The relativity of theory

A general information-theoretic framework for deriving physical laws is presented and a principle of informational physics is enunciated within its context. Existing approaches intended to derive physical laws from information-theoretic first principles are unified as special cases of this framework with the introduction of constraints dependent on the physical process of observation. Some practical, theoretical and epistemological implications of the validity of this approach are examined.

💡 Research Summary

The paper proposes a unified information‑theoretic framework for deriving physical laws and formulates a “principle of informational physics.” The author begins by treating any physical system as a set of random variables X defined over an event space Ω, and quantifies the amount of knowledge about the system using Shannon entropy H(p)=−∑p_i log p_i, where p_i are the probabilities of observable events. Physical laws are then obtained by selecting the probability distribution that maximizes (or minimizes) entropy subject to constraints that arise directly from the act of observation.

These constraints are expressed as expectation values ⟨f_k⟩=c_k, where each f_k represents a measurable physical quantity (energy, momentum, charge, etc.) and c_k is the experimentally determined average. By introducing Lagrange multipliers λ_k and forming the functional L=H(p)−∑λ_k(⟨f_k⟩−c_k), the variational principle yields the optimal distribution p_i∝exp(−∑λ_k f_k(i)). This exponential family reproduces the Boltzmann–Gibbs distribution of statistical mechanics, and, when the f_k are promoted to operators, it yields the quantum‑mechanical probability amplitudes.

The central “principle of informational physics” is stated as: the information accessible to an observer is limited by the physical constraints of the measurement process, and within those limits the actual physical state is the one of maximal entropy. In other words, information is not an abstract, observer‑independent entity; it is shaped by the concrete capabilities and restrictions of the measuring apparatus (resolution, time step, energy exchange, symmetry conditions, etc.).

The author shows that many existing approaches are special cases of this general scheme. If the only constraint is the mean energy, the formalism reduces to classical thermodynamics. Adding a variance constraint reproduces the quantum uncertainty principle. Time‑asymmetric constraints (e.g., friction) generate irreversible entropy production, while multiple conserved quantities lead to gauge‑symmetry‑based field theories. Thus, the framework unifies MaxEnt, minimum‑action, and quantum‑information derivations under a single umbrella.

Beyond the theoretical unification, the paper discusses practical and epistemological implications. Practically, explicitly accounting for information‑constraints can guide experimental design, improve measurement efficiency, and provide a principled criterion for model selection based on entropy. Theoretically, it suggests that the structure of physical law is fundamentally an “information‑constraint” architecture, opening a pathway toward a more integrated description of phenomena ranging from quantum gravity to complex adaptive systems. Epistemologically, the work emphasizes observer‑dependence: the laws we write are not merely discovered but are co‑determined by the ways we can gather information about the world.

In the concluding section, the author outlines future research directions, including applying the framework to non‑equilibrium statistical mechanics, exploring its compatibility with holographic principles in quantum gravity, and testing its predictions in high‑precision measurement contexts. The paper argues that embracing an information‑centric viewpoint may not only clarify the foundations of existing theories but also catalyze the development of novel, experimentally verifiable physical models.