10+1 dimensions, a spinor has 32 real components. The
minimal supersymmetry has 32 supercharges (components) and in higher
dimensions, the minimal amount is bigger.
If you have 32, everything is fine. A BPS object (such as the graviton
multiplet) preserves 16 supercharges. The remaining 16 supercharges can be
used to lower or raise the z-projection of spin: you pair them into 8
creation and 8 annihilation fermionic (complex) operators. Each of the
creation operators is able to raise the spin j_z by 1/2 - so eight is
precisely enough to go between -2 and +2. The graviton multiplet has spin
2 and higher spin is not possible; this fact has been discussed here a
while ago. Therefore 32 is the maximum number of supercharges and 11 is
the maximum dimension of a low-energy supersymmetric theory that admits a
free limit.
11 dimensions is a kewl world. Graviton has 9.10/2.1-1 = 44 polarizations,
the gravitino has (9-1).16=128 and the three-form potential C3 has
9.8.7/3.2.1=84 polarizations, so that the bosons and fermions match.
Green, Schwarz and Witten wrote in their "Superstring theory", volume 2,
Cambridge University Press 1987, that "11-dimensional supergravity remains
an enigma. It is hard to believe that the existence of such a beautiful
structure is just an accident. It will take time to understand what is its
role in the scheme of things" - or something like that. Witten had to
think for 8 years to understand the depth of his sentence from 1987. ;-)
It was known that type IIA supergravity in 10 dimensions was the
dimensional reduction of 11-dimensional supergravity. Many things were
known - such as the tension of membranes in 11 dimensions. But people had
to wait for Witten who realized that the strong coupling limit of type IIA
superstring theory (=the consistent completion of type IIA supergravity at
all scales) is an 11-dimensional theory, a completion of 11-dimensional
supergravity, called M-theory.
With M-theory, the relation is clear. Membranes wrapped on the extra
circle are type IIA strings, membranes which are not wrapped are
D2-branes. Wrapped M5-branes are D4-branes and non-wrapped M5-branes are
NS5-branes of type IIA. All the tensions agree, physics is understood both
at weak and strong coupling.
M-theory in 11 dimensions can be used to obtain more than just type IIA
strings (by compactifying the 11-th direction on a circle). If the 11-th
direction is a line interval, the world has two boundaries. Each of them
must carry a single E8 gauge supermultiplet, to cancel anomalies, as was
shown by Horava and Witten in late 1995. If the boundaries are close to
each other, physics is that of E8 x E8 heterotic string theory in 10
dimensions (one E8 per each boundary). M-theory can be compactified in
many ways. Because its dimension is higher than the dimension of 5
perturbative string "theories", people feel that it is "more fundamental"
although one can also say that this limit of TOE is as fundamental as
others.
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.
t...@rosencrantz.stcloudstate.edu
Charles Francis <cha...@clef.demon.co.uk> wrote:
>In article <55644811.01072...@posting.google.com>, Ann Marie
>Aoki <marier...@earthlink.net> writes
>>How did Mr. Hawking theorize his eleven dimensions? Thank you very much,
>>Ann M. Aoki.
>>
>I don't know that Prof Hawking was the originator of this model,
I'm reasonably sure he wasn't. There seems to be a general phenomenon
in popular reporting on physics that anything sufficiently
weird-sounding gets attributed to Hawking. Presumably this is because
he's one of the few contemporary physicists anyone's heard of, and
everyone knows that he says weird things!
Similar things have happened to Einstein's name in the past.
-Ted
Aaron J. Bergman
>
>I don't know that Prof Hawking was the originator of this model, but the
>way Michio Kaku describes it in Hyperspace it appears to be based on his
>failure to understand the distinction between a dimension and an
>independent variable. That would make it a matter of incompetence.
So, what is the difference, Charles?
Just curious, you know.
J. J. Lodder
Actually, there is no real math or 'proof' to it.
It is 'experimental math':
many things are tried, some work better than others,
hence -it is believed- that there -may be- some sort of physical reality
associated with the easiest model that happens to have certain desirable
properties.
Best,
Jan
Bagnoud Maxime
> How did Mr. Hawking theorize his eleven dimensions? Thank you very much,
> Ann M. Aoki.
Dear Ann,
checking the last ten years of archives, I've seen no articles from Hawking
where the title refer to an eleventh dimension. Although, the research in
M-theory is aimed at an eleven-dimensional description of the forces of
nature, as far as I know, Hawking hasn't written anything on that matters.
Can you explain us what you are referring to in particular, so that we can
address your question?
Rgeards,
Maxime
Squark
<Pine.SOL.4.10.101072...@physsun9.rutgers.edu>):
>Green, Schwarz and Witten wrote in their "Superstring theory", volume 2,
>Cambridge University Press 1987, that "11-dimensional supergravity remains
>an enigma. It is hard to believe that the existence of such a beautiful
>structure is just an accident. It will take time to understand what is its
>role in the scheme of things" - or something like that.
I think it must more interesting to understand the role of 4 dimensions in
the scheme of things, just to toss some would into the fire... ;)
Best regards,
Squark.
-------------------------------------------------------------------------------
Write to me at:
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dSdqudarkd_...@excite.com
Toby Bartels
>How about this: In susy qm the supercharges are related to the exterior
>derivatives. So we have N=1 on real manifolds, N=2 on complex manifolds, N=4
>on quaternionic manifolds (?) and N=8 on octonionic manifolds (??) and
>that's presumably it since there are no hexadeconions... Maybe there is a
>relation?
Well, there *are* hexdeconions (the standard name is "sedenions"),
but they lose many of the important properties of the others.
For example, they are not a division algebra;
multiplication by a constant (non0) sedenion is not (always) an isomorphism,
so you can't divide in general, which screws up a lot of things.
See <http://math.ucr.edu/home/baez/week59.html>,
also <http://www.arXiv.org/abs/math.RA/0105155>.
-- Toby
to...@math.ucr.edu
Urs Schreiber
news:9jsggj$pbb$1...@glue.ucr.edu...
> Urs Schreiber wrote:
>
> >How about this: In susy qm the supercharges are related to the exterior
> >derivatives. So we have N=1 on real manifolds, N=2 on complex manifolds,
N=4
> >on quaternionic manifolds (?) and N=8 on octonionic manifolds (??) and
> >that's presumably it since there are no hexadeconions... Maybe there is a
> >relation?
>
> Well, there *are* hexdeconions (the standard name is "sedenions"),
> but they lose many of the important properties of the others.
> For example, they are not a division algebra;
> multiplication by a constant (non0) sedenion is not (always) an
isomorphism,
> so you can't divide in general, which screws up a lot of things.
So this means that there is no such thing as a "sedenionic manifold", since
there are in general no invertible sedenionic transition functions, right?
Aaron Bergman
wrote:
A year or so ago, I got an invitation (along with everyone else in the
department, I think) to join a Yahoo club ostensibly devoted to string
theory. On the page for it, it listed essentially every development in
strings in the last five or six years, ending with the sentence, "these
ideas are all due to Brian Greene."
Ah well.
Aaron
Lubos Motl
> I think it must more interesting to understand the role of 4 dimensions in
> the scheme of things, just to toss some would into the fire... ;)
Well, too bad, :-) I agree with you. I know one consistent theory that
does not assume the dimension of spacetime already at the beginning but
offers a natural way to connect vacua with different numbers of large
dimensions. A theory that makes the number of dimensions a dynamical
question. The theory is string/M-theory.
There could be an explanation why we live in 4 large spacetime dimensions.
But I can also imagine that there is no explanation like that - except for
some anthropic ideas (a hydrogen atom in higher dimensions - with a
potential 1/r^k for k>1 - is unstable; a 2-dimensional dog is halved if it
eats a lunch; 3+1 dimensions is the only viable possibility). More
concretely, I believe that the (supersymmetric) vacua of string theory in
high enough dimensions (such as 6,7,8,9,10,11) are consistent and nothing
will change about that. We will be forced to imagine that we live in a
sector of the world that has 4 large dimensions - but there are also other
"regions" in the world with a different number of spacetime dimensions.
However it is also possible that after supersymmetry is broken, Nature
chooses its ground state almost uniquely and the broken SUSY fixes even
the dimension of spacetime...
Well, this is a typical example of a question that we cannot answer by
solid arguments. If someone knows of a nice answer, I will be more than
happy to see it! :-)
Charles Francis
Bergman <aber...@Princeton.EDU> writes
>In article <qjU5MeAC...@clef.demon.co.uk>, Charles Francis wrote:
> the
>>way Michio Kaku describes it in Hyperspace it appears to be based on his
>>failure to understand the distinction between a dimension and an
>>independent variable.
>So, what is the difference, Charles?
Hi, Aaron,
Yeah, ok, so it's not an easy question. The use of mathematics in
physics requires that we abstract from the physical situation a number
of formal rules which are then used to define a mathematical structure.
Abstraction means that we leave out everything which is not part of the
chosen formal rules. When we take abstraction to a high degree two
things which are quite different may obey the same mathematical law. But
that only means the mathematical law is the same, it does not mean they
are the same thing. Otherwise you could conclude that apples are oranges
because apples and oranges obey the same laws of integer arithmetic. So
the real distinctions apply not in the mathematical structure, but the
physical situation.
In the case of these many dimensions we are really only looking at the
properties of basis for Hilbert space, as distinct from the type of
physical measurement which gives you a dimension, as distinct from
isospin or something else. We are really leaving out most of the physics
when we look at things this way, certainly most of the empirical
physics. There is a sense in which your apparently casual challenge may
be likened to saying "distinguish between apples and oranges using only
the laws of integer arithmetic". I wouldn't be able to do it.
But in this instance the mathematical laws are not that close the same -
dimensions are continuum variables (or at least have that appearance),
whereas most of the additional dimensions discussed by Kaku appear to
take only a few discrete values. Discussion of how these additional
dimensions existed in the early life of the universe and have become
"curled up" merely adds to the feeling that this is a model which has to
be fixed by quite extraordinarily ad hoc language, non-empirical
phenomena, and wildly speculative hypotheses about the physical
behaviour of matter.
Moreover speculation about many dimensions runs quite contrary to what I
perceive as the course of science as we head towards more unified
theory. In relativity we reduce space-dimension to measurement of time.
I expect space dimension to disappear altogether at a deeper level of
space-time structure, not increase from three to eleven. Even now it is
possible to formulate physics so that space dimension appears only as a
relationship, not as a fundamental entity. But there is still a need for
independent variables to describe different types of particle.
Regards
--
Charles Francis
John Gonsowski
Lubos Motl wrote:
The best anthropic idea I think is simply that spacetime had to have
four dimensions so that it could have an associative division algebra
to go with it (a non-associative history would be wierd). These
ideas say why we have to live in four dimensions but as you say it
doesn't say how we got here. String theory allows the possibility of
getting to four dimensions but it as you say isn't known to force us
to four. I know Tony Smith is into something called MetaClifford
algebras which may be related to dimensional reduction to four but
it is still in the early development stage. I personally (just me not
Smith) am into the idea that the large-compact spacetime dimension
differentiation is related to the negative-positive ends of the E7
seventh axis (E7 being related by Smith, Smolin and others to
bosonic M-theory). I have a paper for this to be "published" in an
online journal. I can send it to you if you want but you would
have to wade through alot of non-physics stuff. What does
breaking symmetry (or supersymmetry) mean to you? You
referred earlier to E6 as a good Grand Unified theory. How would
breaking symmetry effect this E6. Would it be equivalent to
some slices/projections of E6 root vectors being given special
attention?... pretending E6 was a cube it would be like choosing
particular axes to call x and y and then picking a particular way
to project the z into this x/y plane... Tony Smith seems to do
something like this up through D4 and I would think it could
extend up through E6 and even E8 (I do some of this in my paper
also, I just wish I understood this better from other than a
root vector point of view). I also wish I understood the Spin(8)
triality better; for Tony Smith this Spin(8) triality seems to
effect D5 through E8 and for me and my paper it seems to
effect even D3. I wish there was a direct way to go from root
vector "symmetry breaking" to things like Lagrangians...
John
Lubos Motl
> ... On the page for it, it listed essentially every development in
> strings in the last five or six years, ending with the sentence, "these
> ideas are all due to Brian Greene." Ah well.
Let me say a few comments about this phenomenon from my perspective. First
of all, it is clear that the laymen tend to think that the authors of
popular books - and more generally physicists who like to talk to laymen -
are the best physicists in the world while the experts who write a lot of
complex equations are less interesting.
Many people think that Stephen Hawking is the brightest living physicist.
Some readers of Lee Smolin's books think the same about Lee Smolin. And
finally many readers of The Elegant Universe think that the only candidate
for the smartest physicist can be Brian Greene. He is as bright as
Feynman, I have read. I do not want to hide that this is probably the most
reasonable claim of all although Hawking's discoveries of black hole
thermodynamics would deserve a Nobel prize. Unfortunately, there are not
too many light black holes around.
Laymen are not able to appreciate technicalities necessary to judge who is
really a great physicist. And therefore they use a simpler framework and
criteria. The players in NHL appear in the public and people like them.
They also like Madonna, for instance. And the authors of popular books are
always in the risk that they become more like Madonna.
Almost anyone who writes popular books becomes more popular among laymen
but less respected by the colleagues.
Sometimes such a change is natural. However, I think that sometimes such a
development is not fair. Brian Greene's book is honest and balanced.
However some people try to sell (wrong and silly) scientific speculations
to the laymen because it is much easier than to convince the fellow
physicists.
Concerning Brian Greene. I think that he is probably the most important
physicist who contributed to our understanding of the topology change in
string theory. Although topology change is not the only interesting
development (and AdS/CFT, String Field Theory or Matrix Theory are at
least equally important as the topology change), it is certainly a topic
comprehensible to the general public but scientifically interesting and
deep.
Witten and Atiyah just published their paper with 100 pages of stuff
concerning the topology changes of conically singular 7-dimensional
manifolds with G2 holonomy in M-theory. It is a very interesting paper.
But at the same moment, it is an "appendix" of the papers by Greene,
Aspinwall, Morrison - and by Greene, Morrison, Strominger. Of course,
there were many other people involved and many of them are mentioned in
The Elegant Universe.
Brian Greene is an extremely skillful and scientifically honest writer and
speaker and the scientific community should be very happy that someone
like that exists. The general public can get a balanced idea what physics
is really about in spite of that Brian Greene's discoveries and papers
were focused primarily on some subtle features of the Calabi-Yau manifolds
such as mirror symmetry and the topology change.
There is a gap between the way how laymen look at science and how
scientists judge their colleagues. I think that this gap should not grow.
It is extremely important for science as a human activity that it has some
natural "spokesmen" who can communicate important facts to the public.
Science without such personalities always goes down the hill. Its funding
decreases. Einstein and Feynman are two examples of great physicists who
were very popular among the laymen, too. Physics needs to go in this way.
Aaron J. Bergman
[snip much ontology]
>But in this instance the mathematical laws are not that close the same -
>dimensions are continuum variables (or at least have that appearance),
>whereas most of the additional dimensions discussed by Kaku appear to
>take only a few discrete values.
This is simply incorrect.
