Does Bohmian Mechanics Redefine Our Understanding of Spacetime?

[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)

 

[PeterDonis]

if we remove spacetime then the distance between all particles will become zero

No, the concept of "distance between particles" will be meaningless. Zero is not meaningless; it's a definite value, and requires a spacetime metric.

 

[Ostrados]

No, the concept of "distance between particles" will be meaningless. Zero is not meaningless; it's a definite value, and requires a spacetime metric.

Ok it will be Null. Better?

 

[PeterDonis]

it will be Null

What does "Null" mean? If it means "meaningless", then yes, the distance between particles will be "Null" (meaningless). But it seems like a roundabout way to say it, since "Null" is ambiguous in this context while "meaningless" is not.

If "Null" means "zero", then no. But I already told you that. So I still don't see the point.

 

[Demystifier]

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.

Is your point that it is not defined what does it mean to "disappear"? I think it can be well defined. This is a metric $g_{\mu\nu}(t,{\bf x})$ with the property that it is non-zero for $t<t_0$ and zero for $t\geq t_0$, which means that the metric disappears at $t=t_0$.

 

[Demystifier]

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

I don't think that spacetime metric appears in the path integral with topological action.

 

[martinbn]

Is your point that it is not defined what does it mean to "disappear"? I think it can be well defined. This is a metric $g_{\mu\nu}(t,{\bf x})$ with the property that it is non-zero for $t<t_0$ and zero for $t\geq t_0$, which means that the metric disappears at $t=t_0$.

I don't see how becoming zero is the same as disappearing. But if that's what he meant, that's what he should have said. I am convinced it is not what he meant. He talked about the spacetime suddenly disappearing. You also said you had no idea what that meant.

 

[Demystifier]

I don't see how becoming zero is the same as disappearing. But if that's what he meant, that's what he should have said. I am convinced it is not what he meant. He talked about the spacetime suddenly disappearing. You also said you had no idea what that meant.

Initially I had no idea what that meant, but later (post #56) it was clarified.

Anyway, to understand a layman one must make himself think like a layman.

 

[PeterDonis]

I don't think that spacetime metric appears in the path integral with topological action.

Isn't the path integral $\int d^4 x \sqrt{-g} e^{iS}$ in a general curved spacetime? (Without the factor of $\sqrt{-g}$ the integrand is not diffeomorphism invariant.)

 

[Demystifier]

Isn't the path integral $\int d^4 x \sqrt{-g} e^{iS}$ in a general curved spacetime?

No it isn't. Even in Minkowski spacetime, the path integral is not $\int d^4 x e^{iS}$. I guess you should refresh your knowledge about path integrals in QM and QFT.

 

[PeterDonis]

I guess you should refresh your knowledge about path integrals in QM and QFT.

Can you recommend a reference?

 

[vanhees71]

My QFT manuscript contains some basics about path integrals. The introductory chapter is about path-integrals in non-relativistic QT. The QFT case is in Sect. 4.5.

http://th.physik.uni-frankfurt.de/~hees/publ/lect.pdf

 

[Demystifier]

Can you recommend a reference?

I would recommend Ryder
https://www.amazon.com/dp/0521478146/?tag=pfamazon01-20
because it derives in detail the path integral formulation for both QM and QFT.

 

[PeterDonis]

I would recommend Ryder

Thanks!

 

[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?

Hello, I posted the following at #26 without response:

"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."

I have reflected since on whether in fact sentience (consciousness, or what ever you want to call it) might indeed necessarily be a consequence of collapse or whether it might, in fact, be essentially inherent in the wave function. In other words whether it might not actually be a constituent part of the universe, which yet the world of physics (it seems to me) attempts all the time to leave out, ignore, and/or disregard. Despite that experiments such as the Double Slit evidence that sentience plays an independently hugely significant roll in the world, still the discipline of physics seems uncomfortable with its inclusion in considerations. How is anybody ever going to get anywhere (in real terms) if we are happy to pretend that major factors don't exist?

 

[PeterDonis]

I posted the following at #26 without response

You probably did not get a response because your statement basically amounts to either a personal theory or non-mainstream physics, neither of which are suitable topics of discussion here. The mainstream position, as I understand it, is that "sentience" is a physical process, and can in principle be described in terms of the same fundamental constituents as any other physical process. We don't currently know how to do that in detail, but the same is true for many macroscopic physical processes.

experiments such as the Double Slit evidence that sentience plays an independently hugely significant roll in the world

No, they don't. Measurements are physical processes, and now that we understand decoherence, we understand that those processes are going on all the time, whether there is sentience present or not. Measurements do not require sentient observers, and claims that they do, which were made by many early researchers into QM, are simply outdated.