The relationship between chance and determinism has been analyzed by philosophy, mathematics, and physics.With the aim of identifying the intersection between the two, the Law of Probability Equilibrium (LPE) was demonstrated.When the probabilities of natural phenomena differ from zero and one, the LPE shows that the observed probability is empirical and that the cumulative probability functions of these phenomena measure the imminence of their occurrence ("energy concentration").These functions behave like waves that carry information about the probabilistic ("energetic") potential for the materialization of such phenomena.Probability functions exhibit properties analogous to quantum systems, such as complementarity, superposition, uncertainty, collapse, duality, interference, and entanglement.The findings indicate that chance and determinism converge at a cumulative limit of 1/2, forming a self-regulating equilibrium within the probabilistic field.This implies both the certainty of occurrence and the unpredictability of its timing.Even events with infinitesimal probabilities will inevitably occur.The LPE shows that the probability potential decreases until it reaches zero ("maximum entropy").Accumulated randomness is restricted to a maximum value of 1/2, allowing for causal processes (e.g., emission and absorption).Each probabilistic event, before being observed, exists in two superposed states: presence and absence, and it possesses a simultaneous and distinct probabilistic duality.One of these values is derived from the density function at the final instant, while the other is accumulated and remains stationary at 1/2.Upon measurement, the two probability density functions collapse into presence or absence (1 or 0) ("particle modality").Meanwhile, the two cumulative probability distribution functions remain entangled, each How to cite this paper: Traversa, I.
The relationship between chance and determinism has been analyzed by philosophy, mathematics, and physics.With the aim of identifying the intersection between the two, the Law of Probability Equilibrium (LPE) was demonstrated.When the probabilities of natural phenomena differ from zero and one, the LPE shows that the observed probability is empirical and that the cumulative probability functions of these phenomena measure the imminence of their occurrence ("energy concentration").These functions behave like waves that carry information about the probabilistic ("energetic") potential for the materialization of such phenomena.Probability functions exhibit properties analogous to quantum systems, such as complementarity, superposition, uncertainty, collapse, duality, interference, and entanglement.The findings indicate that chance and determinism converge at a cumulative limit of 1/2, forming a self-regulating equilibrium within the probabilistic field.This implies both the certainty of occurrence and the unpredictability of its timing.Even events with infinitesimal probabilities will inevitably occur.The LPE shows that the probability potential decreases until it reaches zero ("maximum entropy").Accumulated randomness is restricted to a maximum value of 1/2, allowing for causal processes (e.g., emission and absorption).Each probabilistic event, before being observed, exists in two superposed states: presence and absence, and it possesses a simultaneous and distinct probabilistic duality.One of these values is derived from the density function at the final instant, while the other is accumulated and remains stationary at 1/2.Upon measurement, the two probability density functions collapse into presence or absence (1 or 0) ("particle modality").Meanwhile, the two cumulative probability distribution functions remain entangled, each How to cite this paper: Traversa, I.
The source of inspiration for doing quantum probability lies in the ingenious methods adopted by physicists to compute probabilities of events concerning the subatomic world of elementary particles where the laws of classical mechanics break down and the distinction between a particle and a wave becomes vague. These methods lead to a generalisation of classical probability which may be described as a study of observable quantities concerning any system subject to chance and exhibiting the following basic features: (i) each observable quantity behaves like a classical real valued random variable on a probability space and hence has a probability distribution on the real line; (ii) it may be impossible to measure simultaneously two individually observable quantities in the sense that measurement of one may interfere with and destroy already existing information about the value of the other; (iii) bounded observable quantities constitute a real linear space in which the vectorial sum of two individually observable quantities interfering with each other is different from the arithmetic sum of their actual values. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
