Author: Ranger McCoy
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A Categorical No-Embedding Theorem for McGucken Geometry Underlying The McGucken Principle that the Fourth Dimension is Expanding at the Velocity of Light dx₄/dt = ic: The Moving-Dimension Manifold Category 𝓜 Is the Terminal Subcategory of Axis-Dynamics Frameworks Satisfying the Formal Privileged-Element Predicates
Dr. Elliot McGucken · Light, Time, Dimension Theory · elliotmcguckenphysics.com · drelliot@gmail.com “More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet.” — John Archibald Wheeler, Joseph Henry…
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The McGucken Geometry: A Novel Mathematical Category Exalted by the Physical Principle dx₄/dt = ic, Wherein an Axis Such as x₄ Is Physically Expanding in a Spherically Symmetric Manner Relative to Three Other Axes x₁, x₂, x₃: A New Geometric Category with Equivalent Differential-Geometric, Jet-Bundle, and Cartan-Geometric Formulations
Dr. Elliot McGucken · Light, Time, Dimension Theory · elliotmcguckenphysics.com · drelliot@gmail.com “More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet.” — John Archibald Wheeler, Joseph Henry…
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Connes’ Spectral Triple Geometry derived as Theorems of the McGucken Principle dx₄/dt = ic: McGucken Space, the McGucken–Dirac Spectral Triple, the Spectral Distance Theorem, the Spectral Action–Lagrangian Correspondence, and the Riemannian Reconstruction Theorem as Theorems of dx₄/dt = ic, with the Almost-Commutative Internal Algebra A_F as Empirical-Input Encoding
Dr. Elliot McGuckenLight, Time, Dimension Theoryelliotmcguckenphysics.comdrelliot@gmail.com “More intellectual curiosity, versatility, and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student… Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet.” — John Archibald Wheeler, Joseph Henry Professor of Physics, Princeton University Abstract…
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Novel Reciprocal-Generation McGucken Category McG built on dx₄/dt = ic: Three Theorems on the Source-Pair (ℳ_G, D_M) — Mutual Containment, Reciprocal Generation, and the Containment-Generation Equivalence, Establishing a New Categorical Foundation for Mathematical Physics which Completes the Erlangen Programme
Dr. Elliot McGucken Light, Time, Dimension Theory elliotmcguckenphysics.com drelliot@gmail.com “More intellectual curiosity, versatility, and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student… Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet.” — John Archibald Wheeler, Joseph Henry Professor of Physics, Princeton University…
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The McGucken Principle dx4/dt=ic Necessitates the Wick Rotation and i Throughout Physics: A Reduction of Thirty-Four Independent Inputs of Quantum Field Theory, Quantum Mechanics, and Symmetry Physics to a Single Physical Principle, with the Imaginary Unit i Identified Across All of Physics — Including Penrose’s Twistors, the Arkani-Hamed–Trnka Amplituhedron, Feynman Diagrams, AdS/CFT, String Theory, and the Extra Dimensions of Kaluza–Klein, String Theory, M-Theory, and AdS/CFT — as the Algebraic Signature of the Fourth Expanding Dimension
Dr. Elliot McGuckenLight, Time, Dimension Theoryelliotmcguckenphysics.comdrelliot@gmail.com “More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet…” — Dr. John Archibald Wheeler, Joseph Henry Professor of Physics, Princeton University “Behind it…
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The McGucken Cosmology dx4/dt = ic Outranks Every Major Cosmological Model in the Combined Empirical Record (and McGucken accomplishes this with Zero Free Dark-Sector Parameters): First-Place Finish in All Available Rankings Across Twelve Independent Observational Tests for Dark-Sector and Modified-Gravity Frameworks — The Empirical Signature of the McGucken Symmetry, Lagrangian, and Principle dx4/dt = ic
Dr. Elliot McGucken elliotmcguckenphysics.com “More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet.”— John Archibald Wheeler, Joseph Henry Professor of Physics, Princeton University “It doesn’t matter how…
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The Double Completion of Klein’s 1872 Erlangen Programme via the McGucken Principle dx4/dt=ic: Two Structurally Independent Routes from dx4/dt=ic to the Klein Pair (ISO(1,3),SO+(1,3)) and Its Categorical Subsumption, with a Unification of Group Theory and Category Theory via the Physical McGucken Principle
The Double Completion of Klein’s 1872 Erlangen Programme via the McGucken Principle dx4/dt=ic:Two Structurally Independent Routes from dx4/dt=ic to the Klein Pair (ISO(1,3),SO+(1,3)) and Its Categorical Subsumption, with a Unification of Group Theory and Category Theory via the Physical McGucken Principle Dr. Elliot McGuckenLight, Time, Dimension Theoryelliotmcguckenphysics.com “More intellectual curiosity, versatility, and yen for physics than Elliot McGucken’s I have never…
