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International Journal of Modern Physics B

COMPLEMENTARY HISTORIES AND COLLAPSE INTO THE PAST IN STANDARD QUANTUM MECHANICS

Yuri F. Orlov

Published Aug 10, 1999• 0 citations
Publisher

Abstract

It follows from the standard quantum formalism that in the time between any two noncommuting measurements there are two quantum states of the same system representing two complementary, forward and backward histories, histories that may be observed in two complementary experiments. It follows from this in turn that all interpretations of quantum mechanics based on the idea of a single state between measurements should be rejected. The non-existence of a faster-than-light nonlocality and of paradoxes in EPR-type experiments1 can be proved in the frame of the standard formalism when the reality of backward histories is taken into account.

DOI
10.1142/s0217979299002551

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It follows from the standard quantum formalism that in the time between any two noncommuting measurements there are two quantum states of the same system representing two complementary, forward and backward histories, histories that may be observed in two complementary experiments. It follows from this in turn that all interpretations of quantum mechanics based on the idea of a single state between measurements should be rejected. The non-existence of a faster-than-light nonlocality and of paradoxes in EPR-type experiments1 can be proved in the frame of the standard formalism when the reality of backward histories is taken into account.
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We introduce quantum history states and their mathematical framework, thereby reinterpreting and extending the consistent histories approach to quantum theory. Through thought experiments, we demonstrate that our formalism allows us to analyze a quantum version of history in which we reconstruct the past by observations. In particular, we can pass from measurements to inferences about what happened in a way that is sensible and free of paradox. Our framework allows for a richer understanding of the temporal structure of quantum theory, and we construct history states that embody peculiar, non-classical correlations in time.
A new interpretation of quantum mechanics, similar to the Copenhagen interpretation, is developed from time-symmetry arguments and commonly held principles concerning time and causality. These principles, which are grounded in ideas outside of quantum mechanics, suggest that the strange features and paradoxes of quantum mechanics come from backward causation, in which future events can change the past. Using these principles this paper gives a better understanding of (and reasons for) stationary states, tunneling, wave-particle duality, the measurement problem with the collapse of the state vector, Hardy's paradox, non-locality, and the EPR paradox. These are only a few of the interpretational successes, and the model will be contrasted to other popular and/or recent interpretations. Unfortunately, this model is metaphysical, without any predictive power.
When a single photon is split by a beam splitter, its two `halves' can entangle two distant atoms into an EPR pair. We discuss a time-reversed analogue of this experiment where two distant sources cooperate so as to emit a single photon. The two `half photons,' having interacted with two atoms, can entangle these atoms into an EPR pair once they are detected as a single photon. Entanglement occurs by creating indistinguishabilility between the two mutually exclusive histories of the photon. This indistinguishabilility can be created either at the end of the two histories (by `erasing' the single photon's path) or at their beginning (by `erasing' the two atoms' positions).
We have seen, in Section 2.5, how the superposition principle leads to the existence of entangled states of two or more quantum systems. Such states are characterized by the existence of correlations between the systems, the form of which cannot be satisfactorily accounted for by any classical theory. These have played a central role in the development of quantum theory since early in its development, starting with the famous paradox or dilemma of Einstein, Podolsky, and Rosen (EPR). No less disturbing than the EPR dilemma is the problem of Schrödinger’s cat, an example of the apparent absurdity of following entanglement into the macroscopic world. It was Schrödinger who gave us the name entanglement; he emphasized its fundamental significance when he wrote, ‘I would call this not one but the characteristic trait of quantum mechanics, the one that enforces the entire departure from classical thought’. The EPR dilemma represents a profound challenge to classical reasoning in that it seems to present a conflict between the ideas of the reality of physical properties and the locality imposed by the finite velocity of light. This challenge and the developments that followed have served to refine the concept of entanglement and will be described in the first section of this chapter. We start by recalling that a state of two quantum systems is entangled if its density operator cannot be written as a product of density operators for the two systems, or as a probability-weighted sum of such products. For pure states, the condition for entanglement can be stated more simply: a pure state of two quantum systems is not entangled only if the state vector can be written as a product of state vectors for the two systems. In the discipline of quantum information, entanglement is viewed as a resource to be exploited. We shall find, both here and in the subsequent chapters, that our subject owes much of its distinctive flavour to the utilization of entanglement.