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American Journal of Physics

An apparent paradox at the heart of quantum mechanics

Jose Luis Cereceda

Published Apr 1, 1996• 1 citation
Publisher

Abstract

A simple conceptual experiment which seems to violate the general principles of quantum mechanics is reported. The reasoning leading to this contradiction contains a trick which makes the paradox possible. By discussing the failure of the argument the author wishes to draw attention to a fundamental feature of the wave function which is frequently overlooked. Finally, in light of this discussion, a kind of delayed-choice experiment is described, and an analysis of the related issue of complementarity is made.

DOI
10.1119/1.18192

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A simple conceptual experiment which seems to violate the general principles of quantum mechanics is reported. The reasoning leading to this contradiction contains a trick which makes the paradox possible. By discussing the failure of the argument the author wishes to draw attention to a fundamental feature of the wave function which is frequently overlooked. Finally, in light of this discussion, a kind of delayed-choice experiment is described, and an analysis of the related issue of complementarity is made.
In recent years there has been an upsurge in the discussion of so-called delayed-choice experiments, as exemplified in the interferometer experiment discussed by Wheeler [1]. In commenting on this experiment Bohm et al. [2] claim that their quantum potential interpretation gives results entirely compatible with Bohr's views on wholeness and complementarity. It seems to me, however, that this discussion to a large extent completely misses the fundamental point in Bohr's argumentation as given in his famour answer [3] to Einstein, Podolsky and Rosen as well as in his paper on his discussions with Einstein [4]. Expressing it a bit paradoxically one might say that in the examples discussed the experiments are not sufficiently delayed. I shall therefore here discuss a different thought experiment, much closer to Bohr's own examples, which brings out this point.
Abstract. This paper proposes a resolution of the delayed-choice paradox of the Conven-tional Theory of quantum mechanics, where a particle seems to know what will happen in the future, and changes its present behavior accordingly. A comparison of the Conventional Theory with an Advanced Theory and a Symmetrical Theory of the same delayed-choice experiment suggests that the apparent paradox is caused by an incorrect assumption about the interaction of a wavefunction with a beam-splitter. Once this assumption is corrected, there is no delayed-choice paradox in any of the three theories. 1.
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.
In most textbooks, measurement does not receive the full attention it deserves and sometimes is even not treated at all, apart a brief and cryptic mention of the “reduction of the wave packet.” However, in the last decades, the situation has profoundly changed and it is time to consider measurement a fundamental part of quantum mechanics, even, to a certain extent, an important generalization of the traditional theory (see also Chs. 14–15). This chapter consists of three major parts. In the first block (Secs. 9.1–9.4) we develop the main physical features of the measurement process: the heart of the argument is here represented by the aspects related to the interpretation. In the second part (Secs. 9.5–9.8) we discuss several special (and partly interdependent) topics of measurement: the heart here is represented by experimental aspects. In the third part (Secs. 9.9–9.12) we deal with the measurement process on a more formal plane, making use, in particular, of the generalization represented by the concepts of effect and positive operator valued measure (POVM). As we have said, the measurement problem is one of the most fundamental issues in the conceptual structure of quantum mechanics (as described in Sec. 9.1) and has a long history that will be examined in Sec. 9.2. In this context, the existence of apparently paradoxical quantum states comes about: the so-called Schrödinger cat states (see Sec. 9.3).