The problem of objectification in quantum mechanics

Peter Mittelstaedt

Paul Busch, PEKKA J. LAHTI, Peter Mittelstaedt

Guruprasad Kar, S. Roy

Fedor Herbut

The problem of objectification of measurement is investigated in orthodox quantum mechanics, that is assuming the validity of the Schrodinger equation (and the other postulates) for the composite object-plus-measuring-instrument system. It is argued that by giving physical meaning to basic entities, the positivist and the realist positions must be explicitly distinguished. It is shown that the objectification problem is satisfactorily solved within quantum mechanics for the positivist, but not for the realist. For the latter, a partially satisfactory solution is obtained by assuming that the quantum mechanical description of individual systems is incomplete and, by assuming further, that the pointer observable has definite values prior to any measurement in any quantum state (a so-called beable).

Peter Mittelstaedt

The concept of objectification Weak and strong objectification Let S be a quantum system that is prepared in a pure state φ and A a discrete nondegenerate observable with eigenvalues a i and eigenstates φ a i . If the preparation φ is not an eigenstate of A , then quantum mechanics does not provide any information about the value of the observable A . The pair 〈φ, A 〉 merely defines a probability distribution p (φ, a i ), the experimental meaning of which is given by the statistical interpretation of quantum mechanics: the real positive number p (φ a i ) is the probability of obtaining the result a i after a measurement process of the observable A . This means that if one were to perform a large series of N measurements of this kind, then the relative frequency f N (φ, a i ) of the result a i would approach for almost all test series the probability p (φ, a i ), for N → ∞ (cf. chapter 3). One could, however, in addition to these well-established results tentatively assume that a certain value a i or even an eigenstate φ a i of A pertains objectively to the system S but that this value or state is subjectively unknown to the observer, who knows only the probability p (φ, a i ) and hence the distribution of possible measurement outcomes. The probability would then express the subjective ignorance (or knowledge) about an objectively decided value or eigenstate of A . The hypothetical attribution of a certain value or eigenstate of A to the system S will be called objectification .