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Results for “p-adic” 21 papers
Adelic Zitterbewegung: p-Adic Regularization of Dirac Trembling Motion and the Product-Formula Cancellation at Macroscopic Scales
Zitterbewegung (ZBW) — the trembling motion of Dirac wave packets at the Compton scale — is conventionally treated as a purely Archimedean interference effect between the positive- and negative-energy branches of the free Dirac equation. Missing from the standard account is any mechanism by which…
Finite-Distinction Quantum Mechanics: Unitary Evolution and Superposition as the Large-Distinction Limit of Stochastic Thermodynamics
The continuum is an infinite-information object: a single real coordinate specifies infinitely many yes/no distinctions, and a finite-entropy world cannot contain such coordinates. This paper assembles the consequences of that observation into a three-part thesis. First, the finite-information…
Frequency as Valuation Theory: The Rational Ratio at the Heart of Physical Law
Physics expresses frequency as a real number — 5.783 × 10^14 Hz, 1420.405751768 MHz. Yet in dimensionless Planck units (h = c = G = k_B = 1), frequency reduces to a ratio of two integers: count-of-oscillations per count-of-Planck-times. This is a rational number q = a/b in Q — not an Archimedean…
Radix-Agnostic Detection of Discrete Scale Invariance: A Certified Three-Stage Protocol and a Null Result from Planck 2018
Discrete scale invariance (DSI) — invariance under a discrete set of rescalings $x \to \lambda^n x$ — predicts log-periodic oscillations whose angular frequency in the logarithmic coordinate $u = \ln x$ is $\omega_0 = 2\pi/\ln\lambda$. When the scaling radix $\lambda$ is unknown, a radix-locked…
The Valuation Reading of the Qubit Delusion: Is the Adelic Kernel Load-Bearing?
The Qubit Delusion (https://papers.qnfo.org/papers/paper-the-qubit-delusion/) argues that the qubit-gate-circuit model of quantum computation imports a particle ontology inconsistent with quantum field theory, and that the field's failure to deliver commercially viable hardware after $35 billion of…
Searching for P-Adic Log-Periodic Signatures in the Cosmic Microwave Background Bispectrum: Upper Bounds from Planck 2018
Discrete scale invariance under integer rescalings of scale — the observable fingerprint of a p-adic (ultrametric) structure in the primordial fluctuation field — predicts log-periodic oscillations in the cosmic microwave background (CMB) statistics. The two-point angular power spectrum was already…
The Ostrowski Dimensionless Reformulation: A Systematic Compilation of Fundamental Physics Equations in Planck Units
We present the definitive edition of the Ostrowski Dimensionless Reformulation (ODR) — a systematic compilation, dimensionless reformulation, and detailed derivation of 53 fundamental physics equations across ten disciplines. The central claim is refined from the original v2.0 compilation:…
Counterfactual Physics: What If p-Adic Methods Had Won?
