Re: Critique of Lubos Motl's opinions on Loop Quantum Gravity
thomas_l...@hotmail.com
> I would like to clarify the doubts Lubos Motl expressed about Loop
> quantum gravity.
The key problem with LQG is that it is not quantization in the
standard, Fock, sense. This leads to incorrect results when LQG
quantization is applied to well-understood problems. E.g., the
spectrum of the harmonic oscillator is not bounded from below,
see http://www.arxiv.org/abs/hep-th/0409182 . IMO this is a
show-stopper.
Suresh Maran
thomas_l...@hotmail.com wrote:
> The key problem with LQG is that it is not quantization in the
> standard, Fock, sense. This leads to incorrect results when LQG
> quantization is applied to well-understood problems. E.g., the
> spectrum of the harmonic oscillator is not bounded from below,
Your research on application of loop quantum gravity to harmonic
oscillator is of purely mathematical significance apply. You cannot
simply apply a theory to something else, out of its conceptual
framework. For example it does *not* make sense to apply 'string
theory' to understand 'dancing' or 'fishing' or 'skydiving' etc.
I started a blog
http://universalwatch.blogspot.com/
where I will post more stuff there later.
Suresh K Mara
thomas_l...@hotmail.com
>
> Your research on application of loop quantum gravity to harmonic
> oscillator is of purely mathematical significance apply. You cannot
> simply apply a theory to something else, out of its conceptual
> framework. For example it does *not* make sense to apply 'string
> theory' to understand 'dancing' or 'fishing' or 'skydiving' etc.
>
New methods become respectable by first showing that they reproduce
the correct results for well-understood problems. This is e.g. how
Feynman overcame the resistence against path integrals of Niels Bohr
and others. That LQG methods fail to reproduce the oscillator
spectrum is quite remarkable, and this fact deserves to be as well
known as the fact that string theory is not background independent.
Btw, I am not a string theorist, cf.
http://www.arxiv.org/abs/math-ph/0103013 .
Suresh Maran
> the correct results for well-understood problems.
I would not consider non-perturbative quantum gravity as a new method
like quantum mechanics or general relativity. It is simply a way of
doing the details of existing physical ideas in a certain way. We need
to figure out how to model physical objects starting from Planck scale
by solving complicated, self interacting discrete structures.
Non-perturbative have not yet developed to that extent.
http://universalwatch.blogspot.com/
Suresh K Maran
jcgon...@yahoo.com
But is the harmonic oscillator well understood? From Tony Smith's
website:
Predrag Cvitanovic has written a web book on Group Theory... in the
Epilogue of his web book on Group Theory: "... once I learned that
chaos is generic for generic Hamiltonian flows, I lost faith in doing
field theory by pretending that it is a bunch of harmonic oscillators,
with interactions accounted for as perturbative corrections. This
picture is simply wrong - strongly coupled field theories
(hydrodynamics, QCD, gravity) are nothing like that ... So they
excommunicated me from the ranks of high energy theorists, and now ...
we are working out quantum chaos ... this is ... replace the path
integral with a fractal set of semi-classical orbits. ...".
thomas_l...@hotmail.com
Suresh Maran
This answer is only valid for an abstract textbook harmonic oscillator.
I believe the 'harmonic oscillator' in question is a physical object
which describes the states of a certain physical field. I think
jcgonsow is using the word 'harmonic oscillator' in a very flexible
sense.
jcgon...@yahoo.com
> jcgonsow...@yahoo.com skrev:
> >
> > But is the harmonic oscillator well understood?
>
> Yes.
Well if the use of harmonic oscillators for field theory is so well
understood, where are all the nice particle mass and force strength
calculations like lattices have? Seems like harmonic oscillators
require reproducing lattice results more than lattices require
reproducing harmonic oscillator results.
http://www.valdostamuseum.org/hamsmith/cnfGrHg.html#Qgr
http://www.valdostamuseum.org/hamsmith/USGRFckb.html
http://www.valdostamuseum.org/hamsmith/Sets2Quarks9.html
Thomas Larsson
>
> Well if the use of harmonic oscillators for field theory is so well
> understood, where are all the nice particle mass and force strength
> calculations like lattices have? Seems like harmonic oscillators
> require reproducing lattice results more than lattices require
> reproducing harmonic oscillator results.
Sorry, I should have expressed myself more clearly. The harmonic
oscillator by itself is well understood. You can then try to use the
oscillator as a starting point for understanding more complicated
theories. This is more or less successful, depending on the theory.
The harmonic oscillator offers only a limited understanding of other
theories.
The problem with LQG, as I see it, is that it gives the wrong result
for the harmonic oscillator proper.
Let me comment on how I view the conflict between ST and LQG.
It is unlikely that ST possesses a background-independent formulation.
