What was different about Planck's quantization of light compared to Einstein's?

Question

In describing black body radiation Planck assumed that the energy that can be absorbed or emitted by charges is quantized, i.e., they can only absorb or emit certain quantities of energy. But it was Einstein, who postulated the photon. I have two questions relating to this:

1. Did Planck think these energies travelled in wave packets (if not, then how)? And why is his quantization of the energy of light different from Einstein's quantization of light?

2. If Planck thought that energies of EM radiation, which weren't multiples of Planck's constant with frequency could exist, what if one of these interacted with a charge that could according to him only absorb certain energies of light? What did he think would happen to this radiation?

Answer 1

Unlike Einstein, Planck did not quantize electromagnetic waves themselves, only the exchanged energies, and even them only statistically. So the other two questions have no satisfactory answer because he was not dealing with specifics of emission/absorption at the level of individual quanta. The quanta were meant as mathematical fictions for the purposes of a statistical count, like Boltzmann's boxes. It was Einstein, who acknowledged them as real physical entities in 1905, postulating that electromagnetic waves split into wave packets carrying quanta of energy. But this was not a coherent picture either since Maxwell's electrodynamics does not allow such stable packets, and Einstein declared in 1911 "I insist on the provisional character of this concept, which does not seem reconcilable with the experimentally verified consequences of the wave theory."

Planck's derivation of the radiation formula was a convoluted affair, that started in 1894 with him taking interest in emission experiments conducted in Berlin's Physikalisch-Technische Reichenstalt by a number of young researchers, see Did light bulb companies commission Planck to study black body radiation? After several unsuccessful attempts Planck finally derived the correct formula in October 1900, without any energy quantization. But in his eyes it lacked foundational insight. He considered thermodynamics to be more fundamental than Boltzmann's statistical mechanics, a common sentiment at the time, but could not extract the correct formula from it despite trying for 6 years.

Contrary to a popular belief, Planck was not concerned by the "ultraviolet catastrophe" (Ehrenfest's nickname from 1911) in black body radiation, when the energy gets converted into higher and higher frequency waves in ether, which is a commonly given back engineered motivation. This "catastrophe" is related to the equipartition theorem of statistical mechanics, and does not occur in the thermodynamical approach of Wien, which Planck originally followed.

Turning to discrete statistics with "quanta" of energy in November 1900 was "an act of despair", and he hoped to dispense with them in the end by taking a continuous limit. The last part did not work out. This thread on Physics.SE discusses Planck's struggles in more detail. A key qoute comes from his 1931 letter to Wood:

"...one finds that the continuous loss of energy into radiation can be prevented by assuming that energy is forced at the outset to remain together in certain quanta. This was purely a formal assumption and I really did not give it much thought except that no matter what the cost, I must bring about a positive result." (boldface mine)

If "energy is forced at the outset to remain together in certain quanta" then presumably non-multiple energies do not occur. But this is a later self-interpretation, long after Einstein's and Bohr's inputs. In Black-Body Theory and the Quantum Discontinuity, 1894-1912 Kuhn paints a messier picture based on the inspection of contemporary evidence, which became the consensus among historians.

Answer 2

You should really read Douglas Stone's "Einstein and the Quantum: The Quest of the Valiant Swabian." It's a brilliant work insofar as Prof. Stone shows precisely how Planck went about deriving the eponymously named Planck's law and why the quantum revolution did not beging with Planck but with Einstein. In the book Prof. Stone (Head of Applied Physics at Yale), having read T.S. Kuhn's work on the Black Body Problem and Quantum Discontinuity, as well as all of Planck's original papers and correspondence on the issue, in addition to all of Einstein's original papers and correspondence between 1879 and 1929, essentially argues that Planck's law arose as a mathematical fudgefactor. On the one end you had Rayleigh's law in the lower limit, and on the other Wien's law in the higher limit; Planck, having asserted to the Prussian Academy of Science that he had derived a formula directly from the second law of thermodynamics found himself in a dire quandary. His formula did not fit Kurlbaum's data and Planck, a very capable mathematician, simply guessed at an interpolation formula that fit Kurlbaum's new data.

One Problem, however, he couldn't explain it and buried it for 5 years - in fact, no scientist in Europe brought it up again for 5 years - until Einstein launched quantum theory in earnest in 1905 and AGAIN in 1906 with one of the most underrated papers (as Walther Nernst later acknowledged) in the history of Quantum Mechanics titled "On the Specific Heat of Solids."

The irony, of course, is that Bohr, his later sparring partner in the interpretation of QM, didn't actually believe in quantum theory for years, maintaining that "the wave model of electromagnetism is tried and tested and any theory to the contrary cannot possibly fit experiment" (or something to that effect, I'l' have to dig up the quote but Bohr was definitely not an instant believer).

After completing General Relativity, in 1917 Einstein rederives Planck's Law as well as Bohr's Frequency Rule in a completely novel way (crystallized in the A & B coefficients) and in so doing conjectures inherent randomness in quantum theory, a conceptual postulate that has remained with the theory ever since.

Watch a lecture Stone gives on the topic. Quite enlightening: http://www.grassrootstv.org/view?showID=12681

One last word on the topic. Contrary to popular opinion, Einstein's foray into revolutionizing physics didn't begin in 1905 but rather between 1902 and 1903. This is where you see the genesis of his unconventional genius. He wrote a brilliant trilogy of papers in those years deriving the foundations of statistical mechanics from first principles (a work that would make J.W. Gibbs a legend - and Gibbs work, Einstein noted, was superior but also, in a way, less daring). Einstein didn't know of Gibbs work at the time as it hadn't been properly translated into German. But even so you can see the rudiments of Einstein's thinking on light quanta and how he, and not Planck, made the leap in 1905 that light, and indeed all energy and matter, is quantized. His complete mastery of statistical mechanics and thermodynamics comes to the fore again and again throughout his development on quantum theory. It's interesting: http://faculty.poly.edu/~jbain/heat/readings/98Navarro.pdf