Lorentz Transformation on a Wave Function

[bobc2]

Let's say an observer A in his rest system has a wave function for an electron double slit experiment (psi function of x and t). Would there be any inconsistencies between QM and relativity coming out of a QM analysis performed by observer A and some other observer, B, who is moving at relativistic speed relative to A (B applies Lorentz Transformation on the wave function)?

 

[Mentz114]

No, I don't think so. Dirac's equation for the electron is relativistically invariant.

 

[bobc2]

No, I don't think so. Dirac's equation for the electron is relativistically invariant.

Thanks for the comment, Mentz114. Of course you are certainly right about Dirac's equation being relativistically invariant.

As I was pondering Roger Penrose's concept of the electron wave function representing the objective reality of the electron (as opposed to the collapsed wave function), I was wondering about any implications coming out of Lorentz transforming the actual wave function for different observers. I had never thought about applying a coordinate transformation to a wave function (maybe I was absent or sleeping in class the day the prof mentioned it) and thought I'd probe for any ideas here before launching into it (of course we would be working with Hilbert space).

 

[Mentz114]

Phase is preserved by LT in any wave, because a change in the interference pattern as seen by different observers could lead to a causal paradox ( being a scalar it is automatically invariant, of course ).