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).
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).
In this work we analyze the deep link between the 20th Century positivist re-foundation of physics and the famous measurement problem of quantum mechanics. We attempt to show why this is not an "obvious" nor "self evident" problem for the theory of quanta, but rather a direct consequence of the empirical-positivist understanding of physical theories when applied to the orthodox quantum formalism. In contraposition, we discuss a representational realist account of both physical 'theories' and 'measurement' which goes back to the works of Einstein, Heisenberg and Pauli. After presenting a critical analysis of Bohr's definitions of 'measurement' we continue to discuss the way in which several contemporary approaches to QM --such as decoherence, modal interpretations and QBism-- remain committed to Bohr's general methodology. Finally, in order to expose the many inconsistencies present within the (empirical-positivist) presuppositions responsible for creating the quantum measurement problem, we show how through these same set of presuppositions it is easy to derive a completely analogous paradox for the case of classical mechanics.
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 .
Abstract Given an ontological model of a quantum system, a “genuine measurement,” as opposed to a quantum measurement, means an experiment that determines the value of a beable, i.e., of a variable that, according to the model, has an actual value in nature before the experiment. We prove a theorem showing that in every ontological model, it is impossible to measure all beables. Put differently, there is no experiment that would reliably determine the ontic state. This result shows that the positivistic idea that a physical theory should only involve observable quantities is too optimistic.
We present a historical-epistemological analysis of the foundations of quantum mechanics, highlighting the relationships between quantum mechanics and scientific realism, as well as the influence of the neo-positivist philosophy of the first decades of the 20th century. The great significance of the measurement process in the context of quantum mechanics is underlined as an essential element in providing a coherent description of reality, moving from micro to macrocosm, as well as the role that the measurement apparatus and the consciousness of the observer assume during the act of measurement, the related ontological problems, the question of the objectification of the wave function, and that of the definition of discernibility. We consider also an overview of the most important alternative proposals to the standard interpretation of quantum mechanics (Copenhagen interpretation), with particular reference to hidden variable theories and other alternatives to standard quantum mechanics philosophical approach, that are modifying the vision of reality, such as the Everett’s many-worlds theory, the QBism and unified holistic approaches, such as the Primordial Dynamic Space.
Pekka Lahti is a prominent exponent of the renaissance of foundational studies in quantum mechanics that has taken place during the last few decades. Among other things, he and coworkers have drawn renewed attention to, and have analyzed with fresh mathematical rigor, the threat of inconsistency at the basis of quantum theory: ordinary measurement interactions, described within the mathematical formalism by Schrödinger-type equations of motion, seem to be unable to lead to the occurrence of definite measurement outcomes, whereas the same formalism is interpreted in terms of probabilities of precisely such definite outcomes. Of course, it is essential here to be explicit about how definite measurement results (or definite properties in general) should be represented in the formalism. To this end Lahti et al. have introduced their objectification requirement that says that a system can be taken to possess a definite property if it is certain (in the sense of probability 1) that this property will be found upon measurement. As they have gone on to demonstrate, this requirement entails that in general definite outcomes cannot arise in unitary measuring processes. In this paper we investigate whether it is possible to escape from this deadlock. As we shall argue, there is a way out in which the objectification requirement is fully maintained. The key idea is to adapt the notion of objectivity itself, by introducing relational or perspectival properties. It seems that such a “relational perspective” offers prospects of overcoming some of the long-standing problems in the interpretation of quantum mechanics.
This work presents a historical-epistemological analysis of the foundations of quantum mechanics. From a philosophical point of view, the relationships between quantum mechanics and scientific realism are highlighted, as well as the influence of the neo-positivist philosophy of the first decades of the 20th century. The great significance of measurement in the context of quantum mechanics is underlined, as an essential element in providing a coherent description of reality moving from the microcosm to the macrocosm, as well as the role that the measurement apparatus and the consciousness of the observer assume during the act of measurement, the ontological problem, the problem of the objectification of the wave function and the problem of the definition of discernibility. This is followed by an overview of the most important alternative proposals to the standard interpretation (Copenhagen interpretation), with particular reference to hidden variable theories, and other alternatives to standard quantum mechanics that profoundly modify the vision of reality, such as the Everett’s many-worlds theory, the QBism, the unified holistic approach.