# Lorentz Transformation on a Wave Function

• bobc2
In summary, the conversation discusses the potential inconsistencies between quantum mechanics and relativity when an observer A, in a rest system, analyzes the wave function for an electron double slit experiment. The concept of applying Lorentz Transformation on the wave function for different observers is brought up, but it is determined that Dirac's equation for the electron is relativistically invariant. The preservation of phase by LT in any wave is also mentioned as a potential cause for causal paradoxes.
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)?

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 ).

## What is a Lorentz Transformation on a Wave Function?

A Lorentz Transformation on a Wave Function is a mathematical tool used to describe the behavior of a wave function in different frames of reference. It takes into account the effects of time dilation and length contraction in special relativity.

## Why is a Lorentz Transformation necessary for describing wave functions?

In special relativity, the laws of physics must be the same in all inertial frames of reference. This means that the behavior of a wave function should also be the same, even when observed from different frames. The Lorentz Transformation allows us to accurately describe the wave function in different frames.

## How do you perform a Lorentz Transformation on a Wave Function?

The Lorentz Transformation involves applying a set of equations to the wave function, which take into account the relative velocity between the frames of reference, the time elapsed, and the distance between the two frames. The transformed wave function will have different values for time and position, but its physical properties will remain the same.

## What are some applications of Lorentz Transformation on Wave Functions?

Lorentz Transformation on Wave Functions is used extensively in the study of quantum mechanics and special relativity. It is used to describe the behavior of particles with high velocities, such as particles in particle accelerators. It is also crucial in understanding the behavior of electromagnetic fields and the propagation of electromagnetic waves.

## Are there any limitations to the Lorentz Transformation on Wave Functions?

While the Lorentz Transformation is a powerful tool, it is only applicable in special relativity and does not take into account the effects of gravity. It also assumes that the frames of reference are inertial, meaning they are not accelerating. In situations where the frames are accelerating, more complex transformations such as the Rindler Transformation may be required.

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