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The Double Completion of Felix Klein’s Erlangen Programme via the McGucken Principle in Both Group Theory and Category Theory: dx4/dt=ic as the Source Law of Mathematical Physics, with a Unification of GT & CT
Dr. Elliot McGucken Light Time Dimension Theory elliotmcguckenphysics.com goldennumberratio@gmail.com “More intellectual curiosity, versatility, and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student…Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet.” — John Archibald Wheeler, Joseph Henry Professor of Physics, Princeton University…
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The McGucken Space and McGucken Operator Generated by dx4/dt=ic: Simultaneous Space-Operator Generation and the Source Structure of All Mathematical Physics — A New Category Completes the Erlangen Programme
Dr. Elliot McGuckenLight, Time, Dimension Theoryelliotmcguckenphysics.com “More intellectual curiosity, versatility, and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student…Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet.” — John Archibald Wheeler, Joseph Henry Professor of Physics, Princeton University Abstract For the…
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The McGucken Operator DM : The Simplest, Most Complete, and Most Powerful Source Operator in Physics: A Formal Theory of How dx4/dt=ic Co-Generates Space, Dynamics, Time Evolution, Wick Rotation, Lorentzian Wave Propagation, Schrödinger Evolution, Dirac Factorization, Gauge Covariance, Commutator Structure, and More
The McGucken Operator DM : The Simplest, Most Complete, and Most Powerful Source Operator in Physics: A Formal Theory of How dx4/dt=ic Co-Generates Space, Dynamics, Time Evolution, Wick Rotation, Lorentzian Wave Propagation, Schrödinger Evolution, Dirac Factorization, Gauge Covariance, Commutator Structure, and More Dr. Elliot McGuckenLight, Time, Dimension Theoryelliotmcguckenphysics.com “More intellectual curiosity, versatility, and yen for physics than Elliot McGucken’s I…
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The McGucken Space ℳG: The Simplest, Most Complete, and Most Powerful Source Space in Physics: A Formal Theory of How dx4/dt=ic Generates Spacetime, Metric Structure, Hilbert Space, Phase Space, Spinor Space, Gauge-Bundle Space, Fock Space, Operator Algebras, and More
Dr. Elliot McGuckenLight, Time, Dimension Theoryelliotmcguckenphysics.com “More intellectual curiosity, versatility, and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student…Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet.” — John Archibald Wheeler, Joseph Henry Professor of Physics, Princeton University Abstract The central…
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The McGucken Symmetry 𝐝𝐱𝟒/𝐝𝐭=𝐢𝐜 — The Father Symmetry of Physics — Completing Klein’s 1872 Erlangen Programme while Deriving Lorentz, Poincaré, Noether, Wigner, Gauge, Quantum-Unitary, CPT, Diffeomorphism, Supersymmetry, and the Standard String-Theoretic Dualities and Symmetries as Theorems of the McGucken Principle
Dr. Elliot McGuckenLight Time Dimension Theoryelliotmcguckenphysics.comgoldennumberratio@gmail.com “More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet.” — John Archibald Wheeler, Joseph Henry Professor of Physics, Princeton University “A theory…
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The McGucken Sphere as Spacetime’s Foundational Atom: Deriving Arkani-Hamed’s Amplituhedron and Penrose’s Twistors as Theorems of the McGucken Principle dx4/dt=ic
Dr. Elliot McGuckenLight Time Dimension Theory, elliotmcguckenphysics.comIncorporating MG-Proof, MG-HLA, MG-PathInt, MG-Born, MG-Wick, MG-Nonlocality, MG-Feynman, MG-Twistor, MG-Witten, MG-Amplituhedron, MG-AmplituhedronComplete, MG-Lagrangian, MG-Commut, MG-Deeper, MG-Duality, MG-QMChain “More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. Originality, powerful motivation, and a can-do spirit make me think that McGucken…
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The McGucken Sphere as Spacetime’s Foundational Atom: A Complete Constructive Derivation of Twistor Space, the Positive Grassmannian, and the Amplituhedron from dx4/dt=ic
Dr. Elliot McGucken, Light Time Dimension Theory / elliotmcguckenphysics.com Contents • Postulate 1: The McGucken Principle • Theorem 1: x4=ictx4=ict Generates the Minkowski Metric • Theorem 2: The McGucken Sphere Is the Future Null Cone and the Foundational Atom of Spacetime • Plain-language meaning • Theorem 3: The Rest-Frame Quantum Phase Follows from x4x4-Evolution • Theorem 4: The Path…
