An inequality stronger than Bell’s inequality

Gutkowski, D.; Masotto, G.

doi:10.1007/bf02737464

Cited by 16 publications

(4 citation statements)

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“…D'Espagnat assumes (as Bell did in 1965) that one has a system like a pair of spin-4 particles in the singlet state, such that one can measure an observable of one of the pair and then infer with absolute certainty the value of a corresponding observable of the other pair (equation (3.2)). The same criticism can also be made of the arguments of Gutkowski and Masotto (1974), Selleri (1978) and Schiavulli (1977) but it should be noted that they derive a number of generalisations of Bell's inequalities which have not been obtained elsewhere.…”

Section: Other Versions Of Bell's Theoremmentioning

confidence: 94%

Bell's theorem. Experimental tests and implications

1978

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Bell's theorem represents a significant advance in understanding the conceptual foundations of quantum mechanics. The theorem shows that essentially all local theories of natural phenomena that are formulated within the framework of realism may be tested using a single experimental arrangement. Moreover, the predictions by these theories must significantly differ from those by quantum mechanics. Experimental results evidently refute the theorem's predictions for these theories and favour those of quantum mechanics. The conclusions are philosophically startling: either one must totally abandon the realistic philosophy of most working scientists, or dramatically revise our concept of space-time.

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Section: Other Versions Of Bell's Theoremmentioning

confidence: 94%

Bell's theorem. Experimental tests and implications

1978

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“…This examples was at the origin of a vast literature (cr. for example [10], [13], [14], [19], [20], [21]) whose results can be framed in the general scheme described above. In fact one can show (cf.…”

Section: The Statistical Invariantsmentioning

confidence: 99%

Some trends and problems in quantum probability

Accardi¹

1984

Quantum Probability and Applications to the Quantum Theory of Irreversible Processes

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From the experimental point of view probability enters quantum theory just like classical statistical physics, i.e. as an expected relative frequency. However it is well known that the statistical formalism of quantum theory is quite different from the usual Kolmogorovian one involving, for example, complex numbers, amplitudes, Hilbet spaces... The quantum statistical formalism has been described, developped, applied, generalized with the contributions of many authors; however its theoretical status remained, until recently, quite obscure, as shown by the widely contrasting statements that one can find in the vast literature concerning the following questions.\ud \ud Is it possible to justify the choice of the classical or the quantum statistical formalism, for the description of a given set of statistical data, on rigorous mathematical criteria rather than on empirical ones

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“…In the standard theory this Boolean representation does not exist for quantities represented by non-commuting operators because the distributivity property of the lattice is violated [5]. A similar conclusion is obtained in axiomatic probability theory, the violation of Bell's inequalities can be shown to reflect the non-existence of a classical probabilistic structure underlying quantum probability [12]. However in the quantum real number model the logic is intuitionistic [1].…”

Section: Basic Postulate 3 Amentioning

confidence: 73%