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Physics Today

Quantum Histories, Mysteries, and Measurements

N. G. van Kampen, Bryce Seligman DeWitt, Sheldon Goldstein, Jean Bricmont, Robert B. Griffiths, Roland L. Omnes

Published May 1, 2000• 3 citations
Publisher
DOI
10.1063/1.883089

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Interpretation problems are eliminated from quantum theory by picturing a quantum history as having been sampled from a probability distribution over the set of histories which are permitted by all relevant boundary conditions. In laboratory physics, the final measurement plays a crucial role in defining the set of allowed histories by constraining the final state to be an eigenstate of the measurement operator. For the universe itself, a final boundary condition can play a similar role. Together with the special big bang initial state, the final constraint may ensure that the universe admits a classical description in the asymptotic future. Acknowledging the role of a future constraint dispels the mysteries of quantum theory without any amendment to the theory itself.

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An increasingly popular interpretation of quantum mechanics holds that in any genuinely chancy situation, all possible outcomes occur.1 For example, if the spin of a typical electron is measured in a given direction, then both 'up' and 'down' results will be registered. (True, 'up' and 'down' won't occur within the same 'branch of reality', for that would be inconsistent. Rather, the idea is that reality comes to contain two elements, with 'up' registered relative to one, and 'down' registered relative to the other.) This kind of 'many worlds' or 'many minds' interpretation of quantum mechanics has advantages and disadvantages. The main advantage is that it avoids any 'collapse of the wave function' and so avoids the measurement problem, mysterious non-local interactions, and the like. The most obvious disadvantage is that its burgeoning world of duplicate histories seems repugnant to common sense. Some commentators think that there is another disadvantage. They argue that this interpretation undermines itself by destroying any notion of objective probability. Quantum mechanics is, if anything, a theory which specifies the objective probabilities of certain results. But in what sense is there an objective probability for 'up' and 'down' in a spin measurement, if both results always happen? (Albert [1]; Albert and Loewer [3], [4]; Healey [5]; Squires [9]; Stein [8].) This looks like a good objection. But I shall show in this note that it is not. The proposed interpretation does leave objective probability as a rather mysterious notion. But it is no more mysterious on the proposed interpretation than on the conventional view of the world. This is not the place to go into details about the 'many minds'2 interpretation of quantum mechanics, but one point may help readers. If both the 'up' and 'down' results occur, why do we experience only one?

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How come such a successful theory like Quantum Mechanics has so many mysteries? The history of this theory is replete with dubious interpretations and controversies. The knowledge of its predictions, however, caused the amazing technological revolution of the last hundred years. In its very beginning Einstein pointed out that there was something missing due to contradictions with the relativity theory. So, even though Quantum Mechanics explains all the physical phenomena, due to its mysteries, there were many attempts to find a way to ``complete it, e.g. hidden-variable theories. In this paper, we present these mysteries, with special attention to the concepts of physical reality imposed by quantum mechanics, the role of the observer, prediction limits, definition of collapse, and how to deal with correlated states (the basic strategy for quantum computers and quantum teleportation). The discussion is carried out by accepting that there is nothing important missing. We are just restricted by the limitations imposed by quantum mechanics. The mysteries are cleared out by a proper interpretation of these limitations. This is done by introducing two interpretation rules within the Copenhagen interpretation.

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arXiv:2105.14448•Springer eBooks•Jan 1, 2023•2 citations
Interpretation problems are eliminated from quantum theory by picturing a quantum history as having been sampled from a probability distribution over the set of histories which are permitted by all relevant boundary conditions. In laboratory physics, the final measurement plays a crucial role in defining the set of allowed histories by constraining the final state to be an eigenstate of the measurement operator. For the universe itself, a final boundary condition can play a similar role. Together with the special big bang initial state, the final constraint may ensure that the universe admits a classical description in the asymptotic future. Acknowledging the role of a future constraint dispels the mysteries of quantum theory without any amendment to the theory itself.
An increasingly popular interpretation of quantum mechanics holds that in any genuinely chancy situation, all possible outcomes occur.1 For example, if the spin of a typical electron is measured in a given direction, then both 'up' and 'down' results will be registered. (True, 'up' and 'down' won't occur within the same 'branch of reality', for that would be inconsistent. Rather, the idea is that reality comes to contain two elements, with 'up' registered relative to one, and 'down' registered relative to the other.) This kind of 'many worlds' or 'many minds' interpretation of quantum mechanics has advantages and disadvantages. The main advantage is that it avoids any 'collapse of the wave function' and so avoids the measurement problem, mysterious non-local interactions, and the like. The most obvious disadvantage is that its burgeoning world of duplicate histories seems repugnant to common sense. Some commentators think that there is another disadvantage. They argue that this interpretation undermines itself by destroying any notion of objective probability. Quantum mechanics is, if anything, a theory which specifies the objective probabilities of certain results. But in what sense is there an objective probability for 'up' and 'down' in a spin measurement, if both results always happen? (Albert [1]; Albert and Loewer [3], [4]; Healey [5]; Squires [9]; Stein [8].) This looks like a good objection. But I shall show in this note that it is not. The proposed interpretation does leave objective probability as a rather mysterious notion. But it is no more mysterious on the proposed interpretation than on the conventional view of the world. This is not the place to go into details about the 'many minds'2 interpretation of quantum mechanics, but one point may help readers. If both the 'up' and 'down' results occur, why do we experience only one?
How come such a successful theory like Quantum Mechanics has so many mysteries? The history of this theory is replete with dubious interpretations and controversies. The knowledge of its predictions, however, caused the amazing technological revolution of the last hundred years. In its very beginning Einstein pointed out that there was something missing due to contradictions with the relativity theory. So, even though Quantum Mechanics explains all the physical phenomena, due to its mysteries, there were many attempts to find a way to ``complete it, e.g. hidden-variable theories. In this paper, we present these mysteries, with special attention to the concepts of physical reality imposed by quantum mechanics, the role of the observer, prediction limits, definition of collapse, and how to deal with correlated states (the basic strategy for quantum computers and quantum teleportation). The discussion is carried out by accepting that there is nothing important missing. We are just restricted by the limitations imposed by quantum mechanics. The mysteries are cleared out by a proper interpretation of these limitations. This is done by introducing two interpretation rules within the Copenhagen interpretation.