Does Bohmian Mechanics Redefine Our Understanding of Spacetime?

[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?

 

[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.

 

[Daisyroots]

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.

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?

 

[mieral]

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.

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

 

[Demystifier]

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

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.

 

[Daisyroots]

Any takers for #3?

 

[A. Neumaier]

Wheeler-DeWitt equation (which is a candidate for quantum gravity)

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

 

[Demystifier]

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

Why do you think so?

 

[Demystifier]

Any takers for #3?

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.

 

[A. Neumaier]

Why do you think so?

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

 

[martinbn]

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.

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?

 

[Daisyroots]

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.

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?

 

[Demystifier]

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?

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).

By the way what selects the preferred time coordinate?

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

 

[Demystifier]

energy, can we say what it is?

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

 

[Demystifier]

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

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.

 

[A. Neumaier]

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

But the wave equation of sound corresponds to a classical effective field theory. Where is the quantum example?

It is ill-defined due to UV divergences, but it certainly doesn't make it "simplified".

The simplified referred to the cases (minisuperspaces) where one can make proper sense out of the equations.

oncerning 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.

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.

 

[Demystifier]

But the wave equation of sound corresponds to a classical effective field theory.

It's quantization gives phonons.

 

[Demystifier]

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.

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.

 

[A. Neumaier]

It's quantization gives phonons.

But the dispersion relation of phonons is not covariant.

 

[Demystifier]

But the dispersion relation of phonons is not covariant.

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

 

[Daisyroots]

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

Demystifier, let's assume for a moment that one of the definitions proved correct, let's say for argument's sake your perhaps preferred and chosen 'eigenvalue of the Hamiltonian'. Would matter, in your view, then equate to its terms? Or is it simply a fact, period, that matter doesn't, as you said, equate to energy? Please, I'm just inquiring and trying to find out.

 

[Demystifier]

Demystifier, let's assume for a moment that one of the definitions proved correct, let's say for argument's sake your perhaps preferred and chosen 'eigenvalue of the Hamiltonian'. Would matter, in your view, then equate to its terms? Or is it simply a fact, period, that matter doesn't, as you said, equate to energy? Please, I'm just inquiring and trying to find out.

There are no correct and incorrect definitions. It's a matter of convenient choice. But according to the definition above, energy doesn't equate matter.

To make it relevant and non-trivial in the context of this thread, let me also add that WdW Hamiltonian is zero even matter is present.

 

[Daisyroots]

There are no correct and incorrect definitions. It's a matter of convenient choice. But according to the definition above, matter doesn't equate energy.

To make it relevant and non-trivial in the context of this thread, let me also add that WdW Hamiltonian is zero even matter is present.

Thanks, Demystifier, for bothering with such a 'Luddite' as I must present.

In the terms of such as myself, I suppose that what you say above, particular with regard to WdW Hamilton at zero, could be translated as: whether or not a wave function happens to have collapsed, there is still (and/or always is) 'something'(?). I'd appreciate a response to that but I'm way out of my depth so I'll leave it there anyway. But I remain very interested in the particulars and the implications of the OP question and might approach it from another direction.

 

[Ostrados]

But according to the definition above, matter doesn't equate energy.

Mass is a consequence of energy (ex1: gluon binding energy is responsible for 99% of proton mass) (ex2: Higgs field mechanism)

 

[Demystifier]

Mass is a consequence of energy (ex1: gluon binding energy is responsible for 99% of proton mass) (ex2: Higgs field mechanism)

I have edited the post you quoted.

 

[Daisyroots]

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?

Hi mieral. It seems to me that, given the circumstance of a collapsed wave function, whether it's an objective collapse or a collapse induced by measurement, sentience is required to objectify the resultant. Wouldn't you say that that, ie. the requisite sentience, is a connecting factor? The sentient being itself of course results from (or constitutes) collapsing wave functions, ie. it isn't as if it's separate from the unfolding events.

 

[mieral]

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.

I've been reading a lot about the Hole Argument. Wasn't it supposed to eliminate all possibility of spacetime metric being objective? For example. Refer to this:

https://en.wikipedia.org/wiki/Hole_argument

Einstein believed that the hole argument implies that the only meaningful definition of location and time is through matter. A point in spacetime is meaningless in itself, because the label which one gives to such a point is undetermined. Spacetime points only acquire their physical significance because matter is moving through them. In his words:

"All our spacetime verifications invariably amount to a determination of spacetime coincidences. If, for example, events consisted merely in the motion of material points, then ultimately nothing would be observable but the meeting of two or more of these points." (Einstein, 1916, p.117)
He considered this the deepest insight of general relativity. When asked by reporters to summarize his theory, he said:

"People before me believed that if all the matter in the universe were removed, only space and time would exist. My theory proves that space and time would disappear along with matter."[

 

[Demystifier]

I've been reading a lot about the Hole Argument. Wasn't it supposed to eliminate all possibility of spacetime metric being objective?

