In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously, so that such a theory could not be Lorentz invariant. Of course, the situation is different if the quantum mechanical predictions are of limited validity. Conceivably they might apply only to experiments in which the settings of the instruments are made sufficiently in advance to allow them to reach some mutual rapport by exchange of signals with velocity less than or equal to that of light. In that connection, experiments of the type proposed by Bohm and Aharonov, in which the settings are changed during the flight of the particles, are crucial.
John Stewart Bell
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More generally, the hidden variable account of a given system becomes entirely different when we remember that it has undoubtedly interacted with numerous other systems in the past and that the total wave function will certainly not be factorable. The same effect complicates the hidden variable account of the theory of measurement, when it is desired to include part of the 'apparatus' in the system. Bohm of course was well aware of these features of his scheme, and has given them much attention. However, it must be stressed that, to the present writer's knowledge, there is no proof that any hidden variable account of quantum mechanics must have this extraordinary character. It would therefore be interesting, perhaps, to pursue some further 'impossibility proofs,' replacing the arbitrary axioms objected to above by some condition of locality, or of separability of distant systems.
John Stewart Bell
THEY who are acquainted with the present state of the theory of Symbolical Algebra, are aware, that the validity of the processes of analysis does not depend upon the interpretation of the symbols which are employed, but solely upon the laws of their combination. Every system of interpretation which does not affect the truth of the relations supposed, is equally admissible, and it is thus that the same process may, under one scheme of interpretation, represent the solution of a question on the properties of numbers, under another, that of a geometrical problem, and under a third, that of a problem of dynamics or optics. This principle is indeed of fundamental importance; and it may with safety be affirmed, that the recent advances of pure analysis have been much assisted by the influence which it has exerted in directing the current of investigation.
George Boole
The powers, and faculties, and principles that are necessary fully to comprehend all that we see and all that surrounds us, exist and have been bestowed on man by his beneficent Creator. Still, it is only by slow degrees that he is to become their master, acquiring knowledge, step by step, as he has need of its services, and learns how to use it. Such seems to be the design of Providence, which is gradually opening to our inquiries the arcana of nature, in order that we may convert their possession into such uses as will advance its own wise intentions. Happy are they who feel this truth in their character of individuals! Thrice happy the nations which can be made to understand, that the surest progress is that which is made on the clearest principles, and with the greatest caution! The notion of setting up anything new in morals, is as fallacious in theory as it will be found to be dangerous in practice.
James Fenimore Cooper