What does Bohr mean in the following letters?
Bohr:
The idea that any observation must necessarily involve an increase in entropy has been much discussed and I remember that already in the discussions with Stern and you in Hamburg, when you helped me with the ‘proofs’ of the old paper on complementarity, I stressed the principal irreversibility of the concept of observation. More specifically, any observation must make use of some registering device, whether through a photographic plate or directly by the retina of the eye, which involves processes of amplification by which free energy is spent. I know that also Teller is interested in these problems which were discussed in Los Alamos. I shall be glad if either you or Stern would write to me what has come out of your discussions in Zurich.
Pauli:
The discussions which I had here with Stern (he left Zurich a few days ago) concerned the quantitative side of the connection of the concepts of entropy and of observation, a connection which, as we all agree, is of a very fundamental character. The problem arises whether there is a well defined minimum of the increase in entropy, independent of the particular experimental arrangement in use, if a certain quantity (‘observable’) is measured. Our discussions seemed to indicate that this is actually the case, although we did not reach yet any final conclusion. The increase in entropy can easily [be] computed if one starts with a ‘mixture’ as initial states and changes it into a ‘pure case’ by constatation of the value of a certain quantity. If, however, before and after the measurement the observed system is in pure cases the situation seems to be more difficult to judge. (Example: a single particle in a closed box. Before the measurement it is supposed to be in a certain eigenstate with a sharply fixed value of the energy. Then one observes the place of the particle in space, perhaps by constatation that it is in a certain partial volume. What one can [can one] say about the amount of the increase in entropy through this measurement, independent of a particular experimental arrangement?) We discussed different experimental arrangements, but we are not sure how general our preliminary results are. Stern and I are both trying to continue the considerations of the problems, possibly by correspondence. Needless to say how anxious I am to hear what you know yourself on this quantitative side of the increase in entropy by observations and how grateful I would be if you could write to me your views on this problem. I feel that you might know the answer already or at least that you may find it out quicker than we.
Bohr:
As regards the problem of the entropy increase connected with observations I have in the last days been thinking anew over the situation and have also revived my reminiscence of earlier discussions on this point. You will remember our talks with Stern in Hamburg at the time you so kindly assisted me in gradually working my first article on complementarity from proof back to manuscript. The question was then of Boltzmann’s ideas regarding the direction of time and my point was that the very concept of observation entails an irreversibility in principle. In the following years, this problem came into the foreground in connection with the question of the consistency of the interpretation of the quantum mechanical formalism and in continuation of our discussions in Warsaw I had during the war some talks in America with v. Neumann who still felt some uneasiness about the apparent arbitrariness in the distinction between the objects and the measuring instruments, and with Teller who just like Stern, as I gather from you, was endeavouring to look for the elucidation of the paradoxes in a more quantitative connection between thermodynamics and the observational problem. After reconsidering the question, I feel myself that the whole question is purely epistemological and therefore of qualitative rather than quantitative character. On the one hand, it is evident that any practical observational arrangements, making use of photographic plates, cloud chambers or direct sensual impressions, involve a mechanism of amplification in the working of which free energy is spent in amounts out of all proportion with the energy exchanges characterizing the individual atomic processes under investigation. On the other hand, it is equally clear that, for the interpretation of [the] quantum mechanical formalism and the elucidation of the paradoxes involved, the problem is how to account consistently for the phenomena defined by means of measuring agencies and recording devices which serve to fix the external conditions and register the experimental results and which, for this purpose, are to be treated as ideal classical instruments.
Of course, it is true that the constitution and operation of the instruments is ultimately subject to the laws of atomic mechanics and that a consideration of this point may perhaps eventually prove a guide for the overcoming of the still unsolved difficulties in quantum theory, but I am sure we agree that this point has as little to do with the questions for which Einstein feels such uneasiness as the final clarification of the still unsolved problems of cosmology has to do with futile criticism of the foundation of relativity
theory.
The irreversibility in any observational problem has its root in a certain degree of complication of the interaction of the object with the measuring agencies and, trying to make the situation more clear to me, I have considered experimental arrangements where the critical element of irreversibility may be arbitrarily far removed from the final macroscopic recording. For instance, we may, for the localization of a particle, instead of catching it directly on a photographic plate, allow it to enter through a small hole in a box from which the probability of escaping is vanishingly small and where, therefore, the presence of the particle can be ascertained in some suitable way at a later time. The degree of irreversibility here depends on the complicated character of the state of motion of the particle in the box, and the problem presents a certain analogy with the entropy increase accompanying irreversible expansion of a gas from a smaller volume u to a larger volume V which for gas molecule is given by \(k\ln\frac{V}u\). From such considerations it follows that there will be a close correspondence between the degree of complexity required and the degree of irreversibility practically demanded and that, under optimal circumstances, the unavoidable entropy increase may be brought down to the order of k, representing the limit for the unambiguous use of the very concept of entropy.
Here, I have in mind such considerations about the complementary relationships between thermodynamical and mechanical concepts as I tried to indicate in my old Faraday lecture. Just as such considerations offer a consistent attitude to the well-known paradoxes of irreversibility in thermal phenomena, so it appears to me that, notwithstanding the obvious qualitative relationship between such phenomena and the irreversibility of observations, we may more adequately regard thermodynamical considerations and the essence of the observational problem as different complementary aspects of the description.
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