Acceleration deforms exponential decays into generalized Zipf-Mandelbrot laws

TL;DR

This paper shows how acceleration can transform exponential decay laws into generalized Zipf-Mandelbrot laws through relativistic effects, with applications in linguistics, biochemistry, and physics.

Contribution

It introduces a kinematic framework that explains exponential decay deformations into Zipf-Mandelbrot laws due to acceleration and relativistic effects, independent of dynamic phenomena.

Findings

Exponential decays appear as generalized power laws under acceleration.

The mathematical framework applies to linguistics and ligand binding.

The effect is purely kinematic, not dynamic.

Abstract

An exponentially decaying system looks as if its decay was a generalized power or double-exponential law, provided one takes into account the relativistic time dilation in a detector, the delay of the emitted signal, and the accelerations of both the source and the detector. The same mathematical formula can be found in generalizations of the Zipf-Mandelbrot law in quantitative linguistics and in the dynamics of ligand binding in heme proteins. The effect is purely kinematic and is not related to the various dynamic phenomena that can accompany accelerated motion of sources or detectors. The procedure used can also be seen as a form of clock synchronization near an event horizon.