Why is QM incompatible with GR and how does string theory solve this? Or M-Theory?

[SeventhSigma]

I always hear that these two things are incompatible but I never really hear why. The most I know is that QM assumes a quantized spacetime whereas GR assumes a dynamic one, but I don't really understand if this is correct (nor do I get what that really means). I don't see how GR would fail, for instance, if you just took the aggregate of quantum effects to the mass-scale such that certain aspects of the quantum world are negligible (much like how quantum effects are negligible when we talk about, say, adding velocities of classical objects).

What happens if you take QM's assumptions to the GR level and vice-versa? How does string theory aim to resolve QM and GR? Is it meant to give a new foundation of assumptions that work under both theories and yet still provide the same level of verifiability/testability/accuracy/etc as QM does in its own realm and as GR does in its own realm?

Any elucidation on the matter would be appreciated.

 

[bcrowell]

I know very little about quantum gravity, so others here can probably give much better technical answers. However, there are some fairly straightforward, albeit non-rigorous, arguments that QM and GR are incompatible. For example, QM has a time-evolution operator that is unitary, so in some sense information is never lost. In GR, you can destroy information by throwing it into a black hole.

For a good nontechnical article on this, see Smolin, "Atoms of Space and Time," Scientific American, Jan 2004. The article can be found (illegally?) on the web by googling.

I don't think it's necessarily true that string theory solves the problem. We want a theory of quantum gravity to have various features, including (1) self-consistency (never gives infinite energies, negative probabilities, etc.), (2) consistency with GR and QM in the appropriate limit, and (3) consistency with at least one experiment for which both GR and QM make incorrect predictions. We have no theory at all that satisfies #3. It is a matter of opinion whether string theory satisfies 1 and 2. There are other theories, such as loop quantum gravity, that also satisfy some of these criteria.

-Ben

 

[SeventhSigma]

I thought the black hole paradox had been resolved and that it really wasn't a paradox at all and that information COULD be retrieved?

 

[bcrowell]

I thought the black hole paradox had been resolved and that it really wasn't a paradox at all and that information COULD be retrieved?

As far as I know, it has not been resolved to the point where the resolution is generally accepted. I believe that Hawking changed his mind, but that doesn't mean that everyone is satisfied.

Even if it does get resolved, or already has been resolved, to many people's satisfaction, that doesn't mean it's not a valid argument for the incompatibility of GR and QM -- the resolution may require ingredients that go beyond standard GR and QM.

 

[martinbn]

Just a small remark. QM does not assume quantized space time.

 

[granpa]

http://en.wikipedia.org/w/index.php?title=Doubly-special_relativity&oldid=288143426

 

[haushofer]

One very interesting aspect of string theory is that the spatial extension of point particles (0-dimensional) to strings (1-dimensional), and the appearance of an infinite tower of particles in the spectrum, renders the theory in the target space finite. So what a naive renormalization procedure on General Relativity can't do, is done by string theory in a sense.

You can discuss how remarkable it is that string theory contains gravity. For me it is quite non-trivial; you start out with a string, choose a vacuum to do perturbation theory (the Minkowski vacuum, which is a vacuum solution of GR), and there appears to be a massless spin 2 particle which by conformal inviarance obeys the vacuum Einstein equations to lowest order. For me, that is a hint that maybe string theory is on the right track :)

 

[Fra]

There are several ways to note the problems.

You can take some naive receipes of "quantization" that does work form normal QM/QFT; and try to just "apply" that to the degrees of freedom of the gravitational field itsel. Then the calculations are first of all ambigous, and hard to make sense of. You get these infinities that are hard to renormalize away using the techqniques that was successful for other interactions. This is somehow a "technical description" whose status is nevertheless unclear since it's by no means obvious that it's correct in the first place to apply these naive "quantisation procedures" to spacetime and gravity itself. This view is just a technical manipulation accoriding to commont practice, that fails and thus gives rise to an incompatibility problem.

The other view is more at conceptual level. The whole point of Quantum theory is to be a theory of measurement, where the predictions are expectations of what a specific observer will observe. Quantum theory in this sense involves a CHOICE of observer. This is related to the CHOICE of background space and vacuum selection problems.

GR OTOH, is not really a measurement theory at all. It is rather a realist theory of how simple measurements by rods and clocks, done by different observers relate. And the physics of GR is the observer invariants! In GR the PHYSICS is the observer invariants and specific observers correspond to gauge choices.

In this sense the measurement theory of QM; and GR are very different. IT is not clear how "predictions of QM" which are expectations conditional on an observer; really does translate to the predictions of GR which are more like only RELATIONS between observers.

Also, in QM, the choice of observer (background) is part of the starting point. It is not dynamically assigned and contains no physics. QM is a purely descriptive theory that describes how an expectations of something follows from the initial information about this. The observer is not dynamical and part of the system in QM. It's only the information state that changes upon observation.

In GR, the observer-background is non-physical. Only relations between observers are defined.

This is a conceptual incompatibility that is more than just technical. In particular is it very doubtful to just "apply procedures" arbitrary. The exact meaning of quantisation and "observation" and what really qualify as observables are the conceptual part of this. This requires deepening the understanding of the foundations of both theories in a way that makes the observer part of the system, and an active player and not just an external non-physical observer that just DESCRIBES the system without having to face consequences of incorrect expectations.

In particular do we need to understand that the process of "CHOOSING the observer" is a physical and highly constrained process. The nature of this, corresponds to the vacuum selection problem om ST; but it also generally relates to the problem of merge the GR-view that observer choices lack physicla significance, and the fundamental role the observer MUST play in a measurement theory.

/Fredrik