Tomography of clock signals using the simplest possible reference

TL;DR

This paper demonstrates that finite physical clocks produce well-behaved signals and that their timing distributions can be reconstructed using only the relative ordering of clock ticks, with a Poisson process serving as an effective reference.

Contribution

It introduces a method to reconstruct clock signals using minimal reference information, specifically employing a Poisson process as the simplest reference clock.

Findings

Finite physical clocks have bounded waiting-time distributions.

Reconstruction of timing distributions is possible from tick orderings alone.

A Poisson process is sufficient as a reference clock for this reconstruction.

Abstract

We show that finite physical clocks always have well-behaved signals, namely that every waiting-time distribution generated by a physical process on a system of finite size is guaranteed to be bounded by a decay envelope. Following this consideration, we show that one can reconstruct the distribution using only operationally available information, namely, that of the ordering of the ticks of one clock with the respect to those of another clock (which we call the reference), and that the simplest possible reference clock -- a Poisson process -- suffices.