Relativistic interpretation of Quantum Mechanics?

[_heretic]

Is there any formulations of quantum mechanics out there that are relativistic? i.e. interpretations that take special and/or general relativity into account when describing the behaviour of quanta? As I understand it, traditional QM is not relativistic, time is just sort of "bolted on" and 'ticks away' in the background. I think I recall reading something by Roger Penrose where he said that when relativity is added to the picture at the quantum level, problems arise; something about a particle going its merry way down its own time dimension (?)

[timo]

Relativistic quantum mechanics is routinely used in e.g. particle physics. As a matter of fact, it is so mainstream that many people erroneously believe that quantum field theory was inherently relativistic. Notable keywords are the "Dirac equation" and the "Klein-Gordon equation".

 

It is the quantum mechanical description of gravity that causes problems. I don't know what Sir Penrose speaks about - but keep in mind that his interest is selling books by writing things that sounds interesting, not expressing himself unambiguously or making sense.

Edited September 26, 2012 by timo

[_heretic]

Relativistic quantum mechanics is routinely used in e.g. particle physics. As a matter of fact, it is so mainstream that many people erroneously believe that quantum field theory was inherently relativistic. Notable keywords are the "Dirac equation" and the "Klein-Gordon equation".

 

It is the quantum mechanical description of gravity that causes problems. I don't know what Sir Penrose speaks about - but keep in mind that his interest is selling books by writing things that sounds interesting, not expressing himself unambiguously or making sense.

 

Ah, I probably just mixed up that paraphrase then.

[timo]

Not sure if you understood me - my post may have been ambiguous at some part. So let me repeat/clarify/elaborate:

 

- Special Relativity (which I tend to call "relativity") is routinely incorporated in QM (except technically saying that QM is incorporated in SR may be more appropriate). Little to no issues left, there.

 

- General Relativity (which I tend to call "our current theory of gravity") has not been formulated on a QM basis, yet. To some extend, one can do QM in a GR background, but (a) I think even this causes some problems, and (b) this is not what people usually mean by "quantum gravity". Quantum gravity, which Sir Penrose presumably refers to (since it sells more pop-sci books than the other real-sci things) indeed is an unsolved issue.

Edited September 26, 2012 by timo

[_heretic]

Not sure if you understood me - my post may have been ambiguous at some part. So let me repeat/clarify/elaborate:

 

- Special Relativity (which I tend to call "relativity") is routinely incorporated in QM (except technically saying that QM is incorporated in SR may be more appropriate). Little to no issues left, there.

 

- General Relativity (which I tend to call "our current theory of gravity") has not been formulated on a QM basis, yet. To some extend, one can do QM in a GR background, but (a) I think even this causes some problems, and (b) this is not what people usually mean by "quantum gravity". Quantum gravity, which Sir Penrose presumably refers to (since it sells more pop-sci books than the other real-sci things) indeed is an unsolved issue.

 

I see. I didn't grab that paraphrase from a book on quantum gravity, however, it was from his book: The Road to Reality: A Complete Guide to the Laws of the Universe, which is about the standard model of particle physics, general relativity, special relativity and possible TOEs.

 

So, anyway, special relativity has been worked out with QM. What about EPR situations?

[ajb]

Relativistic quantum mechanics is routinely used in e.g. particle physics. As a matter of fact, it is so mainstream that many people erroneously believe that quantum field theory was inherently relativistic. Notable keywords are the "Dirac equation" and the "Klein-Gordon equation".

 

We should be a little careful here, the Dirac equation and the Klein-Gordon equation cannot be interpreted as single-particle relativistic wave equations.

 

The root of the problem is that within special relativity energy is conserved (in a specified frame), but mass is not. We also have the problem of negative energy to deal with.

 

The way round this is quantum field theory; basically we have a multi-particle theory with creation and annihilation of particles, rather than a theory of a single particle.