Is a Spin 2 Particle the Key to Understanding Gravitation in Quantum Mechanics?

[Omega0]

I have some questions regarding the expected exchange particles for gravitation.
From my understanding the following was valid:

• We can linearize the equations of GTR for weak fields
• "Quantum mechanics" (Schrödinger, Dirac equations) are linear
• Those linear equations allow eigenstates and eigenvalues
• If we take the linearized equations of GTR we expect a tensor wave, not a dipole
• This fits to a spin 2 particle for the exchange (TT gauge)
• A strongly non-linear Hamiltonian operator like the square root, does not produce an eigensystem

Please let me know if the points above are so far correct.
From a popular scientific book written by a physicist I learned short ago that Feynman tried to derive GTR from the assumption of a spin 2 particle. Here is hopefully the correct material: Feynman Quantum theory of gravitation - UMass Blogs
What I remember from my QFT lessons is that GTR appears to be not renormizable which also Feynman needed to agree with in the discussion above.

My main question is:

How should we know that we have a spin 2 exchange particle for a quantum mechanical description which is not even given as a theory?

I hope I formulated it right, thanks.

 

[Vanadium 50]

I'm not sure what GRT is supposed to be - General Relativity Today? But in any event if you want a quantum theory of gravity to map on to GR at large scales, it needs to couple to the same thing that GR does: the stress-energy tensor. The minimum spin that can do that is 2.

 

[Omega0]

I'm not sure what GRT is supposed to be - General Relativity Today? But in any event if you want a quantum theory of gravity to map on to GR at large scales, it needs to couple to the same thing that GR does: the stress-energy tensor. The minimum spin that can do that is 2.

I changed it to GTR, you are right. In Germany we write ART, this is where the confusion came from. Sorry.

 

[PeterDonis]

How should we know that we have a spin 2 exchange particle for a quantum mechanical description which is not even given as a theory?

You are incorrect; it is given as a theory. The quantum field theory of a massless spin-2 field was worked out in the 1960s and early 1970s by Feynman, Deser, and many others. Its properties, which include the fact that the field equation for this field is the Einstein Field Equation, and therefore the classical limit of this QFT is General Relativity, have been known since those efforts were completed.

 

[PeterDonis]

A good overview of the QFT I described in post #4 is this paper by Deser, which was published in 1970 but which was reprinted and posted to arxiv.org (if only all of the classic historical papers in physics were treated this way):

https://arxiv.org/abs/gr-qc/0411023

 

[PeterDonis]

Here is hopefully the correct material: Feynman Quantum theory of gravitation - UMass Blogs

This is an early paper in the course of the theoretical work I described in post #4.

What I remember from my QFT lessons is that GTR appears to be not renormizable

That's correct. The simplest way to see that is to note that the coupling constant in the theory, which is Newton's gravitational constant (the exact value depends on your choice of units), is not dimensionless; in "natural" units of QFT, in which $\hbar = c = 1$, it has dimensions of (IIRC) inverse length squared. That makes the QFT non-renormalizable by simple power counting arguments.

 

[PeterDonis]

We can linearize the equations of GTR for weak fields

Yes, but doing that leaves out all of the phenomena of gravity other than weak gravitational waves in a flat background spacetime. Which isn't very much to have left.

"Quantum mechanics" (Schrödinger, Dirac equations) are linear

The non-relativistic versions are. However, when we incorporate relativity, we have to use quantum field theory, and for a QFT to be linear, the field must have no self-interaction. That is true of the Maxwell field (i.e., the photon field--the quantum electromagnetic field), but it isn't true of the Einstein field (i.e., the graviton--the quantum gravitational field, in the spin-2 QFT I described in post #4). (It also isn't true of Yang-Mills fields in general; in fact, the Maxwell field is the only commonly used QFT that is linear.)

Those linear equations allow eigenstates and eigenvalues

This isn't really relevant; you can still do things like scattering theory and searching for non-perturbative solutions in a nonlinear QFT.

If we take the linearized equations of GTR we expect a tensor wave, not a dipole

I would say "quadrupole" instead of "tensor"--or, alternatively, you could say "vector" instead of "dipole". Or you could just say "spin-2" and "spin-1", as you note:

This fits to a spin 2 particle for the exchange (TT gauge)

Yes. See above.

