Resolving the Incompatibility of Special Relativity and Quantum Mechanics

[JustinLevy]

Okay, I realize that there are difficulties in combining the theory of GR and quantum mechanics, but I thought SR and quantum could be combined alright (relativistic quantum field theories, etc). If that is not correct, please let me know as it makes the rest of my questions pointless.

My questions here are based on the fact that I am having trouble understanding two issues of "combining" SR and quantum. Any help you can provide would be much appreciated.

1] Since I'm interested in SR, we will consider a spanse of spacetime that is negligibly curved. Observers moving relative to each other should measure the same speed of light and any other physical constants. This means they will agree on c (a speed) AND a unit of length (the Planck length).

How can observers agree on a "universal" speed constant AND a "universal" length constant?

One explanation I've seen in literature is to slightly change the "constancy of the speed of light postulate" of SR to "there exists one velocity upon which all observers agree" and refer to this velocity as the velocity of light in vacuum in the limit the energy -> 0. And then allow for light to have a dispersion relation in vaccuum, and a universal length to be agreed on. Is there another explanation that is simpler? And I'm not really sure how this answers the question in the first place.

2] Another issue is that quantum mechanics has that pesky "measurement postulate". All of quantum mechanics involves unitary and local evolution until you throw a measurement in there. How in the world can you define a "wavefunction collapse" in a lorentz invarient manner? It seems to have a built in "simultaneity" to it.

 

[Parlyne]

Okay, I realize that there are difficulties in combining the theory of GR and quantum mechanics, but I thought SR and quantum could be combined alright (relativistic quantum field theories, etc). If that is not correct, please let me know as it makes the rest of my questions pointless.

My questions here are based on the fact that I am having trouble understanding two issues of "combining" SR and quantum. Any help you can provide would be much appreciated.

1] Since I'm interested in SR, we will consider a spanse of spacetime that is negligibly curved. Observers moving relative to each other should measure the same speed of light and any other physical constants. This means they will agree on c (a speed) AND a unit of length (the Planck length).

How can observers agree on a "universal" speed constant AND a "universal" length constant?

One explanation I've seen in literature is to slightly change the "constancy of the speed of light postulate" of SR to "there exists one velocity upon which all observers agree" and refer to this velocity as the velocity of light in vacuum in the limit the energy -> 0. And then allow for light to have a dispersion relation in vaccuum, and a universal length to be agreed on. Is there another explanation that is simpler? And I'm not really sure how this answers the question in the first place.

The fact that observers agree that there is a fundamental length scale (which, really we should only introduce when trying to involve GR, since it involves Newton's constant) doesn't mean that the observers will agree on what objects actually have that length.

2] Another issue is that quantum mechanics has that pesky "measurement postulate". All of quantum mechanics involves unitary and local evolution until you throw a measurement in there. How in the world can you define a "wavefunction collapse" in a lorentz invarient manner? It seems to have a built in "simultaneity" to it.

Most physicists just avoid that particular issue. IMO, that's a big reason we use field theory instead of trying to formulate relativistic quantum mechanics in terms of wave functions.

That said, wave functions are still an open question. I know that Dr. Y. S. Kim at Maryland has spent significant effort on questions regarding relativistic wave functions; so, if you're up for it, you might try looking at his papers.

 

[robphy]

2] Another issue is that quantum mechanics has that pesky "measurement postulate". All of quantum mechanics involves unitary and local evolution until you throw a measurement in there. How in the world can you define a "wavefunction collapse" in a lorentz invarient manner? It seems to have a built in "simultaneity" to it.

It seems to me that a successful theory of quantum gravity will have to address this issue in a satisfactory way. (IMHO, such a theory will provide us with the correct interpretation of quantum mechanics [in some appropriate limit].)