Classification of Hidden-Variables Theories

Yakir Aharonov, Alonso Botero, Marian O. Scully

Abstract The folklore notion of the "Non-Locality of Quantum Mechanics" is examined from the point of view of hidden-variables theories according to Belinfante's classification in his Survey of Hidden Variables Theories. It is here shown that in the case of EPR, there exist hidden variables theories that successfully reproduce quantum-mechanical predictions, but which are explicitly local. Since such theories do not fall into Belinfante's classification, we propose an expanded classification which includes similar theories, which we term as theories of the "third" kind. Causal implications of such theories are explored. -Pacs: 03.65.Bz

Eduardo Gonzalez-Granda Fernandez

This work investigates the compatibility of hidden-variable modifications with the analytic structure of relativistic quantum field theory (QFT). Working within the framework of tempered distributions, we analyze three fundamental properties: the spectral condition, analyticity in the forward tube, and causal localization. We prove a rigidity result showing that any modification satisfying all three conditions must vanish identically. This establishes a structural obstruction linking analyticity and causal constraints in QFT. Building on this result, we provide a systematic classification of nontrivial hidden-variable extensions according to which analytic assumptions fail. We identify three distinct regimes: (i) delocalized modifications compatible with standard QFT, (ii) causally localized modifications that violate the spectral condition and introduce negative-frequency components, and (iii) localized modifications that necessarily break analyticity. These results show that nontrivial hidden-variable theories cannot be embedded within the standard analytic framework of relativistic QFT without violating at least one of its fundamental structural principles. The work provides a unified analytic perspective on the constraints governing hidden-variable extensions and clarifies the role of analyticity as a rigidity mechanism.

Abner Shimony

Stefan Teufel, Karin Berndl, Detlef Dürr +2 more

Motivated by Popescu's example of hidden nonlocality [Phys. Rev. Lett. 74, 2619 (1995)], we elaborate on the conjecture that quantum states that are intuitively nonlocal, i.e., entangled, do not admit a local causal hidden-variables model. We exhibit quantum states which either (i) are nontrivial counterexamples to this conjecture or (ii) possess a new kind of more deeply hidden irreducible nonlocality. Moreover, we propose a nonlocality complexity classification scheme suggested by the latter possibility. Furthermore, we show that Werner's [Phys. Rev. A 40, 4277 (1989)] (and similar) hidden-variables models can be extended to an important class of generalized observables. Finally, a result of Fine [Phys. Rev. Lett. 48, 291 (1982)] on the equivalence of stochastic and deterministic hidden variables is generalized to causal models.