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Where is an object before you look at it

Marcello Cini, Maurizio Serva

Published Jun 1, 1989• 0 citations
OpenAlex

Abstract

According to the standard interpretation of quantum mechanics (QM), no meaning can be assigned to the statement that a particle has a precise value of any one of the variables describing its physical propertes before having interacted with a suitable measuring instrument. On the other hand, it is well known that QM tends to classical statistical mechanics (CSM) when a suitable classical limit is performed. One may ask therefore how is it that in this limit, the statement, meaningless in QM, that a given variable has always a precise value independently of having been measured, gradually becomes meaningful. In other words, one may ask how can it be that QM, which is a theory describing the intrinsically probabilistic properties of a quantum object, becomes a statistical theory describing a probabilistic knowledge of intrinsically well determined properties of classical objects.

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According to the standard interpretation of quantum mechanics (QM), no meaning can be assigned to the statement that a particle has a precise value of any one of the variables describing its physical propertes before having interacted with a suitable measuring instrument. On the other hand, it is well known that QM tends to classical statistical mechanics (CSM) when a suitable classical limit is performed. One may ask therefore how is it that in this limit, the statement, meaningless in QM, that a given variable has always a precise value independently of having been measured, gradually becomes meaningful. In other words, one may ask how can it be that QM, which is a theory describing the intrinsically probabilistic properties of a quantum object, becomes a statistical theory describing a probabilistic knowledge of intrinsically well determined properties of classical objects.
Identity principle is a fundamental postulate of quantum mechanics. In this paper, from a philosophical point of view, we revisit the identity principle of quantum mechanics. We attribute the identity to the existence of a precision limit for observation: the microscopic objects become indistinguishable when the difference between them is lower than the precision limit. This precision limit is determined not by the measuring apparatus, but by the action quantum h behand the objective physical law. We deduce logically how to relate the identity principle with the probabilistic interpretation, uncertainty principle, quantization in quantum mechanics, attempting to sorting out some logic for quantum theory. The indistinguishability of identical particles makes it impossible to accurately obtain all the details about the microscopic objects at the same time, and consequently the microscopic objects can only be described statistically, leading to the probabilistic determinism and indeterminacy of initial state in quantum mechanics. By reviewing Bohmian mechanics, one of the nonlocal hidden variable theories, we discuss the possibility of restoring determinism and causality in quantum mechanics by restoring the determinacy of initial state. However, any hidden variable theory constructed by using only the terminologies of classical physics cannot reproduce the quantum mechanical predictions. It is the identity principle that makes it impossible to restore causality and determinism, and is the root that makes quantum mechanics different from classical physics. Finally, the boundary between the so-called classical and quantum worlds is discussed. We hope these philosophical arguments can provide a kind of epistemic understanding for quantum mechanics.
While I very much enjoyed Steven Weinberg’s article “Einstein’s Mistakes,” I am puzzled by the author’s statement about quantum mechanics: “The difficulty is not that quantum mechanics is probabilistic—that is something we apparently have to live with. The real difficulty is that it is also deterministic, or more precisely, that it combines a probabilistic interpretation with deterministic dynamics.” Quantum mechanics is an acausal deterministic theory in the sense that a physical system’s state (mathematically described by a state vector) at a given initial time determines its state at a specified later time, but its state is not in one-to-one correspondence with sharp values of all its dynamical variables; that correspondence is probabilistic. Therefore events, identified by sharp values of those variables at one spacetime point, are not causally connected with other events. That is something we have to live with.Why does the combination of these two attributes—acausality and determinism—constitute a special difficulty? Weinberg asks, “So where do the probabilistic rules of the Copenhagen interpretation come from?” Why do they have to come from anywhere other than from human brains? Nature exists out there, independent of human thought, but its mathematical description surely is a human construction rather than an immutable law given to us on a stone tablet.© 2006 American Institute of Physics.
A critical reconsideration of the EPR (Einstein-Podolsky-Rosen) paper shows that the EPR argument can be developed without using the concept of `element of physical reality', thus eliminating any philosophical element in the logical chains of the paper. Deprived of its philosophical ornament, the EPR argument plainly reduces to require what quantum mechanics can not do: to assign definite values to two incompatible physical quantities. Hidden variables theories built up according to Bell - type theorems are formulated on the basis of the assumption that the locality condition implies the statistical independence between two measurements space - like separated. This assumption is valid only with the additional one that statistical dependence between two measurements requires a causal connection between them. This additional assumption rules out the possibility that statistical dependence may due to an intrinsic property of the physical system under study. Therefore, hidden variables theories are built up with a restriction which leads them to be disproved by experiment. Quantum mechanical non - locality, invoked for describing EPR - type experiments, is strictly connected to the hypothesis (NDV hypothesis) according to which the twin photons of entangled pairs do not have a definite polarization before measurements. Both hypotheses are used only for describing EPR experiments and not for making predictions. Therefore, they can be dropped without reducing the predictive power of quantum mechanics concerning entangled photons pairs. Furthermore, both hypotheses can be experimentally tested by a modification of a standard experimental apparatus designed for studying entangled photons pairs.