# B Bohmian Spacetime?

1. Feb 27, 2017

### mieral

If the world is really described by say Bohmian Mechanics or Objective Collapse. does it mean Spacetime is also objective or a substance in some way or absolutely no relationship between the quantum mechanism and spacetime? But then if no connection.. how can one have a wave function that is actual versus a spacetime that is just computations.. how do they couple to each other?

2. Feb 27, 2017

### Demystifier

It depends on quantum gravity, and we do not know what is the correct theory of quantum gravity. In the Bohmian interpretation of Wheeler-DeWitt equation (which is a candidate for quantum gravity), spacetime metric is objective.

3. Feb 27, 2017

### Daisyroots

May I ask what is intended by 'objective'? As I have it - and please correct me - matter equates to energy, which in turn equates to heat/movement, these latter indivisible. Is anybody able to say what it is that might get warm or move?

Last edited: Feb 27, 2017
4. Feb 27, 2017

### mieral

if spacetime metric is objective.. how do you deal with the diffeomorphism invariance.. or the Einstein hole argument of this realistic spacetime?

5. Feb 28, 2017

### Demystifier

Let me be more precise. First, only the space metric is objective. In this Bohmian theory of quantum gravity there is a preferred foliation of spacetime into space and time. Second, the space metric $g_{ij}$ is objective in the same sense in which metric in classical GR is objective. There is still a space diffeomorphism invariance.

6. Feb 28, 2017

### Daisyroots

Any takers for #3?

7. Feb 28, 2017

### A. Neumaier

hmmm, it is only a grossly simplified version of quantum gravity....

8. Feb 28, 2017

### Demystifier

Why do you think so?

9. Feb 28, 2017

### Demystifier

That's quite elementary and not really related to Bohmian mechanics and quantum gravity. So only a short answer: Matter is not equal to energy, energy is not equal to heat/movement, and being indivisible does not mean that it is not objective.

10. Feb 28, 2017

### A. Neumaier

Because it is not a relativistic field theory but an equation for the 3-dimensional spatial metric. Moreover, the quantum version is ill-defined.

11. Feb 28, 2017

### martinbn

That is unusual. In a quantum theory of gravity, where the quantum is based on Bohmian mechanics, there are preferred space and time. But in the classical limit there aren't. Some unification is achieved in the classical limit, isn't that the opposite of what usually happens? By the way what selects the preferred time coordinate?

12. Feb 28, 2017

### Daisyroots

Thanks. If we can say what matter is not, ie. as you say it is not (simply anyway) energy, can we say what it is?

13. Feb 28, 2017

### Demystifier

This is not unusual, especially if you read condensed-matter physics literature. In condensed matter, the "fundamental" theory is non-relativistic quantum mechanics of atoms. From this one can get various quantum and classical effective field theories, which are valid at distances much larger than the size of atom. For instance, the wave equation of sound is Lorentz invariant (with the velocity of sound instead of velocity of light).

In condensed matter, it is the frame in which the atoms are at rest. In Bohmian quantum gravity - nobody knows.

14. Feb 28, 2017

### Demystifier

There are several definitions of energy, one of them is eigenvalue of the Hamiltonian.

15. Feb 28, 2017

### Demystifier

It is ill-defined due to UV divergences, but it certainly doesn't make it "simplified". Concerning the claim that it is not relativistic, this is like claiming that quantum electrodynamics in Coulomb gauge is not relativistic because it is a theory for the 3-dimensional spatial vector potential.

16. Feb 28, 2017

### A. Neumaier

But the wave equation of sound corresponds to a classical effective field theory. Where is the quantum example?
The simplified referred to the cases (minisuperspaces) where one can make proper sense out of the equations.
No. In QED one can (and has to!) prove covariance of the quantum version in Coulomb gauge by exhibiting (in perturbation theory) an explicit set of operators generating the Poincare group. To do the same for the Wheeler-deWitt equations would require to exhibit (in perturbation theory) an explicit set of local operators generating the local Lorentz groups, and another set of operators generating the diffeomorphism group. I don't think anyone has done this.

17. Feb 28, 2017

### Demystifier

It's quantization gives phonons.

18. Feb 28, 2017

### Demystifier

The classical limit of WdW equation is Hamilton-Jacobi equation for GR, which is certainly consistent with standard formulation of GR. But you are probably right that in the quantum case there are additional problems. Loop quantum gravity (LQG) is a canonical quantization of gravity which is supposed to eliminate those problems, but for LQG it is not clear that it gives the right classical limit. Unfortunately, we do not longer have Marcus with us, who could say more.

19. Feb 28, 2017

### A. Neumaier

But the dispersion relation of phonons is not covariant.

20. Feb 28, 2017

### Demystifier

It is in the long distance limit (small $k$).