Entropic Dynamics Offers New Approach to Relational Mechanics and Time.

Entropic Dynamics constructs relational models of mechanics using probability, entropy and geometry. These non-relativistic models, retaining absolute simultaneity and Euclidean geometry, define constraints on expectation values post-quantization and circumvent the problem of time analogous to that encountered in general relativity.

The persistent challenge of reconciling quantum mechanics with our understanding of time and relationality receives focused attention in new research applying the principles of Entropic Dynamics (ED) – a framework that posits entropy as fundamental to physical processes – to the foundations of relational quantum mechanics. This approach seeks to define physical quantities not in absolute terms, but relative to an observer, addressing long-standing conceptual difficulties within the quantum realm. Ariel Caticha and Hassaan Saleem, both from the Department of Physics at the University at Albany–SUNY, detail their development of non-relativistic models within this framework in their article, ‘Entropic Dynamics approach to Relational Quantum Mechanics’, demonstrating a potential pathway to resolving the ‘problem of time’ – a key obstacle in formulating a complete theory of quantum gravity – and clarifying the appropriate formulation of constraints following quantization.

Relational Entropic Dynamics: Reconstructing Quantum Mechanics from Information

Recent research details a relational framework for both quantum mechanics and gravity, predicated on the principles of entropic dynamics (ED). This approach demonstrates that the temporal evolution of a quantum system does not necessitate a pre-defined Hamiltonian – the operator describing total energy – but instead arises from maximising entropy – or equivalently, minimising free energy – subject to constraints representing available information. This challenges the conventional concept of absolute time, proposing instead that time emerges from relationships between systems and increasing disorder.

The framework employs a statistical manifold – a mathematical space representing all possible states of a system – to describe a quantum system’s state. This manifold evolves via Hamilton-Killing flows, geometric transformations that preserve key structural properties. Critically, the authors establish that the constraints within ED represent relationality – the dependence of properties on the observer’s frame of reference – and should be imposed on expectation values after the process of quantization – the transition from classical to quantum descriptions. This contrasts with traditional methods and allows for the construction of non-relativistic models that are spatially relational, respecting rigid translations and rotations.

The research addresses the longstanding ‘problem of time’ in quantum gravity – the difficulty of reconciling the static nature of general relativity with the dynamic nature of quantum mechanics – offering a potentially consistent path towards a unified theory. By framing dynamics through entropy maximisation and relational constraints, the framework circumvents the need for an external time parameter. The resulting models retain elements of classical mechanics, such as definite particle positions, facilitating adaptation of existing intuitions from related work, notably Barbour’s shape dynamics – a theory proposing that the universe is fundamentally timeless and spatial relationships define reality.

This work builds upon decades of research, notably that of Arnowitt, Deser, and Misner, whose work on the Hamiltonian formulation of general relativity provides a foundational basis for the framework. It also draws inspiration from the relational approaches to classical physics pioneered by Barbour and Bertotti, and Rovelli’s relational quantum mechanics, which frames quantum mechanics within a probabilistic and relational context.

The framework establishes a strong connection between quantum mechanics and statistical physics, suggesting that quantum mechanics may not be a fundamental theory in itself, but rather an emergent consequence of underlying statistical behaviours. This perspective opens new avenues for exploring the foundations of quantum mechanics and potentially unifying it with other areas of physics.

Furthermore, the framework resonates with Mach’s Principle – the hypothesis that inertia arises from interactions with the rest of the universe – suggesting that time itself emerges from the system’s dynamics and relational information. Future research will focus on extending this framework to incorporate gravity, exploring the implications for cosmology, and developing new methods for testing these ideas experimentally. The authors anticipate that this work will contribute to a deeper understanding of the fundamental laws of nature and the origins of the universe.