DESCRIPTION This work presents a complete, deterministic framework for quantum mechanics derived entirely from a single, testable postulate: the density of quantum space. The Core Problem For over a century, quantum mechanics has been interpreted as a theory of fundamental randomness, wave-particle duality, instantaneous jumps, and irreducible uncertainty. The standard Copenhagen interpretation treats the wave function as a probability amplitude, measurement as a "collapse" of that probability, and the Heisenberg uncertainty principle as a fundamental limit of nature. This work demonstrates that all these "mysteries" are not properties of nature—they are artifacts of our limited perception. We observe quantum phenomena through slow, macroscopic instruments that cannot resolve the actual continuous dynamics occurring in a space that is 6.54 trillion times denser than what we perceive as "empty space." The Fundamental Postulate The foundation of this work is a single, geometrically derived constant: ρ = (number of Planck lengths in 1 mm) / (number of millimeters in 1 light-year) = 6.54 × 10¹² Physical Meaning: One millimeter of physical space contains 6.54 trillion times more quantum spatial units than one light-year contains millimeters. What we perceive as "empty space" is actually a dense, discrete, information-rich medium. The entire observable universe (93 billion light-years in diameter) maps to only 0.014 light-years in quantum space—well within our Solar System. Consequence: The density inversion explains why quantum phenomena appear strange: we are observing a dense, fast, discrete reality through slow, coarse, macroscopic instruments. The apparent "weirdness" is not in nature—it is in our perception. The Comprehensive Law From the density postulate and classical physics (Newton, Coulomb, Maxwell, Einstein), a single comprehensive law is derived that contains all known physics as limit cases: E(t,v,n) = (m₀c²/ρ) · ‖n‖ · √(1 + (γv/c)²) · sin(2πt/T) This formula contains: Einstein's E = mc² as the limit ρ → 1, ‖n‖ → 1, sin → 1, v ≪ c Newtonian mechanics as the limit v ≪ c Special relativity as the limit ρ → 1, ‖n‖ → 1, sin → 1 Quantum mechanics as the discrete geometry n ∈ ℤ³ and resonance sin(2πt/T) Each term has a precise physical meaning: the rest mass energy (m₀c²) is scaled by the quantum space density (1/ρ), modified by the position relative to the absolute zero point Z₀ (‖n‖), adjusted for relativistic motion (√(1 + (γv/c)²)), and modulated by temporal resonance (sin(2πt/T)). Resolution of All Quantum Paradoxes Wave-Particle Duality = Optical Illusion The electron is always a localized particle with a definite trajectory. The "wave" is the charge density distribution—a standing wave in the dense quantum medium. From the standing wave condition 2πr = nλ, the Poynting vector in the far field is exactly zero (S = 0), meaning the electron does not radiate. The apparent "wave behavior" is an optical illusion caused by the density ρ smearing the point-like trajectory in our low-resolution projection. Wave Function = Energy Density, Not Probability The squared modulus of the wave function |Ψ|² is the energy density fraction, not a probability density. The particle itself follows a deterministic trajectory y(t) = v₀t - ½g₀t². Probability appears only because we cannot resolve the trajectory (due to t_total = 118 as ≪ Δt_instr) and we do not know the initial phase φ of the oscillation. Schrödinger Equation = Effective Approximation The Schrödinger equation is an effective, averaged description of how the energy density evolves. The fundamental law is classical motion in the dense quantum medium. The Schrödinger equation emerges when we average over the fast oscillation sin(2πt/T), ignore the density force F_ρ, and treat trajectories statistically. Quantization = Resonance, Not Arbitrary Jumps Energy levels are the resonant harmonics of the quantum space medium. The standing wave condition 2πr = nλ gives E_n = -13.6 eV/n²—exactly the same physics as a vibrating string. Only frequencies that satisfy the standing wave condition are stable. The transition between levels is not an instantaneous "jump" but a continuous trajectory y(t) = v₀t - ½g₀t² with total duration t_total = 118 as. The apparent "instantaneous jump" is an artifact of our slow instruments. Heisenberg Uncertainty = Collision, Not Fundamental Limit The uncertainty product depends on the measurement geometry: Δx·Δp = h·tan(θ/2), where θ is the scattering angle of the measurement photon. As θ → 0 (forward scattering with perfect detection), the product approaches zero. There is no fundamental lower bound. The uncertainty is a practical limitation of invasive measurement—we disturb the particle's trajectory when we hit it with a photon. Quantum Randomness = Ignorance Residual "quantum randomness" is simply unmodeled environmental force noise. The apparent randomness arises from three sources: temporal resolution (t_total = 118 as ≪ Δt_instr—we cannot resolve the trajectory), initial phase ignorance (we do not know the phase φ of sin(2πt/T)), and measurement perturbation (we do not know the exact collision parameters). If we could measure the outgoing photon completely and know the initial phase, the outcome would be fully deterministic. Randomness is in our ignorance, not in nature. Five Testable Predictions The theory makes five clear, quantitative predictions that distinguish it from standard quantum mechanics: Prediction 1 - Electron Transit Time: The electron transit time during the n=1 → n=2 transition in hydrogen is 118 ± 5 attoseconds. Standard quantum mechanics predicts zero duration (instantaneous jump). Testable with attosecond pump-probe spectroscopy. Prediction 2 - Heisenberg Product Can Approach Zero: With better detectors, the uncertainty product Δx·Δp can approach zero, not ħ/2. Standard quantum mechanics predicts Δx·Δp ≥ ħ/2 always. Testable with weak measurement experiments. Prediction 3 - Energy Oscillation at 116 kHz: The energy of gold-197 oscillates at 116 kHz with amplitude 1.252 × 10⁻²⁶ J. Standard quantum mechanics