A strongly non-linear Hamiltonian operator like the square root, does not produce an eigensystem

While a square root does appear in the simplest relativistic Lagrangian for a single point particle, that isn't really relevant to the spin-2 QFT I described in post #4. The Lagrangian for that QFT is simply the Einstein-Hilbert Lagrangian, which has no square root.

 

[Demystifier]

What I remember from my QFT lessons is that GTR appears to be not renormizable which also Feynman needed to agree with in the discussion above.

My main question is:

How should we know that we have a spin 2 exchange particle for a quantum mechanical description which is not even given as a theory?

The theory does not need to be renormalizable in order to be given as a theory. A non-renormalizable theory can still be used as an effective theory, applicable at low energies.

 

[Omega0]

The theory does not need to be renormalizable in order to be given as a theory. A non-renormalizable theory can still be used as an effective theory, applicable at low energies.

True, but if the theory is non-renormizable it can never be used at high energies, or in other words: It does not describe gravitation correctly.
Right?

 

[malawi_glenn]

True, but if the theory is non-renormizable it can never be used at high energies, or in other words: It does not describe gravitation correctly.
Right?

What does even "correctly" mean?

All QFT's (of point particles) are today seen as some effective theory at some point. It all boils down to at what energy scales you are interested in and what accuracy you demand.

 

[PeterDonis]

f the theory is non-renormizable it can never be used at high energies

In principle this is true, but what "high energies" means can vary greatly with the theory. In the case of the QFT of a massless spin-2 field, "high energies" means Planck scale energies. In other words, energies many orders of magnitude higher than we can either observe anywhere in our universe or create in experiments ourselves, now and for the foreseeable future.

in other words: It does not describe gravitation correctly.

More precisely, it cannot be a correct fundamental theory of gravity at the energy scales where the non-renormalizability becomes significant. As above, that is the Planck scale for the spin-2 QFT for gravity. So the theory can't be the correct description of gravity at that scale. But that does not in any way prevent it from being a very accurate description of gravity at lower energy scales--like all of the energy scales we have ever observed or will be able to observe for the foreseeable future.

 

[LCSphysicist]

I have some questions regarding the expected exchange particles for gravitation.
From my understanding the following was valid:

• We can linearize the equations of GTR for weak fields
• "Quantum mechanics" (Schrödinger, Dirac equations) are linear
• Those linear equations allow eigenstates and eigenvalues
• If we take the linearized equations of GTR we expect a tensor wave, not a dipole
• This fits to a spin 2 particle for the exchange (TT gauge)
• A strongly non-linear Hamiltonian operator like the square root, does not produce an eigensystem

Please let me know if the points above are so far correct.
From a popular scientific book written by a physicist I learned short ago that Feynman tried to derive GTR from the assumption of a spin 2 particle. Here is hopefully the correct material: Feynman Quantum theory of gravitation - UMass Blogs
What I remember from my QFT lessons is that GTR appears to be not renormizable which also Feynman needed to agree with in the discussion above.

My main question is:

How should we know that we have a spin 2 exchange particle for a quantum mechanical description which is not even given as a theory?

I hope I formulated it right, thanks.

I think it is cool to mention that, while seen as a particle, the graviton indeed provides non-renormalizable results. But, if avaliated as a string excitation, and then the Feynman diagrams being smooth 2-dimensional surfaces, there are no ultraviolet divergences at all.

 

[PeterDonis]

f avaliated as a string excitation, and then the Feynman diagrams being smooth 2-dimensional surfaces, there are no ultraviolet divergences at all.

Yes, this has always been one of the big selling points of string theory, that it gives a nice simple underlying model that leads to the ordinary QFT of a massless spin-2 field as an effective theory for energies below the Planck scale. Unfortunately, string theory has not produced any testable predictions that would help us to evaluate whether this underlying model is actually true.

 

[malawi_glenn]

this underlying model is actually true

I know that you know that "true" is the wrong word here. Models can never give us the truth about nature.

 

[PeterDonis]

I know that you know that "true" is the wrong word here. Models can never give us the truth about nature.

If you like, read "makes accurate predictions" instead of "true".

 

[Omega0]

If you like, read "makes accurate predictions" instead of "true".

Which accurate prediction has been measured to be true so far?

 

[PeterDonis]

Which accurate prediction has been measured to be true so far?

