Relativity Considerations for Measurements on a Free Particle

[phyahmad]

Suppose I have an initially localized free particle at x0 then I measure its momentum it will become a plane wave so there is a probability that if I measure its position again to find it far away from its initial position if the time between the two measurements were T isn't finding the particle at xo+2cT for example violate relativity ....because of that I imagine that an initially localized particle must be modeled to be a particle in infinite box with width equals 2ct but I was told that this isnt a true model but why?

 

[PeroK]

Standard QM is non relativistic and is not compatible with SR. You can see this directly from the Schrodinger equation, which is not covariant, as the derivatives with respect to time and spatial coordinates are different.

And, indeed, it's possible to find a particle outside its future light cone. To patch this up, you need a relativistic theory, such as the Dirac equation. Or, fully fledged relativistic Quantum Field Theory. Of which standard QM is a non-relativistic approximation.