>Discussion of how these additional
>dimensions existed in the early life of the universe and have become
>"curled up" merely adds to the feeling that this is a model which has to
>be fixed by quite extraordinarily ad hoc language, non-empirical
>phenomena, and wildly speculative hypotheses about the physical
>behaviour of matter.
You can have all the prejudices you want -- you still haven't described
to me an experiment that can, say, distinguish between one of the
composite dimensions of Georgi and Arkani-Hamed and a "real" dimension.
Charles Francis
>>
>>I don't know that Prof Hawking was the originator of this model, but the
>>way Michio Kaku describes it in Hyperspace it appears to be based on his
>>failure to understand the distinction between a dimension and an
>>independent variable. That would make it a matter of incompetence.
>
>So, what is the difference, Charles?
>
>Just curious, you know.
>
>Aaron
Hi, Aaron,
Yeah, ok, so it's not an easy question. The use of mathematics in
physics requires that we abstract from the physical situation a number
of formal rules which are then used to define a mathematical structure.
Abstraction means that we leave out everything which is not part of the
chosen formal rules. When we take abstraction to a high degree two
things which are quite different may obey the same mathematical law. But
that only means the mathematical law is the same, it does not mean they
are the same thing. Otherwise you could conclude that apples are oranges
because apples and oranges obey the same laws of integer arithmetic. So
the real distinctions apply not in the mathematical structure, but the
physical situation.
In the case of these many dimensions we are really only looking at the
properties of basis for Hilbert space, as distinct from the type of
physical measurement which gives you a dimension, as distinct from
isospin or something else. We are really leaving out most of the physics
when we look at things this way, certainly most of the empirical
physics. There is a sense in which your apparently casual challenge may
be likened to saying "distinguish between apples and oranges using only
the laws of integer arithmetic". I wouldn't be able to do it.
But in this instance the mathematical laws are not that close the same -
dimensions are continuum variables (or at least have that appearance),
whereas most of the additional dimensions discussed by Kaku appear to
take only a few discrete values. Discussion of how these additional
dimensions existed in the early life of the universe and have become
"curled up" merely adds to the feeling that this is a model which has to
be fixed by quite extraordinarily ad hoc language, non-empirical
phenomena, and wildly speculative hypotheses about the physical
behaviour of matter.
(BTW I do not regard Kaku as authorative on string theory. It is just
that he has done a great deal of publicising many dimensions, presumably
to help sell his books. The real arguments from gauge theory appear far
more compelling, and my disagreement with them is considerably more
subtle.)
Regards
--
Charles Francis
Ralph E. Frost
news:9kce86$ehv$1...@news.state.mn.us...
Independent or ad hoc?
Charles Francis
Bergman <aber...@Princeton.EDU> writes
>You can have all the prejudices you want -- you still haven't described
>to me an experiment that can, say, distinguish between one of the
>composite dimensions of Georgi and Arkani-Hamed and a "real" dimension.
That sounds rather easy. I can measure a real dimension experimentally
with a ruler.
Regards
--
Charles Francis
Aaron Bergman
Charles Francis <cha...@clef.demon.co.uk> wrote:
What makes you think you can't measure a composite dimension with a
ruler?
Aaron
Charles Francis
Bergman <aber...@Princeton.EDU> writes
Please will you describe an experiment in which you use a set square to
define four or more independent space dimensions, and in which you can
identify points whose specification require four or more independent
values which can be read off a ruler.
Regards
--
Charles Francis
John Gonsowski
> Moreover speculation about many dimensions runs quite contrary to what I
> perceive as the course of science as we head towards more unified
> theory. In relativity we reduce space-dimension to measurement of time.
> I expect space dimension to disappear altogether at a deeper level of
> space-time structure, not increase from three to eleven. Even now it is
> possible to formulate physics so that space dimension appears only as a
> relationship, not as a fundamental entity. But there is still a need for
> independent variables to describe different types of particle.
Even particles aren't independent variables. The 10 De Sitter gravitons
are bivectors made from a collection of only five vectors and those five
vectors aren't even independent in that two are at the opposite end of
an axis from two others. In the Tony Smith model I like, spacetime itself
shows up as D5 bivectors (in an SU(5) GUT kind of way). Matter and
antimatter show up at E6 (in a superstring E6 subgroup of E8xE8 kind
of way). E6 isn't limited to bivectors but it is just as non-independent
as the bivectors. To get something independent you kind of have to
look at the Clifford algebra that the LIE algebra is derived from and
even then it's messy. You kind of have 8 independent variables due
to the Clifford 8-fold periodicity rule but in a strict sense the number
of independent variables would be more like the number of Clifford
information bits needed to describe all that could be (a rather large
number). John
A.J. Tolland
A ruler made of what...?
zirkus
>I know Tony Smith is into something called MetaClifford
> algebras which may be related to dimensional reduction to four but
> it is still in the early development stage.
Hi, are these "MetaClifford algebras" related to Pezzaglia's new
derivation [1] of the Papapetrou equations as autoparallels in a
Clifford manifold ? Please note that I am *not* in any way endorsing
this particular view, only mentioning it.
> (E7 being related by Smith, Smolin and others to
> bosonic M-theory).
Perhaps you will be interested to know that E7 (as well as E6 and E8)
are also important in the new M-theory paper by Atiyah and Witten. See
page 97 of [2].
zirkus
>First
> of all, it is clear that the laymen tend to think that the authors of
> popular books - and more generally physicists who like to talk to laymen -
> are the best physicists in the world while the experts who write a lot of
> complex equations are less interesting.
It is a paradox of much popular scientific writing that the only
people who might really understand it are those who are already
experts in the subject. (IMO, it is impossible to really understand
theoretical physics without also understanding the relevant math that
is involved with the physics, but I don't want to start a discussion
about this point.)
>And
> finally many readers of The Elegant Universe think that the only candidate
> for the smartest physicist can be Brian Greene.
IMHO, the current theorists with the greatest and most original
thoughts which might be important for high energy physics are Edward
Witten for string theory, Alain Connes and Shahn Majid for
noncommutative geometry, and John Baez for spin foams, octonions,
catgories etc. (but I know very little about LQG approaches).
> Concerning Brian Greene. I think that he is probably the most important
> physicist who contributed to our understanding of the topology change in
> string theory.
I agree because, IMO, topology change in string theory cannot be very
realistic unless it can also be dynamically driven and, AFAIK, Brian
Greene is the only theorist who has really studied this issue
(although I have only heard of his work and am not myself familiar
with it). However, in M-theory, I believe that the topology of
spacetime should only be a relative concept so I myself am not sure
how fundamentally significant topology change could be.
>Although topology change is not the only interesting
> development (and AdS/CFT, String Field Theory or Matrix Theory are at
> least equally important as the topology change),
Perhaps I do not understand or am missing something, but I don't know
if these ideas are all that important because no one really
understands if M-theory is compatible with a realistic theory of QG in
a realistic setting such as de Sitter space or some type of
quintessence model. No one that I know of seriously believes that our
actual universe is AdS. These issues (including a mention of the
limitations of Matrix theory) are discussed some in Witten's paper on
QG and de Sitter space. See especially pages 6 and 17 of his paper
[1]. ( Maybe it could be important, though, that both AdS/CFT and
Matrix theory might be based on the conversion of an open string into
a closed string under a strong coupling limit [2] ).
> There is a gap between the way how laymen look at science and how
> scientists judge their colleagues. I think that this gap should not grow.
If even the experts do not really understand M-theory then it is
almost certain that laymen will not understand it either. But I do
agree for various reasons that it is important for at least a few
quality theorists such as Brain Greene or Michael Duff to reach out to
the public. Perhaps their efforts will even inspire some young people
to want to study math or physics.
Aaron Bergman
Charles Francis <cha...@clef.demon.co.uk> wrote:
> >What makes you think you can't measure a composite dimension with a
> >ruler?
>
> Please will you describe an experiment in which you use a set square to
> define four or more independent space dimensions, and in which you can
> identify points whose specification require four or more independent
> values which can be read off a ruler.
Well, that's trivially done for extra dimensions in string theory if
those extra dimensions were large enough to fit your ruler. As for the
rest, why not just read the discussion in the paper:
hep-th/0104005
Aaron
zirkus
> You can have all the prejudices you want -- you still haven't described
> to me an experiment that can, say, distinguish between one of the
> composite dimensions of Georgi and Arkani-Hamed and a "real" dimension.
Hi, would you happen to know if the string theory community still
considers seriously Arkani-Hamed's theory about large extra
dimensions? I myself don't give this theory much credence for two
reasons:
(1) I agree with Newton that we should not clutter our view of
Nature with extra and unnecessary assumptions (even if this means that
perhaps it could be harder to understand string theory or to verify it
experimentally).
(2) Recent experiments [1] done at UW reveal that, so far, there is
no deviation from Newton's gravitational law at submillimeter scale.
Personally, I will choose Newton over Arkani-Hamed. ( I don't mean
this in any way as an insult against Arkani-Hamed. It's just that
Newton is Newton).
A.J. Tolland
> In article <abergman-9A8FC8...@cnn.princeton.edu>, Aaron
> Bergman <aber...@Princeton.EDU> writes
> >In article <rJJZWVAC...@clef.demon.co.uk>,
> > Charles Francis <cha...@clef.demon.co.uk> wrote:
> >
> >> In article <slrn9mk7l6....@phoenix.Princeton.EDU>, Aaron J.
> >> Bergman <aber...@Princeton.EDU> writes
> >> >You can have all the prejudices you want -- you still haven't described
> >> >to me an experiment that can, say, distinguish between one of the
> >> >composite dimensions of Georgi and Arkani-Hamed and a "real" dimension.
> >>
> >> That sounds rather easy. I can measure a real dimension experimentally
> >> with a ruler.
And what are rulers made out of, Charles?
--A.J.
Toby Bartels
>Aaron J. Bergman wrote:
>>Charles Francis wrote:
>>>the
>>>way Michio Kaku describes it in Hyperspace it appears to be based on his
>>>failure to understand the distinction between a dimension and an
>>>independent variable.
>>So, what is the difference, Charles?
>dimensions are continuum variables (or at least have that appearance),
>whereas most of the additional dimensions discussed by Kaku appear to
>take only a few discrete values.
Then I would hesitate to call them "independent variables" either.
So I don't see the difference either.
(Of course, my limited knowledge of string theory suggests that
Aaron is right to say of what you wrote, "This is simply not true.",
but my comments apply if Aaron is wrong and it is true.)
-- Toby
to...@math.ucr.edu
Aaron Bergman
zir...@my-deja.com (zirkus) wrote:
> Lubos Motl <mo...@physics.rutgers.edu> wrote:
>
> > Concerning Brian Greene. I think that he is probably the most important
> > physicist who contributed to our understanding of the topology change in
> > string theory.
>
> I agree because, IMO, topology change in string theory cannot be very
> realistic unless it can also be dynamically driven and, AFAIK, Brian
> Greene is the only theorist who has really studied this issue
> (although I have only heard of his work and am not myself familiar
> with it).
Eek. Plenty of people have studied this stuff. Witten, Strominger,
Aspinwall and Morrison come to mind off the top of my head. Probably a
bunch of others, too.
> However, in M-theory, I believe that the topology of
> spacetime should only be a relative concept so I myself am not sure
> how fundamentally significant topology change could be.
I'm not sure what you mean. M-theory still has 11D SUGRA as a low energy
limit, so we can still talk about topology change.
Aaron
Charles Francis
, A.J. Tolland <a...@hep.uchicago.edu> writes
The abstract concept "ruler" does not specify the material, merely that
it is made of rigid material.
Regards
--
Charles Francis
Toby Bartels
>zirkus wrote:
>>However, in M-theory, I believe that the topology of
>>spacetime should only be a relative concept so I myself am not sure
>>how fundamentally significant topology change could be.
>I'm not sure what you mean. M-theory still has 11D SUGRA as a low energy
>limit, so we can still talk about topology change.
Perhaps this will clarify things for zirkus:
Even if you believe that spacetime topology won't be fundamental
in the ultimate version of M theory,
nevertheless it will appear as a derived concept in some limit
(if not in the entire range of the theory).
So topology change will still be an important issue,
only an issue dealing with this derived concept.
Since our currently well tested theories of physics (GR & QFT)
include spacetime topology as a fundamental component,
understanding how spacetime topology appears as a derived concept in M theory
will be of fundamental importance to understanding
the relationship of the theory to today's physics,
if nothing else.
-- Toby
to...@math.ucr.edu
John Gonsowski
zirkus wrote:
Funny my Tony Smith response to your comments on F4
(which you related to the Atiyah and Witten paper) got
posted at the same time as this post. That Pezzaglia paper
seems to be a nice endorsement for Clifford algebra in
general. MetaClifford algebra as I understand it is like
first using Clifford algebra on a vector space to create a
Clifford algebra space and then use Clifford algebra again
on the Clifford algebra space to create a MetaClifford
algebra space. Here's a link for MetaClifford algebras:
http://www.innerx.net/personal/tsmith/metaclif.html
The Smith-Smolin use of E7 is for the 27-dim space of
bosonic string M-theory itself. The Atiyah-Witten
use seems to be for singularities and thus for
branching that can occur within the M-theory space
(for bosonic strings or superstrings). Here is the
Tony Smith view of E8 for the singularities/branching:
http://www.innerx.net/personal/tsmith/WeyLie.html#coxnotlie
The triple/triality, vector-spinor supersymmetry, and
octonion stuff that keeps coming up in your comments/links
is related to the basic SO(8) triality supersymmetry of
an octonion vector and two octonion half-spinors.
Unfortuneately it seems even the experts can't connect
all the manifestations of this in a mathematically rigorous
way. One can't even rigorously be sure that all the things
that look like manifestations really are.
John
Toby Bartels
>A.J. Tolland wrote:
>>A ruler made of what...?
>The abstract concept "ruler" does not specify the material, merely that
>it is made of rigid material.
We've known since 1905 (at least) that there is no such material ^_^.
The practical relevance of A.J.'s question is this:
That your desk ruler made of wood or plastic
can't measure the rolled up Calabi Yau dimensions
is easily explained by the (relatively) huge size
of wood and plastic molecules.
So we need a ruler made of some smaller material.
For example, we might use a molecule itself as a ruler;
some periodic molecule (think of DNA) can serve as a ruler.
But even this is too large for the Calabi Yau dimensions,
since those are smaller than the atoms making up any molecule.
So we could use a single atom. But this is still too large.
So we could use a subatomic particle. But this is still too large.
So we could use what subatomic particles are made of;
if string theory is correct, then this is strings.
These are *not* too large! And string theory suggests that
we can measure the sizes of curled up dimensions using strings.
This hardly proves that the Calabi Yau dimensions exist.
I don't believe in string theory myself, after all.
But it hardly seems reasonable to me to object to this feature of it
when it suggests its own way to meet your objection.
If we ever get experimental confirmation of string theory,
then we should be able to experimentally measure the tiny dimensions,
using strings as rulers, as string theory suggests.
And yes, we are getting less and less rigid as we go down this scale,
but since even your wooden or plastic desk ruler isn't perfectly rigid,
this is a problem of degree, not of kind.
