Exploring the Relationship Between Bohmian Mechanics and Spacetime

[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.

 

[mieral]

I don't even know what that means.

I mean in your room or around objects, if spacetime suddenly vanished.. and there was no minkowski or lorentzian metric.. what would happen to matter.. don't the atoms use any metric to define its place or position.. but atoms don't have time (time is symmetric) and quantum has no position.. remember Mach asked something along this line too although pre-Einstein

 

[PeterDonis]

What I really meant is that there are always coordinates (called Gaussian normal coordinates) such that

$$
ds^2 = - dt^2 + g_{ij} dx^i dx^j
$$

Ok, that makes it clearer. I'm not sure that "the curvature is all in space, not in spacetime" is an apt ordinary language description of this, though.

First, spacetime is curved in the cases under discussion, so the contrast should be between "curvature in space" and "curvature in time" (though that has issues too, see below).

Second, there are spacetimes which are curved but in which $g_{ij} = \delta_{ij}$ in these coordinates, i.e., space is flat (the critical density matter-dominated FRW universe is one such case). Such cases are sometimes described as having "the curvature all in time", but that can be misleading as well. This is one of those cases where there really isn't a good way of describing what you're saying in ordinary language.

 

[PeterDonis]

If say Spacetime suddenly disappear

It is pointless to pose hypotheticals that violate the laws of physics.

 

[Demystifier]

I mean in your room or around objects, if spacetime suddenly vanished.. and there was no minkowski or lorentzian metric.. what would happen to matter.. don't the atoms use any metric to define its place or position.. but atoms don't have time (time is symmetric) and quantum has no position.. remember Mach asked something along this line too although pre-Einstein

What do you mean "there was no minkowski or lorentzian metric"? Do you mean $g_{\mu\nu}=0$?

 

[Demystifier]

It is pointless to pose hypotheticals that violate the laws of physics.

By that argument, in 19th century one might argue that it is pointless to study curved spacetime.

One can always study exotics mathematically, and you never know whether it can lead to new physics which might be valid in some extreme conditions, like distances smaller than Planck length.

 

[mieral]

What do you mean "there was no minkowski or lorentzian metric"? Do you mean $g_{\mu\nu}=0$?

Yup. Or is QFT forever tied with spacetime because Dirac use spacetime to create QFT... But then wheeler said.. "Spacetime tells matter how to move; matter tells spacetime how to curve".. as if they could be independent.. so maybe without spacetime.. matter doesn't move?

 

[martinbn]

It is pointless to pose hypotheticals that violate the laws of physics.

One can always study it mathematically, and you never know whether it can lead to new physics which might be valid in some extreme conditions, like distances smaller than Planck length.

Yes, but in this case the question, as formulated, not only violates the laws of physics, it is also meaningless.

 

[Demystifier]

Yup. Or is QFT forever tied with spacetime because Dirac use spacetime to create QFT... But then wheeler said.. "Spacetime tells matter how to move; matter tells spacetime how to curve".. as if they could be independent.. so maybe without spacetime.. matter doesn't move?

Yes, by keeping everything else the same and putting $g_{\mu\nu}=0$, one would obtain that nothing changes with time and nothing depends on the position in space.

 

[mieral]

Yes, but in this case the question, as formulated, not only violates the laws of physics, it is also meaningless.

Just clarying what Mach and Wheeler said (see above).

 

[mieral]

Yes, by keeping everything else the same and putting $g_{\mu\nu}=0$, one would obtain that nothing changes with time and nothing depends on the position in space.

So what would happen to matter like a piece of coin.. would it just dissolve into a blob or would become like the Dewitt Wheeler Equation where time stand still (and matter too).

But I'm asking because I read matter itself created spacetime.. called emergent gravity.. so I guess this is a trek to beyond the standard model thread now..

 

[Demystifier]

Yes, but in this case the question, as formulated, not only violates the laws of physics, it is also meaningless.

Why do you think it's meaningless? Take for example Chern-Simons action that does not depend on spacetime metric.

 

[Demystifier]

But I'm asking because I read matter itself created spacetime

That's not really true. Minkowski spacetime does not need matter to exist. In this sense, Mach principle is wrong.

 

[mieral]

That's not really true. Minkowski spacetime does not need matter to exist. In this sense, Mach principle is wrong.

That's why I mentioned this is follow up to Mach question... Does Lorentzian spacetime (GR) need matter to exist? Wonder what a post-GR Mach would comment on this. But in Loop Quantum Gravity.. matter made up spacetime.. so here can we say Minkowski spacetime does not need matter to exist?

 

[PeterDonis]

in Loop Quantum Gravity.. matter made up spacetime

Where are you getting that from?

 

[Demystifier]

Does Lorentzian spacetime (GR) need matter to exist?

No.

But in Loop Quantum Gravity.. matter made up spacetime..

No it didn't.

Matter only tells spacetime how to curve.

 

[martinbn]

Why do you think it's meaningless? Take for example Chern-Simons action that does not depend on spacetime metric.

But the question wasn't "What if the description of nature doesn't need the notion of spacetime or metric?". It was what if they disappear.

 

[PeterDonis]

Take for example Chern-Simons action that does not depend on spacetime metric.

The action doesn't, but what happens when you do the path integral?

 

[Ostrados]

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..

Maybe you will get singularity (pre big bang state).

 

[PeterDonis]

Maybe you will get singularity (pre big bang state).

"Singularity", as has been pointed out in a number of recent threads, is just shorthand for "our models break down at this point and we don't know what actually happens". So this isn't a possible way things could have been before the big bang; it's just a recognition of the limits of our current knowledge.

 

[Ostrados]

"Singularity", as has been pointed out in a number of recent threads, is just shorthand for "our models break down at this point and we don't know what actually happens". So this isn't a possible way things could have been before the big bang; it's just a recognition of the limits of our current knowledge.

I thought about it this way: if we remove spacetime then the distance between all particles will become zero and thus matter will be crushed and condensed in an infinitesimal point (singularity)