New Prospects for a Causally Local Formulation of Quantum Theory (2402.16935v1)

Abstract: It is difficult to extract reliable criteria for causal locality from the limited ingredients found in textbook quantum theory. In the end, Bell humbly warned that his eponymous theorem was based on criteria that "should be viewed with the utmost suspicion." Remarkably, by stepping outside the wave-function paradigm, one can reformulate quantum theory in terms of old-fashioned configuration spaces together with 'unistochastic' laws. These unistochastic laws take the form of directed conditional probabilities, which turn out to provide a hospitable foundation for encoding microphysical causal relationships. This unistochastic reformulation provides quantum theory with a simpler and more transparent axiomatic foundation, plausibly resolves the measurement problem, and deflates various exotic claims about superposition, interference, and entanglement. Making use of this reformulation, this paper introduces a new principle of causal locality that is intended to improve on Bell's criteria, and shows directly that systems that remain at spacelike separation cannot exert causal influences on each other, according to that new principle. These results therefore lead to a general hidden-variables interpretation of quantum theory that is arguably compatible with causal locality.

• The paper replaces Bell's local causality with a refined principle using directed conditional probabilities to realign quantum dynamics.
• The research introduces a unistochastic formulation where transition probabilities from unitary operations underpin deterministic quantum behavior.
• The study offers practical insights to reconcile quantum interference and measurement challenges through a clearer, causally local stochastic framework.

An Examination of a Causally Local Formulation of Quantum Theory

The paper "New Prospects for a Causally Local Formulation of Quantum Theory" by Jacob A. Barandes investigates a reformulation of quantum theory aimed at resolving long-standing issues related to causal locality. The research proposes a unistochastic framework, diverging from conventional approaches that revolve around the complexities of wave functions. At its core, this framework is conceived as an attempt to clarify causal relationships on a microphysical level, rekindling the discourse on causation within quantum mechanics which has been elusive under the traditional, interventionist lens.

Context and Objectives

Historically, quantum theory's relationship with nonlocality has been intensely debated. The Einstein-Podolsky-Rosen (EPR) paradox and Bell's theorem have suggested that quantum mechanics entails some form of nonlocal interaction, whether through "spooky action at a distance" as posited by Einstein or the implicatory conclusions of Bell's work on hidden variables. One of the critical challenges has been formulating coherent criteria for causal locality amidst quantum entanglement and the violation of inequalities predicted by local theories.

Barandes embarks on this reformulation by defining the processes in quantum mechanics as governed by directed conditional probabilities. These probabilities act as microphysical laws for stochastic processes, decoupling from the reliance on entangled wave functions or differential equations typically used in describing quantum systems. This novel presentation draws from Bayesian networks that model causal structures in terms of directed graphs, offering a language wherein causal inference aligns with probabilistic dependencies.

Major Claims and Contributions

• Replacement of Bell's Criterion: The paper critiques and subsequently replaces Bell's criterion of local causality with a refined principle. Barandes proposes that systems remaining at spacelike separation during a quantum process can be viewed as not exerting causal influences on one another within this new framework. This perspective challenges Reichenbach's principle of common causes by offering stochastic interactions as the basis of causal linkages, which need not conform to classical factorization.
• Unistochastic Formulation: The introduction of a unistochastic matrix, wherein transition probabilities correspond to the square magnitudes derived from unitary operations, provides a deterministic underpinning that realigns quantum probabilities with classical configurations. This theoretical construct aims to reconcile the algebra of measurement probabilities with the dynamics of quantum evolution.
• Microphysical Causation: By employing the directedness inherent in conditional probability, Barandes develops a framework where causation is neither obscure nor erroneously interventionist. The character of causality thus derived becomes analytically tractable, permitting an examination of quantum systems as inherently stochastic entities.
• Practical and Theoretical Implications: The approach practically mitigates many of the interpretational struggles with phenomena like superposition, interference, and the measurement problem. Theoretically, it suggests the plausibility of a hidden-variables model that remains compatible with the constraints of causal locality, contradicting the predominant assumption that quantum mechanics inherently defies local realism.

Significance and Future Directions

The significance of Barandes' unistochastic model lies in its potential to offer a reformulation of quantum theory that better harmonizes with intuitive notions of causality and locality. While the paper does not purport to overhaul quantum mechanics radically, it presents an innovative approach that challenges entrenched views and opens the door to further exploration of quantum causal dynamics. Future research pathways may include deeper empirical scrutiny or computational simulations validating the unistochastic model against quantum correlation data and potentially developing practical algorithms or technologies guided by this reformulation.

In essence, this reformulation embodies a rigorous effort to provide clearer causal underpinnings to quantum mechanics, fostering an environment where contemporary interpretations can be tested against a framework designed for clarity and causal coherence.