What we actually have to do is to ensure that our ruler
doesn't change size by more than our measurement's intended precision
over the course of the measurement,
and we can get arbitrarily close to perfection on this score
(assuming that string theory is correct in the first place).
-- Toby
to...@math.ucr.edu
Aaron J. Bergman
>aber...@Princeton.EDU (Aaron J. Bergman) wrote:
>
>> You can have all the prejudices you want -- you still haven't described
>> to me an experiment that can, say, distinguish between one of the
>> composite dimensions of Georgi and Arkani-Hamed and a "real" dimension.
>
>Hi, would you happen to know if the string theory community still
>considers seriously Arkani-Hamed's theory about large extra
>dimensions?
Which one? The original one or this one? For the former, it depends a
lot on the string theorist. For the latter, it seems like a neat trick,
but I don't really know where you go with it.
>I myself don't give this theory much credence for two
>reasons:
>
>(1) I agree with Newton that we should not clutter our view of
>Nature with extra and unnecessary assumptions (even if this means that
>perhaps it could be harder to understand string theory or to verify it
>experimentally).
That would be Ockham, not Newton. But, in the absence of pretty much any
experimental data that contradicts our current theories, pretty much
anything is going to be an extra hypothesis. I don't see, in particular,
why we shouldn't look at everything. The LED stuff is interesting even
oustide of a string theory context.
>(2) Recent experiments [1] done at UW reveal that, so far, there is
>no deviation from Newton's gravitational law at submillimeter scale.
Sure, but you can always go a bit smaller. If they go another order of
magnitude or two, though, the idea loses some of its appeal, ie, weak
scale gravity.
Aaron J. Bergman
>
>The abstract concept "ruler" does not specify the material, merely that
>it is made of rigid material.
Well, then, no such a thing exists, so why should we talk about it? We
should talk about experiments one can actually do.
A.J. Tolland
> > A ruler made of what...?
>
> The abstract concept "ruler" does not specify the material, merely that
> it is made of rigid material.
Rigid material? There isn't really any such thing.
--A.J.
Charles Francis
Bergman <aber...@Princeton.EDU> writes
>In article <9ks03v$1jf$1...@news.state.mn.us>, Charles Francis wrote:
>>
>>The abstract concept "ruler" does not specify the material, merely that
>>it is made of rigid material.
>
>Well, then, no such a thing exists, so why should we talk about it? We
>should talk about experiments one can actually do.
The concept rigid exists in physics to good approximation. Good
approximation is all that any scientist could claim of any physical
theory. You could put numbers on it and define a precise meaning of 99%
rigid if you so desired. But for you to claim on these grounds that an
ordinary ruler and set square cannot measure the familiar three
dimensions, and that a ruler does indeed behave identically with respect
to these three dimensions as it does with respect to extra ones, seems
somewhat bizarre.
Now do you really want to go on saying that there is no experiment you
can do to distinguish the familiar three dimensions from the extra
string theoretic ones. Perhaps you should have your eyes tested.
Regards
--
Charles Francis
Aaron J. Bergman
>In article <slrn9n31qv....@phoenix.Princeton.EDU>, Aaron J.
>Bergman <aber...@Princeton.EDU> writes
>>In article <9ks03v$1jf$1...@news.state.mn.us>, Charles Francis wrote:
>>>
>>>The abstract concept "ruler" does not specify the material, merely that
>>>it is made of rigid material.
>>
>>Well, then, no such a thing exists, so why should we talk about it? We
>>should talk about experiments one can actually do.
>
>The concept rigid exists in physics to good approximation.
Not really. The best you're going to get is v_s ~ c.
> Good
>approximation is all that any scientist could claim of any physical
>theory. You could put numbers on it and define a precise meaning of 99%
>rigid if you so desired. But for you to claim on these grounds that an
>ordinary ruler and set square cannot measure the familiar three
>dimensions, and that a ruler does indeed behave identically with respect
>to these three dimensions as it does with respect to extra ones, seems
>somewhat bizarre.
I claimed no such thing.
>Now do you really want to go on saying that there is no experiment you
>can do to distinguish the familiar three dimensions from the extra
>string theoretic ones. Perhaps you should have your eyes tested.
Again, I have claimed no such thing. There are plenty of experiments
that could detect extra dimensions. Measuring the power falloff for
gravity at short distances is being done in atleast two places as we
speak. If there were large extra dimensions and TeV scale gravity, it
should be possible to see gravitons at LHC. If we were to imagine a
hypothetical universe in which the extra dimensions of string theory
were quite large and we weren't confined to a brane of some sort, then
you could measure those extra dimensions with a ruler from your third
grade class if you'd like.
Uncle Al
http://www.mazepath.com/uncleal/eotvos.htm
Table VI and references
If we go for M-Theory 10+1 dimensions and require seven of them
to be compactified, then modeling suggests extra dimension
scaling around the proton Compton wavelemgth, about 2x10^(-15)
meters or 2x10^(-6) nanometers.
http://www.slac.stanford.edu/pubs/slacpubs/8000/slac-pub-8071.pdf
First couple of pages.
Proposed compactified dimension span is 10^[(30/n)-19] meters
where n is the number of compactified dimensions. Planetary
orbits rule out n=1; Adelberger's work rules out n=2. The chiral
Eotvos experiment probes n=3.... Nuclear accelerators' collision
results pretty much rule out down to n=7 - no results anomalous
vs Standard Model predictions even at very small distances.
It would preliminarily appear that *only gravity* is potentially
affected by compactified dimensions, or that there are no
interactive compactified dimensions.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
Charles Francis
Bergman <aber...@Princeton.EDU> writes
Well I have had a look at the paper, and it does not appear to be as you
say. There is no indication that it has any bearing on empirical science
whatsoever. I do not wish to know how a multidimensional being in
science fiction fantasy is trivially able to measure four or more
independent dimensions by using a set square and ruler. I want you to
give a simple explanation of how I can physically do this myself. If you
cannot, then I hope you would not claim your theory is science, and I
hope you would not post here.
Actually your claim is stronger. You have claimed to be able to measure
these extra dimensions in exactly the same way as the familiar three
dimensions, so that there is no way to distinguish one from the other.
Now, seriously, is this physics?
Regards
--
Charles Francis
[Moderator's note: Let's not turn this into a meta-discussion about
what is or is not appropriate for posting here, please. -MM]
zirkus
> > I agree because, IMO, topology change in string theory cannot be very
> > realistic unless it can also be dynamically driven [....]
> Eek. Plenty of people have studied this stuff. Witten, Strominger,
> Aspinwall and Morrison come to mind off the top of my head. Probably a
> bunch of others, too.
By "dynamically driven" I mean that the topology change is driven by
field equations. Otherwise, what kind of dynamics would the topology
change have? Perhaps others have studied this issue but I myself don't
know if they include the authors you mention (although maybe one of
them has written a paper about this).
> I'm not sure what you mean. M-theory still has 11D SUGRA as a low energy
> limit, so we can still talk about topology change.
This may depend on whether we believe in de Sitter space. Maldacena
and Nunez have an important no- go theorem in the second part of paper
[1] about the inability of obtaining various SUGRAs in dS. It looks
like there could be some way of circumventing this no- go theorem but
I don't yet understand how this is supposed to be done.
zir...@my-deja.com
says...
>Which one? The original one or this one? For the former, it depends a
>lot on the string theorist. For the latter, it seems like a neat trick,
>but I don't really know where you go with it.
I had meant the original theory. I'm not familiar with the newer one.
>That would be Ockham, not Newton.
Newton said it too, although I wouldn't be surprised if some ancient philosopher
also had the same opinion long before Ockham.
>But, in the absence of pretty much any
>experimental data that contradicts our current theories
I thought there was supposed to be astronomical data which contradicts the idea
that our universe could be AdS (and I also referred to data which contradicts
the idea that there are deviations from Newton's gravitational law at a certain
submillimeter range).
Jim Jastrzebski
> If we were to imagine a
> hypothetical universe in which the extra dimensions of string theory
> were quite large and we weren't confined to a brane of some sort, then
> you could measure those extra dimensions with a ruler from your third
> grade class if you'd like.
Would you situate this ruler in a direction perpendicular to
all old 3 dimensions or in some other direction?
-- Jim
Lubos Motl
> Hi, would you happen to know if the string theory community still
> considers seriously Arkani-Hamed's theory about large extra
> dimensions?
Sure, the string community still considers the scenarios with large
dimensions to be a viable alternative to the classical scenarios whose
fundamental scale is close to the Planck scale. Arkani-Hamed et al. wrote
a model currently called "the old large dimensions" because the more
recent papers by Lisa Randall and Raman Sundrum ("new large dimensions" or
"warped geometry") became even more popular.
> I myself don't give this theory much credence for two reasons:
>
> (1) I agree with Newton that we should not clutter our view of
> Nature with extra and unnecessary assumptions (even if this means that
> perhaps it could be harder to understand string theory or to verify it
> experimentally).
Well, I myself don't give this paragraph much credence for two reasons.
First of all, the Occam's razor was invented by Occam, not Newton. :-)
Second, Newton was probably the greatest *scientist* so far. Although he
also believed some Christian dogmas (just like many other people that
surrounded him), he certainly preferred rational arguments over
philosophical speculations and ideology.
From a rational point of view, one must argue and think in a similar way
as string theorists do. The extra dimensions are predicted by the only
consistent theory of quantum gravity that we know of; they are certainly
not "extra and unnecessary assumptions" but rather an essential
ingredience to explain a falling apple in this quantum world! Furthermore,
there is a clear hierarchy (gap) between the four-dimensional Planck scale
and the electroweak scale, for example. This gap must be explained by a
large parameter in your theory. Large dimensions are very natural from
this point of view and they predict physics that agrees with everything we
observe.
The huge ratio between the 4D Planck scale and the electroweak scale is
then reduced to the large volume of the large dimensions expressed in the
fundamental units.
While there are many unsolved puzzles (the stabilization problem etc.),
almost everyone who is doing physics and not philosophy will agree that so
far, the models with large dimensions (smaller than 10 microns) and a
fundamental scale 10 TeV or higher are consistent with everything we have
learned about the Universe. I have some partly emotional and partly
rational reasons why I still prefer the "conventional" scenarios from the
80s with the Planckian extra dimensions - just like many people in the
community. But all of us know that there is no rational evidence ruling
the large dimensions out, at least if the fundamental scale is above 50
TeV (to be more certain).
> (2) Recent experiments [1] done at UW reveal that, so far, there is
> no deviation from Newton's gravitational law at submillimeter scale.
Well, this means that the large dimensions must be smaller than 50 microns
or so (this is where the submillimeter gravitational experiments operate
today). It does not mean what you said. Of course, people tried to
construct models which predict new phenomena "just behind the corner" i.e.
models whose extra dimensions are the largest possible etc. The reason why
people like to do this is that if their proposals turn out to be correct,
it would be exciting and they would be given the Nobel prize soon. :-)
Of course, Nature does not care about this motivation. The fundamental
scale can be at 100 TeV, 10^{10} TeV or 10^{16} TeV. Maybe we will be able
to see the phenomena at the fundamental scale directly in this century,
maybe we won't. The scenarios that will make the 21st century particle
physics more exciting or less exciting are equally likely. There is no
rational argument that prefers one possibility over the other.
> Personally, I will choose Newton over Arkani-Hamed. ( I don't mean
> this in any way as an insult against Arkani-Hamed. It's just that
> Newton is Newton).
Well, I think that your text is primarily an insult against Newton :-)
because you tried to convince the reader that Newton would agree with your
unjustified arguments and interpretations. Of course that he would not.
Newton was a great scientist and if he learned string theory, he would
think approximately the same what Witten does. I wonder whether you really
think that Newton's agreement from the 17th century with some philosophy
of the 14th century implies that a specific model of particle physics from
the end of the 20th century is unlikely - I hope that you are just
kidding.
Although Newton might have been a smarter guy than any living physicist,
it is true that even if Newton had really written a couple of sentences
that could be interpreted as being "against the large dimensions", it
would be absolutely irrelevant for physics today. Maybe someone won't
believe me but physics has changed "a bit" during the last three centuries
and Newton did not know most things that we know today (and he "knew" many
wrong things) - his knowledge was not enough to answer questions of 20th
century particle physics.
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.
ba...@rosencrantz.stcloudstate.edu
> Aaron Bergman <aber...@Princeton.EDU> wrote:
>
> > > I agree because, IMO, topology change in string theory cannot be very
> > > realistic unless it can also be dynamically driven [....]
> > Eek. Plenty of people have studied this stuff. Witten, Strominger,
> > Aspinwall and Morrison come to mind off the top of my head. Probably a
> > bunch of others, too.
> By "dynamically driven" I mean that the topology change is driven by
> field equations.
I have no idea what this means.
> Otherwise, what kind of dynamics would the topology
> change have?
Same here. The statement that I can make is that there exist physically
smooth processes in string theory wherein spacetime begins with one
topology and ends up with another.
[...]
> > I'm not sure what you mean. M-theory still has 11D SUGRA as a low energy
> > limit, so we can still talk about topology change.
>
> This may depend on whether we believe in de Sitter space.
Er, huh?
When did we start talking about de Sitter space? And what does it have
to do with topology change?
Aaron
Aaron Bergman
zir...@my-deja.com wrote:
> In article <slrn9n31o4....@phoenix.Princeton.EDU>, Aaron J. Bergman
> says...
>
[...]
> >That would be Ockham, not Newton.
>
> Newton said it too, although I wouldn't be surprised if some ancient
> philosopher also had the same opinion long before Ockham.
It's almost universally associated to Ockham, though, ie, Ockham's razor.
>
> >But, in the absence of pretty much any
> >experimental data that contradicts our current theories
>
> I thought there was supposed to be astronomical data which
> contradicts the idea that our universe could be AdS (and I also
> referred to data which contradicts the idea that there are deviations
> from Newton's gravitational law at a certain submillimeter range).
What exactly does that contradict? It's certainly not a prediction of
string theory that either the universe is asymptotically AdS or that the
extra dimensions are large.
Aaron
Aaron Bergman
Jim Jastrzebski <Jim...@aol.com> wrote:
Along some direction that you'd come back to yourself.
Aaron
zirkus
says...
>> I thought there was supposed to be astronomical data which
>> contradicts the idea that our universe could be AdS (and I also
>> referred to data which contradicts the idea that there are deviations
>> from Newton's gravitational law at a certain submillimeter range).
>What exactly does that contradict? It's certainly not a prediction of
>string theory that either the universe is asymptotically AdS or that the
>extra dimensions are large.
I agree with you that these do not have to be predictions of string theory, but
I was making the point that in the past string theorists have considered these
two scenarios which we now know to be false (to a certain degree). IOW,
experiments may be helping to constrain the development of string theory in the
right direction.
zirkus
>> By "dynamically driven" I mean that the topology change is driven by
>> field equations.
>
>I have no idea what this means.
Not surprisingly, Brian Greene can explain this better than I can so please read
the first paragraph in Section 4 on page 7 of:
http://arxiv.org/abs/hep-th/0011059
>When did we start talking about de Sitter space?