The objective thing is the equivalence class of all metrics related by a diffeomorphism. That's different from the claim that metric itself is objective, but not that much different. For instance, the distance between two nearby points is objective.

 

[mieral]

The objective thing is the equivalence class of all metrics related by a diffeomorphism. That's different from the claim that metric itself is objective, but not that much different. For instance, the distance between two nearby points is objective.

You mean even in a formulation of relativistic Bohmian Field Theory, time is like in Quantum Mechanics where time occurs in the background.. this is in contrast to QFT where time is the coordinate?

 

[Demystifier]

You mean even in a formulation of relativistic Bohmian Field Theory, time is like in Quantum Mechanics where time occurs in the background.. this is in contrast to QFT where time is the coordinate?

Yes, but this is not necessarily different from QFT. QFT can also be formulated in terms of a functional Schrodinger equation with a "background" time. See e.g. the book by Hatfield
https://www.amazon.com/dp/0201360799/?tag=pfamazon01-20

 

[mieral]

Yes, but this is not necessarily different from QFT. QFT can also be formulated in terms of a functional Schrodinger equation with a "background" time. See e.g. the book by Hatfield
https://www.amazon.com/dp/0201360799/?tag=pfamazon01-20

Cool book. You mean if gravity is not geometry in formulation of relativistic Bohmian field theory, it is a field or a force? But can you model a black hole using just a force or field? I thought the idea of force was outdated in GR.. but how could formulation of relativistic Bohmian field theory resurrect it?

 

[Demystifier]

You mean if gravity is not geometry in formulation of relativistic Bohmian field theory, it is a field or a force?

No, that's not what I mean.

 

[martinbn]

You mean if gravity is not geometry in formulation of relativistic Bohmian field theory, it is a field or a force?

Relativistic quantum field theory (Bohmian or not) doesn't have gravity.

 

[Demystifier]

Relativistic quantum field theory (Bohmian or not) doesn't have gravity.

Actually it does (in the sense of effective field theory), but it's just not renormalizable.

 

[martinbn]

Actually it does (in the sense of effective field theory), but it's just not renormalizable.

This is over my head. What I meant was that the spacetime used is Minkowski.

 

[A. Neumaier]

This is over my head. What I meant was that the spacetime used is Minkowski.

Quantum field theory can be defined in curved spacetime. There is a lot of work on this by Wald, Hollands, Fredenhagen.

 

[martinbn]

Quantum field theory can be defined in curved spacetime. There is a lot of work on this by Wald, Hollands, Fredenhagen.

Yes, but as far as I know, not in general. And when people say relativistic quantum field theory, they don't mean that. If they mean that, they say qft on curved spacetimes or something like that.

 

[A. Neumaier]

Yes, but as far as I know, not in general. And when people say relativistic quantum field theory, they don't mean that.

That's not true. They mean the quantization of a classical relativistic field theory. And the latter can take many forms, in flat spacetime, in curved spacetime, or even with dynamical gravity.

 

[mieral]

Yes, but this is not necessarily different from QFT. QFT can also be formulated in terms of a functional Schrodinger equation with a "background" time. See e.g. the book by Hatfield
https://www.amazon.com/dp/0201360799/?tag=pfamazon01-20

Oh by the way. How about in General Bohmian Relativity (counterpart of General Relativity).. can time be background too like you said above "QFT can also be formulated in terms of a functional Schrodinger equation with a "background" time".. but if time is a background.. can it become curved spacetime? I thought spacetime only occur when time is a coordinate especially in General Relativity. I am still trying to understand how time is in background (meaning Euclidian and not even Minkowski) yet spacetime can curve (producing GR)?? You are implying Euclidian spacetime can curve producing gravity?? Is this even possible? Let's sort out all this. Thanks.

 

[Demystifier]

Oh by the way. How about in General Bohmian Relativity (counterpart of General Relativity).. can time be background too like you said above "QFT can also be formulated in terms of a functional Schrodinger equation with a "background" time".. but if time is a background.. can it become curved spacetime? I thought spacetime only occur when time is a coordinate especially in General Relativity. I am still trying to understand how time is in background (meaning Euclidian and not even Minkowski) yet spacetime can curve (producing GR)?? You are implying Euclidian spacetime can curve producing gravity?? Is this even possible? Let's sort out all this. Thanks.

In GR coordinates can always be chosen such that all curvature is only in space, not in spacetime. Canonical formulation of GR is based on this fact.

