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By J. S. Bell
This e-book contains all of John Bell's released and unpublished papers within the box of quantum mechanics, together with papers that seemed after the 1st variation used to be released. It additionally includes a preface written for the 1st version, and an advent by way of Alain point that places into context Bell's nice contribution to the quantum philosophy debate. one of many major expositors and interpreters of recent quantum concept, John Bell performed an immense function within the improvement of our present figuring out of the profound nature of quantum innovations. First version Hb (1987): 0-521-33495-0 First version Pb (1988): 0-521-36869-3
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Extra info for Speakable and Unspeakable in Quantum Mechanics (Collected Papers on Quantum Philosophy)
Example text
Therefore, dispersion free states are impossible. If the state space has more dimensions, we can always consider a two-dimensional subspace; therefore, the demonstration is quite general. The essential assumption can be criticized as follows. At first sight the required additivity of expectation values seems very reasonable, and it is rather the non-additivity of allowed values (eigenvalues) which requires explanation. Of course the explanation is well known: A measurement of a sum of noncommuting observables cannot be made by combining trivially the results of separate observations on the two terms - it requires a quite distinct experiment.
Now we can quickly rule out dispersion free states by considering a twodimensional subspace. In that the projection operators are the zero, the unit operator, and those of the form 6 Speakable and unspeakable in quantum mechanics where a is a unit vector. In a dispersion free state the expectation value of an operator must be one of its eigenvalues, 0 or 1 for projections. cr> Let a and P be any noncollinear unit vectors and with the signs chosen so that =
Thirdly, and finally, there is no difficulty in reproducing the quantum mechanical correlation (3) if the results A and B in (2) are allowed to depend on b and a respectively as well as on a and b. For example, replace a in (9) by a', obtained from a by rotation towards b until l - - 0 ' = cos0, n where 9r is the angle between a' and b. However, for given values of the hidden variables, the results of measurements with one magnet now depend on the setting of the distant magnet, which is just what we would wish to avoid.