There has been renewed interest in considering de Sitter space because we now
know that our real universe is not AdS.
>And what does it have
>to do with topology change?
Neither SUGRA nor maybe even M-theory might be compatible with a
realistic theory of QG in de Sitter space. No one seems to know for
sure and if you don't believe me then read Witten's recent paper on
the subject, especially page 17. Since we don't know what a realistic
theory of QG is (e.g. in de Sitter space or some type of quintessence
model) then I cannot be sure how important toplogy change really is
for a realistic theory of QG.
zirkus
Motl says...
>Well, I myself don't give this paragraph much credence for two reasons.
>First of all, the Occam's razor was invented by Occam, not Newton. :-)
It's not as if Occam's opinion was so unique that he was the only one who
uttered it, and Newton said it too. (Btw, there was an ancient group of Chinese
thinkers who postulated Newton's first and third laws, but they never developed
the concept of rate, calculus, F=ma etc.).
>From a rational point of view, one must argue and think in a similar way
>as string theorists do. The extra dimensions are predicted by the only
>consistent theory of quantum gravity that we know of; they are certainly
>not "extra and unnecessary assumptions" but rather an essential
>ingredience to explain a falling apple in this quantum world!
Your statement does not necessarily apply to *large* extra dimensions - which is
what I was talking about.
>While there are many unsolved puzzles (the stabilization problem etc.),
>almost everyone who is doing physics and not philosophy will agree that so
>far, the models with large dimensions (smaller than 10 microns) and a
>fundamental scale 10 TeV or higher are consistent with everything we have
>learned about the Universe.
Since it seems that English is not your native language perhaps you do not know
that the word "credence" means "belief". I was not saying that I can rule out
the possibility of large extra dimensions, only that I choose not to believe in
them which is what you yourself say below. I don't know what your "partly
rational reasons" are, but I myself will continue to believe in Newton's
gravitational law (at submillimeter scale) until there is *very* good
experimental evidence to the contrary.
>I have some partly emotional and partly
>rational reasons why I still prefer the "conventional" scenarios from the
>80s with the Planckian extra dimensions - just like many people in the
>community.
>> (2) Recent experiments [1] done at UW reveal that, so far, there is
>> no deviation from Newton's gravitational law at submillimeter scale.
>Well, this means that the large dimensions must be smaller than 50 microns
>or so (this is where the submillimeter gravitational experiments operate
>today). It does not mean what you said.
It means *exactly* what I said because I qualified my remark with the phrase "so
far". If you would, please show me some experiments which contradict Newton's
law at submillimeter scale.
>Well, I think that your text is primarily an insult against Newton :-)
>because you tried to convince the reader that Newton would agree with your
>unjustified arguments and interpretations. Of course that he would not.
I'm pretty sure that Newton is smart enough to continue believing in his own
valid results (as I do) until there is very good ccontrary evidence.
>Newton was a great scientist and if he learned string theory, he would
>think approximately the same what Witten does.
If string theory is ever verified then I suspect that Witten is smarter than
Newton, especially because Newton actually spent most of his time with alchemy
and theology and then, later in life, quit doing science and, IIRC, worked for
Britain's Treasury where he helped to get counterfeiters executed etc.
Andy Neitzke
Bergman wrote (replying to zirkus):
>> By "dynamically driven" I mean that the topology change is driven by
>> field equations.
>
> I have no idea what this means.
>
>> Otherwise, what kind of dynamics would the topology change have?
>
> Same here. The statement that I can make is that there exist physically
> smooth processes in string theory wherein spacetime begins with one
> topology and ends up with another.
Well, I think there might be a real question here. In the arguments I
have seen for the statement "spacetime topology change is allowed in
string theory," that phrase is usually a macro for something like the
following:
"There exist pairs of Calabi-Yau threefolds M1, M2 such that the low
energy limits of the supersymmetric sigma models into M1 and M2 are
connected by a smooth path in the moduli space of d=2, N=(2,2)
superconformal field theories."
That's an important statement -- I guess we can interpret it as saying
that spacetime topology change is allowed in some kind of "adiabatic"
limit. (Maybe it would be more accurate to say "space topology change.")
But one might hope to be able to answer questions like "how long does it
take for the topology change to occur?" or "what is the amplitude for the
topology changing process?" I have never seen any calculations of this
type -- I guess these questions are probably hard, considering how little
we seem to know about the problem of choosing a vacuum in string theory.
But I would be very pleased to hear that I am wrong -- does anyone know of
any results on this kind of question? Anyway, I think that might be the
kind of thing zirkus is asking for.
-Andy
Aaron Bergman
zirkus<zir...@my-deja.com> wrote:
> In article <abergman-4DA99F...@cnn.princeton.edu>, Aaron Bergman
> says...
>
> >> I thought there was supposed to be astronomical data which
> >> contradicts the idea that our universe could be AdS (and I also
> >> referred to data which contradicts the idea that there are deviations
> >> from Newton's gravitational law at a certain submillimeter range).
>
> >What exactly does that contradict? It's certainly not a prediction of
> >string theory that either the universe is asymptotically AdS or that the
> >extra dimensions are large.
>
> I agree with you that these do not have to be predictions of string
> theory, but I was making the point that in the past string theorists
> have considered these two scenarios which we now know to be false (to
> a certain degree).
People consider things all the time which we know to be false. I guess I
don't see the point.
> IOW, experiments may be helping to constrain the
> development of string theory in the right direction.
Setting upper bounds on the size of extra dimensions unfortunately
doesn't constrain much of anything. One can hope that understanding the
parameters of the weak SUSY breaking lagrangian (assuming they even find
it) at LHC could give some guidance.
Aaron
Charles Francis
Lubos Motl <mo...@physics.rutgers.edu> writes
>From a rational point of view, one must argue and think in a similar way
>as string theorists do. The extra dimensions are predicted by the only
>consistent theory of quantum gravity that we know of;
Since string theory is not the whole of research into quantum gravity,
this claim, persistently made by string theorists, only leads me to
doubt their credentials.
General relativity has shown gravity to be a theory of geometry, and
geometry is a set of relationships between the results of observation of
space and time. To produce a quantum theory of gravity we would
therefore have to treat space in the manner of observable in quantum
mechanics. String theory does not seem to have taken on this basic idea,
and without that I do not think it can be seen as a serious contender
for a theory of quantum gravity.
Regards
- --
Charles Francis
zirkus
>But I would be very pleased to hear that I am wrong -- does anyone know of
>any results on this kind of question?
Hi, please consider the paper I just referred Aaron to in my last post. Another
paper which is more comprehensive is "Dynamical topology change in M-theory"
[1]. Btw, there have been discussions on the web and in usenet about B. Greene's
popular book, "The Elegant Universe", but I don't know if there are also
descriptions somewhere of his other ideas that would be accessible to
non-experts.
[1] http://arxiv.org/abs/hep-th/0010207
Aaron Bergman
>
>>When did we start talking about de Sitter space?
>
>There has been renewed interest in considering de Sitter space because we now
>know that our real universe is not AdS.
Sure, but that has nothing to do with whether or not we can talk
about topology change in string theory.
>>And what does it have
>>to do with topology change?
>Neither SUGRA nor maybe even M-theory might be compatible with a
>realistic theory of QG in de Sitter space. No one seems to know for
>sure and if you don't believe me then read Witten's recent paper on
>the subject, especially page 17. Since we don't know what a realistic
>theory of QG is (e.g. in de Sitter space or some type of quintessence
>model) then I cannot be sure how important toplogy change really is
>for a realistic theory of QG.
I've read Witten's paper and I've listened to the talk. It still
doesn't have anything to do with whether we can talk about
topology change in string theory. We don't know how to do string
theory in dS space (although there is a proposed dS/CFT
correspondence), but that doesn't stop us from discussing what we
can do.
Toby Bartels
>Lubos Motl wrote:
>>From a rational point of view, one must argue and think in a similar way
>>as string theorists do. The extra dimensions are predicted by the only
>>consistent theory of quantum gravity that we know of;
>Since string theory is not the whole of research into quantum gravity,
>this claim, persistently made by string theorists, only leads me to
>doubt their credentials.
Well, you know that Lubos is more extremem in this claim
than the other string theorists on this board
(even if, as Lubos might suggest,
he merely says out loud what others feel in their hearts ^_^).
Really, whether string theory is necessary (I don't think so either)
is not the issue; it's whether string theory is possible.
If in the framework of string theory,
there's a way to measure to curled up dimensions,
then those dimensions exists if string theory is right.
Now we just have to wait for experiment to confirm or refute this.
Lubos is confident that experiment will confirm it, while you and I aren't.
But that doesn't matter; we'll find out eventually if we live long enough.
There remains no logical inconsistency in string theory
or in its claim that the extra dimensions do exist as dimensions.
Lubos' first sentence is right, although the second sentence isn't the reason;
the reason is simply that it's string theory itself that you're evaluating.
-- Toby
to...@math.ucr.edu
Leong Chung Wei Bernard
Hi Andy,
> I have never seen any calculations of this type -- I guess these
> questions are probably hard, considering how little we seem to know
> about the problem of choosing a vacuum in string theory. But I would
> be very pleased to hear that I am wrong -- does anyone know of any
> results on this kind of question? Anyway, I think that might be the
> kind of thing zirkus is asking for.
As far as I can recall, this is the only paper which I am aware of
that mentions about choosing a vacuum in string theory.
Title : Vacuum Configurations for Superstrings
By P. Candelas (Texas U. & Santa Barbara, ITP), Gary T. Horowitz (UC,
Santa Barbara), Andrew Strominger (Princeton, Inst. Advanced Study),
Edward Witten (Princeton U.). NSF-ITP-84-170, (Received Mar 1985). 28pp.
Published in Nucl.Phys.B258:46-74,1985
Hope that helps.
yours sincerely,
Bernard Leong
your ex-Part III classmate
"The good life is one inspired by love and guided by knowledge."
- Bertrand Russell
John Baez
Andy Neitzke <nei...@fas.harvard.edu> wrote:
>In article <abergman-EBD53F...@cnn.princeton.edu>, Aaron
>Bergman wrote (replying to zirkus):
>>> By "dynamically driven" I mean that the topology change is driven by
>>> field equations.
>> I have no idea what this means.
Take "field equations" in the broadest sense, to mean: some
equations governing string theory. The question, then, is whether
we can use these equations to compute something like the transition
amplitude for one topology of space to turn into another after a
certain amount of time.
So far, it seems not: one treats the changing topology of space as a
background structure, not a dynamical structure - i.e. something you
tell the theory, not something it tells you. Neitzke summarizes
the state of the art pretty well, as far as I can tell:
>In the arguments I have seen for the statement "spacetime topology change
>is allowed in string theory," that phrase is usually a macro for something
>like the following:
>
>"There exist pairs of Calabi-Yau threefolds M1, M2 such that the low
>energy limits of the supersymmetric sigma models into M1 and M2 are
>connected by a smooth path in the moduli space of d=2, N=(2,2)
>superconformal field theories."
>That's an important statement -- I guess we can interpret it as saying
>that spacetime topology change is allowed in some kind of "adiabatic"
>limit. (Maybe it would be more accurate to say "space topology change.")
Right: we assume the geometry of space changes so slowly with time
that we can get away with pretending the geometry is *static*. Then,
in this approximation, we see that certain very slow changes in geometry
take us all the way from one topology to the other while physically
observable quantities change in a smooth way.
(This is just an attempt to state the quoted phrase above in less
technical language. In particular, the "slow change in geometry"
is really a slow change in the associated superconformal field theory:
when we flop over from one topology of Calabi-Yau to another, it
doesn't make sense to say that the geometry is changing slowly, but
vacuum expectation values of observables are changing slowly.)
Anyway, my point is this: we just *postulate* these very slow changes
in geometry: the theory doesn't tell us how these changes occur, at
what rate they occur, or anything like that. That's the sense in
which they are not "dynamically driven".
>But one might hope to be able to answer questions like "how long does it
>take for the topology change to occur?" or "what is the amplitude for the
>topology changing process?" I have never seen any calculations of this
>type [....]
Neither have I, and when I talked to Brian Greene about this a year
ago, he didn't mention any progress on these questions.
It seems there is *something* one could do without massive improvements
in our understanding of string theory. Namely, if one found the right
Riemannian metric on the moduli space of superconformal field theories,
one could interpret a geodesic on this space as the classical motion of
the background as time passes - at least in this adiabatic approximation.
It's sort of like a Born-Oppenheimer approximation where you treat the
nuclei as "classical" and "slow-moving", while treating the electrons
as "quantum" and "fast-moving".
With this, you could start space off at a given topology and geometry,
give it a gentle nudge, and calculate how it slides over to another
topology and geometry... just like a glorified analog of the free point
particle. Or maybe there is also a potential. This isn't as good as
computing transition amplitudes for topology change, but it's better than
nothing.
Similar things have been worked out for the moduli space of n-monopole
solutions in Yang-Mills-Higgs theory, so this idea is not completely nuts,
I don't think. Has anyone tried it?
Aaron J. Bergman
>In article <9lcoqo$g99$1...@news.fas.harvard.edu>,
>Andy Neitzke <nei...@fas.harvard.edu> wrote:
>
>>In article <abergman-EBD53F...@cnn.princeton.edu>, Aaron
>>Bergman wrote (replying to zirkus):
>
>>>> By "dynamically driven" I mean that the topology change is driven by
>>>> field equations.
>
>>> I have no idea what this means.
>
>Take "field equations" in the broadest sense, to mean: some
>equations governing string theory. The question, then, is whether
>we can use these equations to compute something like the transition
>amplitude for one topology of space to turn into another after a
>certain amount of time.
Of course, I think that it's a bit harder to define a transition
amplitude that that. On the other hand, there is the Greene paper which
was referenced earlier that talks about topology change in terms of the
field equations. In terms of trying to define a transition amplitude, it
seems to me that it might be possible to do in the context of
holography. Along this lines, there seems to be 9807241 abd 9808177, but
I haven't really looked at them.
>So far, it seems not: one treats the changing topology of space as a
>background structure, not a dynamical structure - i.e. something you
>tell the theory, not something it tells you.
Only in the sense that we are doing perturbation theory, after all. I
could well make the argument tha, as the string sees the flop transition
as being no different than anywhere else in the moduli space, then, if
string theory does lift to a full theory of quantum gravity and that
said quantum theory of gravity includes dynamics wherin a cycle begins
to shrink, then this theory of quantum gravity should include topology
change.
zirkus
> Sure, but that has nothing to do with whether or not we can talk
> about topology change in string theory.
Okay, I agree with you on this point, but I also happen to agree with
John Baez who said that there do not seem to be any ironclad reasons
for why topology change should occur or not occur in a realistic
theory of QG. The importance of topology change in string theory is
something for experts like Brian Greene to think about, but it is not
a topic I am going to consider anymore - at least until there is more
evidence that string theory is compatible with a realistic theory of
QG.
It is possible that a realistic theory of QG might be very important
because future technology that might stem from it could perhaps enable
us to:
save our species from extinction
conduct trade with extraterrestial civilizations
traverse the universe to meet alien babes
Lubos Motl
> Well, you know that Lubos is more extremem in this claim
> than the other string theorists on this board
> (even if, as Lubos might suggest,
> he merely says out loud what others feel in their hearts ^_^).
