Spin and polarizations in momentum space

[Azurite]

What does it mean for "reality" to have a particular "dimension"?

In the sense of the extra large dimensions and compactified small dimensions of for example string theory. Is the 3N configuration space of quantum mechanics saying that the larger dimensions is equal to the 3N configuration space of QM?

 

[PeterDonis]

In the sense of the extra large dimensions and compactified small dimensions of string theory.

Ok, then those are spacetime dimensions, so they're not the same as the dimensions of QM configuration space. But we don't have any way of knowing which, if either, is the "dimensions" of "reality". We don't even know if that makes sense.

 

[PeterDonis]

the 3N configuration space of quantum mechanics

It's also worth nothing that this "3N configuration space" is for a non-relativistic quantum system consisting of N particles. But that's only an approximation anyway. Our best fundamental quantum theory is quantum field theory, which, to the extent the idea of "number of dimensions of configuration space" makes sense at all, has a continuous infinity of dimensions of its "configuration space".

This is an example of why I find philosophers' commentaries on physics to be not worth reading. Philosophers of QM are still talking about a version of QM that has been outdated since the late 1920s, as though it were the latest, most exact version of QM, the one that physicists think best describes "fundamental reality". But no physicist thinks that, or has since, as I said, the late 1920s.

 

[Azurite]

Ok, then those are spacetime dimensions, so they're not the same as the dimensions of QM configuration space. But we don't have any way of knowing which, if either, is the "dimensions" of "reality". We don't even know if that makes sense.

If we don't know how to tell.. you mean the dimensions of QM configuration space can become the spacetime dimensions? Does this make sense?

 

[PeterDonis]

you mean the dimensions of QM configuration space can become the spacetime dimensions?

No. I mean that all of these "dimensions" are properties of abstract models. We don't know which, if any, of these "dimensions" are the "dimensions of reality". We don't even know if "reality", whatever it is, can even be usefully described as having "dimensions".

 

[Azurite]

No. I mean that all of these "dimensions" are properties of abstract models. We don't know which, if any, of these "dimensions" are the "dimensions of reality". We don't even know if "reality", whatever it is, can even be usefully described as having "dimensions".

spacetime dimensions = lorentzian spacetime manifold
QM configuration dimensions = non-lorentzian spacetime manifold

Is there a way to relate configuration dimensions to spacetime manifold?

 

[PeterDonis]

spacetime dimensions = lorentzian spacetime manifold

Yes.

QM configuration dimensions = non-lorentzian spacetime manifold

No. Configuration space is not spacetime, not even a non-lorentzian spacetime.

Is there a way to relate configuration dimensions to spacetime manifold?

It depends. For the non-relativistic case of $N$ particles, if space (not spacetime, since we're non-relativistic) has $D$ dimensions, then the configuration space of the quantum system has $N * D$ dimensions.

But in the relativistic case, where we have to use quantum field theory, there is a continuous infinity of "dimensions" (degrees of freedom would be a better term) in "configuration space" (which isn't a good term here because it isn't the space of configurations of anything), and there's no way to tell from this how many dimensions spacetime itself has.

 

[Azurite]

Yes.
No. Configuration space is not spacetime, not even a non-lorentzian spacetime.

I meant QM configuration dimensions = non-"lorentzian spacetime manifold".

It depends. For the non-relativistic case of $N$ particles, if space (not spacetime, since we're non-relativistic) has $D$ dimensions, then the configuration space of the quantum system has $N * D$ dimensions.

Since relativity is true and it should be spacetime.. then it's not space (which I understood as Newton space)... meaning "space" is incomplete formalism. But then is it not we can still go back to absolute time by making the length contraction and time dilation occurring in the object? So Newton space is still valid if the relativistic mechanics is really occurring in the atomic processes? Is this a right distinction?

But in the relativistic case, where we have to use quantum field theory, there is a continuous infinity of "dimensions" (degrees of freedom would be a better term) in "configuration space" (which isn't a good term here because it isn't the space of configurations of anything), and there's no way to tell from this how many dimensions spacetime itself has.

