An experimentally testable proof of the discreteness of time

TL;DR

This paper presents an experimentally testable proof that time is discrete, with Planck time as the smallest unit, based on paradoxes in quantum mechanics and relativity, impacting quantum gravity and computational limits.

Contribution

It introduces a novel, testable proof of time discreteness rooted in quantum and relativistic paradoxes, linking system size and speed to the temporal unit.

Findings

Time cannot change within Planck time.

Larger and slower systems have larger time units.

The proof constrains quantum gravity theories and computational speeds.

Abstract

By proposing a paradox between the impossibility of superluminal signal transfer and the normalization condition of wavefunctions, we predict that when a change happens to the conditions that determining the status of a quantum system, the system will show no response to this change at all, until after a certain time interval. Otherwise either special relativity or quantum mechanics will be violated. As a consequence, no physical process can actually happen within Planck time. Therefore time is discrete, with Planck time being the smallest unit. More intriguingly, systems with a larger size and a slower speed will have a larger unit of time. Unlike many other interpretations of the discreteness of time, our proof can be tested, at less partly, by experiments. Our result also sets a limit on the speed of computers, and gives instruction to the search of quantum gravity theories.