predicts constant energy for a given state. Testable with precision spectroscopy. Prediction 4 - Bell Inequality Violations Decrease with Measurement Strength: As measurement impulse strength decreases, Bell inequality violations decrease. Standard quantum mechanics predicts violations are independent of measurement strength. Testable with weak measurement entanglement experiments. Prediction 5 - Quantum Randomness is Environmental Noise: Residual "quantum randomness" equals unmodeled environmental force noise. Full force accounting restores classical determinism. Standard quantum mechanics predicts randomness is fundamental and irreducible. Testable with complete force reconstruction in closed quantum systems. The Absolute Zero Point Z₀ This work introduces Z₀ = (0,0,0) as a universal, absolute reference point in quantum space. Every point in space has a discrete address: n = (n_r, n_θ, n_φ), ‖n‖ = √(n_r² + n_θ² + n_φ²) Z₀ is physically grounded in the cosmic microwave background (CMB) rest frame, vacuum energy (the lowest possible energy state), and the geometric center of the quantum space lattice. This eliminates the relativity of reference frames—providing an absolute coordinate system that standard physics lacks. Mathematical Consistency The work provides rigorous derivations of: The density ρ from first principles (Planck length, electron mass, fine structure constant) The quantum coordinate norm ‖n‖ from the discrete metric of quantum space The oscillation period T from the de Broglie relation The coupling constant ε from fundamental constants The regularized metric eliminating all singularities The thermodynamic properties of quantum space (entropy, temperature, heat capacity) The covariant Einstein equation in quantum space The connection to quantum anomalies and topological invariants The Lamb shift from quantum space density oscillation Dark energy from quantum space density variation Comparison with Other Approaches String theory requires approximately 10⁵⁰⁰ free parameters and offers no testable predictions with current technology, while introducing new physics such as strings, extra dimensions, and supersymmetry. Loop quantum gravity requires approximately 10 parameters and also offers no testable predictions, introducing spin networks and loop quantization. Both approaches have difficulty connecting to the Standard Model. In contrast, this theory has only one parameter (ρ, which is derived from fundamental constants rather than being free), offers five testable predictions with current or near-future technology, requires no new physics beyond standard physics applied in a dense medium, and connects directly to the Standard Model through the energy-momentum tensor. The Core Message Quantum mechanics is not magic. It is not a new kind of physics. It is the same old physics—Newton, Maxwell, Coulomb—operating in a space that is 6.54 trillion times denser than we perceive. Three things to remember: Space is dense, not empty. What we call "empty space" is actually a dense, discrete medium. We are the ones who are sparse—not the universe. The particle has a trajectory. Every particle follows a precise, continuous path. We don't see it because our instruments are too slow. The path exists—we just can't resolve it. Energy breathes. Energy is not a static number. It oscillates in time, like a heartbeat. The universe is alive with resonance. Conclusion This work demonstrates that quantum mechanics is not a theory of fundamental randomness and irreducible uncertainty. It is the low-resolution, static-space approximation of a deeper, deterministic, dynamic reality. The deeper reality is quantum space—dense, discrete, resonant, and absolute. The final statement of this
Quantum Energy: Confined & Oscillatory Dual Equilibrium Modes of the Quantum Field This paper takes the globally continuous quantum field as the fundamental carrier medium of the universe, and proposes the inherent collapse-attraction and repulsion-diffusion dual tendencies of all quantum energy units as the endogenous driving force of all physical phenomena. It defines two exclusive native eigenstates of energy: the confined state under low energy density and weak field potential, and the oscillatory state formed by persistent stress imbalance in high-density superimposed strong fields. All wave-particle duality phenomena, microscopic quantum behaviors and macroscopic cosmic evolution are uniformly interpreted as two modal transformations regulated by local energy density and field potential intensity, without introducing extra mathematical hypothetical constructs such as wave function collapse or superposition. The theory establishes a complete logical closed loop covering quantum field ontology, microscopic dual-state dynamics, double-slit interference mechanism, fundamental interaction origin and cosmic large-scale evolution. It fully matches all verified experimental observations, only reconstructs the underlying physical causal logic, and does not overthrow objective measured conclusions. Meanwhile, it distinguishes the computational practicability of hierarchical mathematical modeling from the natural unity of cosmic physical laws, and criticizes the cognitive bias of prioritizing mathematical description over physical ontology in mainstream research paradigms. This monistic energy framework serves as the general outline for the complete P1–P11 series of collapse-repulsion dynamic theories. Version 2: Add full English manuscript, V1 keeps original Chinese file unchanged.
