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arXiv:quant-ph/0203131

FAQ about the "contextual objectivity" point of view

Philippe Grangier

Published Mar 27, 2002• 1 citation
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Abstract

We discuss some Frequently Asked Questions about the ``contextual objectivity" point of view on quantum mechanics introduced in two previous preprints quant-ph/0012122 and quant-ph/0111154.
DOI
10.48550/arxiv.quant-ph/0203131

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In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in such a way that it may be given an "objective reality". Here we use some ideas about the system dimensionality, taken from quant-ph/0101012, to propose a possible axiomatic approach to QM. In this approach the structure of QM appears as a direct consequence of the non-commutative character of the (classical geometrical) group of "knobs transformations", that relate between themselves the different positions of the measurement apparatus.
Recently, there has been a discussion on the origin of the quantum probability rules (Deutsch quant-ph/9906015, Polley quant-ph/9906124, Barnum et al. quant-ph/9907024, Finkelstein quant-ph/9907004). This contribution, which is a slightly reformulated version of a paper published in Int.J.Theor.Phys. 33, 171 (1994), points out the follwoing: To an experimenter the world is a persistent stream of discrete data. All that is certain is that with each observation he/she knows more than before, simply because he/she can now answer the question "Which of the possible outcomes have you just registered?", while this was not possible before the observation. One can ask whether this relentless increase of information entails a specific structure. In particular, how must different observations be related in order to ensure that predictions become ever more accurate, the more past observations serve as input? This leads to the quantum rule for adding the complex square roots of probabilities, and not to adding the probabilities themselves, as classical probability would have it.