Something like that. I just want to express the "official" opinion of
science - so that some readers won't get lost in the plethora of the
"alternative" approaches - and you are invited to believe that people such
as Ed Witten, Joe Polchinski or David Gross would agree with essentially
everything I wrote.
> Really, whether string theory is necessary (I don't think so either)
> is not the issue; it's whether string theory is possible.
String theory is both possible and necessary and both facts are the issue. ;-)
> Lubos is confident that experiment will confirm it, while you and I aren't.
I wrote something unclearly. I personally prefer the conventional scenario
with a very high unification (or fundamental) scale. In this scenario, we
won't see the extra dimensions directly. But before the experiment decides
which scenario is correct (classical / old large / Randall-Sundrum), we
must rely on string-theoretical arguments (and not Newton's arguments from
the 17th century).
Charles Francis
writes
>Charles Francis wrote in part:
>
>is not the issue; it's whether string theory is possible.
>If in the framework of string theory,
>there's a way to measure to curled up dimensions,
>then those dimensions exists if string theory is right.
>Now we just have to wait for experiment to confirm or refute this.
>
>Lubos is confident that experiment will confirm it, while you and I aren't.
>But that doesn't matter; we'll find out eventually if we live long enough.
>There remains no logical inconsistency in string theory
>or in its claim that the extra dimensions do exist as dimensions.
The criterion for the validity of an axiom set in mathematics is
"freedom from contradiction". But that is not sufficient for a
scientific test of physical theory. As we have been saying elsewhere,
there is no logical inconsistency either in the axiom of choice or its
contradiction, and no experimental test will ever tell us which is
"right".
Likewise with string theory and extra dimensions. Perhaps there is no
logical inconsistency in the structure, but it does not follow from that
that the structure is empirically testable. There may be tests
describable in string theory for extra dimensions, but if those tests
are not also describable in terms of established scientific theory, then
we cannot carry them out. I have never heard of a testable prediction of
string theory, or an experiment to test such a thing, and until people
start actually describing experiments instead of simply speculating that
there may be experiments, or, worse, claiming that there are experiments
which they disdain from describing, I regard the whole thing as unduly
speculative. (Note: this is a personal opinion and has no bearing on
moderator policy as to what is or is not speculative).
As it happens I very much doubt that string theory is really consistent
to the degree which I would require of a scientific theory. Of course
almost any axiom system can be consistent if it is small enough or
incomplete enough, but that does not make the axioms true of anything
other than themselves. If the axioms of string theory are not properly
and fully expressed (and there are so many versions of it that I don't
see how they can be) then it does not, in my view, fulfil the basic
requirement on which to make a claim of consistency.
Moreover if it is to be a unification theory, then string theory does
not simply need to be consistent with itself. It also has to be
consistent with the rest of physics. Conceptually I do not think that
any model in which gravity is a transmitted force perceived against a
background is consistent with the background free notions of general
relativity. Of course, now I believe they are claiming background free
versions of string theory, but there are substantial historical
precedents for theories which prove nothing and go on and on being
altered so much and appearing in so many versions, that you cannot say
what the actual theory is. String theory appears to me to be of much the
same mould as phlogiston, and let us not forget that phlogiston was
adhered to by great scientists of historical importance, such as
Priestley, even though his own experiments were instrumental in refuting
the theory.
Regards
--
Charles Francis
theos ek mechanes
M-Theory" [1]
Abstract
We study topology change in M theory compactifications on Calabi-Yau
three-folds in the presence of G flux (the four form field strength).
In particular, we discuss vacuum solutions in strongly coupled
heterotic string theory in which the topology change is inevitable
within a single spacetime background. For rather generic choices of
initial onditions, the field equations drive the Kahler moduli outside
the classical moduli space of a Calabi-Yau manifold. Consistency of
the solution suggests that degenerate flop curves - just as wrapped M
theory fivebranes - carry magnetic charges under the four form field
strength
[1] http://arXiv.org/abs/hep-th/0010207
Best
Lubos Motl
> The criterion for the validity of an axiom set in mathematics is
> "freedom from contradiction". But that is not sufficient for a
> scientific test of physical theory.
It is true that consistency is not enough to test a physical theory
scientifically. However, surprisingly, it turns out that consistency is
most likely sufficient to construct a quantum theory of gravity. This task
seems to have a unique solution.
> I have never heard of a testable prediction of string theory, or an
> experiment to test such a thing, and until people start actually
> describing experiments instead of simply speculating that there may be
> experiments, or, worse, claiming that there are experiments
Well, it is hard to hear about testable predictions of string theory
without listening to physicists and reading their papers. Actually there
exists a huge literature of a few thousands papers concerning string
phenonenology. This literature strongly expanded after the scenarios with
large dimensions were proposed. All of those papers are closely connected
with experiments; in fact, this is a definition of phenomenology. Every
phenomenologist is able to tell you how a specific model manifests itself
on accelerators or submillimeter gravitational experiments, for example.
The last sentence follows from the definition of a "phenomenologist".
Today we know a lot about the theoretical structure of string theory. We
know less about the way how is it embedded in this Universe. Henceforth,
there are many models for string phenomenology. In various models, the
submillimeter gravity is altered in various specific ways; new particles
are predicted for the accelerators (the superpartners are the most generic
ones) and various models predict details about the production of the black
holes at LHC etc. We are not sure which model is correct; none outside
string theory is sure either. String theorists however work with a rigid
structure.
> which they disdain from describing, I regard the whole thing as unduly
> speculative. (Note: this is a personal opinion and has no bearing on
> moderator policy as to what is or is not speculative).
String theory is just the other way around. When understood completely, it
predicts everything that can be observed and nothing else. And we have
already seen this property at many places although there is a long way to
go before we can see it everywhere.
> As it happens I very much doubt that string theory is really consistent
> to the degree which I would require of a scientific theory.
If you add a valid idea about this hypothetical inconsistency of string
theory and you write a paper about that, you will become extremely famous!
Good luck. ;-) I said a "valid" idea because an "idea" is not enough. Our
colleagues at sci.physics.relativity who say why Einstein was wrong have
not become famous so far and there is a good reason behind it.
> Of course almost any axiom system can be consistent if it is small
> enough or incomplete enough, but that does not make the axioms true of
> anything other than themselves.
That's correct. A much more difficult thing is to construct a theory
described in 10,000 technical papers that unifies the Standard Model with
General Relativity and describes everything that anyone has seen so far.
> If the axioms of string theory are not properly and fully expressed
> (and there are so many versions of it that I don't see how they can
> be) then it does not, in my view, fulfil the basic requirement on
> which to make a claim of consistency.
String theory - as we know it - is not an abstract collection of
mathematical axioms. It is a theory of physics. Therefore its insights are
expressed in terms of physics (and physical mathematics), not in terms
axiomatic mathematics. This fact also implies what is the correct way to
learn about it.
> Moreover if it is to be a unification theory, then string theory does
> not simply need to be consistent with itself. It also has to be
> consistent with the rest of physics.
Right!
> Conceptually I do not think that any model in which gravity is a
> transmitted force perceived against a background is consistent with
> the background free notions of general relativity.
This mistake has been clarified in many posts here and everyone who is
ready and capable to understand this issue has already understood it.
Physics at low energies, predicted by string theory, is in absolute
agreement with all the principles and predictions of general relativity.
> Of course, now I believe they are claiming background free
> versions of string theory, but there are substantial historical
> precedents for theories which prove nothing and go on and on being
> altered so much and appearing in so many versions, that you cannot say
> what the actual theory is.
String theory is difficult enough so that laymen can be confused, but the
fact is that we study the absolutely identical theory that was constructed
by Ramond, Neveu and Schwarz in the early 70s, in an attempt to
incorporate fermions into the old bosonic string theory. Superstring
theory was never modified. The reason is that it is impossible to modify
or "deform" string theory. There is one string theory only. The different
"versions" are just different formulations of the same theory.
> String theory appears to me to be of much the same mould as
> phlogiston, and let us not forget that phlogiston was adhered to by
> great scientists of historical importance, such as Priestley, even
> though his own experiments were instrumental in refuting the theory.
This is a beautiful collection of implications. However, one of the
starting points (namely that "string theory appears to you to be of much
the same mould as phlogiston") has no relevance for physics. Your
conclusions have consequently the same value: phlogiston in, phlogiston
out. :-)
BTW phlogiston is nothing else than the chemical energy (relative to the
minimal energy of the same elements arranged in the energetically minimal
way). All flammable materials contain phlogiston. :-) This paradigm is
similar to the idea of "heat" that was once thought to be another
material. Joseph Priestly was the last alchemist who helped to create
chemistry as we know it today. An idea of phlogiston is something that we
could forgive him in the 18th century.
Urs Schreiber
news:9lrcbo$ah9$1...@glue.ucr.edu...
[...]
I know little about the "moduli space of superconformal field
theories", but by now I know a little more about 11-d supergravity,
which should have some relation. In particular, I have studied
homogeneous cosmologies derived from the 11d-sugra action both in the
classical limit and quantum mechanically and I have played around
with some numerical simulations. In 11d sugra minisuperspace (so to
say, actually this is the configuration space of the homogeneous 11d
metric *and* the homogeneous 3-form field in the bosonic sector) I
can make my computer regard an initial "universe point", give it a
nudge, and watch as it follows a geodesic in this kind of moduli
space. Therefore I'd really like to understand if the possibility of
topology change might have any relevance in such a setup.
In particular, I need to know the answer to a question that was
brought up here a while ago by Demian Cho, but which had not been
answered by anyone: In theories of gravity the metric tensor is a
dynamical field, but the notion of topology does not appear as an
object of the theory. Then how could one read off topology change
from only looking at the metric tensor? (Is this a well posed
question, anyway?) I do not know the answer, but I have two guesses:
1) Whenever the metric tensor becomes degenerate a change of topology
is implied. (?)
2) The metric tensor gaining or loosing some sort of periodicity is a
signal for a change of multiple connectedness. (?)
There is not much room for point 2) in a crude homogeneous setup, but
the metric becoming degenerate can easily be observed already in the
homogeneous case. In fact, in my numerical calculations I have
observed that when I turn on all the components of the 3-form field
the dilaton fields (logarithms of radii of internal dimensions) tend
to "explode" (to the effect that the numerical calculation breaks
down). I have regarded this as a nuisance so far, but maybe it's a
virtue?
Charles Francis
u>, Lubos Motl <mo...@physics.rutgers.edu> writes
>On Wed, 22 Aug 2001, Charles Francis wrote:
>> The criterion for the validity of an axiom set in mathematics is
>> "freedom from contradiction". But that is not sufficient for a
>> scientific test of physical theory.
>It is true that consistency is not enough to test a physical theory
>scientifically. However, surprisingly, it turns out that consistency is
>most likely sufficient to construct a quantum theory of gravity. This task
>seems to have a unique solution.
I actually believe that this is true, at least if the meaning of
consistency is extended to include consistency with observation, and if
we can legitimately disallow non-essential complications. Given a
working theory it is always possible to introduce a set of variables and
a formula such that the variables have no affect on the observable
results of the theory. But I am not happy that string theory can answer
this. For one thing, how do you distinguish whether the gauge symmetry
on which it is based is a fundamental symmetry of nature, or whether it
is really just a meaningless variable which has no affect on
predictions? I would like to see that question answered before going too
far down that road.
>Today we know a lot about the theoretical structure of string theory. We
>know less about the way how is it embedded in this Universe. Henceforth,
>there are many models for string phenomenology.
This seems rather a fundamental problem. It is a unique theory, but one
which we do not know how to apply to physics. How can we be sure it is
physics? That question should be answered in the assumptions made by
string theory, not the calculations. But I don't see the discussion.
By calling it one theory, many phenomenologies, you are merely making a
semantic distinction which I don't accept. One theory, many
phenomenologies just sounds to me like many theories. Especially as it
is in the phenomenology that you hope to relate the theory to physics.
>If you add a valid idea about this hypothetical inconsistency of string
>theory and you write a paper about that, you will become extremely famous!
I couldn't. But that has much to do with the absence of clearly laid out
assumptions, which means there is an absence of clearly defined theory.
Inconsistencies are more likely to be found between what one person
thinks of it and what another thinks, and a paper about that is scarcely
physics. I could not even describe what any one string theorist thinks,
and hope to represent it reasonably, let alone pinpoint inconsistencies.
>> Of course almost any axiom system can be consistent if it is small
>> enough or incomplete enough, but that does not make the axioms true of
>> anything other than themselves.
>That's correct. A much more difficult thing is to construct a theory
>described in 10,000 technical papers that unifies the Standard Model with
>General Relativity and describes everything that anyone has seen so far.
That sounds like an impossible task. If the theory has not been
constructed, then the 10,000 technical papers cannot guarantee to
describe anything at all.
>> If the axioms of string theory are not properly and fully expressed
>> (and there are so many versions of it that I don't see how they can
>> be) then it does not, in my view, fulfil the basic requirement on
>> which to make a claim of consistency.
>String theory - as we know it - is not an abstract collection of
>mathematical axioms. It is a theory of physics. Therefore its insights are
>expressed in terms of physics (and physical mathematics), not in terms
>axiomatic mathematics. This fact also implies what is the correct way to
>learn about it.
As far as I can see, the correct way to learn about it is to recognise
that there is, in qed, a fundamental problem with the notion of
continuous interactions of point-like particles. Strings certainly
appear to give a way of avoiding that problem, but before going too far
down that road I think you have to be quite sure that there are no other
ways of avoiding the problem. You can't claim that your solution is
uniquely possible simply because it is the only known solution. You also
have to show that no other solution is possible. At the moment you can
only say that a range of solutions people have thought of don't work.
What if there is a solution that has not been tried? You cannot rule out
that which has not been thought of, so you cannot claim uniqueness, and
as far as I can see you have not produced a model based on definite
assumptions and producing precise results, so you don't even have a
theory.
>> Conceptually I do not think that any model in which gravity is a
>> transmitted force perceived against a background is consistent with
>> the background free notions of general relativity.
>This mistake has been clarified in many posts here and everyone who is
>ready and capable to understand this issue has already understood it.
>Physics at low energies, predicted by string theory, is in absolute
>agreement with all the principles and predictions of general relativity.
Low energy predictions are not particularly impressive here. Basically
you are just looking for an inverse law of potential so that you can fix
an arbitrary constant. The inverse law is very simple and comes about
rather easily in a lot of false theories. The conceptual requirement of
gtr covers all energies, and if you have not satisfied it then you are
wrong to claim that you have agreement.
>> Of course, now I believe they are claiming background free
>> versions of string theory, but there are substantial historical
>> precedents for theories which prove nothing and go on and on being
>> altered so much and appearing in so many versions, that you cannot say
>> what the actual theory is.
>> String theory appears to me to be of much the same mould as
>> phlogiston, and let us not forget that phlogiston was adhered to by
>> great scientists of historical importance, such as Priestley, even
>> though his own experiments were instrumental in refuting the theory.
