Comments on Generalized Mechanics

Sumiyoshi Abe

In their Comment on the paper [Abe and Okuyama, Phys. Rev. E 83, 021121 (2011)], González-Díaz and Díaz-Solórzano discuss that the initial state of the quantum-mechanical analog of the Carnot cycle should be not in a pure state but in a mixed state due to a projective measurement of the system energy. Here, first the Comment is shown to miss the point. Then, second, multiple projective measurements are discussed as a generalization of the Comment, although they are not relevant to the work commented.

T. E. Phipps

M. Yussouff

Tullio Levi-Cività

Hilary Putnam

The Margenau and Wigner ‘Comments’ (1962) on my ‘Comments on the Paper of David Sharp’ (Putnam, 1961; Sharp, 1961) is a strange document. First the authors say, in effect, ‘had anything been wrong (with the fundamentals of quantum mechanics) we should certainly have heard’. Then they issue various obiter dicta (e.g. the ‘cut between observer and object’ is unavoidable in quantum mechanics; the – highly subjectivistic – London-Bauer treatment of quantum mechanics is described, along with von Neumann's book, as ‘the most compact and explicit formulation of the conceptual structure of quantum mechanics’). My assumption 2 (that the whole universe is a system) is described as ‘not supportable’, because ‘the measurement is an interaction between the object and the observer’. The ‘object’ (the closed system) cannot include the observer. The issues involved in this discussion are fundamental ones. I believe that the conceptual structure of quantum mechanics today is as unhealthy as the conceptual structure of the calculus was at the time Berkeley's famous criticism was issued. For this reason – as much to emphasize the seriousness of the present situation in the foundations of quantum mechanics as to remove confusions that may be left in the mind of the general reader upon reading the Margenau and Wigner ‘Comments’ – I intend to restate the main points of my previous ‘Comments’, and to show in detail why the Margenau and Wigner remarks fail completely to meet them.