Planck's Mistake

Known in 1900 Max Planck first guessed the correct formula for the radiation of the black body. Then he searched frantically for the theoretical justification of this formula. Months later he found the solution. This is regarded as the birth of quantum mechanics.

The derivation, which is now offered in the textbooks is not complicated and, with the consideration of Einstein's light quantum hypothesis, plausible. But Planck did things differently, and his calculation will be wrong... That I did not know until I read John Gribbin's book "In Search Of Schrodinger's Cat". The author writes that Planck did not understand the Boltzmann equation and therefore does not use it correctly. And only when Einstein took up the case, it became obvious importance of the work of Planck.

Although at present the derivation of Planck's radiation formula through using Einstein's light quantum hypothesis was refined, can this interpretation be not correct. While the derivation is obviously forgot what was the original physical model. It examines a closed box with reflecting walls. Inside can arise standing waves with different frequencies. According to thermodynamics can have any of them mean energy kT:

Well as long hv < kT there is obviously no problem, because a standing wave can consist of several light quanta. But for hv > kT we have the problem that a single photon no longer fits into a standing wave. So it should actually spread partly on a different wave, but it's already from another frequency! 
Yes, you can considered instead of kT the mean photon energy:

however, does not help, because mean photon number

at hv > kT is less than 1. What are we to do with the fractions of the photons in a box? In addition, the photons as particles may not be divided. 
Therefore, Planck's radiation formula, as it was initially, remains mainly an empirical approach.
You must not think that I've just now at once discovered this error. Why the scientists of that time must have the quantum theory, I do not know, but they were probably relieved after Max Born in 1926 offered the probability interpretation. At least then they need no longer think of shredded photons, but since then there is the probability that these photons are present in the box.
By and large this is an abuse of the mathematical means to justify the unphysical description. It is one thing, if one speaks of the probability that all the air molecules accumulate only in one half of the room. Although the probability is very small, but  the process itself is quite possible, as long the total volume of all molecules is less than the volume of the half room. And it is completely another thing, if for example claims that an elephant made of flesh and blood with a certain probability can fit into a box of matches. It is physically impossible even for a tiny moment. But in fact this trick is the basis of quantum theory and aroused great enthusiasm among the people (for whatever reason).

Walter Orlov, 2011