The electrons preserve their individuality amid the most diverse vicissitudes, is it the same with the atoms of energy?  We have, for instance, three quanta of energy in a resonator whose wave-length is 3; this passes to a second resonator whose wave-length is 5; it now represents not 3 but 5 quanta, since the quantum of the new resonator is smaller and in the transformation the number of atoms and the size of each has changed.”

If, however, we replace the atom of energy by an “atom of action,” these atoms may be considered equal and invariable.  The whole study of thermodynamic equilibrium has been reduced by the French mathematical school to a question of probability.  “The probability of a continuous variable is obtained by considering elementary independent domains of equal probability....  In the classic dynamics we use, to find these elementary domains, the theorem that two physical states of which one is the necessary effect of the other are equally probable.  In a physical system if we represent by q one of the generalized coordinates and by p the corresponding momentum, according to Liouville’s theorem the domain [double integral]_dpdq_, considered at given instant, is invariable with respect to the time if p and q vary according to Hamilton’s equations.  On the other hand p and q may, at a given instant take all possible values, independent of each other.  Whence it follows that the elementary domain is infinitely small, of the magnitude dpdq....  The new hypothesis has for its object to restrict the variability of p and q so that these variables will only change by jumps....  Thus the number of elementary domains of probability is reduced and the extent of each is augmented.  The hypothesis of quanta of action consists in supposing that these domains are all equal and no longer infinitely small but finite and that for each [double integral]_dpdq_ equals h, h being a constant.”

Put a little less mathematically, this simply means that as energy equals action multiplied by frequency, the fact that the quantum of energy is proportional to the frequency (or inversely to the wave-length as stated above) is due simply to the fact that the quantum of action is constant—­a real atom.  The general effect on our physical conceptions, however, is the same:  we have a purely discontinuous universe—­discontinuous not only in matter but in energy and the flow of time.  M. Poincare thus puts it:  “A physical system is susceptible only of a finite number of distinct states; it leaps from one of these to the next without passing through any continuous series of intermediate states.”

He notes later: 

“The universe, then, leaps suddenly from one state to another; but in the interval it must remain immovable, and the divers instants during which it keeps in the same state can no longer be discriminated from one another; we thus reach a conception of the discontinuous variation of time—­the atom of time.”