>This is a beautiful collection of implications. However, one of the
>starting points (namely that "string theory appears to you to be of much
>the same mould as phlogiston") has no relevance for physics.
There are identifiable behaviours among scientists during periods of
scientific crisis, which precede scientific revolution. The scientific
revolution comes when someone produces an idea that resolves the issues
leading to crisis, but it is invariably an idea that no one has been
working with. During this period there is a studied phenomenology on the
development of alternative schools, which will be replaced by the
revolution. String theory fits that phenomenology.
>Your
>conclusions have consequently the same value: phlogiston in, phlogiston
>out. :-)
Strings in, strings out?
>BTW phlogiston is nothing else than the chemical energy (relative to the
>minimal energy of the same elements arranged in the energetically minimal
>way).
I know. Usually when I point that out, people don't get it. But your
expression is more precise than mine.
>Joseph Priestly was the last alchemist who helped to create
>chemistry as we know it today. An idea of phlogiston is something that we
>could forgive him in the 18th century.
As I say.
Regards
--
Charles Francis
theos ek mechanes
this kind of stuff is at Chern-Simons Theory. The metric can
thought of as resulting from a connection visa a tetrad and
one can look at points in the moduli space at which the met-
ric becomes degenerate, then look at the topological invar-
iants that are computable using the CS Theory and the connec-
tion and look how they change along the path in moduli space
generated by your code.
For example, to see the relation between the metric and the
connection take a look a Wald 3.4b. Let us know how it works
out...
PS: I am sure there are some loop gravity people on this list
who can tell you alot more about such things than myself.
Best
"Urs Schreiber" or his evil twin wrote...
> [snip]
>
> In theories of gravity the metric tensor is a dynamical field,
> but the notion of topology does not appear as an object of the
> theory. Then how could one read off topology change from only
> looking at the metric tensor?
>
> [snip]
theos ek mechanes
worried that your approach will not yield meaningful
results....
Consider a field theory of a metric $g_{ab}$. It has
an action:
%
\eqn\One
{
S(g_{ab}) \equiv \int_{M} {\cal L} \sqrt(-g) d^n x
}
%
Varying this with respect to $g_{ab}$ yields GR for
this theory.
%
\eqn\Two
{
{\delta S(g_{ab}) \over \delta g_{ab}} = 0
}
%
Now consider a new theory in which the action is:
%
\eqn\Three
{
S'(g_{ab}) \equiv S(g_{ab}) + Q T(g_{ab})
}
%
where is $T(M)$ a topological invariant of $M$, such
as an index, and Q is a constant. As the variation of
$T(M)$ with respect to $g_{ab}$ is identically zero,
classically $S$ and $S'$ are equivalent.
But one can crank up $Q$ to any value one choses, such
that the theories $S'$ and $S$, which are classically
equivalent, "quantum mechanically" yield theories of a
very different nature.
In $S'$ large $T(M)$ are suppressed while in $S$ there
is no preference for small or large $T(M)$.
If one evolves $S$ and $S'$ classically, then no selec-
tion on $T(M)$ is observed and classically a topology
change may occur which is quantum mechanically highly
suppressed. So, no meaningful results will follow...
Best
Redlum Xohp
> . We are not sure which model is correct; none outside
> string theory is sure either. String theorists however work with a rigid
> structure.
>
In fact string theory is so much constrained that is makes infinitely
many predictions (though not exactly in the zero mode sector);
if we could measure at the Planck scale and beyond, we could pin
it down (or disprove) for sure. Requesting that we should be able to do
experiments today is a bit anthropocentric; why should nature care about whether
we would
be able to test string theory at this time, by present-day means ?
Analogously electromagnetic waves exist independently of whether some ants
are able to measure them or not.
We are not engineers who build machines and can redesign them if their clients
don't like them (though certain string model builders behave this way); rather
we have no choice other than to try to see how far we can go.
Almost every theory of gravity and grand unification has this problem
of large energy scales, whether we like this or not..
One way out may be the large extra dimension scenario,
which by the way has per se nothing to do with strings (though is
compatible with it); thus it may be
confusing to discuss string theory under this thread. In fact this scenario _is_
highly
speculative, as there is no convincing reason why nature should be like that;
it is mainly wishful thinking what drives this approach.
Iin contrast, for string theory there is number of good reasons; for example,
the state count in black holes turned out exactly as predicted by string theory,
and there is no other known theory of gravity that has achieved that. Any
competing
theory of gravity better comes up with the same state count (... which makes it
likely that it is a theory that is equivalent to string theory).
>Charles Francis wrote in part:
>
> > If the axioms of string theory are not properly and fully expressed
> > (and there are so many versions of it that I don't see how they can
> > be) then it does not, in my view, fulfil the basic requirement on
> > which to make a claim of consistency.
There is such an _enormous_ number of non-trivial consistency features that are
satisfied that there there can't be any doubt that the whole model makes sense and
is
consistent as a physical model. Whether it describes nature is another question.
FM
Peter Woit
> In fact string theory is so much constrained that is makes infinitely
> many predictions (though not exactly in the zero mode sector);
> if we could measure at the Planck scale and beyond, we could pin
> it down (or disprove) for sure. Requesting that we should be able to do
> experiments today is a bit anthropocentric; why should nature care about whether
> we would
> be able to test string theory at this time, by present-day means ?
I'm interested to hear that string theory makes infinitely many
predictions. Could you tell us what one of them is? Assume that we're
magically given the ability to accelerate and collide particles at
arbitrarily high energies. Pick any energy and tell us exactly what
string theory predicts will be seen by arbitrarily sophisticated
detectors.
Peter
Lubos Motl
> I'm interested to hear that string theory makes infinitely many
> predictions. Could you tell us what one of them is? Assume that we're
> magically given the ability to accelerate and collide particles at
> arbitrarily high energies. Pick any energy and tell us exactly what
> string theory predicts will be seen by arbitrarily sophisticated
> detectors.
Dear Prof. Woit,
nice to see you here. BTW with another person who likes to participate in
the discussions here, we had some confusion concerning your information
about the reactions to your "evaluation of string theory". Could you
please clarify what have the people really written you?
If you were able to calculate effects of string theory accurately, you
could predict anything at any energy. For example, we have a full
nonperturbative definition of string theory in the 11-dimensional vacuum
(Matrix theory), so we can in principle calculate precisely the cross
sections at arbitrary energies. Similarly, we have a perturbative
formulation of string theory meaningful for any consistent background.
Therefore, for any such background, we can calculate the precise
perturbative power series for such cross sections etc. The main missing
thing is a formulation that is both nonperturbative and
background-independent. This would allow us to calculate the vacuum
selection questions and predict anything. Stay tuned.
But anyway I would like to point out that the claim that string theory has
infinitely many constraints/predictions is not the same as the claim that
string theory can predict everything! ;-)
For example, there are infinitely many prime integers greater than 1000.
But it does not mean that all the numbers must be prime integers greater
than 1000.
I hope that this note will help you in your research.
Best
Lubos
Aaron J. Bergman
>Redlum Xohp wrote:
>> In fact string theory is so much constrained that is makes infinitely
>> many predictions (though not exactly in the zero mode sector);
>> if we could measure at the Planck scale and beyond, we could pin
>> it down (or disprove) for sure. Requesting that we should be able to do
>> experiments today is a bit anthropocentric; why should nature care about
>> whether we would
>> be able to test string theory at this time, by present-day means ?
>I'm interested to hear that string theory makes infinitely many
>predictions. Could you tell us what one of them is?
An easy example is the Regge trajectory of massive particles above the
string scale.
>Assume that we're
>magically given the ability to accelerate and collide particles at
>arbitrarily high energies. Pick any energy and tell us exactly what
>string theory predicts will be seen by arbitrarily sophisticated
>detectors.
Assuming the Planck scale is the string scale (something that's not
obviously true), then string theory predicts more than four dimensions
and the Regge trajectory of particles mentioned above, just to name a
few.
Redlum Xohp
Peter Woit wrote:
Strings have infinitely many excitations, however very tightly
constrained; you can't remove any single one without spoiling the
consistency of the theory. . If we were able to measure at arbitrary
high energies, we certainly could see the characteristic string
excitation spectrum, involving states with arbitrary but correlated
high spins and masses, and in particular observe the characteristic
growth of density of states. Thus would not be shared by some other
theory of quantum gravity (if it would exist at all).
In terms of an effective lagrangian at low energies, there are
infinitely many corrections to the Einstein (plus Yang-Mills + more)
lagrangian which are suppressed by inverse powers of the Planck
scale. The tight constraints imply that these terms are not arbitrary
but are correlated with each other. Some of such terms have the form
of powers of Riemann curvature tensors, say L ~ R^n, (the leading of
such corrections are easy to compute explicitly), and could be
measured by eg graviton scattering. If we go up in energy, we could
assess also the interaction terms of the massive states.
These infinitely many specific predictions of course depend on the
particular vacuum states chosen; it is well-known that that there is
enormous amount of choices and that's why we cant make any useful
predictions at low enegies. But for any given such vacuum state there
are infinitely many predictions that could in principle be used to
find out whether nature is governed by string theory or not.
There was also an email complaining about the state count in black
holes not being specific to string theory. My answer is: tell me how
you compute this in some "other", microscopic theory of quantum
gravity (which one do you take ? I am interested to hear).
-FM
Peter Woit
> nice to see you here. BTW with another person who likes to participate in
> the discussions here, we had some confusion concerning your information
> about the reactions to your "evaluation of string theory". Could you
> please clarify what have the people really written you?
Hi Lubos,
In brief, I heard from about 50 people. Almost all wrote to say
that they agreed strongly with what I had written and were glad to
see that someone was publicly making these points. A handful
mainly wanted to tell me about their TOE's and there were exactly
two who wanted to defend string theory. Besides you, the other
one was a string theory graduate student who was more interested
in telling me that I was incompetent than in addressing the issues
raised in my article. It seems that you're the most senior member
of the physics community willing to argue the case for string theory,
you deserve congratulations for this!
Both the original poster and you agree that the
infinite number of predictions of string theory being referred to
depend upon a choice among the (infinite? very large?) number
of known perturbative (and non-perturbative) ground states. Under
the circumstances I wish string/M theorists would stop referring
to "predictions of string/M theory" until you have a real one. For
an example of the kind of dangerous confusion this is causing, go to
http://online.itp.ucsb.edu/online/mt01teach/meeting
where you can hear a high school teacher who has just been
through a day-long NSF funded program to teach him
about string theory say that he has learned that "we may
have to come up with new standards of what it means to
say we know something in science". David Gross's
response to this teacher was basically to chuckle nervously
and go on to someone else.
> The main missing
> thing is a formulation that is both nonperturbative and
> background-independent. This would allow us to calculate the vacuum
> selection questions and predict anything. Stay tuned.
I've been tuning into this show since it came on the air 17 years ago. The
plot always seemed pretty implausible to me, but in the first few
seasons there were some characters I grew to like a lot (mainly
WZW models and their supersymmetric and gauged cousins). For the
last six seasons the plot has revolved around the mysterious "Mr. M"
who is supposed to show up someday and make sense of everything.
Besides the "Mr. M" story line, lots of time seems to be taken up
with the antics of the various "Brane-world" characters, who I've
always assumed were put on for comic relief.
Peter
zirkus
>where you can hear a high school teacher who has just been
>through a day-long NSF funded program to teach him
>about string theory say that he has learned that "we may
>have to come up with new standards of what it means to
>say we know something in science".
I happen to think there is at least some truth or useful insights to be
gained from string theory, but I also think that it is fine for
non-string theorists to not take string theory too seriously at least
until it starts to make some 'testable' predictions. It is okay to tell
high school students something about string theory but I don't think
that they should be taught about a "science" for which there is no
experimental evidence, and also because they would not understand it. If
there are kids who are interested in studying string theory then they
should probably be studying valid math since string theory is very math
intensive.
From the perspective of non-string theorists, what do you think could be
the biggest problems with string theory other than a lack of certain
uniqueness or testable predictions? My answer would be:
1) Astronomical evidence indicates that our actual universe is something
like de Sitter space or some type of quintessence model, but it is not
clear if string theory can be made compatible with a realistic theory of
QG in such scenarios.
2) String theory purports to be a physical TOE but it does not explain
certain things about the nature of QM. For instance, I personally do not
see how string theory can be made compatible with a correct explanation
of the appearance of Berry phase in QM (whatever such an explanation
is). (Berry phase is a purely kinematical effect in the time evolution
of quantum systems and I like to think of it as a generalization of the
Aharanov-Bohm effect). I'm not sure if this is really a significant
problem for string theory but it still bugs me occasionally, as well as
the broader issue of kinematics vs. dynamics in string theory.
Btw, has anyone studied whether string theory is compatible with
emergent complexity in the large scale structure of the universe? I ask
because when I took an astronomy course I wrote my report about these
international studies which showed that our universe is like a giant 3
dimensional chessboard - with 80 percent of the universe's matter in the
'white' cubes and the other 20 percent mostly near the edges of the
void-like 'black' cubes.
I told Stephen Wolfram about this and other examples in emergent
phenomenon such as stochastic resonance because Wolfram supposedly still
has a book coming out which might explain emergent complexity from the
very small to the very big. It is rumored that his work might be
applicable to various fields of science and math, and I am still waiting
to see if he explains some of the things I asked him about as well as
things that are probably more interesting (he has delayed publication
for quite a few years supposedly because he kept coming up with new
things and wants to get everything just right to his satisfaction).
Aaron J. Bergman
>
>2) String theory purports to be a physical TOE but it does not explain
>certain things about the nature of QM. For instance, I personally do not
>see how string theory can be made compatible with a correct explanation
>of the appearance of Berry phase in QM (whatever such an explanation
>is).
After a little bit of thought, the best response I can come up with to
this is: huh?
What on earth are you talking about? I mean, I've heard a whole lot of
objections to string theory, and this one is rather oroginal....
[...]
>Btw, has anyone studied whether string theory is compatible with
>emergent complexity in the large scale structure of the universe?
That sounds like a buzzword. If you're talking about is string theory
compatible with large scale structure, that's so far out of the realm
where string theory is important that's it's tough to respond to. The best
I can come up with is that if string theory can replicate our current
ideas about the early universe and CDM, then, all the current calculations
go through.
>I ask
>because when I took an astronomy course I wrote my report about these
>international studies which showed that our universe is like a giant 3
>dimensional chessboard - with 80 percent of the universe's matter in the
>'white' cubes and the other 20 percent mostly near the edges of the
>void-like 'black' cubes.
It's my impression that the CDM model accounts for almost everything
seen in large scale structure. Gravity does tend to condesnse things,
after all. There are some interesting recent observations about not
having enough CDM in the centers of large objects which seem to be
interesting, bu the astro guy telling us about seemed to indicate that
more observations ar really needed to see if the results (ie, prevalence
of MaCHOs in the galactic core) hold up.
[snip Wolfram's amazing discovery that simple rules can give rise to
complicated behavior. To which the best response, I think, is: duh.]
