How does string theory address problem of time GR vs QM?

[ensabah6]

I'm reading this:

==quote==

Einstein's theory of gravity, General Relativity, and our theory which governs the sub-atomic world, Quantum Theory, give seemingly inconsistent accounts of the nature of time. According to General Relativity, each observer will have a separate notion of time, based upon his or her 'trajectory' within the spacetime history of the universe. According to Quantum Theory, there is only one notion of time which governs the evolution of physical systems. The inconsistency leads to considerable problems when attempting to write down a theory which incorporates both gravity and the quantum.

The attempt to reconcile the role played by time in quantum theory, with the principle of general covariance of General Relativity, leads many to consider a radical departure from our every day intuitive understanding of the concept, such as regarding it as an illusory phenomenon, or that the histories which enter the gravitational path integral are of Euclidean signature rather than Lorentzian.

==quote==


It's said string theory is the only consistent theory of quantum gravity, and reproduces GR in the semi classical regime.

String theory is an extension of SUSY-QFT and "only one notion of time which governs the evolution of physical systems."

So how does string theory get from "only one notion of time which governs the evolution of physical systems." to reproduce GR ""each observer will have a separate notion of time, based upon his or her 'trajectory' within the spacetime history of the universe"

Does it also reproduce GR's general covariance? Does it regard QM's understanding of time as more fundamental? If so, how does string theory reproduce GR "each observer will have a separate notion of time, based upon his or her 'trajectory' within the spacetime history of the universe" from a QM description that is based on "only one notion of time which governs the evolution of physical systems."

 

[tom.stoer]

There is no such inconsistency. The time measured by an observer and the time according to which a Hamiltonian flow is constructed is indeed different already in classical GR; that's not an inconsistency but simply a different definition of different entities. No problem so far.

There ARE inconsistencies between (classical) GR/gracity and quantum theory which requires new methods in deriving a consistent theory of quantum gravity, but I haven't seen any approach which lists the problem of time as such an obstacle during the construction or a source of inconsistencies. Yes, one has to find an interpretation of the the Hamiltonian flow and one has to find something like "clock time", but that's afaik not a problem in the fundamental approach.

"It's said string theory is the only consistent theory of quantum gravity, " is a bold statement; you will certainly find supporters within the string theory community, but of course there are other successful approaches as well. The sattement is strange as string theory still has major problems when it comes to calculations for fully dynamical spacetime where weak-field or perturbative approximations are no longer reasonable. This is the problem of "background independence" and I think that most string theorists would agree that this is one of the open issues in string theory.

 

[ensabah6]

There is no such inconsistency. The time measured by an observer and the time according to which a Hamiltonian flow is constructed is indeed different already in classical GR; that's not an inconsistency but simply a different definition of different entities. No problem so far.

There ARE inconsistencies between (classical) GR/gracity and quantum theory which requires new methods in deriving a consistent theory of quantum gravity, but I haven't seen any approach which lists the problem of time as such an obstacle during the construction or a source of inconsistencies. Yes, one has to find an interpretation of the the Hamiltonian flow and one has to find something like "clock time", but that's afaik not a problem in the fundamental approach.

"It's said string theory is the only consistent theory of quantum gravity, " is a bold statement; you will certainly find supporters within the string theory community, but of course there are other successful approaches as well. The sattement is strange as string theory still has major problems when it comes to calculations for fully dynamical spacetime where weak-field or perturbative approximations are no longer reasonable. This is the problem of "background independence" and I think that most string theorists would agree that this is one of the open issues in string theory.

I have wondered if string theory as a theory of quantum gravity gives a prediction in the Planck scale on the properties of gravity or inside the black hole.


"General Relativity, and our theory which governs the sub-atomic world, Quantum Theory, give seemingly inconsistent accounts of the nature of time. According to General Relativity, each observer will have a separate notion of time, based upon his or her 'trajectory' within the spacetime history of the universe. According to Quantum Theory, there is only one notion of time which governs the evolution of physical systems. The inconsistency leads to considerable problems when attempting to write down a theory which incorporates both gravity and the quantum."

