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- Thread starter cnidocyte
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mathman

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the assumption of quantized amounts of photon energy is used to produce the black-body radiation spectrum. This result is the justification of that assumption.

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Born2bwire

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Planck looked at the Wien and Rayleigh-Jeans results and proposed an interpolation between the two results. This was the same as the resulting Placnk distribution. It then took him several weeks to find a physical and theoretical reasoning behind this and this was done by throwing out the classical equipartition theory and devising a new one that required the energy to be quantized. Actually, quantization of energy was done by Boltzmann as a tool for derivations but with Boltzmann the quantization did not affect the final results. However, removing the quantization in Planck's derivation simply results in the Rayleigh-Jeans distribution again. Thus, Planck's use of quantization was essential. In addition to the quantization, Planck used a different method for counting the elements which is consistent with what is now called Bose-Einstein statistics (as opposed to the Maxwell-Boltzmann statistics that gave rise to the Rayleigh-Jeans).

So basically Planck found a way to fit an equation that matched the Wien and Rayleigh-Jeans distributions and was able to a posteriori derive this distribution by using a new equipartition theorem. This matched the suspicions of other physicists at the time that the classical statistical equipartition theory may be the problem.

Milonni has a few sections in his Quantum Vacuum book that discusses this in detail.

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