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.
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.
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.
This paper introduces a novel theoretical framework that bridges discrete and continuous descriptions in physics through a unified probabilistic approach. At its core, the framework demonstrates how continuous forms naturally emerge from discrete entities via probability distributions, providing fresh insights into phenomena ranging from classical mechanical systems to quantum mechanics. The work develops a rigorous mathematical formalism that includes a geometric interpretation through Riemannian metrics and extends naturally to relativistic systems.What sets this approach apart is its ability to describe transitions between discrete and continuous regimes using a single mathematical structure, while maintaining compatibility with both classical and quantum mechanical descriptions. The framework introduces a continuity probability function that characterizes systems across all scales, offering new perspectives on wave-particle duality and the emergence of continuous forms in nature. By providing a unified mathematical language for describing such phenomena, this work opens up new possibilities for understanding the relationship between discrete and continuous aspects of physical reality.
The absence of a common mathematical structure underlying quantum theory and relativistic physics remains a central obstacle to unification. While relativity is formulated in terms of spacetime geometry and covariance, quantum theory is intrinsically probabilistic, relying on amplitudes, uncertainty, and statistical interpretation. Existing unification programs typically attempt to quantize geometry or to geometrize quantum fields, but the probabilistic structure itself is rarely treated as a fundamental geometric object. In this paper, we propose a unified description of relativistic and quantum dynamics based on probabilistic geometry. Probability densities are taken as primary variables and are endowed with an intrinsic information–geometric structure defined by the Fisher–Rao metric. Within this framework, physical motion is described as the covariant evolution of probability distributions on a statistical manifold rather than as trajectories in a preassigned phase space or Hilbert space. The central result is a unified probabilistic–geometric field equation in which the relativistic d’Alembertian acting on the probability density is coupled to the scalar curvature of the associated information manifold. In an appropriate nonrelativistic limit, this equation reproduces the quantum potential as a curvature term, establishing a direct correspondence between quantum effects and informational geometry. Relativistic covariance is preserved throughout, allowing quantum and relativistic structures to appear as different regimes of a single probabilistic equation. The proposed framework does not introduce new particles, interactions, or quantization postulates. Instead, it provides a structural unification in which quantum and relativistic features emerge from the geometry of probability itself.
The traditional path integral formulation of quantum mechanics relies on complex probability amplitudes and the principle of least action, which has conceptual ambiguities in interpreting microphysical mechanisms — serving merely as effective mathematical statistical tools. Based on the Unified Cosmic Mechanics Evolution Theory — where the momentum unit (m₀·c) is the only physical reality, the field is an interaction protocol, and the particle is a momentum encapsulation structure — this paper reconstructs the mathematical description of multi-slit experiments. The new formulation replaces the complex path integral with a dual-integral system: the self-integral describes momentum unit self-evolution along their intrinsic direction, endowing linear motion; the interaction integral describes momentum flow interaction with the slit wall's electromagnetic field, realizing multi-path distribution and direction deflection. These two integrals together constitute the momentum flow distribution integral, interpreting "interference" as the superposition of real momentum flows dominated by the interaction integral. Key insight: Just as a stone falling from a height depends on the perceptual cross-section 1/(4πr²) for its integral result, all forces should be similarly understood — their underlying dynamics must be reduced to the perceptual cross-section mechanism. The interaction integral follows this logic: the relativistic mass-energy equation is a space-time state shaping equation, where the emergent space-time integral reflects Pythagorean conservation (Lorentz covariance); general relativistic integrals involve variable space-time redundancy under field strength; special relativistic integrals arise from perceptual space-time window compression during motion. For micro-particles in multi-slits, this paper primarily adopts the interaction integral mechanisms of special relativity, electromagnetism, and photoelectricity. This framework remains consistent with existing experimental phenomena and proposes testable predictions including slit thickness-dependent deflection and multi-slit interference fringe modulation.
