The idea of the preferred frame as a remedy for difficulties of the relativistic quantum mechanics in description of the non-local quantum phenomena was undertaken by physicists such as J. S. Bell and D. Bohm. The possibility of the existence of a preferred frame was also seriously treated by P. A. M. Dirac. In this paper, we propose an Einstein-Podolsky-Rosen–type experiment for testing the possible existence of quantum preferred frame. Our analysis suggests that to verify whether a preferred frame of reference in the quantum world exists, it is enough to perform an EPR-type experiment with a pair of observers staying in the same inertial frame and with use of the massive EPR pair of spin–one-half or spin-one particles.
The idea of the preferred frame as a remedy for difficulties of the relativistic quantum mechanics in description of the non-local quantum phenomena was undertaken by physicists such as J. S. Bell and D. Bohm. The possibility of the existence of a preferred frame was also seriously treated by P. A. M. Dirac. In this paper, we propose an Einstein-Podolsky-Rosen–type experiment for testing the possible existence of quantum preferred frame. Our analysis suggests that to verify whether a preferred frame of reference in the quantum world exists, it is enough to perform an EPR-type experiment with a pair of observers staying in the same inertial frame and with use of the massive EPR pair of spin–one-half or spin-one particles.
In this paper the relativistic quantum mechanics (QM) is considered in the framework of the nonstandard synchronization scheme, which preserves the Poincar\'e covariance but (at least formally) distinguishes an inertial frame. This enables one to avoid the problem with a strong formulation of local causality related to the breaking of Bell's inequalities in QM. Our analysis has been focused mainly on the problem of the existence of a proper position operator for massive particles. We have proved that in our framework such an operator exists for particles with arbitrary spin. This operator is Hermitian and covariant, it has commuting components, and its eigenvectors (localized states) are covariant too. We have found an explicit form of the position operator and demonstrated that it coincides with the Newton-Wigner one in the preferred frame. We have also defined a covariant spin operator and constructed an invariant spin squared operator. Moreover, full algebra of observables consisting of position, four-momentum, and spin operators is manifestly Poincar\'e covariant in this framework. Our results support expectations of other authors [J. S. Bell, in Quantum Gravity, edited by C. J. Isham, R. Penrose, and D. W. Sciama (Oxford University Press, Oxford, 1981), p. 611; P. H. Eberhard, Nuovo Cimento B 46, 392 (1978)] that a consistent formulation of quantum mechanics demands the existence of a preferred frame.
In this paper the localization problem in the relativistic quantum mechanics is considered in the framework of a nonstandard synchronization scheme for clocks. Such a synchronization preserves Poincaré covariance but (at least formally) distinguishes an inertial frame. Our analysis has been focused mainly on the problem of existence of a proper position operator for massive particles. We have found the explicit form of the position operator and have demonstrated that in the preferred frame our operator coincides with the Newton–Wigner one. Moreover, full algebra of observables consisting of position operators and fourmomentum operators is manifestly Poincaré covariant in this framework. Our results support expectations of other authors (Bell [1], Eberhard [3]) that a consistent formulation of quantum mechanics demands existence of a preferred frame.
It may well be that a relativistic version of the theory, while Lorentz invariant and local at the observational level, may be necessarily non-local and with a preferred frame (or aether) at the fundamental level. – John Bell [1] Introduction Bell's theorem establishes a contradiction between locality (and a few other assumptions) and certain predictions of quantum mechanics [2]. There have been two main issues surrounding the deep implications of this celebrated theorem. The first issue is basic, and it concerns whether the theorem really establishes that nonlocality is a necessary feature of any empirically viable theory and hence a feature of nature itself. One aspect of the issue concerns exactly what the underlying assumptions of Bell's theorem are. For example, some argue that these assumptions include the assumption of counterfactual definiteness [3–5], while others disagree [6–8]. The other aspect of the issue concerns which assumption should be dropped due to the resulting contradiction. Some believe that standard quantum mechanics may avoid nonlocality by denying counterfactual definiteness [3–5]. The second issue is much deeper, and it concerns how to make sense of the strange nonlocality when assuming that Bell's theorem establishes that our world is nonlocal. In particular, it has yet to be determined whether such quantum nonlocality is compatible with the theory of relativity, e.g., whether the nonlocality requires the existence of a preferred Lorentz frame [7, 9, 10]. It seems that “there is a preferred frame of reference, and in this preferred frame of reference things do go faster than light … Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant” [11]. But it also seems possible that the existence of a preferred Lorentz frame is an illusion, since it cannot be detected according to standard quantum mechanics. A more subtle issue is whether quantum nonlocality permits superluminal signaling. It is widely thought that the answers to these questions will lead to a deeper understanding of Bell's theorem and quantum nonlocality. In this paper, we will present a new analysis of quantum nonlocality and its apparent incompatibility with relativity.
Bohmian Mechanics (BM) posits a deterministic quantum framework where particle trajectories are guided by a wave function within a preferred Lorentz frame, a dependence starkly revealed by a novel EPR-Bohm experiment with reversible measurements. Unlike Bell tests, where BM’s predictions align with standard quantum mechanics regardless of frame, this experiment demonstrates that the Born rule’s application in the preferred frame determines whether Alice’s intermediate measurement statistics are random or deterministic. This reliance on a preferred frame—a measure-zero set in the continuum of Lorentz frames—exposes BM’s fundamental deficiency, as it is experimentally undetectable, lacks physical justification, and violates special relativity’s frame equivalence. Collapse theories, such as GRW and CSL, face analogous issues, requiring a preferred frame for non-local collapse events. This analysis highlights the inherent tension between single-world quantum theories and relativistic constraints, raising significant doubts about their viability as alternative quantum theories. The findings underscore the need for quantum interpretations that reconcile realism with relativity, suggesting that the Many-Worlds Interpretation, which provides a Lorentz-invariant framework without requiring a preferred frame, may offer a more robust and consistent foundation for quantum mechanics.
As shown in the famous EPR paper (Einstein, Podolsky e Rosen, 1935), Quantum Mechanics is non-local. The Bell theorem and the experiments by Aspect and many others, ruled out the possibility of explaining quantum correlations between entangled particles using local hidden variables models (except for implausible combinations of loopholes). Some authors (Bell, Eberhard, Bohm and Hiley) suggested that quantum correlations could be due to superluminal communications (tachyons) that propagate isotropically with velocity v t > c in a preferred reference frame. For finite values of v t , Quantum Mechanics and superluminal models lead to different predictions. Some years ago a Geneva group and our group did experiments on entangled photons to evidence possible discrepancies between experimental results and quantum predictions. Since no discrepancy was found, these experiments established only lower bounds for the possible tachyon velocities v t . Here we propose an improved experiment that should lead us to explore a much larger range of possible tachyon velocities V t for any possible direction of velocity of the tachyons preferred frame.
EPR correlations exist and can be observed independently of any a priori given frame of reference. We can even construct a frame of reference that is based on these correlations. This observation-based frame of reference is equivalent to the customary a priori given frame of reference of the laboratory when describing real EPR experiments. J.S. Bell has argued that local hidden parameter theories that reproduce the predictions of Quantum Mechanics cannot exist, but the counterfactual reasoning leading to Bell's conclusion is physically meaningless if the frame of reference that is based on EPR-correlations is accepted as the backdrop for EPR-type experiments. The refutal of Bell's proof opens up for the construction of a viable hidden parameter theory. A model of a spin h/2 particle in terms of a non-flat metric of space-time is shown to be able to reproduce the predictions of quantum mechanics in the Bohm-Aharonov version of the EPR experiment, without introducing non-locality.