Of the two major problems found near the end of the nineteenth century regarding the “classical” understanding of electromagnetism (that is, light) – The Ultraviolet Catastrophe of black-body radiation and the photoelectric effect – the former was solved first, in 1900.
That very appropriate year – the first of the new century – marked an important turning point in theories of physics. Though at that time the true value of what was being shown wasn’t yet understood, this solution sparked the beginning of the revolution of quantum mechanics.
The Problem
It had become a well-tested fact that the greatest amount of energy being ‘radiated’ from a black body falls somewhere right near the middle of the electromagnetic spectrum. The classical theories, however, had held that the greatest should be in the ultraviolet region, where the amount of radiation should theoretical reach into the levels of the infinite.
These results had plagued physicists for years. In the classical theories, the results of experiments seemed to make absolutely no sense. After all, doesn’t it seem like perfectly reasonable logic that as more energy goes into the black-body, more heat will radiate back out again?
Max Planck’s Solution
Where most physicists refused to accept the experimental results, attempting to find a way to show that somehow the curve itself had to be wrong, Max Planck decided to be bold, and go searching for a mathematical formula that would seek to explain this phenomenon. The only problem was that he would have to dispense with all classical notions regarding electromagnetism in order to do it.
This was no problem, of course, just as long as the two could later be reconciled in some way.
What Planck came up with was quite a deceptively simple, yet revolutionary little equation (called, appropriately, Planck’s law of black-body radiation):
E=hv
Where E is the radiation (energy/heat) produced by a black-body, v (which is actually the Greek letter “nu”) is the frequency of the electromagnetism being released, and h is a new constant, dubbed Planck's constant (which has a very tiny estimated value of somewhere very close to 6.626068 x 10^-24. And that's it. All of this trouble just to find that it can all be answered by this one simple equation.
The question remained, though – what does the equation mean?
Planck’s Constant
The true nature of the beast lies in Planck's constant itself.
What exactly does this number represent?
It’s possible that at the time when he first came up with his formula, not even Planck himself knew the answer to this. It’s a very, very small number, and clearly says something fundamental about the relationship between the amount of energy being released by a black-body which relates directly to the frequency of the electromagnetism – but it didn’t seem to represent any sort of physical thing... which is probably why Planck himself had so much trouble with it.
Planck’s constant seemed to be simply a random, small number which happened to fit well in this particular equation for explaining this particular problem, but not much more.
Search a little bit deeper, however, and the truth behind what Planck’s constant actually represents is rather startling. While on the surface it’s merely a number, if one takes the next step in really asking what it means, it seems to imply that the entire idea of electromagnetism in a classical sense had been wrong – specifically the nineteenth century view, beginning with Thomas Young, that light moved only as waves.
Photons: The First Quanta
Planck’s constant represented the smallest possible unit of radiation. A photon.
Planck realized this consequence himself, but he did his best to ignore it.
You see, according to Planck's new law of black-body radiation, electromagnetism isn't emitted from a source in the form of continuous waves (as had been thought since the wave theory had gained acceptance, half a century earlier). If it was, then the classical notion of black-body radiation should indeed hold up.
Instead, in order to explain this phenomenon, the light emitted from a body must be done so in “chunks” or “packets” of energy. In terms of light, these packets, the smallest piece of energy that can possibly exist, are photons (which we have mentioned previously). Light waves, as it turned out, were somehow discontinuous.
This new theory where light was “quantized” found itself being forced into some odd combination of light theories, where light waves were relegated to travel only in specified chunks of energy (the size of which was denoted by Planck’s constant) at a time. Light was not made of waves. It was made of tiny little individual things which happened to give off the appearance of traveling in waves. So in essence, Planck’s equation was somehow endorsing both theories.
Planck’s Incredulity
Planck had a difficult time in truly believing his own findings, even though they seemed to explain the great mystery of black-bodies. To him, the equation itself was little more than a mathematical fluke which helped to solve this one particular conundrum (which it did well), yet it was just that – a fluke – and not necessarily to be taken seriously by physicists as a general rule regarding the way things work. While Planck knew his equation was the only possible answer to the Ultraviolet Catastrophe! he, like everyone else, refused to accept the idea that electromagnetism should have to be “quantized” as a general rule.
It would take the work of Albert Einstein five years later – applying Planck’s equation to another problem that would give this new “quantum” theory the boost it needed.
References:
Einstein, A. (1905). On a Heuristic Point of View about the Creation and Conversion of Light. Annalen der Physik .
Gribbin, J. (1994). In Search of Schrodinger's Cat: Quantum Physics and Reality. New York, NY: Bantam Books.
Herbert, N. (1985). Quantum Reality. Garden City, NY: Anchor Press/Doubleday.
