The Pauli exclusion principle is one of the fundamental laws of modern physics. It determines the structure of atoms, the stability of matter, the properties of fermionic systems, and macroscopic phenomena ranging from chemistry to astrophysics. In standard quantum mechanics (QM), this principle is formulated as an axiom of antisymmetry: the wave function of two fermions must change sign under the exchange of coordinates. However, the origin of this antisymmetry remains unexplained within QM itself. Within ZEBTS — the Law of Unity of Being of the Triune Substance — the Pauli principle acquires a geometric and topological foundation. In this ontology, fermions are not treated as elementary particles but as topological modes of the operator metric, arising from the spectral structure of quantum geometry. Antisymmetry and the prohibition of identical states emerge as consequences of: the non‑commutativity of the operator metric, the topological charge λ, the spectral non‑intersection of eigenvalues, holographic constraints on information density. Thus, ZEBTS derives the Pauli principle as a topological law of quantum geometry, rather than a postulate.
The Pauli Exclusion Principle and the Spin-Statistics Theorem from Worldline Non-Injectivity: Exchange Phase, Rapidity, and Topological Sheet Structure For nearly a century, the Pauli exclusion principle (PEP) and the spin-statistics theorem have stood as foundational postulates of quantum mechanics and relativistic quantum field theory. The PEP dictates that no two identical fermions can occupy the same quantum state, determining the structure of atoms, the stability of matter, and the properties of neutron stars and white dwarfs. The spin-statistics theorem connects the intrinsic spin of a particle to its statistical behavior: half-integer spin particles (fermions) obey Fermi-Dirac statistics, while integer spin particles (bosons) obey Bose-Einstein statistics. Despite their universal success, these principles have never been derived from a more primitive geometric or topological principle — until now. This paper demonstrates that both the Pauli exclusion principle and the spin-statistics theorem emerge naturally and rigorously from a single geometric fact: the **non-injectivity of a timelike worldline** for Lorentz factors exceeding a critical threshold,
γ>γcrit. In this regime, a single worldline intersects a constant-time hypersurface
Σt in
N>1 distinct spatial points, generating a multi‑sheet spacetime structure. This phenomenon, known as **worldline non-injectivity**, is the foundation of the TPST–DGQ framework. **Key results and logical flow:** 1. **Multi‑sheet structure for a single particle:** For
γ>γcrit, a particle's worldline produces
N(ϵ)∼ϵ−(d−2) topological sheets, each carrying the same physical properties (mass, charge, spin) via the Ontological Identity Principle. 2. **Composite worldline for two identical particles:** By combining two identical particles into a composite worldline in configuration space, we obtain a two‑particle sheet structure. Identical particles share isomorphic sheet structures, reducing the
N×N sheet pairs to
N independent pairs. 3. **Exchange as a permutation of sheet blocks:** The exchange operator
P12 swaps the sheet blocks associated with the two particles. This permutation is a topological operation in the two‑particle configuration space. 4. **Exchange phase from winding number:** The exchange path corresponds to half of a complete winding cycle around the fold structure of the composite worldline. The accumulated topological phase is
Φexchange=πw, where
w is the **winding number** of the worldline. Hence the exchange phase factor is
η=eiπw=(−1)w. 5. **Spin from winding number:** The winding number
w is directly related to the spin
s by the requirement that a
4π rotation returns the physical state to itself (single‑valuedness). This yields
w=2s. Therefore
η=(−1)2s: half‑integer spin gives
η=−1 (fermions, antisymmetric), integer spin gives
η=+1 (bosons, symmetric). This is the spin‑statistics theorem derived from geometry. 6. **Pauli exclusion principle:** For two identical fermions (
η=−1) at spatial coincidence, the two‑particle amplitude satisfies
A=ηA, forcing
A=0. Thus no two fermions can occupy the same quantum state. The PEP is no longer a postulate; it is a theorem. 7. **Rapidity as inter‑sheet phase measure:** The rapidity
ζ=artanh(v/c) is shown to be a monotonic function of the inter‑sheet phase difference
Φn. The non‑injectivity threshold
γ>γcrit corresponds to
ζ>ζcrit. The speed of light
c emerges as the asymptotic limit where the inter‑sheet phase diverges, making
v=c unreachable for massive particles. 8. **Universal cancellation identity:** The same algebraic identity
