The Weird Mistake in Planck's Law

By examining Planck's equation E=hν, one finds an analogy with accounting billing for electricity. Frequency and power have a physical dimension T-1, so one obtains an energy value accounted for over a time interval by multiplying them by this time interval. By investigating this analogy, one finds a surprising mistake in Planck's law for the frequency of black body radiation: confusion between two contexts, one for radiation power and one for a timeless energy density. One goes from one to the other by an accounting-type transformation: a multiplication by 4π/c or c/4π. Correcting this mistake makes a Planck constant h timeless, invalidating the photon definition and de Broglie’s wave-particle duality. Despite this mistake, one obtains the same value for the black body radiation; it goes unnoticed. Consequently, the Planck relation becomes P=hν, with the energy of a cycle equal to h, whatever the frequency. One can consider this cycle as a new photon, which behaves like a particle by its radiation pressure. Its energy-mass equivalence h=mɣc2 gives a mass of 4.134883524·10-15 eV, in the range referenced by the Particle Data Group. This correction of Planck's relation calls quantum physics into question.