Relativistic dilation and contraction of the probabilities of quantum states of light at angular incidence

Abstract

In this work we propose a formulation for the treatment of quantized states of light in photon-matter interaction. It is built in the multidimensional Hilbert space to describe the orbital angular momentum states, in such that probabilities naturally arise in a relativistic setting. Our findings indicate that the classical-relativistic variability of the probabilities can describe the quantized states of light, with the state variable being the variation of the photon angular momentum. It was verified that the probability to find a specific quantized state of light at angular incidence can be treated by relativistic probabilities. Interestingly, our results indicate that, when both states have equal odds, there is a synchronization between source and observer. We found that the relativistic effect in the perspective of the source referential is able to change the odds of an event occurring, dilating and contracting the probabilities of finding a quantized state of light at angular incidence.