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Henri Poincaré, Quanta hypothesis: The law of radiation

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Physicists did not at first concern themselves with these difficulties, but two new facts changed the face of things; the first is what is called the law of black radiation. A perfectly black body is one whose absorption coefficient is equal to 1; such a body brought to incandescence emits light of all wavelengths, and the intensity of this light varies according to a certain law as a function of the temperature and the wavelength. Direct observation is not possible, because there are no perfectly black bodies, but there is a way to turn the difficulty: one can enclose the incandescent body in a completely closed enclosure; the light it emits can not escape and undergoes a series of reflections until it is fully absorbed; when the state of equilibrium is reached, the temperature of the enclosure has become uniform and the enclosure is filled with radiation which follows the law of black radiation.

It is clear that this is a case of statistical equilibrium, the energy exchanges having continued until each part of the system gains on average, in a short space of time, exactly what it loses. But it is here that the difficulty begins. The material molecules contained in the enclosure are in finite number, though very large, and they have only a finite number of degrees of freedom; on the contrary, the ether has an infinity, because it can vibrate in an infinite number of ways corresponding to the various wavelengths with which the speaker is in resonance. If the equipartition law applied, then the ether should take all the energy and leave nothing to the matter.

The freedom of the ether could be restricted by imposing bonds on it, which would render it, for instance, incapable of transmitting too short waves; it would thus escape the contradiction indicated, but would still arrive at a law which, to be no longer absurd, would still be contradicted by experience. It is the Rayleigh law, according to which the radiated energy, for a given length, would be proportional to the absolute temperature and for a given temperature, inversely to the fourth power of the wavelength.

The true law, demonstrated by experience, is Planck’s law; the radiation is much less for the small wavelengths, or for the low temperatures, than the law of Rayleigh, in accordance with the law of equipartition.

The second fact results from the measurement of the specific heats of solid bodies at very low temperatures, in air or in liquid hydrogen. These specific heats, far from being appreciably constant, diminish rapidly as to cancel themselves at absolute zero. It is as if these molecules lose degrees of freedom as they cool, as if some of their joints eventually freeze.


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