The Bell's theorem revisited: geometric phases in gauge theories

David H. Oaknin

The Bell's theorem stands as an insuperable roadblock in the path to a very desired intuitive solution of the EPR paradox and, hence, it lies at the core of the current lack of a clear interpretation of the quantum formalism. The theorem states through an experimentally testable inequality that the predictions of quantum mechanics for the Bell's polarization states of two entangled particles cannot be reproduced by any statistical model of hidden variables that shares certain intuitive features. In this paper, we show, however, that the proof of the Bell's theorem involves a subtle, though crucial, assumption that is not required by fundamental physical principles and, hence, it is not necessarily fulfilled in the experimental setup that tests the inequality. Indeed, this assumption can neither be properly implemented within the standard framework of quantum mechanics. Namely, the proof of the theorem assumes that there exists a preferred absolute frame of reference, supposedly provided by the lab, which enables to compare the orientation of the polarization measurement devices for successive realizations of the experiment and, hence, to define jointly their response functions over the space of hypothetical hidden configurations for all their possible alternative settings. We notice, however, that only the relative orientation between the two measurement devices in every single realization of the experiment is a properly defined physical degree of freedom, while their global rigid orientation is a spurious gauge degree of freedom. Hence, the preferred frame of reference required by the proof of the Bell's theorem does not necessarily exist. In fact, it cannot exist in models in which the gauge symmetry of the experimental setup under global rigid rotations of the two detectors is spontaneously broken by the hidden configurations of the pair of entangled particles and a non-zero geometric phase appears under some cyclic gauge symmetry transformations. Following this observation, we build an explicitly local model of hidden variables that reproduces the predictions of quantum mechanics for the Bell's states.

Akihiro Tanaka, Keisuke Totsuka, Xiao Hu

The physics underlying the magnetization process of quantum antiferromagnets is revisited from the viewpoint of geometric phases. A continuum variant of the Lieb-Schultz-Mattis-type approach to the problem is put forth, where the commensurability condition of Oshikawa et al. derives from a Berry connection formulation of the system's crystal momentum. We then go on to formulate an effective field theory which can deal with higher dimensional cases as well. We find that a topological term, whose principle function is to assign Berry phase factors to space-time vortex objects, ultimately controls the magnetic behavior of the system. We further show how our effective action maps into a ${\mathbf{Z}}_{2}$ gauge theory under certain conditions, which in turn allows for the occurrence of a fractionalized phase with topological order.

David S. Simon

At Wien

Gyula Bene

Using a new approach to quantum mechanics we revisit Hardy's proof for Bell's theorem and point out a loophole in it. We also demonstrate on this example that quantum mechanics is a local realistic theory.