How was E mc 2 found
Was Albert Einstein the first to formulate E = mc2?
The investigations received even greater attention when Fritz Hasenöhrl made a thought experiment in 1904 on thermal energy in a moving cavity. Even if Hasenöhrl has now been forgotten by most, with the exception of Einstein's critics, he was better known at the time than the later Nobel Prize winner. As one of Austria's leading physicists, he wrote an award-winning trilogy of essays entitled "On the theory of radiation in moving bodies", the last two of which appeared in the "Annalen der Physik" in 1904 and 1905. In the first treatise, he looked at a perfectly reflective, cylindrical cavity with two plates at the ends serving as radiators. If these were switched on, they generated enormous heat in the cavity - called black body radiation in physics. Applied to this situation, Newton's third law ("For every action there is an equally large but opposite reaction") says that all photons released by the heating surfaces must exert a reaction force against the heating surfaces themselves. In order to keep the latter in place, an external force has to act on it (we imagine that these external forces hold the plates on the cylinder). But because identical photons are emitted from both ends, the forces are equal, at least for someone who observes the processes from inside the cavity.
Red and blue
Hasenöhrl next asked what would happen if the whole system was moving at a constant speed relative to an observer in the laboratory. It is known from basic physics that emitted light, the source of which is moving towards the viewer, shifts in the direction of the blue spectral range. The observer discovers a shift into red when the source moves away from him: the so-called Doppler shift. Photons from one end of the plate are therefore more likely to appear blue to the observer, while those from the other end appear more red. Blue photons have a higher momentum than red ones, so the two external forces have to be different if the cavity is to keep moving at constant speed. The difference in work created by the kinetic energy forces of the cavity can be offset by a simple application of the "work-energy theorem". It allowed Hasenöhrl to conclude that the black body radiation has a mass m = (8/3) E / c2 owns. In his second essay, Hasenöhrl looked at the slow acceleration of a cavity that was already filled with radiation - and came to the same conclusion. After a remark by Abraham, however, he discovered a calculation error and in his third publication corrected both results to m = (4/3) E / c2.
By taking mass as a component of heat as a given, Hasenöhrl extended his previous considerations beyond the electromagnetic field of charged objects to a more general thought experiment that was very similar to Einstein's considerations of the following year, from which E = mc2 emerged. Of course, Hasenöhrl wrote the essays before the theory of relativity was formulated, so a wrong result seems understandable. But it's not that simple. Together with astronomer Stephen Boughn, I carefully analyzed Hasenöhrl's trilogy and found that the usual claim that "he forgot to take into account that the forces of the envelope itself hold the endplates in place" is not the problem at all. The biggest mistake in Hasenöhrl's first thought experiment was another one: He did not realize that the end disks lose mass when they emit heat. So, ironically, he overlooked exactly what leads to the equivalent of mass and energy - which, as is well known, he wanted to prove. After all, Hasenöhrl's considerations were so fundamental that Max Planck declared in 1909 that "black body radiation has mass inertia and that Hasenöhrl was the first to point this out". Black body radiation, i.e. heat, has mass.
What is even more surprising is that Hasenöhrl's considerations in his second thought experiment - in which the cavity is already filled with radiation and the end faces do not radiate - are obviously not wrong at all, even when applying the theory of relativity. Einstein's famous publication on E = mc2 from 1905 is entitled "Does the inertia of a body depend on its energy content?". The treatise only looks at a single particle that emits a charge pulse of radiation and, like Hasenöhrl, asks what the system would look like when viewed from a moving frame of reference. Hasenöhrl's ideas about a cavity of finite length were more daring or perhaps more careless. Extended bodies have given the special theory of relativity a major headache, as has the fact that the mass of a classical electron is also m = (4/3) E / c2 corresponds to. When applying correct mathematics in the sense of the theory of relativity, this is a result that primarily contradicts the usually expected and preferred answers. Discussions are still going on today about how this problem could reasonably be resolved.
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