Later
in the same section of the book, Planck says, “These statements define
completely the way in which the radiation processes considered take place, as
time goes on, and the properties of the stationary state. … It
is true that we shall not thereby prove that this hypothesis represents the
only possible or even the most adequate expression of the elementary dynamical
law of the vibrations of the oscillators.
On the contrary I think it very probable that it may be greatly improved
as regards form and contents.”
In
the years since Planck’s book was published in 1912, the form of the quantum
harmonic oscillator problem has been greatly formalized, especially by Dirac in
the 1920s, but I don’t think the “contents” or basic ideas have been improved
upon yet. We still don’t have the answer
to Einstein’s concern about the “mechanism of energy transfer” between matter and radiation. In quantum mechanics, we really don’t deal with trying to find mechanisms,
which are physically sensible mental pictures.
We deal instead with finding mathematical formalisms.
Planck’s
idea of a stationary state of an electromagnetic oscillator could be called the first quantum mechanical idea, but it's probably also the
last quantum mechanical idea that attempts to give a physical picture of the energy
transfer between matter and radiation. As quoted in my journal entry above, he says, “While the oscillator is
absorbing it must also be emitting, for otherwise a stationary state would be
impossible.”
Compare this with Bohr’s model
of the hydrogen atom, published only a few months after Planck’s book: the electron undergoing centripetal acceleration
as it orbits the nucleus in the ground state doesn’t radiate, so the ground state is stable, but when the electron has been kicked to an excited state and then falls back to the ground state, there is no consideration of the proton-electron attraction as being involved in this event. Thus, there's no causality associated with the emission process: it is spontaneous, and this is the name Einstein gave it in his 1916-17 derivation of the Planck spectrum.
The
success of quantum theory depends on the acceptance of the idea that electrons
can be in stationary states without radiating away their energy. But there is no physical mechanism in
quantum theory to account for this lack of radiation in a stationary state. At least Planck had an idea that could physically account for
the existence of an electromagnetic stationary state. (See last paragraph below.)
This model of continuous absorption and quantized emission is from Planck's "second theory" put forth in a paper in 1912 as well as in his book. He was trying to make his theory less of a radical departure from classical physics, or in any case he wanted to make it more intuitively understandable. One result of his 1912 work, however, was that he discovered the zero-point energy term in the electromagnetic spectral density formula, a result that later was found unavoidable as a result of the uncertainty principle. So he found an even more radical departure from classical physics rather than his hoped-for less radical approach.
But, on the other hand, zero-point energy can also be understood in the context of classical electromagnetism, as pointed out in this 2015 article by Timothy H. Boyer, among other places. And zero-point fluctuations of the e.m. field itself (around its zero average value in the vacuum) are by many physicists nowadays thought to be the cause for spontaneous emission. But that's not all there is to the story.
This model of continuous absorption and quantized emission is from Planck's "second theory" put forth in a paper in 1912 as well as in his book. He was trying to make his theory less of a radical departure from classical physics, or in any case he wanted to make it more intuitively understandable. One result of his 1912 work, however, was that he discovered the zero-point energy term in the electromagnetic spectral density formula, a result that later was found unavoidable as a result of the uncertainty principle. So he found an even more radical departure from classical physics rather than his hoped-for less radical approach.
But, on the other hand, zero-point energy can also be understood in the context of classical electromagnetism, as pointed out in this 2015 article by Timothy H. Boyer, among other places. And zero-point fluctuations of the e.m. field itself (around its zero average value in the vacuum) are by many physicists nowadays thought to be the cause for spontaneous emission. But that's not all there is to the story.
