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Il Nuovo Cimento B

Special relativity, EPR, and the collapse of the wave function

M. Socolovsky

Published May 1, 2003• 0 citations
Publisher

Abstract

We discuss a paradox which appears in EPR experiments when the collapse of the wave function is analyzed in moving reference frames: the collapse can occur before the actual measurement of the spin component (or polarization) of one of the particles. We show that the paradox can be solved using the instantaneity of the reduction process in all reference frames. Using the same concept, we illustrate with an example the impossibility of defining, in certain circumstances, a covariant state vector in all regions of space-time.

DOI
10.1393/ncb/i2002-10004-3

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We discuss a paradox which appears in EPR experiments when the collapse of the wave function is analyzed in moving reference frames: the collapse can occur before the actual measurement of the spin component (or polarization) of one of the particles. We show that the paradox can be solved using the instantaneity of the reduction process in all reference frames. Using the same concept, we illustrate with an example the impossibility of defining, in certain circumstances, a covariant state vector in all regions of space-time.
We provide a reasonable explanation for measurement where no wave function in the sense of quantum mechanics is collapsed. The wave functions of the particles in the measuring device should be considered together with the measured particle as one system. The measurement is actually a physical process which makes the wave functions of different paths orthogonal. The collapsed wave function is just an equivalent one to explain certain physical phenomena. Our understanding of measurement also provides reasonable explanations for both EPR paradox and the experiments of delayed quantum eraser.
This paper outlines a ‘paradox’ in quantum measurement theory, illustrated with two different types of systems. If this paradox cannot be resolved in ordinary quantum mechanics (as I currently think), it is alarming. If it can be resolved, it can be added to a long list of examples that show the internal consistency of quantum mechanics, and in this case I hope the correct analysis will be an interesting example for students. The immediate paradox involves a failure of Lorentz invariance for measurements on certain types of single particle systems. It seems to show that an absolute frame of reference is required to describe wave function collapse. But if the argument is correct, quantum measurement theory is not merely dependant on the frame of collapse - it is inconsistent, and experimental tests would have to be done to verify whether the apparent non-local effects predicted are real.
Causality and the relativity of simultaneity seem at odds with the apparently sudden, acausal state-vector changes ("collapses") characteristic of quantum phenomena. The problem of how physical phenomena can be causally determined, have the probabilities predicted by quantum theory, and be consistent with special relativity appears to be solved by the assumption, essentially the same as one first used by Aharonov, Bergmann, and Lebowitz to address a different problem, that the "initial" and "final" state vectors of a phenomenon or observation, along with certain other state vectors, all represent the system's state at all times. Each member of such an aggregate of state vectors is postulated to represent a different aspect of a physical state rather than a state, so that most of the state vectors in effect constitute a set of nonlocal hidden variables. Various implications of this assumption are illustrated through several physical situations. Among the results is a somewhat surprising resolution of a paradox in a three-spin Greenberger-Horne-Zeilinger experiment (a "three-particle EPR" experiment), which involves a logical consequence that differs from familiar ideas of quantum physics that has no practical experimental consequence, and the prediction of new experimental phenomena related to the Zou-Wang-Mandel superposed-idler system. The potential value of the concepts described as heuristics for new predictions and for developing physical intuition by clarifying the interrelation and coherence of physical principles that would otherwise seem contradictory is briefly discussed.
Analyzing the EPR paradox, Schrodinger concluded that the problem lies in the way time is used in quantum mechanics. The Schrodinger wave equation, which was the focus of most of the discussion surrounding EPR, is not relativistically invariant and treats time in an essentially classical way. For example it assumes that there can be a well‐defined before and after the collapse of the wave function. Once the wave function collapses into a particle, the event is irreversible. On the contrary, when the relativistically invariant wave equation (Klein‐Gordon’s equation) is taken into account, there is no collapse of the wave function. In this paper a time symmetric interpretation, proposed by the mathematician Luigi Fantappie in 1941, is presented and four experiments which support this interpretation and challenge the Copenhagen Interpretation are discussed. In Cramer’s Transactional Interpretation and in de Beauregard’s Advanced‐Action Interpretation the EPR paradox disappears when advanced waves are considered to be real physical entities.
This report discusses the following: The analysis of the singlet state of separate fermions proves that the EPR contradicts QM. The violation of special relativity. The Schroedinger equation and the EPR. The conservation of angular momentum. The proposal of collapse. The factorization of the spin states. The superposition principle. No paradox exists within the theory. The original state of Einstein et al is not a valid example of the EPR, and it seems impossible to construct a valid linear momentum example. This is another indication that the EPR contradicts QM. Actions at a distance, the model of Einstein et al for particles with mass, and Bell's inequalities and their physical meaning.
This report discusses the following: The analysis of the singlet state of separate fermions proves that the EPR contradicts QM. The violation of special relativity. The Schroedinger equation and the EPR. The conservation of angular momentum. The proposal of collapse. The factorization of the spin states. The superposition principle. No paradox exists within the theory. The original state of Einstein et al is not a valid example of the EPR, and it seems impossible to construct a valid linear momentum example. This is another indication that the EPR contradicts QM. Actions at a distance, the model of Einstein et al for particles with mass, and Bell`s inequalities and their physical meaning.