Contextual Inferences, Nonlocality, and the Incompleteness of Quantum Mechanics

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.

Principles of local realism in a Friedmann universe

The problem of time is a statement of the inability to establish the standard model according to a consistent physical framework based on a valid starting point provided from either the concept of time in quantum mechanics (QM) or general relativity (GR). Using the deterministic local realism approach of Bell’s inequality experiment, a valid mathematical starting point incorporating both QM and GR can be established using the concept of energy conservation within a volume of spacetime. Because Friedmann established a system that correlates the energy level within the volume of spacetime with the proximity between energy mass, with two opposing universal forces that must act on the reconfiguration of particles when considering a realism-based definite position as they evolve in time independent of observation, it is possible to consider QM time evolution as a form of deterministic thermodynamic work. Considering this volume of spacetime in terms of the local realism interpretation allows one to consider the act of time evolution as a reconfiguration that occurs along with the expansion of volume which allows one to establish an energy conservation argument using only the particles that exist within the volume of spacetime to account for both the gravitational energy and the divergent energy usually attributed to the cosmological constant. With this argument time evolution must cost system energy. For energy to be conserved the use of system energy must be for the act of gravitation as a particle evolves in time. The definition of local realism allows Minkowski spacetime diagrams to pertain to the unseen intervals between measurements. This allows a center frame observer to serve as a background clock to measure time rates in correlation to scale factor expansion. This allows one to consider time rates in terms of work that must occur over an interval of a background clock. In the case of local realism, Minkowski mathematics allow a direct correlation between QM time evolution and the second Friedmann equation.

Bell inequalities, counterfactual definiteness and falsifiability

We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical property of Bell’s probabilistic model. Although the amendment does not alter the relevance of the theorem regarding local realism, it brings back Bell theorem from the realm of philosophical discussions about counterfactual conditionals to the concrete experimental arena.

A local-realistic model for quantum theory

We provide a rigorous definition of local realism. We show that the universal wave function cannot be a complete description of a local reality. Finally, we construct a local-realistic model for quantum theory.

Experimentally friendly approach towards nonlocal correlations in multisetting N-partite Bell scenarios

In this work, we study a recently proposed operational measure of nonlocality by Fonseca and Parisio [Phys. Rev. A 92, 030101(R) (2015)] which describes the probability of violation of local realism under randomly sampled observables, and the strength of such violation as described by resistance to white noise admixture. While our knowledge concerning these quantities is well established from a theoretical point of view, the experimental counterpart is a considerably harder task and very little has been done in this field. It is caused by the lack of complete knowledge about the facets of the local polytope required for the analysis. In this paper, we propose a simple procedure towards experimentally determining both quantities for N-qubit pure states, based on the incomplete set of tight Bell inequalities. We show that the imprecision arising from this approach is of similar magnitude as the potential measurement errors. We also show that even with both a randomly chosen N-qubit pure state and randomly chosen measurement bases, a violation of local realism can be detected experimentally almost 100% of the time. Among other applications, our work provides a feasible alternative for the witnessing of genuine multipartite entanglement without aligned reference frames.

Oversights in the Respective Theorems of von Neumann and Bell are Homologous

We show that the respective oversights in the von Neumann's general theorem against all hidden variable theories and Bell's theorem against their local-realistic counterparts are homologous. Both theorems unjustifiably assume the additivity of expectation values within hidden variable theories to derive their respective conclusions. However, for non-commuting observables, the equivalence of a sum of expectation values and the expectation value of the sum of measurement results, although respected within quantum mechanics, need not hold for hidden variable theories, regardless of specific characteristics such as local realism they may respect. Once this oversight is ameliorated from Bell's argument and local realism is implemented correctly, the bounds on the CHSH correlator work out to be +/-2\/2 instead of +/-2, thereby mitigating the conclusion of Bell's theorem. Consequently, what is ruled out by the Bell-test experiments is not local realism but the additivity of expectation values.

Quantum Entanglement Results from Quantum State Transition at Fast-Than-Light Speed with Matter Wave’s Phase Velocity

The quantum entanglement, that violates the local realism and other classical physics theories, leads to various counterintuitive phenomena, is a primary feature of quantum mechanics and probably results from the quantum state’s conservation and the quantum state’s transition with the matter wave’s phase velocity at the fast-than-light speed. The quantum state transition of entangled particles proceeds with the phase velocity, while the observer measures the process with the electromagnetic or the light speed. This speed difference makes the causality law no longer fully valid everywhere except in certain areas.