Once Again on the 'demythologizing' of the Clock-in-the-box Debate of Bohr and Einstein *

The reply of de la Torre, Daleo and García-Mata [Eur. J. Phys. 23 (2002) L15–L16] to a criticism of their 'demythologizing' analysis of the clock-in-the-box debate between Einstein and Bohr is commented on. The main point of the reply [1] of de la Torre, Daleo and García-Mata (TDG) to my criticism [2] of their 'demythologizing' analysis [3] of the arguments of Bohr and Einstein concerning the famous clock-in-the-box gedanken experiment is that the criticism suffers from the 'same mistakes' as those which TDG assert have been committed by Bohr: 'the confusion of quantum indeterminacies with experimental uncertainties'. TDG point out that the meaning of the 'quantum indeterminacy' ∆A of an observable A in a state ψ is only given by ∆A = [ψ|A 2 |ψ − ψ|A|ψ 2 ] 1/2 , which is a quantity that is essentially different from the 'ex-perimental uncertainty' δA in a measurement of A, and that while the lack of appreciation of this difference could have been tolerated during the early days of quantum mechanics, there is no excuse for making the mistake of confusing those two quantities today. In the present note, I comment on this and the other points of the reply of TDG. If, as implied by TDG, the experimental uncertainty δA refers to a measurement of the observable A done on a state in which A has an indeterminacy ∆A, then, of course, there is no prescribed relation between δA and ∆A—this is a trivial point which would be almost impertinent to assume Bohr was not aware of. A state in quantum mechanics (which does not have to be a pure state) always can be defined so that the indeterminacy ∆A of a continuous-spectrum observable A takes in this state an arbitrarily given value, and, in principle, the measurement of A in this state can be done with an uncertainty δA such that, for example, δA < ∆A, no matter how small ∆A was. But one thing is to define a state in a formalism, and another one is the physical realization of a such a state. In the standard interpretation of quantum mechanics (the essential features of which are due to Bohr himself), a physical state to be described by the formalism of quantum mechanics arises as the result of a physical procedure that is describable in purely classical terms; such a procedure is usually also called a 'measurement'. Measurement …