N(ϵ)⋅ϵd−2=O(1) that regularizes holographic entropy, Coulomb self‑energy, wavefunction normalization, electromagnetic fields, and the cosmological constant also regularizes the two‑particle exchange amplitude — zero for fermions, finite for bosons. Quantum statistics thus joins the list of phenomena unified under the principle of worldline non‑injectivity. **Implications:** This work completes the derivation of the foundations of quantum mechanics within the TPST–DGQ framework, following previous derivations of the Born rule, the Schrödinger equation, Planck’s constant, and wavefunction collapse. It also establishes a geometric origin for the spin‑statistics connection, a result that in standard physics relies on the heavy machinery of relativistic quantum field theory (unitarity, causality, positivity of energy). Here, it follows from the topology of worldline folds. This manuscript is current in Official Peer Review. Not final version.Copyright©2026 Alex De Giuseppe.All rights reserved. This work is protected by copyright. Any form of plagiarism, unauthorized reproduction, or misappropriation of ideas, mathematically results, or text without proper citation constitutes a violation of academic and intellectual property standards and common laws. No commercial use, adaptation, or derivative works are permitted without explicit written permission from the author. For correspondence, citations, collaboration inquiries, or feedback please contact:degiuseppealex@gmail.com The hash files that determine ownership have been created.
Repulsive phenomena occupy a central place in the structure of the physical world, yet the foundations of repulsion remain poorly understood. The Pauli exclusion principle prohibits fermions from occupying identical quantum states but offers no ontological reason for why such overlap is impossible. Similarly, Coulomb’s law asserts that like charges repel, but the sign and direction of the interaction are inserted into electromagnetic theory rather than derived from deeper principles. In this paper, a unified structural account of repulsion is developed using the Structural Unified Field (SUF) framework, which treats physical entities as layered existence structures required to maintain minimal separability across attribute domains. The non-overlap axiom states that distinct entities cannot project into overlapping configurations without collapsing their structural identity. We show that Pauli exclusion arises from non-overlap in quantum-state space, while Coulomb repulsion emerges from non-overlap in the electrostatic domain. Spatial impenetrability, interatomic repulsion, and degeneracy pressure are likewise interpreted as manifestations of the same structural constraint. This structural ontology reframes repulsion as neither a force nor an axiomatic rule but as a universal consequence of identity preservation. The approach clarifies long-standing foundational issues concerning indistinguishability, the spin–statistics connection, the nature of quantum forces, and the role of structure in physical law. By grounding repulsion in a single ontological principle, the SUF framework provides a conceptually unified basis for diverse repulsive phenomena and suggests new directions for foundational research in quantum mechanics, electromagnetism, and the philosophy of physics.
This work introduces a unified mathematical and physical framework that reinterprets fundamental mathematical constants and quantum transition rules as structural regulators of informational coherence. Within the Viscous Time Theory (VTT) and the Informational Resonance Spiral Viscous Time (IRSVT) framework, we demonstrate that reality is not a collection of static entities but a continuous resolution of informational inconsistencies governed by specific geometric and dynamical attractors.We formalize a new taxonomy of mathematical structures, classifying them as anchors of stability in an informational manifold. The Trott constant is established as a fixed point of representational metamorphosis, serving as an informational attractor where representational shifts (decimal to continued fraction) induce zero loss of coherence. In contrast, the Lambert Ω constant is reinterpreted as a dynamical fixed-point attractor, marking the stable equilibrium of nonlinear feedback processes between growth and damping.Furthermore, we identify constants that function as operational filters and quanta. The Cahen constant emerges as an informational convergence quantum, providing a super-exponential mechanism for error suppression and defining the boundary between divergent instabilities and recoverable regimes. The MRB constant is formalized as a two-sided coherence filter, uniquely capable of suppressing low-frequency drift and high-frequency noise while preserving the structural integrity of high-dimensional informational manifolds.Finally, we extend this framework to quantum dynamics by providing a radical reinterpretation of Fermi’s Golden Rule. Transition rates are no longer viewed as stochastic "jumps" but as flows of informational substance through geometrically constrained channels. In this model of Informational Hydrodynamics, transition rates act as informational conductivities, and the density of states is redefined as recoverable volume, providing a deterministic geometric origin for Pauli blocking and quantum exclusion.Collectively, these results provide the mathematical foundation for a new era of information physics, where constants are not mere numerical curiosities but the visible footprints of universal self-consistency. This work offers immediate applications in predictive control, AI-pilot systems, and the design of ultra-low-dissipation informational engines.
