Lorentz Transformation on a Wave Function

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Discussion Overview

The discussion centers on the implications of applying Lorentz Transformation to a wave function in quantum mechanics, particularly in the context of an electron double slit experiment. Participants explore potential inconsistencies between quantum mechanics and relativity as perceived by different observers, one at rest and another moving at relativistic speeds.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether inconsistencies arise between quantum mechanics and relativity when applying Lorentz Transformation to a wave function from different observers' perspectives.
  • Another participant asserts that Dirac's equation for the electron is relativistically invariant, suggesting no inconsistencies should exist.
  • A later reply reflects on Roger Penrose's idea regarding the wave function representing objective reality, pondering the implications of Lorentz transforming the wave function and expressing curiosity about the application of coordinate transformations in this context.
  • Another participant claims that phase is preserved by Lorentz Transformation in any wave, arguing that changes in the interference pattern observed by different observers could lead to causal paradoxes, thus emphasizing the invariance of phase as a scalar.

Areas of Agreement / Disagreement

Participants express differing views on the implications of Lorentz Transformation on wave functions, with some asserting that no inconsistencies exist while others explore the complexities and potential paradoxes involved. The discussion remains unresolved regarding the broader implications of these transformations.

Contextual Notes

Participants reference the need to work within Hilbert space when discussing wave functions and transformations, indicating potential limitations in understanding or applying these concepts without further clarification on assumptions and definitions.

bobc2
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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)?
 
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No, I don't think so. Dirac's equation for the electron is relativistically invariant.
 
Mentz114 said:
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).
 
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 ).
 

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