A Unified Covariant Framework for Quantum Dynamics, Electromagnetism and Gravity using the Deterministic Computation Law

Carlo Maria Scandolo, Gilad Gour, Barry C. Sanders

We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be stated as follows: If we evolve the dynamical system for n time steps and then disturb it, then it is the same as first disturbing the system with the same influence and then letting the system evolve for n time steps. Applying the powerful machinery of resource theories, we develop a theory of covariant influences both when there is a purely deterministic evolution and when randomness is involved. Subsequently, we provide necessary and sufficient conditions for the transition between states under deterministic covariant influences and necessary conditions in the presence of stochastic covariant influences, predicting which transitions between states are forbidden. Our approach, for the first time, employs the framework of resource theories, borrowed from quantum information theory, to the study of finite discrete dynamical systems. The laws we articulate unify the behavior of different types of finite discrete dynamical systems, and their mathematical flavor makes them rigorous and checkable.

Dean P. Rickles, Xerxes D. Arsiwalla, Hatem Elshatlawy

Geza Szamosi

Chanda Prosper

Prosper's Unified Position Equation (PUPE) is a novel theoretical framework that unifies classical mechanics, special relativity, quantum mechanics, and electromagnetism into a single deterministic model of motion. By integrating a particle’s momentum, wave amplitude, and ambient electromagnetic fields, PUPE provides precise trajectories for particles, removing the need for probabilistic interpretations in quantum mechanics. The framework reproduces established results in various physical regimes and opens new avenues for deterministic modeling of multi-particle systems, quantum field theory, and cosmological phenomena.

N. Ionescu-Pallas, I. Gottlieb

Chanda Prosper

One of the most persistent and profound goals in physics is the unification of its fundamental theories. For centuries, our understanding of the universe has advanced by developing distinct mathematical descriptions for different physical regimes. This specialization, while incredibly powerful, has bequeathed us a fractured portrait of reality, with different laws governing motion in different realms. A unified theory that can seamlessly describe phenomena across all scales—from the subatomic to the cosmological—remains a central objective of modern science.The current landscape of physics separates motion into several distinct domains, each governed by its own set of laws:Classical motion is described by Newton's second law, F = ma.Relativity governs high-velocity motion through the energy-momentum relation.Quantum mechanics describes the subatomic world using the Schrödinger equation and the concept of probability waves.Electromagnetic motion for charged particles is dictated by the Lorentz force laws.While these descriptions work exceptionally well within their intended domains, they are not unified. The PUPE framework proposes a direct solution to this fragmentation. It aims to reconcile these disparate views by defining all motion through a single position equation and a single momentum equation. This is achieved by incorporating relativistic and electromagnetic terms directly alongside a quantum component derived from the wave amplitude R and its gradient, which generates quantum behavior without disrupting the classical and relativistic foundations. This paper will now detail the core mathematical structure of this innovative framework.