The p-adic approach to physics was nearly mainstream. Vladimirov and Volovich developed p-adic quantum mechanics in the 1980s. Freund and Witten connected p-adic string amplitudes to the adelic product formula in 1987. Dragovich extended p-adic methods to cosmology and the Standard Model. Yet by…
The Adelic Physics Program: Epistemological Foundations and Communications Framework
The QNFO Adelic Physics Program proposes that the physically accessible base field of physics is ℚ (the rational numbers), not ℝ (the real numbers). Ostrowski's theorem — a proven result in number theory — then demands that all p-adic completions of ℚ be physically meaningful, transforming the…
Depth, Breadth, and Valuation: A Unified Ontology of the Physical Continuum
The standard mathematical ontology of the continuum — the real numbers the real numbers with their uncountable cardinality and Dedekind-complete order — conflates three distinct properties with different physical status. We decompose the continuum into three axes: depth (Archimedean completeness),…
The Harmonic Paradigm Under Ostrowski’s Theorem: A p-Adic/Adélic Re-Evaluation with Helical Compton Vortex Synthesis
The Harmonic Paradigm (V1.0–V4.0) proposed the harmonic oscillator as the universal IR attractor of quantum theory, spanning an 8-rung ladder from transmon anharmonicity to quantum gravity. Its bibliography cited Vladimirov-Volovich-Zelenov p-adic QFT (1994) and Ostrowski's theorem (1918), invoking…
Consilience Between Physics and Number Theory: Convergent Theses from Ostrowski's Theorem to Adelic Quantum Mechanics
We synthesize convergent evidence from physics (quantum mechanics, quantum field theory, zitterbewegung, quantum error correction, the Standard Model mass spectrum) and number theory (Ostrowski's theorem, Tate's thesis, the Riemann zeta function, Bruhat-Tits buildings, the adele ring) into a unified…
Zitterbewegung: From Archimedean Puzzle to Adelic Observable
The structural underdetermination of the position operator in relativistic quantum mechanics -- manifested at the Archimedean place as zitterbewegung (the Newton-Wigner no-go) and at p-adic places as a discrete Bruhat-Tits observable -- arises from a single representation-theoretic origin: the…
p-Adic Anyon Fusion and Braiding: Quantum Groups at Roots of Unity, Verma Modules, and Ultrametric Anyon Models
Phases 1–2 established the p-adic braid group $B_n(\mathbb{Q}_p)$ on Bruhat-Tits buildings and identified the Temperley-Lieb parameter $\delta$ as a p-adic cyclotomic unit, yielding a p-adic Markov trace and Jones polynomial $V_L^p(t) \in \mathbb{Z}_p[\zeta_{2p^k}]$. In this third phase, we complete…
Zitterbewegung as the Physical Realization of p-Adic Anyon Braiding
The p-Adic Anyons program (Phases 1-4) developed the mathematical framework for anyons whose braid statistics are defined on Bruhat-Tits trees rather than in continuous spacetime. The ZBW program (P1-P3) demonstrated that Zitterbewegung — the rapid trembling motion of Dirac fermions at the Compton…
Adelic Synthesis: The Pattern-Particle Correspondence and the Complete Arithmetic Theory of Anyons
The prior three phases of this program constructed p-adic anyon theories at individual finite places: p-adic braid groups on Bruhat-Tits buildings (Phase 1), the Temperley-Lieb parameter as p-adic cyclotomic units with the p-adic Jones polynomial (Phase 2), and anyon fusion and braiding via…
Zitterbewegung as a p-Adic Observable: Ultrametric Readout and Intrinsic Topological Protection for Majorana Qubits
The Zitterbewegung (ZBW) of a Dirac fermion — the rapid oscillatory motion at the Compton frequency arising from interference between positive- and negative-energy states — has resisted direct experimental observation for nearly a century. The standard interpretation attributes this to the Compton…
Bruhat-Tits Readout Protocol: Measuring the ZBW Z2 Invariant in Majorana Systems
The companion papers "Zitterbewegung as a p-Adic Observable" (P1, https://papers.qnfo.org/papers) and "Majorana Zitterbewegung Current Correlator" (P2, https://papers.qnfo.org/papers) establish that the Zitterbewegung contribution to the current-current correlator is a $\mathbb{Z}_2$ topological…
Computational Simulation Approach to Non-Archimedean Quantum Architectures
The prevailing quantum computing paradigm is fundamentally constrained by the continuous analog fragility inherent to Archimedean spaces, resulting in uncontrolled linear error accumulation that demands massive active correction overheads. To address this structural bottleneck, we propose a…
From Force to Fractal
The transition from force-based epistemic placeholders to a purely geometric ontic bedrock represents the defining trajectory of modern theoretical physics. By synthesizing Ontic Structural Realism with contemporary developments in Invariant Set Theory, we propose a unified framework where reality…
Ultrametric Relaxation Dynamics in Topological Quantum Memory
The scalability of Topological Quantum Computing (TQC) is currently impeded by a “Thermodynamic Wall,” where the entropy generation from active error correction cycles scales exponentially with logical qubit count. This paper proposes a paradigm shift from active gate synthesis to passive…
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