Did Poincar\'e explore the inertial mass-energy equivalence?

TL;DR

The paper examines the historical development of the concept of inertial mass-energy equivalence, highlighting Einstein's pioneering work and Poincaré's earlier considerations related to electromagnetic energy and recoil effects.

Contribution

It clarifies that Poincaré did not explicitly explore inertial mass-energy equivalence before Einstein's 1905 work, emphasizing the historical context and conceptual distinctions.

Findings

Poincaré considered electromagnetic recoil effects but did not connect them to mass-energy equivalence.

Einstein established the relation E=mc^2, linking energy change to inertial mass.

Historical analysis clarifies the timeline of ideas leading to mass-energy equivalence.

Abstract

Einstein was the first to explore the inertial mass-energy equivalence. In 1905 Einstein showed that a change in energy is associated with a change in inertial mass equal to the change in energy divided by c2. In 1900 Poincar\'e considered a device creating and emitting electromagnetic waves. The device emits energy in all directions. As a result of the energy being emitted, it recoils. No motion of any other material body compensates for the recoil at that moment. Poincar\'e found that as a result of the recoil of the oscillator, in the moving system, the oscillator generating the electromagnetic energy suffers an "apparent complementary force". In addition, in order to demonstrate the non-violation of the theorem of the motion of the centre of gravity, Poincar\'e needed an arbitrary convention, the "fictitious fluid". Einstein demonstrated that if the inertial mass E/c2 is associated with the energy E, and on assuming the inseparability of the theorem of the conservation of mass and that of energy, then - at least as a first approximation - the theorem of the conservation of the motion of the centre of gravity is also valid for all systems in which electromagnetic processes take place. Before 1905 (and also afterwards) Poincar\'e did not explore the inertial mass-energy equivalence. In 1908 Einstein wrote the German physicist Johannes Stark, "I was a little surprised to see that you did not acknowledge my priority regarding the relationship between inertial mass and energy".