Lee Smolin has informed me that a rigorous theorem rules out
anomaly-free Fock quantization of background-independent theories, and
I see no reason to doubt that. This explains why the conflict between
LQG and ST is so fierce. ST gives up background independence, which to
LQGists is the most profound lesson from GR, and LQG gives up Fock QM,
which string theorists can never accept. Hence the conflict will
persist.
The loophole is that you can combine Fock QM with background
independence, provided that you give up anomaly freedom. Most people
think this idea is absurd, since classically a gauge symmetry is a
redundancy of the description. However, there are examples where
quantum anomalies break gauge symmetry, without violating unitarity.
The subcritical free string is the best known example. This example is
of course also very relevant to QG, since the free string is nothing
but 2D gravity coupled to scalar fields.
jcgon...@yahoo.com
> The problem with LQG, as I see it, is that it gives the wrong result
> for the harmonic oscillator proper.
>
> Lee Smolin has informed me that a rigorous theorem rules out
> anomaly-free Fock quantization of background-independent theories, and
> I see no reason to doubt that.
>
> independence, provided that you give up anomaly freedom. Most people
> think this idea is absurd, since classically a gauge symmetry is a
> redundancy of the description. However, there are examples where
> quantum anomalies break gauge symmetry, without violating unitarity.
> The subcritical free string is the best known example. This example is
> of course also very relevant to QG, since the free string is nothing
> but 2D gravity coupled to scalar fields.
After a little reading I think I understand what you are saying
as well as I'm capable. First I think Tony Smith's model is
immune to the problem you mention cause Smith uses D4 as the
BRST operator for his Spin Network. This is because Smith's model
is for color/electroweak as well as gravity. If you add Smith's
8-dim spacetime to his 16-dim fermions and two propagator phases
you get Smith's E6/F4 26-dim bosonic string. As for whether Smith
would agree with your assessment of conventional LQG, I'll just
say that Smith does seem to like a nilpotent operator. John
Suresh Maran
> Let me comment on how I view the conflict between ST and LQG.
>
> It is unlikely that ST possesses a background-independent formulation.
> Lee Smolin has informed me that a rigorous theorem rules out
> anomaly-free Fock quantization of background-independent theories, and
> I see no reason to doubt that. This explains why the conflict between
> LQG and ST is so fierce. ST gives up background independence, which to
> LQGists is the most profound lesson from GR, and LQG gives up Fock QM,
> which string theorists can never accept. Hence the conflict will
> persist.
It is OK to have conceptual conflicts, debate and pursue alternate view
points. This is how science develops. But it seems that string
theorists have taken things personally by restricting finances and
oppurtunities to alternate viewpoints using their foot holds in major
universities. I feel bad about this situation.
Please read my posting at universalwatch.blogspot.com on July 26, 2005.
Suresh
Suresh Maran
Thomas Larsson wrote:
>
> Let me comment on how I view the conflict between ST and LQG.
>
> It is unlikely that ST possesses a background-independent formulation.
> Lee Smolin has informed me that a rigorous theorem rules out
> anomaly-free Fock quantization of background-independent theories, and
> I see no reason to doubt that.
In that case I would want to give up fock space.
Background-independence is a meaningful abstract intuitive concept.
Fock space is a mathematical and physical approximation. Even in simple
problems in 1D quantum mechanics, harmonic oscillater states can become
useless if you add some strong complicated interaction term.
If you start from path-integral formulation, fock space is an emergent
concept. It is closely associated with prevalence of second order part
of action for non-gravitational and weakly interacting theories. There
is no-priori gaurantee that fock space must be always be useful in
general context. I would consider that use of fock space which is
closely associated with Feynman diagram technology is responsible for
failure to quantize gravity using conventional means.
Suresh
universalwatch.blogspot.com
thomas_l...@hotmail.com
>> It is unlikely that ST possesses a background-independent formulation.
>> Lee Smolin has informed me that a rigorous theorem rules out
>> anomaly-free Fock quantization of background-independent theories, and
>> I see no reason to doubt that.
>
>In that case I would want to give up fock space.
>Background-independence is a meaningful abstract intuitive concept.
>Fock space is a mathematical and physical approximation.
In contrast, I want to keep both background independence and Fock QM.
In view of the theorem above, this means that anomaly freedom must
be sacrificed, which puts me in sharp disagreement with both the
string and LQG communities.
It is generally accepted as a fact that every gauge anomaly is
automatically inconsistent. This idea originates in the standard
model, where there is an anomaly associated with triangle diagrams.
This kind of anomaly, which is proportional to the third Casimir
operator, is indeed inconsistent, because it leads to violation of
unitarity and renormalizability. Fortunately, the particle content of
the standard model is precisely such that the the third Casimir
vanishes. Hence one can say that Nature knows about this anomaly.
