Entangled Systems Reveal Reversible Information Exchange, Defining the Flow of Time

Paul L. Borrill, affiliated with DÆDÆLUS, and colleagues present a new framework, termed ‘subtime’, which formalises reversible information exchange within entangled systems and elucidates how our perception of classical time arises from the process of decoherence. The framework sharply advances our understanding by unifying disparate concepts, including Wheeler, Feynman absorber theory and Shannon’s communication theory, under a single symmetry principle. By introducing the concept of Perfect Information Feedback, the team demonstrates that entropy quantifies the degree to which causality becomes irreversible. This suggests the arrow of time reflects the universe’s key imperfections in causal reflection.

Information Preservation and the Emergence of Temporal Asymmetry from Reversible Causal Structures

Mutual information conservation demonstrates 100% preservation of information within closed causal loops, a feat previously unattainable within standard decoherence models. This finding is significant because traditional decoherence models typically predict information loss as systems interact with their environment, leading to the emergence of a preferred direction of time. The ability to maintain complete information preservation within a closed loop suggests that the arrow of time isn’t an inherent property of the system itself, but rather emerges from its interaction with irreversibility. Establishing that entropy quantifies unreflected causality offers a new metric for understanding temporal asymmetry, effectively measuring the degree to which causal relationships fail to perfectly mirror their duals. A perfect reflection would imply complete reversibility, while any deviation, quantified by entropy, indicates the emergence of an irreversible process and thus, a direction of time. Naren Manjunath from the Perimeter Institute and colleagues employed the photon clock model, a single photon bouncing between ideal mirrors, to formalize ‘subtime’, a reversible exchange of information, and link it to classical time’s emergence through decoherence. The photon clock serves as a simplified, controllable system for investigating the fundamental principles governing time and causality, avoiding the complexities of many-body systems.

Open Atomic Ethernet, a communication protocol, showed that a functioning bidirectional link should exhibit zero net entropy production, with entropy only appearing where the link interacts with irreversible systems. This result highlights the importance of isolating systems from irreversible processes to maintain information integrity and potentially achieve reversible computation. The protocol’s design, based on atomic transitions and quantum entanglement, aims to minimise entropy generation during information transfer. Experiments utilising quantum switches suggest that alternating causal protocols suppress entropy growth compared to superposition-based protocols, preserving information more efficiently. Alternating causal protocols involve sequentially activating different causal pathways, while superposition-based protocols attempt to utilise multiple pathways simultaneously, leading to increased decoherence and entropy production. This difference in performance suggests that controlling the order of causal events is crucial for minimising information loss. This framework unifies diverse theoretical approaches, including Wheeler-Feynman’s absorber theory and Shannon’s communication theory, under a single symmetry principle, paving the way for experiments in reversible digital links and switch designs. Wheeler-Feynman’s theory proposes that particles emit waves both forwards and backwards in time, while Shannon’s theory provides a mathematical framework for quantifying information and its transmission; the unification of these seemingly disparate concepts suggests a deeper connection between information, causality, and time.

Process Matrix Formalism and Time-Reversal Duality in Photon Clock Decoherence

The process matrix formalism proved central to modelling this investigation, functioning much like a detailed weather forecast predicting multiple potential outcomes for a quantum system. Unlike traditional quantum state descriptions which provide a single probability amplitude for each possible outcome, the process matrix provides a complete description of the system’s evolution, including all possible transitions between states. This technique maps every possible state a system can occupy, allowing researchers to move beyond simply predicting a single future and instead describe the probabilities of all potential evolutions. The process matrix is a positive operator-valued measure.