Read · Light quanta: from entropy to an energy scale · Results

§4 · dilute radiation and the volume law

Follow all nine sections: the classical allocation problem, the Wien entropy calculation, independent configurations, the heuristic move, and three energy-transfer applications.

Newly authored explanatory preview in modern notation; editorial and physics review are pending. The introduction and all nine numbered sections have explanatory treatments below, but this is not a German transcription, an aligned English translation, or a complete critical edition. Source faces remain in preparation. The headings and argument units are editorial, not a verified paragraph-by-paragraph source inventory.

The constant cannot simply be dropped

Inverting Wien’s law and integrating gives the entropy density plus a frequency-dependent constant. Requiring zero entropy density at zero radiation fixes that constant; it does not cancel automatically.

Compare two states, not a compression movie

For the same energy and narrow frequency band, Wien radiation gains entropy logarithmically with accessible volume. Both endpoint states must remain in the admitted regime.