 

[PeterDonis]

is it not we can still go back to absolute time by making the length contraction and time dilation occurring in the object?

No. Length contraction and time dilation are perspective effects, like the way the apparent size of an object changes when you view it from different angles. They are not actual things that happen to the object.

So Newton space is still valid if the relativistic mechanics is really occurring in the atomic processes?

No, because "relativistic mechanics is really occurring in the atomic processes" is wrong. See above.

 

[Azurite]

No. Length contraction and time dilation are perspective effects, like the way the apparent size of an object changes when you view it from different angles. They are not actual things that happen to the object.

I know the above is vintage original Einstein Special Relativity. But is it not in Lorentz Ether Theory.. it occurs in the objects themselves?
https://en.wikipedia.org/wiki/Lorentz_ether_theory

"Lorentz proposed three possible explanations for this relative contraction:[B 3]

The body contracts in the line of motion and preserves its dimension perpendicularly to it.

• The dimension of the body remains the same in the line of motion, but it expands perpendicularly to it.
• The body contracts in the line of motion, and expands at the same time perpendicularly to it."

So absolute time and length contraction occurring in the object is still valid!

No, because "relativistic mechanics is really occurring in the atomic processes" is wrong. See above.

 

[PeterDonis]

is it not in Lorentz Ether Theory

Please read the PF rules; see the section on "non-mainstream theories" here:

https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/

 

[Azurite]

Please read the PF rules; see the section on "non-mainstream theories" here:

https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/

Ah you meant "Attempts to promote or resuscitate theories that have been discredited or superseded (e.g. Lorentz ether theory); this does not exclude discussion of those theories in a purely historical context"

Can you at least point to reference where this Lorentz ether theory is discredited? I thought since LET occurs in all frames.. there is no way to tell.. so it's not actually discredited but just unprovable (there is a difference).. so it's just unprovable and not discredited.. correct? If it's not discredited.. then please let Greg change the wording in the forum rules above.

 

[Azurite]

Yes.
No. Configuration space is not spacetime, not even a non-lorentzian spacetime.
It depends. For the non-relativistic case of $N$ particles, if space (not spacetime, since we're non-relativistic) has $D$ dimensions, then the configuration space of the quantum system has $N * D$ dimensions.

If space is an incomplete formalism. Why should we even mention "configuration space" where it still uses the outdated concept of space I wonder??

But in the relativistic case, where we have to use quantum field theory, there is a continuous infinity of "dimensions" (degrees of freedom would be a better term) in "configuration space" (which isn't a good term here because it isn't the space of configurations of anything), and there's no way to tell from this how many dimensions spacetime itself has.

 

[Nugatory]

If space is an incomplete formalism. Why should we even mention "configuration space" where it still uses the outdated concept of space I wonder??

In the phrase "configuration space", the word "space" is being used in the mathematical sense (a set with some added mathematical structure) and there is nothing outmoded about it.

 

[PeterDonis]

Can you at least point to reference where this Lorentz ether theory is discredited?

No. The phrase you quoted from the rules says "discredited or superseded". LET is superseded (by the standard intepretation of SR, which simply uses Occam's Razor to say that, since the "absolute rest frame" is unobservable, you can just ignore it).

 

[Azurite]

In the phrase "configuration space", the word "space" is being used in the mathematical sense (a set with some added mathematical structure) and there is nothing outmoded about it.

But it's still related to our space. As Peterdonis puts it: "It depends. For the non-relativistic case of $N$ particles, if space (not spacetime, since we're non-relativistic) has $D$ dimensions, then the configuration space of the quantum system has $N * D$ dimensions.

So why is our configuration space still using the concept of Newtonian space?

 

[PeterDonis]

why is our configuration space still using the concept of Newtonian space?

I specifically said "for the non-relativistic case". Which, as I also said in an earlier post, is only an approximation, just as Newtonian physics is only an approximation to relativity.

At this point I am closing the thread since your substantive questions have been answered and the discussion is degenerating into quibbles over language.