It’s a simple device – a set of vanes mounted on a spindle, enclosed in a partially evacuated glass bulb. Each vane is silvered on one side and blackened on the other. When the Crookes radiometer is placed in sunlight or near heat, the vanes spin round. The commonly held view is that it is being driven by particles of light drumming on the vanes. Just as a ball that bounces off a wall imparts twice as much momentum to the wall as one that hits and sticks, photons reflected from the silvered faces push the vanes twice as hard as ones absorbed on the black side. The only problem is the vanes spin the wrong way round. Confused?Then you are in good company. Some of the greatest minds have beenbaffled by Crookes’s radiometer.
THE story of Crookes’s radiometer begins with the discovery of a new element by William Crookes, a chemist who funded a private laboratory in London out of a sizeable inheritance from his father. In 1861, Crookes found thallium by the pattern of light it emitted, exploiting the new-fangled technique of spectroscopy. In 1873, he attempted to weigh his sample, to find out how much heavier it was than the lightest element, hydrogen. This was tricky as he had so little thallium, so he decided to weigh it in a vacuum. It was then that he stumbled on a peculiar effect. Warm samples appeared to weigh less than cold ones. Furthermore, when heated from below a sample poised on the end of a balance moved upwards and when heated from above it moved downwards, just as if heat exerted some kind repulsion on it.
Like all the best scientists, Crookes was always on the alert for anomalous effects that might prove to be important. When his thallium work was done, he began investigating the new force, and quickly discovered that a black surface was repelled more strongly by heat than a silvered one. This led him to devise the radiometer, which demonstrated the effect he had discovered in the most enchanting way. As a toy it created an immediate sensation. During its heyday, from 1875 to 1877, hundreds of articles appeared in scientific and popular journals, often penned by some of the biggest names in 19th-century science. Most were wrong. “Even today, most physicists think they know how it works, while few actually do,” says Andrés Larraza of the Naval Postgraduate School in Monterey, California.
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Among the luminaries who attempted an explanation was James Clerk Maxwell, who in 1864 had captured the bewildering array of electrical and magnetic phenomena in one beguilingly simple set of equations. Maxwell, who refereed Crookes’s paper on the radiometer, was delighted to read his explanation that the pressure of sunlight was driving the vanes. It was Maxwell who, in 1873, had predicted that light would exert such a force.
His excitement about light pressure was evident during the summer of 1874 when Coggia’s comet made a spectacular appearance in the skies of Europe, igniting a debate about whether the pressure of sunlight was pushing its tail away from the sun. According to a visitor to Maxwell’s house, so often was the word “tail” repeated in conversations that Maxwell’s pet terrier became a whirling dervish, perpetually chasing its non-barking end.
Maxwell was mistaken, however, in his belief that light pressure drove Crookes’s radiometer. As he later realised, not only was the light pressure far too feeble to budge the vanes, but the vanes were spinning the wrong way, with the silvered side leading.
A crucial experiment was done by Arthur Schuster, a young physicist working for Osborne Reynolds, famous for the “Reynolds number” that characterises turbulence in fluids. In 1876, at Reynolds’s instigation, Schuster suspended the glass bulb of a Crookes radiometer by delicate fibres and observed that the bulb turned in the opposite direction to the vanes. Sunlight, he concluded, imparted no net momentum to the system, only energy. The vanes were evidently being turned by something inside. Attention turned to the thin veil of gas left by even the best vacuum pump.
An obvious explanation, and one often trotted out by people aware of the inadequacy of light pressure, is that because the black side of a vane absorbs heat better than the silvered side, gas molecules on the black side are moving faster and hit the vane harder than molecules on the silvered side. The problem with this explanation, however, is that although the gas molecules hit harder, when they bounce back out again they are better at impeding, or deflecting, incoming molecules than the molecules on the cold side. The reduced number of molecules hitting the hot side exactly compensates for their higher speed. So there is no net force on the vanes.
The key thing, which Einstein recognised – yes, he too was fascinated by the Crookes radiometer – is that these two effects do not compensate for each other at the extreme edges of the vanes. Here, some fast-moving gas molecules coming in to hit the black side of a vane are hindered to a lesser extent thanks to slow-moving gas molecules that drift over from the cold side. Consequently, the forces on the two sides of the vanes do not balance exactly, and there is a net push on the black side.
But this is not the only effect in play. The other is “thermal transpiration”, which Maxwell laid out in the very last paper he wrote before his premature death from stomach cancer in 1879. Think of a smooth surface with the temperature increasing along it from left to right. Molecules coming in from the right, hitting the surface and leaving to the left will have a higher velocity than molecules of gas near the surface where the warm incoming molecules strike. And molecules coming in from the left, hitting and leaving to the right will have a lower velocity. The average velocity of molecules on the left and right of the surface is therefore unchanged – and there should be no net effect.
If, however, the surface is not smooth but bumpy – which is always the case with a real surface – there will be a net effect. This is because the bumpy surface acts like a microscopic mountain range. The slower moving molecules from the left are less likely to overcome the peaks and consequently reduce the average energy of the molecules near the surface, whereas the faster moving molecules from the right are more likely to overcome the peaks and increase the average energy of the molecules near the surface. The result is that the gas molecules on the right side of the peaks get hotter and hammer on the peaks more violently than the gas molecules on the left. Because action and reaction are equal and opposite, this causes a drift of the gas molecules from left to right along the surface, from the cold end to the hot end.
So on the hot side of the vane, it will be slightly cooler as you move towards the edges, which means molecules will drift from the edges into the centre. And on the cold side, the edges will be slightly warmer, so there will be a drift from the centre out to the edges. The drift from the edges to the centre on the warm side increases the density of molecules hammering on the warm side, boosting the force on that side. “It’s not completely clear whether this effect dominates or the one highlighted by Einstein,” Larraza says.
It was Reynolds who first hit on the idea of thermal transpiration. But Maxwell, who read the paper that he had sent to the Royal Society, developed the idea and published before him. Reynolds was bitterly resentful, but after Maxwell died it became socially unacceptable to criticise the great man.
In a final twist to the story of the Crookes radiometer, Maxwell’s light pressure theory was laid to rest in 1901. That year, Pyotr Lebedev in Russia and Ernest Nichols and Gordon Hull in the US created a far better vacuum than Crookes had achieved. They succeeded in eliminating the action of the gas by using a suspended vane made of two circular disks of thin glass silvered on one side. By measuring the deflections when the glass and silver sides were successively illuminated, they calculated the gas action and determined the effect of light pressure alone. They showed conclusively that it was not enough to drive the vanes, and the light pressure predicted by Maxwell was finally ruled out.