Ultraviolet Catastrophe of Gravity

[quantumfoam]

Hi everyone! I was thinking about gravitational waves and gravitons and I realized that I did not fully understand the purpose of quantizing gravitational waves. I understand that quantizing electromagnetic waves gets rid of the classical physics prediction of the Ultraviolet Catastrophe (UVC) (note that I understand it did not get rid of it. It showed why the UVC problem doesn't happen). But what is the UVC analogue to gravitational waves predicted by classical general relativity?

 

[tom.stoer]

By UV catastrophe you certainly mean the problem in treating black body classically.

Note that this is not an effect on the fundamental level (quantization, single photons, ...) but an effect due to quantum statistical mechanics for the black body of a given temperature radiating photons.

I don't think that we are able to apply the concept of temperature and quantum statistical mechanics to quantum gravity.

 

[Bill_K]

I don't think that we are able to apply the concept of temperature and quantum statistical mechanics to quantum gravity.

What would be wrong with visualizing an object in thermal equilibrium with a gas of gravitons?

 

[tom.stoer]

I don't see a problem with free gravitons; it's just Bose-Einstein statistics and state-counting.

But I do see problems to define (rigorously) an ensemble of interacting gravitons with a certain temperature. I do not know how to define and interpret temperature in the ART / QG context, and I do not know how to define the Hamiltonian H and

$\rho = e^{-\beta H}$

 

[quantumfoam]

Hello guys! I wasn't very specific on my question. What I meant to ask was why quantize gravitational waves? (:

 

[tom.stoer]

Quantizing gravitational waves as perturbations of a spacetime background is known to be inconsistent; a theory of quantum gravity constructed along these lines (well understood for QED, QCD, ...) is not renormalizable, so only the the free quantum field theory of gravitational waves does exist.

However there are several attempts (frequently discussed in the "beyond the standard model forum) to modify this quantization procedure and find a consistent theory of quantum gravity. There is e.g.
- string theory which goes much further and tries to unify all interactions, so quantum gravity is only one aspect
- there are approaches like loop quantum gravity which do not split the gravitational field in a background + perturbations
- there is the asymptotic safety approach aiming for a renormalizable theory, but which does not start with perturbations, either
- ...
All these approaches are work in progress, non of them is a complete theory in the physical sense

 

[The_Duck]

Hello guys! I wasn't very specific on my question. What I meant to ask was why quantize gravitational waves? (:

Once part of your theory of the universe is quantum mechanical, you need to make the rest of it quantum mechanical too. One of the hallmarks of quantum mechanics is that objects can be in superpositions of two different states at once. For example, a mass could exist in a superposition of two different positions. But masses serve as the source of the gravitational field, so if a mass is in a superposition of two positions, then the gravitational field must be in a quantum superposition of two different possible states. So you need a quantum mechanical theory of gravity to account for this.

It is actually quite straightforward to make a quantum mechanical version of general relativity, our current theory of gravity. The only problem is that this quantum mechanical theory turns out to be useless for making predictions above a certain energy scale, called the Planck scale. When people talk about finding a theory of quantum gravity, they mean finding a consistent theory that extends the current theory to make predictions at and above the Planck scale. This turns out to be hard.

If you don't worry about tom.stoer's subtle reservations, classical gravitational waves would indeed suffer from exactly the same UV catastrophe as classical electromagnetic waves, which is resolved in exactly the same way by quantizing gravity so that gravitational waves come in discrete chunks, as gravitons. But IMO this is not nearly as compelling a reason to quantize gravity as the reason I gave above.

 

[quantumfoam]

The_Duck
In your reason of quantizing the gravitational field due to the superposition of a gravitating particle, would quantum field theory in curved spacetime alone take care of modelling that situation?

 

[The_Duck]

The_Duck
In your reason of quantizing the gravitational field due to the superposition of a gravitating particle, would quantum field theory in curved spacetime alone take care of modelling that situation?

No. As far as I'm aware, "quantum field theory in curved spacetime" refers to doing QFT in a fixed classical background spacetime that is independent of the particles that propagate within it. But really these particles should have an effect on the spacetime: they should act as sources for the gravitational field. So QFT in curved spacetime is not quantum gravity. It let's you calculate the behavior of quantum mechanical particles in the essentially classical gravitational field of a large nearby mass, but it leaves out the gravity of these quantum mechanical particles themselves.

 

[quantumfoam]

Okay I see now! Thank you The_Duck! And thank you tom.stoer! I did not know the approaches taken to quantize gravity! Thank you for your time guys(:

 

[Naty1]

The_Duck: dooes this change your view at all?

http://en.wikipedia.org/wiki/Quantum_field_theory_in_curved_spacetime

I'm not suggesting it should, just wondering, because I see only hints of what you are saying there.


There seems to be a quantum theory of gravity for low energies:

[Someone else posted this this in another discussion in these forums, but I did not record which one.]

http://arxiv.org/PS_cache/gr-qc/pdf/9712/9712070v1.pdf

Perturbative Dynamics of Quantum General Relativity
John Donoghue, Department of Physics and Astronomy,
University of Massachusetts, Amherst, MA 01003 U.S.A.

“Since we only know that General Relativity is valid at low energy, the key requirement is that the quantum theory can be applied to gravity at present scales. What goes on beyond the Planck scale is a matter of speculation, but gravity and quantum mechanics had better go together at the scales where they are both valid. The good news is that the quantum theory of General Relativity at low energies exists and is well behaved. It is of the form of a type of field theory... Of course, the effective theory does not answer all the
interesting questions that we have about the ultimate theory...The outcome of this is that we need to stop spreading the falsehood that General Relativity and Quantum Mechanics are incompatible. They go together quite nicely at ordinary energies.

yet as far as I know the Standard Model of particle physics [using QFT] utilizes only flat spacetime...seems like the QFT there does not reflect gravity. I wonder why??.

 

[The_Duck]

The_Duck: dooes this change your view at all?

http://en.wikipedia.org/wiki/Quantum_field_theory_in_curved_spacetime

I'm not suggesting it should, just wondering, because I see only hints of what you are saying there.

The section "Approximation to quantum gravity" is saying just what I said above.