Did Poincar\'e explore the inertial 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".