This paper advances the Unified Quantum Mechanics (UQM) framework by elevating the empirical stability of matter to the status of a cosmological first principle. While previous work established the operator formalism, this work posits that the foundational conflicts of 20th-century physics—Real vs. Complex, Deterministic vs. Probabilistic, and Continuous vs. Discrete—are resolved specifically by this stability axiom. The central innovation is the advancement of the Analyticity Mandate, which constrains all physical wavefunctions to be causal, positive-energy analytic signals (E>0). This mandate is mathematically implemented by identifying the imaginary unit i with the physical, non-local temporal Hilbert transform operator (i≡Ht), transforming the Schrödinger and Dirac equations into deterministic, real-valued field equations—the Unified Real Wave Equation. We uncover a fundamental symmetry at the heart of unification: the analytic signal constraint required to ontologically complete quantum theory simultaneously derives the geometric structure of General Relativity, demonstrating that both paradigms originate from the single axiom of matter stability. We establish that this analytic complexification constitutes a mathematically rigorous and physically necessary procedure, transforming the underlying real spacetime-energy field into a unified dynamical framework that naturally subsumes both quantum phenomena and gravitational evolution. This framework culminates in a unified Theory of Everything described by the fundamental action: SUQM=∫d4x−g(16πGc4(R−2Λ)+LSM), where the Lagrangian density describes both geometry and matter as manifestations of a single real field ψR under the Analyticity Mandate. The complete theory is expressed through the coupled system: Gμν=κTμν[ψR]andψ=ψR−iHt[ψR]withE>0. We present the following quantitative results and mechanisms: (1) We derive the Cosmic Cycle Period Tcycle≈7.14×1011 years for the cubic model (Spherical model: ≈7.00×1011 years) and the maximum expansion factor Zmax≈2.20×1010 (Spherical: ≈1.36×1010), by solving the cosmic equation of state governed by the electron's vacuum stability horizon lcrit≈5.35 cm (Spherical diameter: Dcrit≈6.64 cm). (2) We identify the Fermionic Rigidity mandated by the Pauli Exclusion Principle as the specific geometrodynamic trigger for the non-singular Big Bounce, avoiding the entropy paradoxes of Conformal Cyclic Cosmology. (3) We restore Global Noether Conservation by reinterpreting cosmological redshift as mechanical work performed against the elastic tension of the vacuum plenum (ρΛ). (4) We formalize the \emph{Singh Stability Conjecture}, proposing a hierarchy of verification protocols including a Rapid-Dispersion interferometric experiment designed to test the specific cosmological parameter limits of the vacuum. The resulting ontology is a monistic Spacetime-Energy substance, where the Einstein Field Equation Gμν=κTμν represents the phase equilibrium between the geometry of the vacuum and the density of matter. UQM thus completes Einstein's unification program by providing a deterministic, realist, and geometrically coherent foundation for all physical phenomena. We formally propose a community-wide verification program, defining definitive falsification tests through laboratory experiments, cosmological observations, and Gedankenexperiments. Within this program, we distinguish between parametric constraints and ontological validity, asserting that the ultimate falsification of the framework requires the empirical demonstration of stable negative-energy states.
ABSTRACT Over the past century, modern physics has been bifurcated into the theory of relativity explaining the macro-world and quantum mechanics dealing with the micro-world. In doing so, it has forfeited mechanical causality, relying instead on mathematical probabilities and geometric optical illusions. This paper meticulously identifies the epistemological blind spots and voids of conventional physics and proposes 'Jung Sung-mo's Grand Unified Dynamics,' which penetrates all forces and motions of the universe with a single, overarching mechanical principle. First, this study establishes the 'Theory of Absolute Intrinsic Physical Metric Relativity,' which posits that every object in the universe independently possesses its own intrinsic unit time (T) and unit distance (L). By introducing the independent metrics (Tc, Lc) of a 'Third-party Omniscient Observer ( C)' into the formulation, we present an algebraic formula for deriving relative velocity, thereby completely and mechanically dismantling the inherent contradictions and the Twin Paradox of Einstein's Special Theory of Relativity. Second, the reality of quantum phenomena, previously dismissed as mere probability clouds, is explicitly elucidated through a novel three-step verification framework: [Theoretical Formulation → Algebraic Equation Derivation → 3D Parametric Simulation Verification]. Within the Dynamic Field formed by the intrinsic motion of particles within the Static Field lattice medium, the mechanical cumulative density of multi-dimensionally superimposed and rotating particles is mathematically formulated. In particular, it visually and dynamically demonstrates via a computer simulation (Appendix A) that the geometric configurations of s, p, d, f orbitals—long considered an enigma in quantum mechanics—are not mathematical probability functions, but rather the pure mechanical outcomes of a 'Teardrop Envelope Trajectory' designed for friction avoidance between particles and a 'Surface of Revolution Scanning' across multiple planes. Ultimately, this study declares a paradigm shift toward a grand unified physics that strips away Einstein's spacetime curvature and Schrödinger's probabilistic illusions, thereby fully restoring the authentic mechanical causality of the Field that bridges the macroscopic and microscopic realms of the universe. Keywords: Grand Unified Dynamics, Mechanical Causality, Absolute Intrinsic Metric Relativity, Particle Multi-Dimensional Trajectory Dynamics, Deterministic Trajectory, Orbital Kinematics, Parametric Simulation, Probability Cloud.