Abstract Different approaches to quantum gravity converge in predicting the existence of a minimal scale of length. This raises the fundamental question as to whether and how an intrinsic limit to spatial resolution can affect quantum mechanical observables associated to internal degrees of freedom. We answer this question in general terms by showing that the spin operator acquires a momentum-dependent contribution in quantum mechanics equipped with a minimal length. Among other consequences, this modification induces a form of quantum nonlocality stronger than the one arising in ordinary quantum mechanics. In particular, we show that violations of the Bell inequality can exceed the maximum value allowed in ordinary quantum mechanics, the so-called Tsirelson bound, by a positive-valued function of the momentum operator. We introduce possible experimental settings based on neutron interferometry and quantum contextuality, and we provide preliminary estimates on the values of the physical parameters needed for actual laboratory implementations.
Abstract Different approaches to quantum gravity converge in predicting the existence of a minimal scale of length. This raises the fundamental question as to whether and how an intrinsic limit to spatial resolution can affect quantum mechanical observables associated to internal degrees of freedom. We answer this question in general terms by showing that the spin operator acquires a momentum-dependent contribution in quantum mechanics equipped with a minimal length. Among other consequences, this modification induces a form of quantum nonlocality stronger than the one arising in ordinary quantum mechanics. In particular, we show that violations of the Bell inequality can exceed the maximum value allowed in ordinary quantum mechanics, the so-called Tsirelson bound, by a positive-valued function of the momentum operator. We introduce possible experimental settings based on neutron interferometry and quantum contextuality, and we provide preliminary estimates on the values of the physical parameters needed for actual laboratory implementations.
Candidate theories of quantum gravity predict the presence of a minimal measurable length at high energies. Such feature is in contrast with the Heisenberg Uncertainty Principle. Therefore, phenomenological approaches to quantum gravity introduced models spelled as modifications of quantum mechanics including a minimal length. The effects of such modification are expected to be relevant at large energies/small lengths. One first consequence is that position eigenstates are not included in such models due to the presence of a minimal uncertainty in position. Furthermore, depending on the particular modification of the position–momentum commutator, when such models are considered from momentum space, the position operator is changed, and a measure factor appears to let the position operator be self-adjoint. As a consequence, the (quasi-)position representation acquires numerous issues. For example, the position operator is no longer a multiplicative operator, and the momentum of a free particle does not correspond directly to its wave number. Here, we will review such issues, clarifying aspects of minimal length models, with particular reference to the representation of the position operator. Furthermore, we will show how such a (quasi-)position description of quantum mechanical models with a minimal length affects results concerning simple systems.
Bell's theorem revealed the fundamental incompatibility between the predictions of quantum mechanics and local realism. Bell inequality violations have since demonstrated quantum nonlocality using photons and internal states of massive particles, but never using their motional states. Here we report the first Bell inequality violation in the motional states of massive particles. Using momentum-entangled pairs of metastable helium atoms manipulated by matter-wave interferometry, we measure a Clauser-Horne-Shimony-Holt (CHSH) Bell parameter of S=2.52±0.17, violating the CHSH-Bell inequality (S≤2). Our work completes a long-standing objective in quantum atom optics by extending Bell tests from internal quantum variables to the external degrees of freedom of massive particles, opening a new regime for exploring quantum nonlocality in matter waves and for investigating the interplay between quantum mechanics and gravity.
This study delves into the validity of quantum mechanical operators in the context of quantum gravity, recognizing the potential need for their generalization. A primary objective is to investigate the repercussions of these generalizations on the inherent nonlocality within quantum mechanics, as exemplified by Bell’s inequality. Additionally, the study scrutinizes the consequences of introducing a nonzero minimal length into the established framework of Bell’s inequality. The findings contribute significantly to our theoretical comprehension of the intricate interplay between quantum mechanics and gravity. Moreover, this research explores the impact of quantum gravity on Bell’s inequality and its practical applications within quantum technologies, notably in the realms of device-independent protocols, quantum key distribution, and quantum randomness generation.
The term Bell's theorem refers to a set of closely related results which imply that quantum mechanics is incompatible with local hidden variable theories. Bell's inequality is the statement that if measurements are performed independently on two space-like separated particles of an entangled pair, the assumption that outcomes depend on hidden variables implies an upper bound on the correlations between the outcomes. Quantum mechanics predicts correlations which violate this upper bound. The CHSH inequality is a specific Bell inequality in which classical correlation (i.e. if local hidden variables exist) can take the maximum value of 2. Quantum mechanics violates this bound, allowing for a higher bound on the correlation, which can take the maximum value 22, known as the Tsirelson bound. Popescu and Rohrlich showed that the assumption of relativistic causality allows for an even higher bound on the CHSH correlation, this value being 4. Why is the bound coming from causality higher than the Tsirelson bound? Are there relativistic causal dynamical theories which violate the Tsirelson bound? In the present paper we answer this question in the affirmative. We show that the pre-quantum theory of trace dynamics, from which quantum theory is emergent as a thermodynamic approximation, permits the CHSH correlation to take values higher than 22. We interpret our findings to suggest that quantum theory is approximate, and emergent from the more general theory of trace dynamics.
Abstract Bell nonlocality refers to the nonlocal correlation strength among quantum systems that cannot be duplicated using local hidden variables, and uncertainty relations set the lower bound on the sum or product of variances for incompatible observables within a quantum system. In this work, the study of linking these two fundamental quantum features in terms of statistical characteristics within Bell tests is initiated. Two statistics determine the state‐dependent quantum upper bounds of the Bell values: the expectation values of local observables, and the joint uncertainty that is the product of local uncertainty. Specifically, it is showed that the joint measurement uncertainty determines the upper bounds of covariant Bell inequalities in the quantum region, with more joint measurement uncertainty required for more covariant correlation strengths. Conversely, the covariant Bell value defines the lower bound of joint uncertainty. In addition, given the maximally entangled states, Tsirelson's bounds of Bell inequalities can be achieved when the joint uncertainty reaches the maximum.
Recent experimental studies on human cognition, particularly where non-separable or entangled cognitive states have been found, show that in many such cases Bell or CHSH inequalities have been violated. The implications are that greater non-local correlations than allowed in quantum mechanics (often known as the Tsirelson bound), are found in human cognition. However, it is also evident that surpassing of Tsirelson limit within relativistic physical Spacetime seems impossible. Tsirelson limit is not guaranteed by no-signaling condition, but some deeper feature like indistinguishability of identical quantum particles might be related to such an upper bound in quantum physics, within relativistic Spacetime. We propose in the current paper that a non-local theory of mind is needed in order to account for the empirical findings. This requires a foundationally different approach than the extant ‘quantum-like’ approach to human mind. To account for the surpassing of the Tsirelson bound we propose abandoning the constraint of no-signaling that depends upon spacetime. Thus, we ask; ‘Is mind outside spacetime?’ We discuss a candidate theory of quantum gravity based on nonlocality as fundamental that may accord with our proposal. We are led to suggest a new 6 - part ontological framework linking Mind, Matter, and Cosmos.