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Henri Poincaré, Quanta hypothesis: Quanta of energy

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The explanation of these phenomena must be sought without making a clean sweep of the principles of Thermodynamics; above all, we must admit the possibility of statistical equilibrium, otherwise nothing would remain of Carnot’s principle; we cannot admit, in Thermodynamics, any breach without all collapsing. Mr. Jeans has tried to reconcile everything by supposing that what we are observing is not the definitive statistical equilibrium, but a sort of provisional equilibrium. It is difficult to adopt this view; his theory, foreseeing nothing, is not contradicted by experience, but it leaves without explanation all the known laws which it limits itself to not contradicting and which appear only as the effect of I do not know what a happy coincidence.

Mr. Planck sought another explanation of the law he had discovered; according to him, it is a true equilibrium, and if it does not conform to the equipartition law, it is because Hamilton’s equations are not exact. To arrive at the experimental law, we must introduce into these equations a very surprising modification. How should we imagine a radiant body? We know that a Hertz resonator sends in the ether radio waves which are nothing but luminous waves; an incandescent body will therefore be regarded as containing a very large number of small resonators. When the body heats up, these resonators acquire energy, vibrate and therefore radiate.

Planck’s hypothesis consists in supposing that each of these resonators can acquire or lose energy only by sudden jumps, so that the energy supply which it possesses must always be a multiple of the same constant quantity called quantum, that it must consist of a whole number of quanta. This indivisible unit, this quantum is not the same for all the resonators, it is in inverse proportion to the wavelength, so that the short-lived resonators can swallow energy only in large pieces while long-lived resonators can absorb or release it in small bites. What does it result? It takes great effort to shake a short-lived resonator, since at least a quantity of energy equal to its quantum is required; there is therefore a good chance that these resonators will remain at rest, especially if the temperature is low, and that is why there will be relatively little short wavelength light in the black radiation.

This hypothesis is well aware of the facts provided that we admit that the relation between the energy of the resonator and its radiation is the same as in the ancient theories. And this is a first difficulty; why keep this after destroying everything? But we must keep something, otherwise we would not know what to build on.

The reduction of specific heats is likewise explained; when the temperature drops, a large number of vibrators fall below their quantum, and, instead of vibrating little, no longer vibrate at all, so that the total energy decreases faster than in the old theories . This is only a qualitative glimpse, but one must not give an exaggerated number of pushes to obtain a sufficient quantitative concordance.

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