Question about GR and Quantum gravity

[Ostrados]

First I don't have extensive knowledge about gravity beyond General Relativity, so please forgive my ignorance about this subject. I have confusion about the relation between GR and QM and I just want a general picture so that I can connect the dots.

My questions:
1- Why do we need quantum gravity? and why GR gravity does not work with QM?

2- In GR gravity is just curvature in spacetime it is not a force. So why do we need to quantize gravity if it is not a field? and why the graviton is proposed? doesn't that contradict with GR?

3- The microscopic world is dominated by forces much stronger that gravity, and gravity is already very week at such small scale, so why do we care about gravity at the quantum level?

Thanks,

 

[PeterDonis]

Why do we need quantum gravity? and why GR gravity does not work with QM?

Quantum field theory can be formulated in curved spacetime, so in that sense GR and QM can "work" together. The problem is that such a theory cannot be fundamental; it must be an approximation to some deeper theory. The reason, heuristically, is that, according to QM, if a system has different possible configurations, there should be an amplitude for it to be in each of them. But GR doesn't work like that: it doesn't say there are amplitudes for different possible spacetime geometries, stress-energy tensors, etc. It says there is only one spacetime geometry, stress-energy tensor, etc.--i.e., only one configuration for the system. (This is true of any classical, i.e., non-quantum, theory.)

So any situation in which quantum effects could create different possible spacetime geometries, stress-energy tensors, etc., with amplitudes for each, cannot be properly modeled using GR. But such situations should occur whenever any significant quantity of mass or energy is subjected to quantum superposition. A typical such situation is determining how a mass moves by some quantum process, such as the decay of a radioactive atom.

In GR gravity is just curvature in spacetime it is not a force. So why do we need to quantize gravity if it is not a field? and why the graviton is proposed? doesn't that contradict with GR?

Saying that gravity is "not a force" in the sense of Newtonian physics (but instead is spacetime geometry) is not the same as saying that gravity is not an "interaction" in the sense of quantum field theory. The latter statement could very well be true; and in fact, the simplest approach to quantum gravity is to assume it is true, and to model gravity at the fundamental level using a massless, spin-2 quantum field, for which the "graviton" is the corresponding particle excitation. It was shown in the 1960s and 1970s that the classical limit of such a theory is in fact GR itself--i.e., that the classical limit of the field equation satisfied by such a quantum field is in fact the Einstein Field Equation of GR. So such a theory of quantum gravity is perfectly consistent with GR.

The problem with this theory of quantum gravity is that it is not renormalizable, which basically means that it is not expected to be a complete theory by itself. There should be extra terms in the theory describing extra interactions which only occur at extremely high energies, and which we have no way of probing experimentally. In fact we have no way of even probing the quantum nature of the spin-2 field itself experimentally, since such quantum aspects are not expected to become significant until we reach length scales on the order of the Planck length, some 20 orders of magnitude smaller than the smallest length scales we can currently probe.

The microscopic world is dominated by forces much stronger that gravity, and gravity is already very week at such small scale, so why do we care about gravity at the quantum level?

We don't in any practical sense; as I noted above, the quantum aspects of gravity are much too small for us to probe now or in the foreseeable future. We care because we know, for the reasons given above, that our current theories are not complete, and we would like to try to find more complete theories.

 

[Comeback City]

Quantum field theory can be formulated in curved spacetime, so in that sense GR and QM can "work" together. The problem is that such a theory cannot be fundamental; it must be an approximation to some deeper theory. The reason, heuristically, is that, according to QM, if a system has different possible configurations, there should be an amplitude for it to be in each of them. But GR doesn't work like that: it doesn't say there are amplitudes for different possible spacetime geometries, stress-energy tensors, etc. It says there is only one spacetime geometry, stress-energy tensor, etc.--i.e., only one configuration for the system. (This is true of any classical, i.e., non-quantum, theory.)

So any situation in which quantum effects could create different possible spacetime geometries, stress-energy tensors, etc., with amplitudes for each, cannot be properly modeled using GR. But such situations should occur whenever any significant quantity of mass or energy is subjected to quantum superposition. A typical such situation is determining how a mass moves by some quantum process, such as the decay of a radioactive atom.
Saying that gravity is "not a force" in the sense of Newtonian physics (but instead is spacetime geometry) is not the same as saying that gravity is not an "interaction" in the sense of quantum field theory. The latter statement could very well be true; and in fact, the simplest approach to quantum gravity is to assume it is true, and to model gravity at the fundamental level using a massless, spin-2 quantum field, for which the "graviton" is the corresponding particle excitation. It was shown in the 1960s and 1970s that the classical limit of such a theory is in fact GR itself--i.e., that the classical limit of the field equation satisfied by such a quantum field is in fact the Einstein Field Equation of GR. So such a theory of quantum gravity is perfectly consistent with GR.

The problem with this theory of quantum gravity is that it is not renormalizable, which basically means that it is not expected to be a complete theory by itself. There should be extra terms in the theory describing extra interactions which only occur at extremely high energies, and which we have no way of probing experimentally. In fact we have no way of even probing the quantum nature of the spin-2 field itself experimentally, since such quantum aspects are not expected to become significant until we reach length scales on the order of the Planck length, some 20 orders of magnitude smaller than the smallest length scales we can currently probe.
We don't in any practical sense; as I noted above, the quantum aspects of gravity are much too small for us to probe now or in the foreseeable future. We care because we know, for the reasons given above, that our current theories are not complete, and we would like to try to find more complete theories.

Just a follow-up question I have to build off of this topic:
Would a quantum gravity theory still predict that mass bends spacetime? I'm not sure if mass curving spacetime is something that is already excepted as true without doubt, or simply accepted because general relativity predicts it and is our current best theory of gravity, but does quantum gravity require mass to curve spacetime?

 

[PeterDonis]

Would a quantum gravity theory still predict that mass bends spacetime?

It would say that this is a low energy approximation to the underlying theory.

 

[Comeback City]

It would say that this is a low energy approximation to the underlying theory.

Could you explain what you mean by "low energy approximation"? I'm unfamiliar with that term.

 

[PeterDonis]

Could you explain what you mean by "low energy approximation"?

It means roughly that, if the average energy per particle is low enough, the physics that is present in the underlying theory (quantum gravity in this case) happens too rarely to observe, and the effective physics is limited to that in the approximate theory (GR in this case).

 

[Ostrados]

@PeterDonis Thanks for the detailed answer.

So any situation in which quantum effects could create different possible spacetime geometries, stress-energy tensors, etc., with amplitudes for each, cannot be properly modeled using GR. But such situations should occur whenever any significant quantity of mass or energy is subjected to quantum superposition. A typical such situation is determining how a mass moves by some quantum process, such as the decay of a radioactive atom.

Regarding superposition: let's say we have a particle in superposition in multiple places, then it's gravity effect will also be in superposition too? For example in double slit experiment will we get something analogues to interference pattern in the gravity field?

 

[PeterDonis]

lets say we have a particle in superposition in multiple places, then it's gravity effect will also be in superposition too?

That is what our understanding of QM would tell us, yes. But GR cannot model this; that's the issue.