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Philosophy of Science

The Impossibility of Accurate State Self-Measurements

Thomas Breuer

Published Jun 1, 1995• 77 citations
Publisher

Abstract

It is shown that it is impossible for an observer to distinguish all present states of a system in which he or she is contained, irrespective of whether this system is a classical or a quantum mechanical one and irrespective of whether the time evolution is deterministic or stochastic. As a corollary, this implies that it is impossible for an observer to measure the EPR-correlations between himself or herself and an outside system. Implications of the main result are discussed for how we have to conceive of universally valid theories.

DOI
10.1086/289852

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It is shown that it is impossible for an observer to distinguish all present states of a system in which he or she is contained, irrespective of whether this system is a classical or a quantum mechanical one and irrespective of whether the time evolution is deterministic or stochastic. As a corollary, this implies that it is impossible for an observer to measure the EPR-correlations between himself or herself and an outside system. Implications of the main result are discussed for how we have to conceive of universally valid theories.
I consider the extent to which the applicability of the concept of classical realism is constrained, irrespective of the validity or not of the quantum formalism, by existing experiments both in the EPR–Bell setup, including recent experiments testing ‘nonlocal realistic’ theories, and in the area of ‘macroscopic quantum coherence’. Unless we are willing to sacrifice one or more other intuitively plausible notions such as that of the conventional ‘arrow of time’, it appears impossible, in either context, to maintain the classical notion of realism.
One of the fundamental conceptual difficulties in quantum mechanics arises from the fact that two of the axioms of the theory concerning the evolution of a microscopic system are contradictory. The first axiom assumes that the state of a quantum system evolving undisturbed by any observer obeys a linear deterministic law expressed by the SchrSdinger equation. The second one (wave-packet reduction principle) states that, when the quantum system interacts with an apparatus devised to measure some of its dynamical variables, its state changes abruptly and stochastically, jumping into a normalized eigenstate of the measured variable. This evolution is not deterministic nor linear and cannot be accounted for by the SchrSdinger equation. As a consequence the internal coherence of the theory becomes questionable. On one side the influence of the apparatus on the quantum system cannot be described as an interaction of the quantum constituents of the measuring macroscopic apparatus with the measured quantum system. On the other side, the impossibility of considering a macroscopic object as made by quantum constituents, i .e . the difficulty of quantum mechanics in describing the behaviour of macroscopic systems, is even more dramatic if we consider the evolution of the closed system consisting of the macroscopic apparatus and of the microscopic system. In such a case the appearance of superpositions of macr0scopically distinguishable states related to the apparatus cannot be avoided. These superpositions contradict both our classical experience and wave-packet reduction principle, which provides for statistical mixtures.
The main distinction between classical mechanics and quantum mechanics is the lack in the latter of a full mechanical determinism: different final states can arise from the same physical state, after the measurement. No hidden variable is supposed to exist, nothing can discriminate two apparently identical states even if they give a different result. In this paper we try to put the basis for a more fundamental theory that (approximately) coincides with quantum mechanics when comparing statistics, but it is more fundamental, since it mathematically describes measurement processes giving an explicit time evolution of the wave function during the collapse. The theory is deterministic even if the Heisenberg uncertainty principle is still valid. The theory distinguishes physical states that collapse and physical states that do not collapse. The theory can be made compatible with all experiments done in the past, but new phenomena such as violations of the Born law or the superposition principle could transpire. However, even if we have probably shown that it is possible to build ad hoc a theory that can describe both the wave function collapse and the Schrödinger linear evolution, a simple and unified construction is still missing.
Abstract I think of the development of physics as the growth of relativism. Every increase in relativism is an increase in our understanding of the complexity of the observer, of a number of possible observers, and of the influence of the observer upon the phenomenon. Quantum theory is only the latest stage in this growth of relativism. It is by no means the end of our understanding of the importance of the observer or the experimenter. In fact, I think it’s no longer proper to speak of the observer because that still carries the old implication of someone who observes from outside the phenomenon without changing it. In quantum theory we only have experimenters, people who do things. One of the lessons of relativism is that one should be very careful about assuming the existence of things that in principle cannot be seen. Evidently one of these things is the universe. It’s a physical impossibility, as a matter of principle, for any experimenter to have complete information about the universe. Every experimenter begins by ignoring large parts of the universe, namely, himself or herself. You turn your attention to something by omitting from your attention much more. It is quite possible that the universe will go the way of absolute time or absolute state. I don’t think we have reached the end of this growth in relativism.
There are two known ways around J.S Bell's famous Inequalities. One is to deny Reichenbach's Common Cause Principle (Bell himself understood this). Another is to impose the lone spin average constraint (Samuel Hedemann discussed this in an obscure preprint). In both cases the Bell Inequality and all generalizations thereof (CHSH, CGLMP and others) cannot be derived, which implies the quantum mechanics correlations one presumes for EPR experiments, and observes, are not necessarily indications of Non-Locality (NL) or anti-Realism (AR). Nevertheless, the orthodox consensus is that our universe is still highly non-classical and EPR-like entanglement correlations are at the heart of the behaviour of non-classical elementary systems. This demands, but we can say "invites," a better account of the observed highly non-classical behaviour of entangled systems, which: (1) respects the (very respectable) lone spin average constraint, and (2) mildly disrespects Reichenbach's principle (RCC), and then (3) explains why one can take the view that either Determinism (D) or (RCC) is violated in quantum processes. We provide a preliminary such account using the principles of topological 4-geon theory (T4G) which leans towards only abandoning the weakest version of (D) possible (deterministic time-evolution) but for very good reason. NB: we have no plans to submit this to a peer review journal, but collaborators with journal access are welcome to inquire about contributing to this preprint to further a peer review process.