Acceleration-Induced Nonlocality: Uniqueness of the Kernel

TL;DR

This paper investigates the uniqueness of the kernel in nonlocal theories of accelerated observers, concluding that a specific kinetic kernel form is the only physically acceptable solution based on theoretical and observational considerations.

Contribution

It establishes the uniqueness of the kinetic kernel in nonlocal acceleration theory by analyzing bounded kernels and using observational data.

Findings

Kinetic kernel $K( au , au')=k( au')$ is uniquely acceptable.

Convolution kernels are ruled out due to divergences.

Observational data supports the kinetic kernel as the only viable form.

Abstract

We consider the problem of uniqueness of the kernel in the nonlocal theory of accelerated observers. In a recent work, we showed that the convolution kernel is ruled out as it can lead to divergences for nonuniform accelerated motion. Here we determine the general form of bounded continuous kernels and use observational data regarding spin-rotation coupling to argue that the kinetic kernel given by $K(\tau ,\tau')=k(\tau')$ is the only physically acceptable solution.