16 April 1926

Dear Colleague,

Professor Planck pointed your theory out to me with well justified enthusiasm, and then I studied it too, with the greatest interest. In the process one doubt has arisen which I hope you can dispel for me. If I have two systems that are not coupled to each other at all, and if *E*_{1} is an allowed energy value of the first system and *E*_{2} an allowed energy value of the second, then *E*_{1} + *E*_{2} = *E* must be an allowed energy value of the total system consisting of both of them. I do not, however, understand how your equation

is to express this property.

So that you can see what I mean, I put down another equation that would satisfy this condition:

For, the two equations

(valid for the phase space of the first system)

(valid for the phase space of the second system) have as a consequence

(valid in the combined q- space).

As proof one need only multiply the equations by φ2 and φ1 respectively and add. φ1 φ2 would, therefore, be a solution of the equation for the combined system, belonging to the energy value *E*, + *E*_{2}.

I have tried in vain to establish a relationship of this sort for your equation.

It also seems to me that the equation ought to have such a structure that the integration constant of the energy does not appear in it; this also holds for the equation I have constructed, but despite that I have not been able to assign a physical significance to it, a matter on which I have not reflected sufficiently.

With warmest greetings from

A. Einstein

The idea of your article shows real genius.^{8}