My current favorite story of scientific discovery is probably the origin of Bose-Einstein statistics.
Before the discovery of Planck’s law, there was the problem of ultraviolet catastrophe in applying statistical mechanics to fields: there are many more high frequency modes than low frequency ones, and the equipartition theorem of statistical mechanics predicts that energy should be spread out evenly across all quadratic degrees of freedom. There’s ~ one quadratic degree of freedom for each frequency in a free field, so a naive application led to the Rayleigh-Jeans law for blackbody radiation which predicted an infinite energy flux radiated by a blackbody at nonzero temperature.
People waved this off as statistical mechanics not being applicable to this situation. Then, Planck noticed that if energy comes in discrete packets where the size of each packet scales linearly with frequency, this manages to kill the divergence at high frequencies and give reasonable results for the spectral energy density of blackbody radiation. This is now known as Planck’s law.
Some years later, when Bose was giving a talk about the ultraviolet catastrophe problem to an audience and explaining why Planck’s calculation was actually unjustified under Maxwell-Boltzmann statistics, he made an error in a combinatorial argument and accidentally derived that Planck’s argument was justified. He realized later that the “error” he had made was to assume that photons occupying the same energy level were indistinguishable. Since photons are bosons, this is actually correct, but the discovery was actually made through a calculation mistake.
Bose later submitted this paper to an English journal & got rejected, so he got in touch with Einstein and asked him to translate his article to German so that it could be published in a German journal. Einstein agreed, and that’s where the name of “Bose-Einstein statistics” comes from.
My current favorite story of scientific discovery is probably the origin of Bose-Einstein statistics.
Before the discovery of Planck’s law, there was the problem of ultraviolet catastrophe in applying statistical mechanics to fields: there are many more high frequency modes than low frequency ones, and the equipartition theorem of statistical mechanics predicts that energy should be spread out evenly across all quadratic degrees of freedom. There’s ~ one quadratic degree of freedom for each frequency in a free field, so a naive application led to the Rayleigh-Jeans law for blackbody radiation which predicted an infinite energy flux radiated by a blackbody at nonzero temperature.
People waved this off as statistical mechanics not being applicable to this situation. Then, Planck noticed that if energy comes in discrete packets where the size of each packet scales linearly with frequency, this manages to kill the divergence at high frequencies and give reasonable results for the spectral energy density of blackbody radiation. This is now known as Planck’s law.
Some years later, when Bose was giving a talk about the ultraviolet catastrophe problem to an audience and explaining why Planck’s calculation was actually unjustified under Maxwell-Boltzmann statistics, he made an error in a combinatorial argument and accidentally derived that Planck’s argument was justified. He realized later that the “error” he had made was to assume that photons occupying the same energy level were indistinguishable. Since photons are bosons, this is actually correct, but the discovery was actually made through a calculation mistake.
Bose later submitted this paper to an English journal & got rejected, so he got in touch with Einstein and asked him to translate his article to German so that it could be published in a German journal. Einstein agreed, and that’s where the name of “Bose-Einstein statistics” comes from.