1 4 0 D O C U M E N T 1 1 9 N O V E M B E R 1 9 2 5 never be released. This objection would be absolutely correct, in my opinion, if it only concerned the harmonic oscillator. It is different, though, if, e.g., the harmonic oscillator is being approximated from the oscillations of two atoms or many atoms. As, at sufficiently high energy values, the atoms involved would then fall asunder and a certain “absolute” energy is fixed by the energy of atoms an infinite distance apart, or better: The energy as a function of the distance has, e.g., the form[4] (q = For adequately small values of , we have the harmonic-oscillator problem.[5] Nevertheless, is not simply an additive constant, because, of course, for adequately high values of q the energy becomes . (Naturally, an additive constant is very generally arbitrary, yet it is generally customary to set in the case of purely kinetic energy).— From all of this I would like to conclude that in the problem of the purely harmonic oscillator, the result of the “zero-point energy” actually has no physical meaning, because it cannot be verified ( does not enter into the energy differences the radiation at zero point vanishes) the same applies to the cavity. Also in the case of oscillations of an elec- tromagn. cavity, I do not see how this could ever be observable, since the cavity is, of course, an exact harmonic oscillator. A solid body is different because there the also enters into the energy difference (namely, in the difference between the energy of the normal state and the energy of atoms an infinite distance apart). (That is why, in my opinion, zero-point energy plays an important role in thermodynam- ics according to Nernst.[6] )— Another important objection could probably be raised against this reasoning, namely, that the absolute energy value would be ver- ifiable by means of the mass therefore, that it would be necessary to assign mass to the cavity, if one assigns the energy to it (and even infinitely much mass, be- cause the cavity contains eigen oscillations of arbitrarily high ν). The possible re- buttal to this, however, is that, on the one hand, the theory of this quantum mechanics is not yet developed far enough at the moment to recognize its connec- 1 2m -------p2 a- q5 ---- b q2 ---- - 1 2mp2 ------------- a q0 5 ----- b q0¹ 2 ----- © § · 30a q0 7 -------- - 6b· q0 ----- -– © § q1 2 + + + –+ q0 q1 + q0 5a 2b ----- - 3 = ¹ ·. q1 2 ----- - 1 2m -------p2 E 1 2m ------- p2 = 2 ----- - 2 ----- - 2 ----- - 2 ----- - 2 ----- -
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