Eighteen Years of Doubt — Einstein's Light Quantum, 1905 to 1923

In March 1905 a 26-year-old clerk at the Swiss patent office wrote to a friend that one of his papers was "very revolutionary." In it, Einstein argued that light behaves as though it were a collection of separate lumps of energy. The fixed step of energy that Planck had introduced in 1900 to make his numbers come out right, Einstein reread as a property of light itself. And yet the idea was not accepted, even after experiments showed its predictions were exactly right — the man who tested them did not believe it either. This is part two of five on the old quantum theory: why "confirmed but unconvincing" lasted eighteen years. Part one is here.

It was not "the photoelectric effect paper"

Textbooks usually introduce it as the photoelectric paper — the photoelectric effect being what happens when light shining on a metal knocks electrons out of it. But the article Einstein published in March 1905 was titled "On a Heuristic Viewpoint Concerning the Production and Transformation of Light," and the photoelectric effect appears near the end as one application among several. The same idea also explains why fluorescent light always comes back redder than the light that caused it (Stokes's rule), and why light can strip electrons from a gas.

Most of the paper is spent not on those applications but on an argument from the theory of heat, meant to justify the picture of light as lumps in the first place. Of everything he wrote in 1905 — special relativity and Brownian motion included — this was the paper he called "very revolutionary" in his letter to his friend Conrad Habicht.

Light spread out just the way a gas does

Here is the shape of the argument, with as little mathematics as possible.

The clue Einstein used was entropy. Put simply, entropy measures how many ways a thing can be spread around: for the same amount of energy, the more freedom there is in how it can be arranged, the larger the entropy.

He looked at the short-wavelength region — where Wien's formula, which appeared in part one, works well — took light of a single colour, held its energy fixed, and changed the volume of the box holding it. Then he worked out how the entropy changed. The answer came out in exactly the same form as the answer for n particles flying about independently inside a box: an ordinary gas.

Read Boltzmann's relation — entropy is set by the number of ways a state can be realised — backwards, and the conclusion follows. Light behaves as though it were made of separate lumps of energy flying about, and the size of one lump is proportional to the frequency of the light (how many times a second it oscillates, which is roughly what we see as colour). The step of energy that Planck in 1900 had confined to the devices emitting and absorbing light, Einstein moved onto light itself.

The photoelectric effect then falls out easily. The most energy an electron can carry away from the metal depends not on how bright the light is but only on its frequency: the electron's energy equals one lump's worth of energy, minus the minimum energy needed to pull an electron out of that metal. Faint violet light ejects electrons; intense red light, however much of it you pour on, does not. That well-known oddity simply follows — if a single lump does not carry enough energy, piling on more lumps does not help.

The man who confirmed it did not believe it

The person who tested that relation properly was the American physicist Robert Millikan. Through experiments running from 1912 to 1915, he showed in 1916 that his measurements fell on a straight line, just as predicted, and read Planck's constant off its slope: 6.569×10⁻³⁴ joule·seconds in today's units. That agrees well with the value Planck had extracted from blackbody radiation in 1900.

Yet Millikan himself regarded the idea of light as lumps as unreasonable, and wrote that he had spent ten years on the test. The equation was right, in his view; the picture behind it was wrong.

The recommendation that Planck and his colleagues wrote in 1913, proposing Einstein for membership of the Prussian Academy of Sciences, carries the same air. It praised his work highly, then added that he may sometimes have missed the target in his speculations — as, for example, in his hypothesis of light quanta. The man who had introduced h into physics was against carrying it over to light.

The resistance was not stubbornness

It would be a mistake to read this as conservative scientists disliking a new idea.

That light is a wave had been settled in the nineteenth century. Light passing through two narrow slits produces alternating bright and dark bands on a screen; light bends around the edges of an obstacle; and the theory of electricity and magnetism yields light as a wave. All of it had been confirmed over and over.

Make light a set of lumps and those bands become inexplicable. If lumps simply fly in straight lines, why should bright and dark stripes appear precisely when the light has passed through two slits?

So the idea of light as lumps bought an explanation of one phenomenon at the cost of something known far more securely. On balance it did not pay. That, and not obstinacy, is why physicists held back.

What settled it was not the photoelectric effect

What shifted opinion was, of all things, not about light.

In 1907 Einstein applied the same "energy comes in steps" idea to the heat needed to warm a solid. As the temperature drops, the heat required to raise it by one degree falls away — which classical theory could not explain, since it predicted a constant. Assume that the vibrations of atoms also come in fixed steps and the fall is accounted for. That work, showing that steps of energy were not a peculiarity of light, did more to move his contemporaries than the photoelectric effect did.

The decisive result came in 1923, from Arthur Compton. Fire X-rays (light of very high frequency) at electrons, and the scattered X-rays come back with a longer wavelength, by an amount that depends on the angle. The measured values matched a calculation treating the event as one billiard ball striking another and handing over momentum. Light carries not just energy but the momentum of a colliding particle — direct evidence at last. Eighteen years had passed since 1905.

The 1921 Nobel Prize in Physics, awarded in 1922, went to Einstein not for relativity but "for his discovery of the law of the photoelectric effect." The citation says law, not light quantum, and that choice of word preserves how the field still held the idea at arm's length. The name "photon" was not coined until 1926.

What had been achieved, and what had not

By 1923 it had been established that one lump's worth of energy — frequency times Planck's constant — was not a bookkeeping trick but a quantity attached to light itself. What Planck had chopped up out of necessity turned out to be real.

What had not been achieved was any account of how lump and wave fit together. Compton's experiment did not make the bright and dark bands go away. "Light is both a particle and a wave" remained a statement of the situation rather than an explanation of it.

Someone set that contradiction aside and carried the quantum into a different place entirely — the inside of the atom. Next: Bohr in 1913, and a model of the atom that worked embarrassingly well.