Hidden Parameters in Heisenberg's and Landau-Peierls Uncertainty Relations, Speed of Virtual Particles and Space-Time Metric Types

TL;DR

This paper reveals hidden angular parameters within quantum uncertainty relations, derives a formula for virtual particle speed estimation, and proposes a method to identify space-time geometry in high-energy interactions.

Contribution

It uncovers hidden variables in fundamental uncertainty relations and introduces a novel approach to analyze virtual particle dynamics and space-time structure in quantum field theory.

Findings

Hidden angular variables in uncertainty relations

Formula for virtual particle speed estimation

Method to determine space-time geometry

Abstract

In quantum field theory, virtual particles are carriers of relativistic wave fields, participate in vacuum fluctuations, and are a consequence of the implementation of the quantum uncertainty mechanism. Virtual particles, playing a fundamental role in our understanding and description of interaction processes, are themselves inaccessible to direct observation and measurement of their dynamic characteristics. We prove that the well-known Heisenberg uncertainty relations and Landau-Peierls uncertainty relations implicitly contain new "hidden" angular variables. On the basis of the relations obtained, we derive a formula for estimating the speed $u$ of a virtual particle in indirect measurements. This formula is applicable in cases where the final state is characterized by an incomplete set of variables. Moreover, we present arguments that the speed of a virtual particle is a sensitive indicator of non-linearity of the process dynamics and propose a method for revealing the type of space-time geometry in the interaction region of high-energy particles.