John Baez
Redlum Xohp <redlu...@wanadoo.fr> wrote:
>There was also an email complaining about the state count in black
>holes not being specific to string theory. My answer is: tell me how
>you compute this in some "other", microscopic theory of quantum
>gravity (which one do you take ? I am interested to hear).
In loop quantum gravity one can count states of quantum black
holes as follows:
Abhay Ashtekar, John Baez and Kirill Krasnov, Quantum geometry of
isolated horizons and black hole entropy, preprint available at
http://xxx.lanl.gov/abs/gr-qc/0005126
Here is a more user-friendly introduction to these ideas:
Abhay Ashtekar and Kirill Krasnov, Quantum geometry and black holes,
preprint available as http://xxx.lanl.gov/abs/gr-qc/9804039
John Baez
Aaron J. Bergman <aber...@Princeton.EDU> wrote:
>In article <tEcl7.3908$4z.1...@www.newsranger.com>, zirkus wrote:
>>String theory purports to be a physical TOE but it does not explain
>>certain things about the nature of QM. For instance, I personally do not
>>see how string theory can be made compatible with a correct explanation
>>of the appearance of Berry phase in QM (whatever such an explanation
>>is).
>After a little bit of thought, the best response I can come up with to
>this is: huh?
I'm afraid I must second Aaron's "huh?" here. Berry's phase
comes right out of the fact that the canonical line bundle over
the space of rays in a Hilbert space has a god-given connection
which is not flat. This has the consequence that when you
adiabatically vary a Hamiltonian, carrying it around a loop
in the space of Hamiltonians, any eigenvector will be parallel
transported in such a way that it picks up a "geometrical phase"
by the time it gets back. I don't expect this terse description
to make sense to anyone, but the point is, Berry's phase is built
into quantum theory right from the start, and it's well-understood.
Since string theory is a quantum theory, this means that string
theory is perfectly compatible with the phenomenon of Berry's phase.
It does not "explain" Berry's phase - nor does it explain quantum
theory! - but that is not it's job, so this is no defect.
zirkus
>What on earth are you talking about? I mean, I've heard a whole lot of
>objections to string theory, and this one is rather oroginal....
Actually, I must admit that this argument is not original and instead comes from
Shahn Majid in the context of his discussing the limitations of string theorists
so far only considering the usual CCR or Heinsenberg algebra. Please read page 8
and pages 14-16 of his paper [1], and note on page 16 his mention of the
Aharonov-Bohm effect.
A good and brief intro to the unanswered question of the appearance of Berry
phase in QM is page 1 of [2], but you needn't read beyond page 1 because I am
not asking anyone to accept this paper's particular interpretation.
>It's my impression that the CDM model accounts for almost everything
>seen in large scale structure.
Below, is an intro [3] to what I was taliking about. Note that Robert Kirshner
of Harvard says that "new" physics may be needed to explain how the universe
could have gone from "soup to chowder" so rapidly. Note also that, according to
this brief report, the interpretation of the data is far from certain. However,
a variety of newer papers on this subject have appeared in astro-ph but I have
not done any follow up on this issue beyond the original paper in "Nature".
Perhaps there is some cosmologist/astronomer who will read this post and who
will know more.
Btw, could cosmic strings leave behind regular distributions of matter in the
universe ?
>[snip Wolfram's amazing discovery that simple rules can give rise to
>complicated behavior. To which the best response, I think, is: duh.]
Supposedly, Wolfram has discovered some new "rules" that are profoundly simple
yet widely applicable. We will have to wait and see if his book can live up to
any of the hype. If it has not been delayed again then it should be released
this fall.
[1] http://arxiv.org/abs/hep-th/0006167
[2] http://arxiv.org/abs/quant-ph/0007093
[3] http://www.sciam.com/explorations/012797cosmos/012797horgan.html
zirkus
>I don't expect this terse description
>to make sense to anyone, but the point is, Berry's phase is built
>into quantum theory right from the start, and it's well-understood.
This explanation is not problematic because it is terse but because it is
fundamentally insufficient because the appearance of Berry phase in QT is *not*
well-understood. To see what I mean please read the first 3 pages of the
following paper by C. Anastopoulos and N. Savvidou. These pages will be easy for
you to read, will summarize part of the issue I am talking about and will spare
me from having to type 2-3 pages worth of text. (Also, I prefer to refer readers
to original sources because the authors have much more expertise in their
subject than I do and because original sources provide more context, details and
references.) Please note in my other post (if it gets posted) that I asked Aaron
to read only page 1, but now I would suggest reading only the first 3 pages
because I just noticed that the authors have significantly changed the length
and format of the paper since I first read it.
zirkus
>Since string theory is a quantum theory
Please read my other 2 posts regarding Berry phase and the Aharanov-Bohm effect
but now I would like to comment on a different theme:
It is fine for you to believe that string theory is a QT but I do not think that
you should assert this belief to non-experts or laymen for these reasons:
In [1], G. Veneziano writes "we thus face a kind of paradoxical situation. On
the other hand QM is essential to the success of the KK idea. At the same time,
QFT gives meaningless infinities and spoils the nice semiclassical results. If
the beautiful KK idea is to be saved we need a better quantum theory than QFT."
This proposal might already be problematic since no one really knows what QFT or
string theory is. Btw, for a brief criticism of Veneziano's version of the
S-matrix from the POV of AQFT see my reply to you in the thread "Derived or
contrived?".
E. Witten suggests especially on page 17 of his paper [2] that string theory
might not even be a QT in de Sitter space (and there is no S-matrix in his
version of de Sitter).
Also, paper [3] says on page 12 that "we will have to understand physics at and
beyond the Planck scale to understand precisely why black holes do not gobble up
information. It is likely that there is a subtle interplay between the IR and UV
of the theory in quantum gravity, entailing breakdown of the usual Wilsonian QFT
picture of the impact of UV physics on IR physics. It is also possible that the
*fundamental rules of QM* need to be altered, although there is no clear idea
yet of how this might occur."
Furthermore, papers [4] and [5] suggest that string theory could modify QM.
Please note that all of the authors below are high quality experts in their
field and that none of them are cranks.
So, the moral of this story is that if someone tells you that string theory is a
quantum theory then you can watch them blow out a few neurons by asking them to
define what "quantum theory" and "string theory" mean in a realistic setting
:-)
However, I would tell non-experts and laymen not to worry about this too much
because no one can even demonstrate that string theory is real physics, and
because often when you learn something in physics or math someone ends up
finding a counterexample or generalization for which what you thought you knew
no longer applies (an obvious example would be Euclidean vs. non-Euclidean
geometry).
[1] pp.235-243 in the book "The Geometric Universe" edited by S.A. Huggett et
al.
[2] http://arxiv.org/abs/hep-th/0106109
[3] http://arxiv.org/abs/hep-th/0008241
Lubos Motl
> It does not "explain" Berry's phase - nor does it explain quantum
> theory! - but that is not it's job, so this is no defect.
I agree with everything that John Baez said about Berry's phase and its
relations with string theory. But it could be useful to add a cultural,
speculative comment. We all know that quantum mechanics is an important
part of string theory: the dualities makes sense only if we consider the
full quantum theory; the Green-Schwarz mechanism requires an anomalous
classical transformation rule of some field which is cancelled by a
quantum anomaly; string theory seems to change nothing about the rules of
quantum mechanics - and still, it can describe gravity and the black
holes.
But some people believe that a future definition of string theory will be
capable to do more: to "explain" quantum mechanics; to derive it from
something deeper; to unify stringy physics with quantum concepts into a
generalized "geometric" structure. Only the time shows whether we will
ever find such a formulation of string theory. Maybe one day, John's
sentence "explaining quantum theory is not a job for string theory" will
turn out to be one of many wrong "sceptical" assumptions in history of
physics.
Lubos Motl
> In article <tEcl7.3908$4z.1...@www.newsranger.com>, zirkus wrote:
>> I personally do not see how string theory can be made compatible
>> with a correct explanation of the appearance of Berry phase in QM
>> (whatever such an explanation is).
That's an original objection. I personally understand how string theory
can explain the existence of pianos. But what about the trumpets that have
no strings in it? The answer is that trumpets contain some kind of
D-membranes which are solitons on which open strings can end. :-)
Could I ask you to explain us why do you think that Berry's phase has
something deep to do with string theory - or more precisely why do you
think that string theory has a more serious problem to deal with the idea
of Berry's phase than the Standard Model, for example? And if you admit
that there is no serious difference: do you think that Berry's phase
contradicts the Standard Model and why?
Such arguments sometimes seem that someone wants to hide the truth. So he
says that we should not build nuclear power stations because we do not
know how God created milk. I think that there should be at least some kind
of known or proposed relation between two objects that appear in the same
sentence and are claimed to affect each other seriously. :-)
>> Btw, has anyone studied whether string theory is compatible with
>> emergent complexity in the large scale structure of the universe?
The immediate answer is that the large scale structure of the universe
involves physics that is well described by effective theories that can be
derived from string theory as low energy limits. Therefore whatever works
with those more primitive theories, will work in string theory - and vice
versa: if you want to understand the behavior of those objects in string
theory, you will probably switch to the proper approximations immediately.
However according to the current wisdom, the galaxies and their structure
were born from the fluctuations at the end of the inflation period. To
know the details, one should know the physics at the GUT scale which is
usually associated with the inflation. However I thought that the
simulations (mostly classical) show that one can get a similar pattern for
the large scale structure of the Universe as observed in reality; am I
wrong?
Best wishes
John Baez
zirkus <zir...@my-deja.com> wrote:
>In article <9n9nrh$pvr$1...@glue.ucr.edu>, John Baez says...
>>I don't expect this terse description
>>to make sense to anyone, but the point is, Berry's phase is built
>>into quantum theory right from the start, and it's well-understood.
>This explanation is not problematic because it is terse but because it is
>fundamentally insufficient because the appearance of Berry phase in QT is
>*not* well-understood. To see what I mean please read the first 3 pages of
>the following paper by C. Anastopoulos and N. Savvidou.
>http://arxiv.org/abs/quant-ph/0007093
I feel I understand the origin of Berry's phase quite well. The first
three pages of this paper don't convince me otherwise. Indeed, it
almost seems the authors are trying to make a mystery where none exists.
Sometimes this is useful for the purposes of getting new insights, but
I don't see any new insights here... not in the first three pages, anyway!
For example, when they say the canonical line bundle over a
projectivized Hilbert space is "irrelevant to any probabilistic
aspects of quantum theory", this is very vague. All I can
imagine is that it's a fancy way of saying that phases are
unobservable in quantum mechanics. While there is something
true about this, it can easily be misleading. The superposition
a psi + b phi
can give experimentally distinguishable states depending on the
*relative* phases of the number a and b, and this is how we do
experiments to measure the Berry phase, the Bohm-Aharonov effect,
and other phase effects in quantum theory.
Furthermore, when they complain that the Berry phase has "no
intuitive explanation", they should really be saying that they
*personally* don't have an intuitive understanding of this effect.
Other people do. See this excellent book, for example:
Geometric phases in physics / edited by Alfred Shapere, Frank Wilczek.
Singapore, Teaneck, N.J. : World Scientific, 1989.
Finally, when they talk about a "realist interpretational scheme
for quantum theory" or "contextuality of predictions about properties
of the physical system", I leap to the conclusion that these are
people engaged in the endless and largely pointless argument over
interpretations of quantum mechanics, rather than working physicists
who actually use quantum mechanics to do things. People like this
delight in making up problems where none exist. This makes me unwilling
to read beyond page 3.
Aaron J. Bergman
>In article <slrn9pb4b4....@phoenix.Princeton.EDU>, Aaron J. Bergman
>says...
>
>>What on earth are you talking about? I mean, I've heard a whole lot of
>>objections to string theory, and this one is rather oroginal....
>
>Actually, I must admit that this argument is not original and instead comes from
>Shahn Majid in the context of his discussing the limitations of string theorists
>so far only considering the usual CCR or Heinsenberg algebra.
I wasn't aware we were only considering these algebras.
>Please read page 8
>and pages 14-16 of his paper [1], and note on page 16 his mention of the
>Aharonov-Bohm effect.
His comment is in relation to considering the difference between local
and global effects. String theory is quite well aware of global effects.
Really.
>A good and brief intro to the unanswered question of the appearance of Berry
>phase in QM is page 1 of [2], but you needn't read beyond page 1 because I am
>not asking anyone to accept this paper's particular interpretation.
I did. It still has nothing to do with string theory. From the very
brieg glance I gave at the page, it seems that their point hsa to do
with quantum mechanical epistemology. Now, string theory says nothing
about what quantum mechanics means, but then, neither does anything
else. Regardless of that point, saying that string theory doesn't
explain the Berry phase still makes no sense.
>>It's my impression that the CDM model accounts for almost everything
>>seen in large scale structure.
>Below, is an intro [3] to what I was taliking about.
It looks like that was from 1997.
> Note that Robert Kirshner
>of Harvard says that "new" physics may be needed to explain how the universe
>could have gone from "soup to chowder" so rapidly. Note also that, according to
>this brief report, the interpretation of the data is far from certain. However,
>a variety of newer papers on this subject have appeared in astro-ph but I have
>not done any follow up on this issue beyond the original paper in "Nature".
>Perhaps there is some cosmologist/astronomer who will read this post and who
>will know more.
As far as I know, current computer models with CDM do a very good job.
If COBE hadn't found variations in the CMBR, that would have been bad,
but it found them and the people have rejoiced.
>Btw, could cosmic strings leave behind regular distributions of matter in the
>universe ?
Cosmic strings as catalysts for structure formation are pretty much
dead, I think. I can't remember why, however. I'm sure there are
astro guys here who can give better explanations.
Lubos Motl
through backlog from before the events of Tuesday. -MM]
On Mon, 10 Sep 2001, zirkus wrote:
> In [1], G. Veneziano writes "we thus face a kind of paradoxical
> situation. On the other hand QM is essential to the success of the KK
> idea. At the same time, QFT gives meaningless infinities and spoils
> the nice semiclassical results. If the beautiful KK idea is to be
> saved we need a better quantum theory than QFT."
Maybe you missed the letter "F", zirkus. ;-) I am not sure whether
Veneziano's knowledge and opinions about this question is up-to-date but
what I know is that string theory - in all the respects that people have
learned so far - is a fully quantum theory (unless you talk about some
classical theory before quantization - but we do not call it the full
string theory) while it is not a quantum *field* theory because it is not
based on local fields. Please do not ignore the letter "F". :-) De Sitter
space is complicated and there is absolutely no guarantee that string
theory must admit a consistent description of gravity in de Sitter space;
this fact can be both good or bad. But it is a problem of string theory
and de Sitter space; not a problem of quantum theory.
> It is also possible that the *fundamental rules of QM* need to be
> altered, although there is no clear idea yet of how this might occur."
Yes, it is still possible and Hawking has derived that assuming locality,
the evaporation of black holes implies that pure states can evolve into
mixed states. However, a lot of evidence has been collected that suggests
that string theory does not have to modify the basic rules of QM. It means
that the loophole of Hawking's argument is most likely the assumption of
locality that does not hold in string theory.
> Furthermore, papers [4] and [5] suggest that string theory could modify QM.
> Please note that all of the authors below are high quality experts in their
> field and that none of them are cranks.
