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That there was a relationship between energy and mass was suspected
since the last years of XIX century.
By 1899, Poincaré derived such a relationship by using a thought
experiment with a "light cannon" and its recoil, once it shot a pulse of
light. By equating the energy of the light pulse and the recoil of such
a cannon, it lead him to attribute to electromagnetic radiation a mass
equal to E/c? where E is the total energy of the radiation.
https://www.bjp-bg.com/papers/bjp2019_2_081-093.pdf
But Thomson, Lorentz, Heaviside and many others were closing the
approach to this concept by using measurements of the recently
discovered electron.
This was known by 1900 (values in c.g.s. system):
1. (Lorentz and others): Energy of an electron at rest E = e?/R
2. Charge e (Planck 1900): e = 4.69E-10 esu (g^1/2 cm^3/2 s^-1)
3. Ratio e/m (Thomson 1900): e/m = 6.32766E+17 esu/g
OR m/e = 1.58036E-18 g/esu
4. Mass of electron (1900): m = (m/e) e = 7.4119E-28 g
5. Radius of an electron (1907, Rutherford, others): R = 1.11E-14 cm
6. Energy stored in an electron (1907): E = 1.976E-05 erg or g.cm?/s?
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