Is Planck's Original Deduction Correct by Today's Physics Standards?

[aleazk]

Hi, I need to know if Planck´s original deduction (I mean the one he presented in his 1900 paper) for the black-body spectral power is actually correct from the point of view of today´s physics. I read in my book of modern physics that this demonstration is wrong and that the correct one was really given by Einstein in the 1920´s with his photon gas model and using Bose-Einstein statistics. The book presents Einstein´s proof and I think it´s OK. I´m not a native english speaker, sorry if there is some redaction mistake.

Edit:for the sake of historical accuracy, it was Bose who actually derived Planck's law using the photon gas etc... Einstein supported the idea and, later, he applied the statistics to other cases.

 

[unusualname]

Einstein presented the more fundamental (and physically motivated) derivation in 1917:

Quantentheorie der Strahlung (On the Quantum Theory of Radiation) Physikalische Zeitschrift, 18, 121–128

(http://cua.mit.edu/8.421_S06/Historic%20references%20to%20Einstein.htm)

Einstein used the notion of quanta to derive an equilibrium law, Planck had no understanding of quanta when he derived the (correct) law he just noticed that by assuming the radiation was emitted in discrete units it gave a law closer to experimentally observed values.

 

[aleazk]

Here is a remark from the book: "An interesting aspect is that Planck´s derivation cannot presently be considered as physically sound (which is the reason we have omited it ). In other words, the problem which precipitated the birth of QM was first solved by means of a unsatisfactory method. The problem had to wait several years until the quantum theory was developed along other lines of thought before an adequate method of calculation was found. This revised derivation will be given in section bla bla... (the derivation using B-E statistics)". Alonso-Finn, Vol.3.
The derivation using B-E statistics is crystal clear, at least in my opinion, whereas Planck´s deduction... well, sincerely, I don´t understand it completely. Don´t get me wrong, Planck IS a genius, but today I argued with my teacher because he insisted in presenting Planck´s derivation as the completely correct one, whereas the cited text seems to indicate the contrary. Of course, the final result is the same (and the correct one) for both deductions, but it´s apparent from the above that Planck largely guessed it.

 

[unusualname]

Planck's derivation wasn't "physically sound" because he had no physical reason to suppose discretisation of the energy resonators in his model. He was applying an idea from an earlier paper of Boltzmann, but Boltzmann had not attributed physical significance to his discrete constructs, it was simply to enable combinatorial mathematical manipulations, and then take the limit as the discrete value goes to zero.

You might just say it was a guess rather than a derivation, for a detailed analysis see (for example)

Planck’s Route to the Black Body Radiation Formula and Quantization

 

[unusualname]

If you read through Fowler's analysis linked to above he points out that Einstein noticed Planck had used contradictory assumptions in his derivation - first assuming classical conditions for his resonators and then introducing the non-classical assumption of discretisation to get the correct form for the blackbody radiation law. Einstein's derivation in the 1917 paper is physically correct but Bose showed how to derive it using the assumption of identical particles (bosons) for light quanta, which Einstein immediately saw was correct and furthemore, it predicted the existence of a new state of matter - the Bose-Einstein condensate .

 

[aleazk]

"You might just say it was a guess rather than a derivation"
That´s my point. Correct derivations (i.e. the "physically sound" ones), are those that were presented by Einstein in 1917 and by Bose in the 1920´s.

 

[unusualname]

I suppose so, but otoh...Einstein's argument relied on a probabilistic mechanism for absorption and emission of photons which wasn't clearly understood at the time, and Bose didn't present a physical argument for the existence of his identical particle statistics (which is why the paper was initially rejected). And furthemore, much of the development of Quantum Theory relied on (brilliantly) creative "guesses" before the physical mechanisms were accepted or even experimentally verified, some would say that even the modern theory is just an effective mathematical abstraction without real physical justification (apart from its predictive power)

 

[aleazk]

"much of the development of Quantum Theory relied on (brilliantly) creative "guesses" before the physical mechanisms were accepted or even experimentally verified"
Yes, I agree on that, and it is fine. I´m not trying to dismiss the (original) reasoning of these great scientists, but it is instructive to know the limitations that they could have from the point of view of today´s physics. Even more if you are learning the subject, as I am. For these reasons, in a historical presentation of the theme, the instructor must be careful. Something on what my teacher was not very skilled. I have nothing against guessing an equation or a law. In fact, Einstein, for example, guessed the field equations of GR. He first proposed Rab=k.Tab (in analogy with Poisson equation Δφ=4πGρ), but because Tab;c =0 and Rab;c ≠0, he later changed it by Rab-1/2.R.gab=k.Tab, where (Rab-1/2.R.gab);c=0. Now, this cannot be considered a "deduction", only a plausibility argument. Later, we accept this equation because it predicts the correct results. There is no problem here, given the fact, as far as I know, that this equation cannot be derived from fundamental principles, even today. On the other hand, Planck's law can be derived from the fundamental principles of modern physics, and, when teaching the subject, this should be stressed.