Planck introduced Planck’s constant in his proof of Planck’s law using statistics based on an ad hoc assumption that the “smallest packet of energy” or “quantum of action” of a wave of frequency is equal to . Later appeared in Schrödinger’s wave equation as a measure of the diameter of an atom. Planck’s constant thus has two meanings and the connection has remained a mystery, well supported by a statistical interpretation of the wave function as solution to the wave equation and with the photon as a mysterious particle of energy or .
To seek to resolve the mystery let us consider wave mechanics without reference to statistics presented in Mathematical Physics of Blackbody Radiation and Computational Blackbody Radiation, which offers a New View of blackbody radiation based on a generic wave model of a blackbody (as a web of atoms) with the following radiation spectrum of the principal form of Planck’s law:
- for ,
- for ,
where is temperature in Kelvin, is frequency and and are two parameters with representing a high-frequency cut-off. Radiative equilibrium between two such blackbodies defined by parameters with the same high frequency cut-off, shows that where is a universal constant. The generic wave model thus effectively depends on one parameter, which we take to be as a representation of Planck’s constant. We here assume that Boltzmann’s constant as a measure of energy per degree Kelvin is normalized to 1.
We observe that the cut-off condition has the form
which gives the parameter in the a wave model in computational form the meaning of a mesh parameter which can be connected to the diameter of the atoms forming the web supporting the wave model. We thus have only one meaning of Planck’s constant as a mesh size parameter.
In the New View based on wave mechanics there is no need to give a different meaning as a mysterious smallest “packet of energy or action” of a wave of frequency and there is no need to speak about a particle named photon. According to Ockham’s razor this should be a step forward.
To view as a measure of the size of atoms is rational and thus not mysterious. To view as a measure of “smallest packet of energy” of a wave of frequency is irrational and thus mysterious.
Observing the radiation spectrum from a peephole of a cavity with graphite walls, as a physical wave model of a backbody, allows and to be determined experimentally.
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