Keep what waves explain
Wave optics describes propagation and interference successfully. Einstein asks whether energy exchange with matter needs an additional, explicitly heuristic description.
Read · Light quanta: from entropy to an energy scale · Results
Light quanta: from entropy to an energy scale
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.
A finite window cannot cure an infinite total
At a positive temperature, classical allocation assigns more energy as the frequency cutoff rises. Its all-frequency total has no finite value; the plotting cutoff is not a physical explanation.
A spectral fit is not yet a free-light hypothesis
Matching a spectral coefficient to classical thermal allocation constrains R/N. Quantized resonator energies and independently propagating light quanta are different claims.
A spectrum can determine an entropy derivative
At fixed volume and frequency, the entropy increase per added energy is 1/T. Inverting an admitted spectrum therefore determines an entropy derivative, but not yet its integration constant.
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.
Independence supplies the exponent
For n independent uniformly distributed points, the chance that all lie in a fraction f of a volume is fⁿ. Perfectly locked positions instead give f; the exponent is a statement about independence.
A coefficient suggests an energy element
In the Wien regime, the radiation entropy coefficient has the form associated with independent elements. Reading an energy scale from that match is a heuristic inference, not a proof of every property of light.
An energy budget has conditions
With one absorbed quantum, no extra energy, and a single emitted quantum, the outgoing energy cannot exceed the incoming energy. Extra thermal energy or multiple-quantum input changes those premises.
More electrons is not more energy per electron
In the one-quantum model, frequency sets the maximum electron energy after paying the escape cost. Increasing power at fixed frequency can increase the number emitted without increasing that maximum.
A stopping voltage is a magnitude with a sign convention
The ideal stopping-potential magnitude is Kmax divided by the positive elementary-charge magnitude. Partial transfer or internal losses produce an inequality rather than a larger endpoint energy.
A threshold does not specify a yield
Under a one-quantum ionization assumption, a quantum must meet the required ionization energy. Absorbed energy bounds the count; equality requires that every absorbed quantum causes exactly one counted ionization.