 

[PeterDonis]

coordinates can always be chosen such that all curvature is only in space, not in spacetime

Can you be more specific about what this means, mathematically? As you state it it seems to be saying that every spacetime must have a timelike Killing vector field, which is obviously false.

 

[Daisyroots]

To make it relevant and non-trivial in the context of this thread, let me also add that WdW Hamiltonian is zero even matter is present.

Dear Demystifier, may I please ask, did you intend the latter part of this statement (from your #22) to read: 'that even when WdW Hamiltonian is zero matter is present'. It's just that I can't make sense of it with the wording as it stands. But that may be down to me not having the requisite understanding.

 

[Demystifier]

Can you be more specific about what this means, mathematically? As you state it it seems to be saying that every spacetime must have a timelike Killing vector field, which is obviously false.

I was talking in non-technical language, because I assumed that otherwise OP would not understand me. What I really meant is that there are always coordinates (called Gaussian normal coordinates) such that
$$ds^2=-dt^2 + g_{ij}dx^idx^j$$
https://www.physicsforums.com/threads/gaussian-normal-coordinates.149978/

 

[Demystifier]

Dear Demystifier, may I please ask, did you intend the latter part of this statement (from your #22) to read: 'that even when WdW Hamiltonian is zero matter is present'. It's just that I can't make sense of it with the wording as it stands. But that may be down to me not having the requisite understanding.

See
https://en.wikipedia.org/wiki/Hamiltonian_constraint

 

[mieral]

I was talking in non-technical language, because I assumed that otherwise OP would not understand me. What I really meant is that there are always coordinates (called Gaussian normal coordinates) such that
$$ds^2=-dt^2 + g_{ij}dx^idx^j$$
https://www.physicsforums.com/threads/gaussian-normal-coordinates.149978/

I know Euclidian space + time is not equal to Einstein Spacetime. So in Bohmian Mechanics.. no matter how you foliate space and time.. it is still Spacetime and not Euclidian space+time, Right? In Roderich Tumulka formulaton of Bohmian Mechanics gravity in the following. He is using Spacetime even when he foliate time and space. May you share your gravity paper so I can know if yours is based on Euclidean space + time (is this still possible)?

http://www.perimeterinstitute.ca/videos/incorporating-gravity-bohmian-mechanics-new-approach

 

[Demystifier]

So in Bohmian Mechanics.. no matter how you foliate space and time.. it is still Spacetime and not Euclidian space+time, Right?

Right.

May you share your gravity paper so I can know if yours is based on Euclidean space + time (is this still possible)?

In this thread I was not talking about my paper. I was talking about this paper
https://arxiv.org/abs/gr-qc/0311076
and references therein.

If you want my paper on Bohmian gravity, then see
https://arxiv.org/abs/hep-th/0407228

Both papers have a non-Euclidean space.

 

[mieral]

Right.In this thread I was not talking about my paper. I was talking about this paper
https://arxiv.org/abs/gr-qc/0311076
and references therein.

If you want my paper on Bohmian gravity, then see
https://arxiv.org/abs/hep-th/0407228

Both papers have a non-Euclidean space.

Thanks. If Einstein, Schroedinger, Heisenberg, Dirac were not born and and Bohm was born earlier and all quantum physicists were all Bohmians, I wonder what path they would take to develop a theory of gravity that didn't involve Einstein Field Equations or path to QFT without Minkowski. Any papers on this alternative history appreciated. Thank you.

 

[Demystifier]

Thanks. If Einstein, Schroedinger, Heisenberg, Dirac were not born and and Bohm was born earlier and all quantum physicists were all Bohmians, I wonder what path they would take to develop a theory of gravity that didn't involve Einstein Field Equations or path to QFT without Minkowski. Any papers on this alternative history appreciated. Thank you.

Hahaha!
I think Bohm was fine with Einstein field equations for classical gravity. Concerning quantum gravity, I think there would be no consensus.

My current belief is that quantization of gravity is like quantization of sound. You can introduce phonons/gravitons as quantum quasiparticles, but fundamentally they emerge from quantization of totally different degrees of freedom.

 

[mieral]

Hahaha!
I think Bohm was fine with Einstein field equations for classical gravity. Concerning quantum gravity, I think there would be no consensus.

My current belief is that quantization of gravity is like quantization of sound. You can introduce phonons/gravitons as quantum quasiparticles, but fundamentally they emerge from quantization of totally different degrees of freedom.

Anyway. If say Spacetime suddenly disappear.. would matter still have molecules intact.. or would some properties be lost.. for example.. time is part of coordinate in QFT. Without spacetime, could there still be QFT? What is the answer to this question in orthodox QM and Bohmian Mechanics.. thanks..

 

[Demystifier]

If say Spacetime suddenly disappear..

I don't even know what that means.