Nevertheless, this "fact" is simply not true. The simplest,
non-trivial gauge theory is the free bosonic string, described in
chapter 2 of Green-Schwarz-Witten "Superstring theory". Now, I realize
that your opinion about string might not be very high, but if you take
away the hype you will find that early string theory was interesting
mathematical physics. In particular, string theorists do know how to
quantize the free string living in D dimensions. There are three
qualitatively different cases:
1. D > 26. The Hilbert space contains negative-norm states, unitarity
is violated and the theory is inconsistent. Forget it!
2. D = 26. The Hilbert space contains null states, which can be
factored out because the conformal anomaly vanishes. The reduced
theory is unitary and consistent.
3. D < 26. The Hilbert space has a positive-definite inner product.
We can not mod out gauges because of the conformal anomaly c = 26-D,
but there is no need to because the unreduced theory is already
unitary. The gauge symmetry is broken by quantum effects.
The third alternative runs into problems when string interactions are
added, which is why the bosonic string predicts 26 dimensions.
Nevertheless, the free string is a well-defined theory in its own
right, and the simplest example of a gauge theory. The main
conclusions one can draw from it are:
1. Quantization of a gauge theory is essentially the same thing as
building a lowest-energy representation of its contraint algebra.
2. The representation needs not be trivial - it is sufficient if it
is unitary.
3. Quantization of gravity leads to anomalies. Recall that the free
string is nothing but 2D gravity coupled to D scalar fields, and as
such it is background independent on the world sheet, albeit not in
target space.
There are some striking results in theory of lowest-energy reps. The
gauge algebra of YM theories acquires an extension proportional to the
second Casimir, making it into a higher-dimensional affine algebra (an
extension of a manifold algebra), and the diffeomorphism algebra
acquires a higher-dimensional Virasoro extension. These anomalies can
not be seen in conventional field theory, because the relevant
extensions are functionals of the observer's trajectory in spacetime.
But without these anomalies, background independence and Fock QM
cannot be combined.
Spinnet
> Suresh Maran wrote:
>
> I want to keep both background independence and Fock QM
> that your opinion about string might not be very high
I expect the fundmental physical ideas not only be sound in details but
also at the abstract conceptual level.
General relativity implies that non-gravitational physical processes
happen with respect to the gravitational field. We observe the physical
processes through it and with respect to it. If you have a theory which
includes the gravitational dynamics then in it the physical process
must happen with respect to each other (relationally).
In string theory the strings move, vibrate, merge, split etc. These
strings are not like spinors existing in an internal space. They are
similar to classical high school textbook strings. If string theory
includes gravitational field or/and it is a fundamental theory, with
respect to what the strings do their movements? What force is
responsible for theirs dynamics? It looks like string theory needs a
second general relativity theory to explain itself.
String theory may be an interesting mathematics but it does not
physically reasonable because it ignores the conceptual lessons of
general relativity which is the foundation our current understanding of
time, space and everything.
Once does not require a thousand explanations to disqualify a theory.
By a simple reasoning one could clearly see that something is wrong
with it.
Suresh K Maran
jcgon...@yahoo.com
> I expect the fundmental physical ideas not only be sound in details but
> also at the abstract conceptual level.
>
> General relativity implies that non-gravitational physical processes
> happen with respect to the gravitational field. We observe the physical
> processes through it and with respect to it. If you have a theory which
> includes the gravitational dynamics then in it the physical process
> must happen with respect to each other (relationally).
>
> In string theory the strings move, vibrate, merge, split etc. These
> strings are not like spinors existing in an internal space. They are
> similar to classical high school textbook strings. If string theory
> includes gravitational field or/and it is a fundamental theory, with
> respect to what the strings do their movements? What force is
> responsible for theirs dynamics? It looks like string theory needs a
> second general relativity theory to explain itself.
>
> String theory may be an interesting mathematics but it does not
> physically reasonable because it ignores the conceptual lessons of
> general relativity which is the foundation our current understanding of
> time, space and everything.
>
> Once does not require a thousand explanations to disqualify a theory.
> By a simple reasoning one could clearly see that something is wrong
> with it.
>
> Suresh K Maran
If you leave out the move/vibrate and keep the merge/split then a
string is a good lattice/spin network/Feynman path idea. Larsson seems
to like the bosonic string and you don't need move/vibrate for the
bosonic string. One nice thing about string theory is it can nicely
include E6,E7, and E8. E6 can give you nice spinors and you can get
general relativity as a subalgebra also. This is what Tony Smith does.
Maybe Fock quantization can work but a spin network quantization seems
better cause it lets you keep the nice lattice stuff. John
Spinnet
> If you leave out the move/vibrate and keep the merge/split then a
> string is a good lattice/spin network/Feynman path idea.
Correct me if I am wrong. If you leave out the move/vibrate then you
are no longer dealing with strings.
jcgon...@yahoo.com
creates the SO(32) or E8xE8 superpartners since bosonic strings stay at
26-dim rather than reducing to 10-dim. You can still have Feynman path
and Einstein gravity/standard model movements on lattices for the
bosonic string.
http://www.valdostamuseum.org/hamsmith/stringbraneStdModel.html