What I was saying in post #13, with the substitution I described in post #15, is that string theory has made no accurate predictions--because it has made no testable predictions, period. More precisely, it has made no testable predictions that are not also predictions of current theories, so it gives no way of distinguishing it from those theories.

 

[Omega0]

What I was saying in post #13, with the substitution I described in post #15, is that string theory has made no accurate predictions--because it has made no testable predictions, period. More precisely, it has made no testable predictions that are not also predictions of current theories, so it gives no way of distinguishing it from those theories.

Oh, sorry about the confusion. I wanted to ask: What are the accurate predictions of the Feynman quantum gravity which have been measured so far?

 

[PeterDonis]

I wanted to ask: What are the accurate predictions of the Feynman quantum relativity which have been measured so far?

There aren't any. We have no experimental evidence at all about any quantum aspects of gravity. Nor do we have any expectation of getting any any time soon, since such aspects are not expected to be significant except at the Planck scale. All we know experimentally is that the classical limit of this theory, namely General Relativity, is an accurate description of gravity at all of the scales we can probe.

 

[Omega0]

There aren't any. We have no experimental evidence at all about any quantum aspects of gravity. Nor do we have any expectation of getting any any time soon, since such aspects are not expected to be significant except at the Planck scale.

Would you say that there is another predictive theory avoiding problems at the Planck scale?

 

[PeterDonis]

Would you say that there is another predictive theory avoiding problems at the Planck scale?

I don't know of any predictive theory that covers the Planck scale. All we have are various speculations about quantum gravity (string theory and loop quantum gravity seem to be the two main contenders right now), none of which make any testable predictions.

 

[dextercioby]

I will ask a question somewhat related to the topic. In what way does the analogy (classical) em. waves > photons vs. (classical) gravitational waves > gravitons is true or fails, and a subsequent (equivalent) question: if measurements on em. waves can be seen as probing the collective behavior of photons, can't we interpret recent experimental findings on gravitational waves as probing the collective behavior of gravitons?

 

[Omega0]

can be seen as probing the collective behavior of photons, can't we interpret recent experimental findings on gravitational waves as probing the collective behavior of gravitons?

Isn't this the picture Schrödinger tried to establish, before the Copenhagen picture was accepted? Now in the gravitation world? Why shouldn't we say that we have a pure wave effect where gravitons doesn't play a role?
I think we shouldn't go to the past to save the picture of a wave build by particles.

 

[vanhees71]

I will ask a question somewhat related to the topic. In what way does the analogy (classical) em. waves > photons vs. (classical) gravitational waves > gravitons is true or fails, and a subsequent (equivalent) question: if measurements on em. waves can be seen as probing the collective behavior of photons, can't we interpret recent experimental findings on gravitational waves as probing the collective behavior of gravitons?

It can not! Take the classical limit, i.e., high-intensity states of the em. field. In QED these are described by coherent states and not by "collective behavior of photons".

If there were some quantum-field theory of gravitation in the same sense as for QED, the classical limit were gravitational waves, on the quantum level described by corresponding coherent states rather than "collective behavior of gravitons". Indeed for a few years we can observe classical gravitational waves, but I don't know of any empirical evidence for any quantum behavior.

 

[Omega0]

It can not! Take the classical limit, i.e., high-intensity states of the em. field. In QED these are described by coherent states and not by "collective behavior of photons".

Exactly! Which is the "Copenhagen outcome". Why shouldn't it be different for a QM of gravity? I believe, it should be the same.

 

[vanhees71]

We do not have "a QM of gravity". For sure, it's not QM anyway, because we want a relativistic description. I've also no clue, what this has to do with any of the zillions of unclearly defined Copenhagen interpretations. I'm also pretty sure that the question about a quantum theory of the gravitational interaction won't in any way be solved by any philosophy or metaphysics but by an ingenious mathematica insight by some theorist. The biggest problem is the lack of any empirical evidence for quantum phenomena of gravity.

 

[LittleSchwinger]

If there were some quantum-field theory of gravitation in the same sense as for QED, the classical limit were gravitational waves, on the quantum level described by corresponding coherent states rather than "collective behavior of gravitons". Indeed for a few years we can observe classical gravitational waves, but I don't know of any empirical evidence for any quantum behavior.

In String theory for example, if we have a background spacetime with metric $\eta$ then any other classical metric $g$ is generated from coherent states of spin-2 excitations upon this background.