The paper [5] by Ellis et al. is prior to the duality revolution and so it
may be slightly obsolete today although it might contain interesting stuff
(I do not know this one). Tom's and Ofer's paper [4] suggested a
relatively slight modification of QM, namely the questions how a state can
be localized in time and what conditions of normalizability should we
impose over the test-functions etc.; however it always was pretty
controversial anyway.
> So, the moral of this story is that if someone tells you that string
> theory is a quantum theory then you can watch them blow out a few
> neurons by asking them to define what "quantum theory" and "string
> theory" mean in a realistic setting :-)
We can define quite clearly what "quantum theory" is. ;-) And the reason
why we ask whether string theory is really a standard quantum theory is
that we have still some doubts about the full definition of string theory.
But if we had doubts about both, the question would be fuzzy enough.
> However, I would tell non-experts and laymen not to worry about this
> too much because no one can even demonstrate that string theory is
> real physics, and because often when you learn something in physics...
I think that this approach is just like if you say that people should not
worry about (and buy) Windows XP because people are dying in Africa. They
should not pay much attention to genetical engineering because people are
dying in Africa. Well, the question whether string theory satisfies the
principles of quantum theory does not depend on the question whether it
describes the real world. You cannot answer every question by pointing out
your doubts about the connections between string theory and the real
world. Then you look like a student at basic school who is asked about
biology by his teacher, but always tries to discuss history. ;-)
> ...or math someone ends up finding a counterexample or generalization for
> which what you thought you knew no longer applies (an obvious example
> would be Euclidean vs. non-Euclidean geometry).
String theory has the marvellous property that it admits no deformations
or generalizations. A given piece of physics is either contained in it, or
it is not and it can never be contained. If you want to deform string
theory by a continuous parameter K (analogy of the curvature in
Lobachevsky geometry, for instance), you would have to find a
corresponding scalar field. But if you know that there is none, there is
also no corresponding generalization or deformation of string theory.
theos ek mechanes
for that matter anything that includes GR, isn't
a QT in the sense taught in QFT courses.
Again I go back to my old horse...Consider the
results [1] which indicate that the Heisenberg
uncertainty relation is modified, to something
of the form:
%
\eqn\One
{
\delta x \delta p \ge 1 + Q (\delta p)^2
}
%
where Q is a constant. From standard Hilbert
space arguments this implies that the canoni-
cal commutation relation,
%
\eqn\Two
{
[x,p]= i
}
%
is modified to include a term proportional to
$(\delta p)^2$ on the right-hand side. So, the
canonical quantization, which works for all QT
does not work for spacetime M-Theory...Similar
arguments apply generically, when General Rela-
tivity is included [2].
In addition, with out to much imagination, one
can consider further modifications to \Two\ so
that such modifications include "higher order"
gravitational effects.
[1] Ciafaloni "Plankian Scattering beyond the
Eikonal Approximation" in STRING QUANTUM
GRAVITY AND PHYSICS AT THE PLANCK ENERGY
SCALE International Workshop on Theoreti-
cal Physics Erice, Italy 21 - 28 June 92
[2] http://xxx.lanl.gov/abs/gr-qc/9403008
Best
Gordon D. Pusch
> In article <tEcl7.3908$4z.1...@www.newsranger.com>, zirkus wrote:
>> Btw, has anyone studied whether string theory is compatible with
>> emergent complexity in the large scale structure of the universe?
>
> The immediate answer is that the large scale structure of the universe
> involves physics that is well described by effective theories that can be
> derived from string theory as low energy limits.
I'm sorry, but IMO that claim must be relaxed to ``effective theories that
string theorists fervently _hope_ will be derivable from string theory in
the low energy limit;'' to claim that such a derivation currently exists
is patently untrue. We are still many acts away from the female person of
substance ululating, and to claim otherwise at this time represents a
statement of faith, not of science.
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
zirkus
says...
>I wasn't aware we were only considering these algebras.
I think that we would have to be by default since string theorists do
not seem to have really considered an alternative to the usual CCR
approach. Majid discusses this on page 8 of [1].
>His comment is in relation to considering the difference between local
>and global effects. String theory is quite well aware of global effects.
I apologize for communicating poorly earlier because I made you, JB and
Lubos misunderstand the points I was trying to make which I will try to
mention briefly:
1) I am *not* claiming that string theory is incompatible with Berry
phase nor any other valid physics. I was only saying that I myself do
not understand the compatibility for the following reasons:
2) From what I can understand, pages 2 and 11 of paper [2] make a
compelling argument that Berry phase does not have a classical analogue
in either classical mechanics or classical probability theory, and that
it is not easy to understand the appearance of Berry phase in a
single-time description of QT (however, I do not like the authors'
consistent histories interpretation because having to choose a
particular philosophic-like interpretation of QM feels too ad hoc and
not very fundamental). The (measurable) Berry phase does not formally
correspond to a self-adjoint operator and I also think that Majid makes
an interesting criticism of algebras with self-adjoint operators as
observables on pages 14-16 of his paper [1], and I prefer his view on
bundles, etc. over a more philosophical interpretation of QM.
3) Also, remember that it has already been established that Berry phase
is a generalization of the Aharanov-Bohm effect and now consider what
Majid says on page 55:
"Usually in physics one needs only the local picture with trivial
bundles in each open set - but for a general noncommutative algebra M
there may be no reasonable 'open sets' and one has therefore to develop
the global picture from the start. We need nontrivial bundles to cover
physics such as in the Aharonov-Bohm effect, potential effects such as
the monopole and also to cover homogeneous spaces and the frame bundles
of general 'manifolds'. None of these could be understood without a
global point of view. In particular, the next quantum spaces after
quantum quantum groups and quantum-braided planes are quantum
homogeneous spaces .... "
(Btw, Majid also uses a particular universal calculus to show that any
quantum homogeneous space is also a quantum manifold). It seems that the
only other person to have considered quantum bundles (and independently
too) is M. Durdevich [3], but their approach to noncommutative
differential geometry based on quantum groups does not seem to be
compatible with the usual CCR approach, as Majid mentions on page 8 of
[1].
4) The main point I would like to make is this:
IMHO, string theory either has to incorporate quantum bundles or explain
why such bundles should not be neccessary (but I don't know how to do
this).
>As far as I know, current computer models with CDM do a very good job.
>Cosmic strings as catalysts for structure formation are pretty much
>dead, I think. I can't remember why, however.
I don't know about either of these topics so I don't know if they are
adequate or inadequate explanations.
[1] http://arxiv.org/abs/hep-th/0006167
[2] http://arxiv.org/abs/quant-ph/0007093
[3] http://arxiv.org/abs/math.QA/0004143
Lubos Motl
> I'm sorry, but IMO that claim must be relaxed to ``effective theories that
> string theorists fervently _hope_ will be derivable from string theory in
> the low energy limit;'' to claim that such a derivation currently exists
> is patently untrue.
Well, the low-energy limit of perturbative string theories - such as type
I, IIA, IIB, heterotic SO(32) and heterotic E8 x E8 string theories - can
be derived by a student who has learned at least the basics of string
theory. Nonperturbatively, we are guaranteed to know the effective
low-energy description in all the vacua if the amount of supercharges is
sufficient. If there is less supersymmetry (or none), there is important
nonperturbative physics that we do not know well enough and it hides the
answers to many important questions such as the vacuum selection problem
and the cosmological constant problem.
But once again, we have been able to derive the low-energy limit of string
theories for decades; this is certainly true for all five theories in 10
dimensions as well as the 11-dimensional M-theory that can include many
types of singularities or domain walls.
> We are still many acts away from the female person of
> substance ululating, and to claim otherwise at this time represents a
> statement of faith, not of science.
We are many acts away from whom? :-) Do you mean the Goddess ululating?
Well, such a claim certainly represents a statement of science, not faith. :-)
Goddess bless you
Lubos
______________________________________________________________________________
E-mail: lu...@matfyz.cz Web: http://www.matfyz.cz/lumo tel.+1-617/496-8199
Urs Schreiber
> one can look at points in the moduli space at which the met-
> ric becomes degenerate, then look at the topological invar-
> iants that are computable using the CS Theory and the connec-
> tion and look how they change along the path in moduli space
> generated by your code.
Hm, but to compute these invariants I need to integrate, and to
integrate I need to know the domain of integration, and to get this I
need to know - the topology! Not so?
BTW, talking about topology change: What if the metric changes its
*signature*? Or is there anything that keeps the signature fixed?
zirkus
Lubos Motl says...
>[string theory] is not a quantum *field* theory because it is not
>based on local fields.
As I mentioned earlier in this NG, both S. Weinberg and K-H Rehren have
suggested that string theory (ST) might only be a fancy method for producing
nonperturbative QFTs. I don't agree with them but no one has been able to
rigorously show that they are wrong (remember that AQFT can at least in some
cases involve local algebras rather than merely local field operators).
>De Sitter
>space is complicated and there is absolutely no guarantee that string
>theory must admit a consistent description of gravity in de Sitter space;
>this fact can be both good or bad. But it is a problem of string theory
>and de Sitter space; not a problem of quantum theory.
I agree and didn't say otherwise.
>Yes, it is still possible and Hawking has derived that assuming locality,
>the evaporation of black holes implies that pure states can evolve into
>mixed states. However, a lot of evidence has been collected that suggests
>that string theory does not have to modify the basic rules of QM. It means
>that the loophole of Hawking's argument is most likely the assumption of
>locality that does not hold in string theory.
I might agree with this but for the sake of completeness I would like to tell
those who don't already know that both string theorists and LQG theorists
believe that semi-classical arguments should break down in a full QG theory, but
that no one really knows which arguments would cease to apply nor how.
>The paper [5] by Ellis et al. is prior to the duality revolution and so it
>may be slightly obsolete today although it might contain interesting stuff
>(I do not know this one).
They formulate QG based on non-critical ST with a Liouville field playing the
role of time, and suggest that this model might have observable violations of
QM. There is a new paper [1] about this approach (which involves the
superscattering matrix $ suggested by Hawking).
>Tom's and Ofer's paper [4] suggested a
>relatively slight modification of QM, namely the questions how a state can
>be localized in time and what conditions of normalizability should we
>impose over the test-functions etc.; however it always was pretty
>controversial anyway.
Yes, they themselves admit in their paper that it is not clear how to interpret
their results. We are still left with 3 possibilities: ST does not modify QM,
ST modifies QM slightly, ST modifies QM significantly.
>String theory has the marvellous property that it admits no deformations
I am not sure what this statement means but e.g. the theory of non-critical
strings involves deformations of the sigma model. See page 3 of paper [1].
Aaron J. Bergman
[More on the Berry phase]
> Please note in my other post (if it gets posted) that I asked Aaron to
> read only page 1, but now I would suggest reading only the first 3 pages
> because I just noticed that the authors have significantly changed the
> length and format of the paper since I first read it.
I skimmed a decent chunk of the whole thing. I see nothing to indicate
that the Berry phase is in any way not well understood.
Aaron J. Bergman
>In article <slrn9pod6m....@phoenix.Princeton.EDU>, Aaron J. Bergman
>says...
>
>>I wasn't aware we were only considering these algebras.
>
>I think that we would have to be by default since string theorists do
>not seem to have really considered an alternative to the usual CCR
>approach. Majid discusses this on page 8 of [1].
Just because Majid says something, it doesn't mean it's true, you know.
Just to pick a random example off of the top of my head, fuzzy spheres
show up in string theory. But, more importantly, this is a vacuous
objection. No one is putting noncommutative geometry into string theory;
the noncommutative geometry comes out of the string theory. You seem to
think that there is this huge community of string theorists who, in some
sort of touching form of naivete, know nothing other than noncommutative
Tori and Moyal planes. It just simply isn't true. If you're interested
in looking at highly noncommutative algebras, you're invited to try to
understand the algebra in Witten's open string field theory ('86). In
the meantime, there's been a lot of work done with the Moyal plane
because it's reasonably straightforward to demonstrate that the
Moyal plane (or, if you prefer, the deformation quantization of the
algebra of functions on the plane) arises in a well-described decoupling
limit of string theory. In some sense, it is a toy model for open string
field theory. For example, one can show that there are D-brane-like
solitons that show up in these noncommutative gauge theories.
>
>>His comment is in relation to considering the difference between local
>>and global effects. String theory is quite well aware of global effects.
>
>I apologize for communicating poorly earlier because I made you, JB and
>Lubos misunderstand the points I was trying to make which I will try to
>mention briefly:
>
>1) I am *not* claiming that string theory is incompatible with Berry
>phase nor any other valid physics. I was only saying that I myself do
>not understand the compatibility for the following reasons:
>
>2) From what I can understand, pages 2 and 11 of paper [2] make a
>compelling argument that Berry phase does not have a classical analogue
>in either classical mechanics or classical probability theory,
It's probably not too hard to work out a classical system that has a
geometrical phase in it. As for classical probability theory, who cares?
> and that
>it is not easy to understand the appearance of Berry phase in a
>single-time description of QT (however, I do not like the authors'
>consistent histories interpretation because having to choose a
>particular philosophic-like interpretation of QM feels too ad hoc and
>not very fundamental). The (measurable) Berry phase does not formally
>correspond to a self-adjoint operator and I also think that Majid makes
>an interesting criticism of algebras with self-adjoint operators as
>observables on pages 14-16 of his paper [1], and I prefer his view on
>bundles, etc. over a more philosophical interpretation of QM.
I'm sorry. I find the rest of this paragraph incoherent.
>3) Also, remember that it has already been established that Berry phase
>is a generalization of the Aharanov-Bohm effect and now consider what
>Majid says on page 55:
It's not so much a generalization as yet another example of a
geometrical phase.
>"Usually in physics one needs only the local picture with trivial
>bundles in each open set - but for a general noncommutative algebra M
>there may be no reasonable 'open sets' and one has therefore to develop
>the global picture from the start. We need nontrivial bundles to cover
>physics such as in the Aharonov-Bohm effect, potential effects such as
>the monopole and also to cover homogeneous spaces and the frame bundles
>of general 'manifolds'. None of these could be understood without a
>global point of view. In particular, the next quantum spaces after
>quantum quantum groups and quantum-braided planes are quantum
>homogeneous spaces .... "
Do you somehow think that we don't work with nontrivial bundles all the
time? If not, I fail to see your point.
>(Btw, Majid also uses a particular universal calculus to show that any
>quantum homogeneous space is also a quantum manifold). It seems that the
>only other person to have considered quantum bundles (and independently
>too) is M. Durdevich [3],
If, by "quantum bundles", you mean bundles over a noncommutative space,
I can assure that they are just about as old as quantum mechanics. The
easiest way to define a vector bundle over a noncommutative space is
to have it by a projective module of the C*-algebra.
>but their approach to noncommutative
>differential geometry based on quantum groups does not seem to be
>compatible with the usual CCR approach, as Majid mentions on page 8 of
>[1].
>
>4) The main point I would like to make is this:
>
>IMHO, string theory either has to incorporate quantum bundles or explain
>why such bundles should not be neccessary (but I don't know how to do
>this).
I have absolutely no idea what this is supposed to mean.