Quantum mechanical transformation between reference frames - a discursive spacetime diagram approach

TL;DR

This paper explores quantum mechanical transformations between reference frames using a spacetime diagram approach, highlighting uncertainties and implications for classical and quantum relativity.

Contribution

It introduces a semiclassical spacetime diagram method to analyze quantum transformations, addressing the limitations of classical Poincare transformations.

Findings

Uncertainties arise in quantum reference frame transformations.

Light-cone coordinates have significant implications.

Classical assumptions do not hold at quantum scales.

Abstract

Heisenberg's uncertainty relation means that one observer cannot know an exact position and velocity for another (finite mass) observer. By contrast, the Poincare transformation of classical special relativity assumes that one observer knows the other's position and velocity exactly. The present paper describes a simple-minded way to consider the issue using a semiclassical discussion of spacetime diagrams, and draws out some possible implications. Uncertainties arise in transformations. A consideration is raised regarding the use of light-cone coordinates.