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

Abstract

The tight connection between mass and energy unveiled by Special Relativity, summarized by the iconic formula $E=m{c}^2$, 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.

Revised, extended version: 9 pages, 6 figures

References in corpus (6)

• Trouble with the Lorentz law of force: Incompatibility with special relativity and momentum conservation
• Will a decaying atom feel a friction force?
• Comment on "Trouble with the Lorentz Law of Force: Incompatibility with Special Relativity and Momentum Conservation"
• Trouble with the Lorentz Law of Force: Response to Critics
• The Lorentz force law and its connections to hidden momentum, the Einstein-Laub force, and the Aharonov-Casher effect
• Interaction of a Magnet and a Point Charge: Unrecognized Internal Electromagnetic Momentum

Cited by in corpus (1)

• The Microscopic Ampère formulation for the electromagnetic force density in linear dielectrics