The shift from classical deterministic prediction to quantum distributions does not by itself decide whether the real is intrinsically probabilistic. The argument begins with both the force and the limit of Laplace’s ideal: deterministic dynamics can coexist with incomplete knowledge of the initial conditions, and classical physics already employs probability. The uncertainty relation then requires a distinction between preparation uncertainty, measurement error, and disturbance, preventing a single formula from serving as an ontological verdict. Bell inequalities tighten the constraints by excluding a specific family of local explanations without ruling out deterministic nonlocal dynamics. The objectivity of probability therefore arises from the explanations that the distributions rule out, not from turning probability into substance. An unexpected detector pulse then allows us to follow the transition from a physical record to knowledge: the material configuration may persist while the act of discrimination is ephemeral; only recognition under a protocol requires a distinction between trace, singular inscription, passive mark, and symbol. Finally, the laser shows why technical fruitfulness increases a theory’s epistemic weight, even though rival ontologies may share the same formalism. The remaining interpretative openness is not arbitrary: it is bounded by results that any future account must accommodate.
Theory of Relational Dimensional Coexistence: An Ontological Model of Observation, Light, and the Multiverse Giuseppe Trizzino Abstract This work outlines a theoretical framework of Relational Dimensional Coexistence, proposing that spatial dimensions and physical reality do not possess absolute, independent existence. Existence is modeled as an emergent property generated through observation. By integrating principles of relational quantum mechanics with an asymmetric causal model of perception, it is postulated that energy exists as a static, primordial stock, but that observation via electromagnetic propagation (light) acts as the fundamental tool and medium for its activation: observing implies being observable, thus giving rise to an infinite network of universes in which the primordial energy stock takes on dimensional form through specular relation. 1. Introduction: The Problem of Ontological Independence Traditional physics treats space, time, and energy as pre-existing background metrics within which observers subsequently evolve. However, quantum mechanics—particularly in relational interpretations (Rovelli) and the principle of complementarity (Bohr)—suggests that physical properties materialize only through interaction. This work introduces a radical inversion: the act of observation precedes and conditions the existence of the dimension itself. Without an active observational bridge, energy, light, and spatial dimensions collapse into nothingness. 2. The Principle of Observability and Openness to the Multiverse A fundamental pillar of this model is the ontological reflexivity of observation: Whoever observes, exists and is observable: Observation is never a one-way street or an isolated privilege. The moment a universe (or dimension) A observes a universe B, A activates its own energy field and demonstrates its existence precisely by virtue of the fact that the observer can itself be observed. The probability of infinite universes: Because every act of observation generates space for the observed and legitimizes the existence of the observer within the energy circuit of light, the system is not confined to a single pair of realities. Probabilistically, this opens up an unlimited multiverse: an infinite network of dimensions that watch each other, move reciprocally, and keep each other alive. 3. The Three Hypotheses of Relational Dynamics Within this system of universes, the interaction between two dimensions (e.g., A and B) is articulated in three distinct configurations: First Hypothesis (A observes B): Universe A observes B in an energetically passive manner via light (without exerting mechanical force or violently altering the other). A can only observe without acting, or interact; only B (the observed) can change its reality and dimension. This act allows B to exist and have the freedom to move and mutate its own dimension. At the same time, A lives and justifies its own existence precisely through its act of observing (since observing implies being inserted into the network of observability). Second Hypothesis (If B also observes A): If Universe B begins to observe A, and if A is simultaneously inserted into the visual field of a third element (C), the network expands. This is not a simple sum of isolated gazes, but an ontological chain reaction that expands the multiverse. Third Hypothesis (Reciprocal and Symbiotic Observation): By law, by chance, or by causality, observation becomes perfectly reciprocal and simultaneous. In this state, A observes B and B observes A in the same instant. Observation becomes symbiotic: the two dimensions coexist as a dimension and an anti-dimension (positive and negative), relating in such a way as to allow the coexistence and life of both, without ever being able to "touch" or mechanically destroy the other. 