The author quoted above seems to regard the problem of time as a problem that needs to be accounted for in quantum gravity. How does LQG account for this?

 

[tom.stoer]

As I said: I don't think that one has to solve the problem of time prior to the quantization of gravity; it's a problem that has to be solved after the quantization has been carried out (but that is only my personal opinion).

I have to leave now; regarding time in LQG when I am back ...

 

[ensabah6]

As I said: I don't think that one has to solve the problem of time prior to the quantization of gravity; it's a problem that has to be solved after the quantization has been carried out (but that is only my personal opinion).

I have to leave now; regarding time in LQG when I am back ...

String theory doesn't solve the problem of time prior "the quantization of gravity", it has a string that gives rise to a masssless spin-2 boson, identified as graviton. It starts and ends in "only one notion of time which governs the evolution of physical systems" which makes me wonder how its description of gravity can give rise to "each observer will have a separate notion of time, based upon his or her 'trajectory' within the spacetime history of the universe"

 

[Haelfix]

The 'problem of time' comes from the Hamiltonian treatment of GR, where one can see that it vanishes identically and hence there is a priori a bit of an interpretational puzzle (what is merely gauge and what are 'true dynamics').

This confused a lot of people for a long time, until it was finally treated properly during the 80s and 90s by Henneaux and Teteilboim. They noted that it was not a unique feature of gravity or general covariance perse. Other systems could be generally covariant without the vanishing hamiltonian.

Anyway, a careful method must be followed involving the reduced phase space and constraints, where you have to be clear to formulate all observables in such a way that their bracket with the constraints vanish.

See the opus 'Quantization of gauge systems', although be warned it is not recommended for the beginner.

 

[ensabah6]

The 'problem of time' comes from the Hamiltonian treatment of GR, where one can see that it vanishes identically and hence there is a priori a bit of an interpretational puzzle (what is merely gauge and what are 'true dynamics').

This confused a lot of people for a long time, until it was finally treated properly during the 80s and 90s by Henneaux and Teteilboim. They noted that it was not a unique feature of gravity or general covariance perse. Other systems could be generally covariant without the vanishing hamiltonian.

Anyway, a careful method must be followed involving the reduced phase space and constraints, where you have to be clear to formulate all observables in such a way that their bracket with the constraints vanish.

See the opus 'Quantization of gauge systems', although be warned it is not recommended for the beginner.

Hi to clarify, I'm not alluding to the 'problem of time' comes from the Hamiltonian treatment of GR" i.e canonical formulation, but as described here, the conception of time in string theory which as in QFT ""only one notion of time which governs the evolution of physical systems" as opposed to GR notion of time.

How does string theory's notion of time ""only one notion of time which governs the evolution of physical systems"" give rise to GR's notion of time in the semiclassical limit?


thanks

 

[Haelfix]

Hi Ensabah, I'd like to see a clear gauge invariant formulation of the problem in terms of observables, b/c a priori I don't see it. I don't agree that GR has 'multiple' notions of time, at least not for a physical observer in a frame with given Cauchy data.

I do however see the original 'problem of time' which arose in QC from the Wheeler-DeWitt equation with the same aforementioned solution.

 

[tom.stoer]

Haelfix is right. There are indeed "different times" in GR but they are introduced by hand. Any observer singles out a specific time slicing and therefore its own proper time. The theory still has an internal symmetry to transform between these different times. No problem with that.

The "problem of time" is that "time" seems to vanish completely when treating GR in the canonical formulation. Some people call this "frozen time". So the problem is not that we have to many times, but that we have no time.

There is one approach (e.g. in LQG - but not restricted to that quantization method) which tries to identify a physical time after quantization. This is called "thermal time". More about that when I am back.