The book also states that quantum jumps first appeared in Niels Bohr’s atomic model in 1913, but that idea, too, had appeared in Planck’s 1912 article and in one by Henri Poincaré the same year. For instance, the book wrongly states that Albert Einstein, in 1916, was the first physicist to include probability in quantum theory in fact, Max Planck had already done that in an article published in 1912. S = k logW, where k is Boltzmann’s constant (so named by Planck.However, the historical narrative itself is sometimes imprecise. Planck in 1900 explained the spectral distribution of colors (wavelengths) in blackbody electromagnetic radiation by using Boltzmann’s principle that the entropy S of a gas is related to the probabilities W for the possible random distributions of molecules in different places in its container and with different velocities. The difference is because the radiant energy (the number of photons) increases greatly as temperature goes up, but the number of molecules is held constant. The similarity between the two is the rise to a maximum with a power law on one side and an exponential decline on the other. Note the resemblance between the distribution of blackbody radiation as a function of temperature and the Maxwell-Boltzmann distribution of velocities. nothing more than mathematical juggling." In 1925, he called his work "a fortunate guess at an interpolation formula" and "the quantum of action a fictitious quantity. Planck's assumption was simply a mathematical device to make the distribution of light as a function of frequency (and thus energy) resemble the Maxwell-Boltzmann distribution of molecular velocities in a gas as a function of velocity (and thus energy). ![]() Note the resemblance to the Bohr theory of the atom thirteen years later, where Bohr postulated stationary states of the electron and transitions between those states with the emission or absorption of continuous waves of energy equal to hν! Although the Lorentz theory of the electron was already complete, Planck did not accept electrons and instead described "the energy flowing across a spherical surface of a certain radius containing the resonator." He assumed the resonators could be described as having energy values limited to multiples of hν. His quantization assumption was for an ensemble of "oscillators" or "resonators" that were emitting and absorbing the radiation. ![]() Planck did not actually believe that light radiation itself existed as light quanta. That was the work of Albert Einstein five years later in his photo-electric effect paper (for which he won the Nobel Prize), in which he proposed his "light-quantum hypothesis." For Einstein, the particle equivalent of light (later called a "photon") contains hν units of energy, where h is Planck's constant and ν is the frequency of the light wave. Planck did not suggest that light actually came in quantized (discrete) bundles of energy. Planck solved the great problem of blackbody radiation by applying the statistical mechanics of the Maxwell-Boltzmann velocity distribution law for particles to the distribution of energy in a radiation field. Zenon Pylyshyn Henry Quastler Adolphe Quételet Pasco Rakic Nicolas Rashevsky Lord Rayleigh Frederick Reif Jürgen Renn Giacomo Rizzolati Emil Roduner Juan Roederer Jerome Rothstein David Ruelle David Rumelhartīiosemiotics Free Will Mental Causation James Symposiumī ν (v, T) = (2 hν 3 / c 2) (1 / ( e hν / kT - 1) )
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