4. Light and Energy as Ontological Consequences The model redefines the causal chain of the universe: {Observation / Observability} — {Medium (Light)} — {Energy} — {Dimensional Existence} Light as a Non-invasive Bridge: Observation occurs via light, which acts as a medium of informative and specular connection, devoid of violence or mechanical force, but an absolute potential. Energy as a Product of Relation: We live in a universe made of energy, but energy, as a static primordial stock, acts as a vehicle for dimension and reality. Without the act of observation and the condition of observability, the medium does not "turn on," energy does not manifest, and there can be no dimension. Observation as Tool and Medium: Spatial reality exists and is maintained in life solely by the energy flow triggered by the gaze. The primordial stock is inherently static. It is the act of observation that acts as the tool and medium to unlock that energy, turning on light as an informative vector. 5. Conclusion The Relational Dimensional Coexistence model demonstrates that cosmic loneliness is a physical and logical impossibility. Reality is an immense fabric of mirrors: dimensions exist because they watch one another, reciprocally authorize each other to be, move through the freedom of the observed, and sustain themselves as a single, infinite energy system based on light and reciprocity. How can a dimension or reality be born from an observation? If we state that the energy stock is already there (static and primordial), how does the simple "act of looking" (the gaze) materially bring about a dimension or reality that did not exist before? The answer lies in moving beyond the idea that space is an "empty container" that exists regardless. In our model, a dimension is not a block of matter, but the geometric and relational space that opens up when energy is directed. The vacuum has no coordinates without a relation: Before observation, the primordial energy stock is a "zero-dimensional" entity, an unformed potential, infinite but immobile. It has no "up," "down," "inside," or "outside" because there is no distance to measure. Geometric space (dimension) arises only the moment there is a point of view pointing toward another point. The distance traveled by light traces the inaugural line of space. Light as the "Pencil" of Space: Light is not just information traveling; physically, it is energy in motion. The moment the gaze (via light) departs from A to reach B, that energy beam establishes a coordinate. It creates a living Cartesian axis between the two. Without that beam, the two are in an unformed non-place. With the beam, distance is traced, and tracing a distance means creating dimension. Actualization of Potential: Taking the principle of quantum indeterminacy: a particle is a "cloud of probability" until a measuring instrument forces it to "choose" a defined position. Extending this to a cosmic scale: the primordial energy stock is the infinite probability cloud. Observation is the act of universal measurement that "collapses" potential into a precise geometric reality. Static energy becomes spatiality precisely because the gaze forces it to focus on an axis of relation. Why is everything, nothing, and everything possible? In traditional quantum physics, as long as a system is isolated and unobserved, it exists in a superposition of states (the wave function). It is only interaction with the outside—the act of measurement—that forces the wave function to "collapse," extracting from the chaos of probabilities a unique event. Applying this to our theory: The Chaos of Potential: Without observation, the primordial energy stock fluctuates in a state of pure acausal potential. Everything is in potential and nothing is in act. Observation as "Cosmic Collapse": The act of observing acts as the ultimate measurement tool of reality, forcing primordial energy to exit probabilistic superposition. The Birth of Dimension: The moment the gaze sets the limit and traces the coordinate between universes, the "everything is possible" crystallizes into a precise geometric form. Spatial dimension arises exactly from this collapse: space is nothing more than the distance established and rendered real by the interruption of probability.