Hidden but real: new relativistic "paradox" exposing the ubiquity of hidden momentum

TL;DR

This paper reveals the widespread and fundamental nature of hidden momentum in relativistic systems, demonstrating its observable effects and clarifying longstanding controversies.

Contribution

It introduces a new relativistic paradox that exposes the ubiquity of hidden momentum and shows how it can be observed directly, advancing understanding of relativistic physics.

Findings

Hidden momentum is more common and fundamental than previously thought.

Observable effects can reveal hidden momentum in various systems.

The paradox clarifies misconceptions and resolves debates about hidden momentum's reality.

Abstract

The tight connection between mass and energy unveiled by Special Relativity, summarized by the iconic formula $E = mc^2$, has revolutionized our understanding of nature and even shaped our political world over the past century through its military application. It is certainly one of the most exhaustively-tested and well-known equations of modern science. Although we have become used to its most obvious implication -- mass-energy equivalence --, it is surprising that one of its subtle -- yet, inevitable -- consequences is still a matter of confusion: the so-called hidden momentum. Often considered as a peculiar feature of specific systems or as an artifact to avoid paradoxal situations, here we present a new relativistic "paradox" which exposes the true nature and ubiquity of hidden momentum. We also show that hidden momentum can be forced to reveal itself through observable effects, hopefully putting an end to decades of controversy about its reality.