Contextual Inferences, Nonlocality, and the Incompleteness of Quantum Mechanics

Abstract

It is known that “quantum non locality”, leading to the violation of Bell’s inequality and more generally of classical local realism, can be attributed to the conjunction of two properties, which we call here elementary locality and predictive completeness. Taking this point of view, we show again that quantum mechanics violates predictive completeness, allowing the making of contextual inferences, which can, in turn, explain why quantum non locality does not contradict relativistic causality. An important question remains: if the usual quantum state ψ is predictively incomplete, how do we complete it? We give here a set of new arguments to show that ψ should be completed indeed, not by looking for any “hidden variables”, but rather by specifying the measurement context, which is required to define actual probabilities over a set of mutually exclusive physical events.

A quantum phase-space equivalence leads to hidden causal loops in a model for measurement consistent with macroscopic realism

“…Other unitary interactions however are possible and the meaning of this form of realism is hence more general than that of the hybrid macroscopic-realism model. This model is consistent with contextual explanations of Bell violations [87].…”

“…The deterministic contextual realism model specifies that the interpretation of realism can be given for the final amplified value Gx j (or Gp j ), but only in a context where the measurement choice and setting is specified. Such models have been discussed elsewhere [87][88][89]. A unitary interaction U (θ) is required as the first stage of the measurement, in order to specify the measurement setting, for instance, as in the selection of a polarizer angle θ in a Bell-inequality experiment which measures a spin Ŝθ .…”

Revisiting Born’s Rule through Uhlhorn’s and Gleason’s Theorems

“…We note, however, that our approach leads to some differences with the standard (textbook) one; in particular, the usual quantum state vector is not predictively complete, since it provides a well-defined probability distribution only when “completed” by the specification of a context [ 27 ]. A complete description, also including the contexts requires the use of algebraic methods [ 19 ].…”

Quantifying and Interpreting Connection Strength in Macro- and Microscopic Systems: Lessons from Bell’s Approach

“…Interpreting the meaning of a quantum state, and the question of whether it expresses the objective underlying physical state of a system or rather the possible measurement outcomes and information, is still a matter of debate [19,21,23]. Contextuality becomes an important concept [25,28,[78][79][80][81][82][83] and it can be formalized to some degree, for example, by requiring predictive completeness, which means that the quantum state has to be completed by linking it with a measurement operator as well [29].…”

“…John Bell's seminal work [1][2][3][4][5][6] has triggered a rich tradition of experimental studies [7][8][9][10][11][12][13] as well as theoretical and interpretational work [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. To derive his famous inequalities, he has taken a realist worldview, making the additional assumption of free choice and locality, as formally defined by precise equations in a hidden variable model.…”