Two of the most fundamental structural features of quantum mechanics — the Heisenberg uncertainty principle and the Pauli exclusion principle — are standardly treated as posits: brute facts about the physical world that quantum theory describes but does not explain. This paper argues that both receive principled ontological grounding from Constraint Theory (CT), the thesis established by transcendental argument that constraint is the ontological primitive constitutive of determinate existence as such. On the CT account, determinate physical entities are constituted by their constraint profiles — the specific exclusion relations that individuate them from everything they are not. The Heisenberg uncertainty principle is shown to reflect the conjugate structure of quantum constraint topology: position-space constraint and momentum-space constraint are dual expressions of a single underlying constraint structure, related by Fourier duality, such that closing one dimension of possibility space structurally requires opening the conjugate dimension. The Pauli exclusion principle is shown to be the direct physical expression of CT’s foundational claim that to be is to exclude: fermions are individuated through mutual exclusion, and the impossibility of two fermions occupying the same quantum state is the ontological requirement that distinct entities must differ in their constraint profiles. The fermion/boson distinction is given a unified structural interpretation: fermions are entities individuated by state-exclusion; bosons are entities whose mode of individuation does not proceed through state-exclusion. The paper engages the principal interpretive positions in the philosophy of quantum mechanics and the literature on quantum particle individuality, and argues that the CT account provides explanatory depth that these positions presuppose but do not supply.
Abstract Standard quantum mechanics often describes entanglement as a non-local correlation, presenting persistent conceptual conflicts with relativistic causality. This paper proposes a heuristic geometric hypothesis within a constrained 3+1+2 multitemporal manifold, reinterpreting entanglement not as superluminal information transfer, but as a deterministic consequence of topological continuity across extra transverse-time dimensions. Within this theoretical framework, we hypothesize two distinct geometric mechanisms depending on particle topology. For massless bosons, modeled as open helical solitons, entanglement is proposed as the continuous bifurcation of a single phase-wavefront. This macroscopic splitting conceptually accounts for the energy bisection and wavelength doubling observed in spontaneous parametric down-conversion (SPDC), as the overarching topological tension is distributed across two macroscopic projections while remaining unbroken in the extra dimensions. Conversely, for massive fermions, which are modeled as closed topological rigid bodies, we propose that macroscopic spatial separation (Δx ≠ 0) can mathematically coexist with coordinate overlap in the 2D transverse-time plane (Δτ = 0). It is hypothesized that these rigid particles are strictly meshed together at a singular coordinate within the transverse-time dimension. This direct interlocking is strictly governed by the Pauli exclusion principle, which mandates that the two topological "gears" must mesh with opposite, complementary rotations to avoid metric rupture. Furthermore, SL(4,ℝ) tensor projections mathematically guarantee that this shared geometric state persists independently of any macroscopic spatial distancing. Finally, we suggest that "wave-function collapse" can be reinterpreted as a forced geometric alignment induced by macroscopic mass ("phase-anchors"). We hypothesize that quantum superposition arises from the transverse-time fluctuations of low-mass particles. Upon contact with a phase-anchor, the Pauli exclusion principle dictates a temporary structural meshing that synchronizes the particle's mass with the macroscopic cluster. This instantaneously forces the fluctuating particle to align with the overarching Meta-Time axis, deterministically halting the superposition and severing the entanglement.