Are models of local hidden variables for the singlet polarization state necessarily constrained by the Bell inequality?

The Bell inequality is thought to be a common constraint shared by all models of local hidden variables that aim to describe the entangled states of two qubits. Since the inequality is violated by the quantum mechanical description of these states, it purportedly allows distinguishing in an experimentally testable way the predictions of quantum mechanics from those of models of local hidden variables and, ultimately, ruling the latter out. In this paper, we show, however, that the models of local hidden variables constrained by the Bell inequality all share a subtle, though crucial, feature that is not required by fundamental physical principles and, hence, it might not be fulfilled in the actual experimental setup that tests the inequality. Indeed, the disputed feature neither can be properly implemented within the standard framework of quantum mechanics and it is even at odds with the fundamental principle of relativity. Namely, the proof of the inequality requires the existence of a preferred absolute frame of reference (supposedly provided by the lab) with respect to which the hidden properties of the entangled particles and the orientations of each one of the measurement devices that test them can be independently defined through a long sequence of realizations of the experiment. We notice, however, that while the relative orientation between the two measurement devices is a properly defined physical magnitude in every single realization of the experiment, their global rigid orientation with respect to a lab frame is a spurious gauge degree of freedom. Following this observation, we were able to explicitly build a model of local hidden variables that does not share the disputed feature and, hence, it is able to reproduce the predictions of quantum mechanics for the entangled states of two qubits.

Passing the Einstein–Rosen bridge

A test particle moving along geodesic line in a spacetime has three physical propagating degrees of freedom and one unphysical gauge degree. We relax the requirement of geodesic completeness of a spacetime. Instead, we require test particles trajectories to be smooth and complete only for physical degrees of freedom. Test particles trajectories for Einstein–Rosen bridge are proved to be smooth and complete in the physical sector, and particles can freely penetrate the bridge in both directions.

Integrable Hierarchy from Topological Gauge Theory

By the recursion operator of nonlinear Schrödinger hierarchy, integrable models in 1+1 dimensions are related to the hierarchy of U(1) invariant gauge fixing constraints for the BF gauge theory. The loop algebra structure for the related linear problem with the spectral parameter as a constant valued, zero-strength gauge degree of freedom is derived.

ON THE PATH INTEGRAL QUANTIZATION OF CHIRAL BOSONS

We show that, in the covariant Lagrangian formalism, a proper treatment of the gauge degree of freedom in a model of chiral bosons proposed by Siegel uncovers the presence of a Jacobian (a "Wess-Zumino action"): the group of gauge transformations gets quantized and the anomaly is absorbed.