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The McGucken Duality & THE MCGUCKEN PRINCIPLE AS GRAND UNIFICATION: How dx₄/dt = ic Unifies General Relativity, Quantum Mechanics, and Thermodynamics as Theorems of a Single Physical, Geometric Principle
A Scholarly Synthesis of the Three-Paper Chain Trilogy, Placing the McGucken Framework in the 340-Year History of Foundational Physics, Identifying Where Prior Unification Programs Succeeded and Failed, and Cataloging the Structural Features that Make the McGucken Principle a Unique, Simple, and Complete Foundation Dr. Elliot McGucken Light, Time, Dimension Theory — elliotmcguckenphysics.com April 2026 “More…
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GENERAL RELATIVITY DERIVED FROM THE MCGUCKEN PRINCIPLE: A Unique, Simple, and Complete Derivation of General Relativity as a Chain of Theorems of the McGucken Principle of a Fourth Expanding Dimension dx₄/dt = ic: A Formal Derivation from First Geometric Principle dx₄/dt = ic to the Einstein Field Equations and Their Canonical Solutions, with the Postulates of General Relativity Reduced to Theorems and the Equivalence Principle, Geodesic Hypothesis, Christoffel Connection, Stress-Energy Conservation, and No-Graviton Conclusion All Generated as Parallel Sibling Consequences of a Single Geometric Principle
A Formal Derivation from First Geometric Principle dx₄/dt = ic to the Einstein Field Equations and Their Canonical Solutions, with the Postulates of General Relativity Reduced to Theorems and the Equivalence Principle, Geodesic Hypothesis, Christoffel Connection, Stress-Energy Conservation, and No-Graviton Conclusion All Generated as Parallel Sibling Consequences of a Single Geometric Principle Dr. Elliot McGucken…
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QUANTUM MECHANICS DERIVED FROM THE MCGUCKEN PRINCIPLE: A Unique, Simple, and Complete Derivation of Quantum Mechanics as a Chain of Theorems of the McGucken Principle of a Fourth Expanding Dimension dx₄/dt = ic: A Formal Derivation from First Geometric Principle dx₄/dt = ic to the Schrödinger and Dirac Equations, the Born Rule, Quantum Nonlocality, and the Full Feynman-Diagram Apparatus, with the Postulates of Quantum Mechanics Reduced to Theorems and the Hamiltonian–Lagrangian, Heisenberg–Schrödinger, Wave–Particle, and Locality–Nonlocality Dualities Generated as Parallel Sibling Consequences of a Single Geometric Principle
A Formal Derivation from First Geometric Principle dx₄/dt = ic to the Schrödinger and Dirac Equations, the Born Rule, Quantum Nonlocality, and the Full Feynman-Diagram Apparatus, with the Postulates of Quantum Mechanics Reduced to Theorems and the Hamiltonian–Lagrangian, Heisenberg–Schrödinger, Wave–Particle, and Locality–Nonlocality Dualities Generated as Parallel Sibling Consequences of a Single Geometric Principle Dr. Elliot…
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THERMODYNAMICS DERIVED FROM THE MCGUCKEN PRINCIPLE: A Unique, Simple, and Complete Derivation of Thermodynamics as a Chain of Theorems of the McGucken Principle of a Fourth Expanding Dimension dx₄/dt = ic
A Formal Derivation from First Geometric Principle dx₄/dt = ic to the Probability Measure, Ergodicity, the Second Law, the Five Arrows of Time, the Dissolution of the Past Hypothesis, and Black-Hole Thermodynamics, with Einstein’s Three Gaps T1–T3 in the Boltzmann-Gibbs Program Closed as Theorems and Hawking-Bekenstein Black-Hole Entropy Recovered through the McGucken Wick Rotation Dr.…
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A Unique, Simple, and Complete Derivation of General Relativity as a Chain of Theorems of the McGucken Principle of a Fourth Expanding Dimension dx₄/dt = ic
A Formal Derivation from First Geometric Principle dx₄/dt = ic to the Einstein Field Equations and Their Canonical Solutions, with the Postulates of General Relativity Reduced to Theorems and the Equivalence Principle, Geodesic Hypothesis, Christoffel Connection, Stress-Energy Conservation, and No-Graviton Conclusion All Generated as Parallel Sibling Consequences of a Single Geometric Principle Dr. Elliot McGucken…
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The Exhaustiveness of the Seven McGucken Dualities: A Three-Form Proof via Closure-by-Exhaustion, Categorical Terminality, and Empirical Audit — Establishing that the Seven Dualities of Physics (Hamiltonian/Lagrangian, Conservation/Second Law, Heisenberg/Schrödinger, Wave/Particle, Locality/Nonlocality, Mass/Energy, Time/Space) Form a Closed and Terminal Catalog of Kleinian-Pair Dualities Descending from dx4/dt = ic
The Exhaustiveness of the Seven McGucken Dualities A Three-Form Proof via Closure-by-Exhaustion, Categorical Terminality, and Empirical Audit — Establishing that the Seven Dualities of Physics (Hamiltonian/Lagrangian, Conservation/Second Law, Heisenberg/Schrödinger, Wave/Particle, Locality/Nonlocality, Mass/Energy, Time/Space) Form a Closed and Terminal Catalog of Kleinian-Pair Dualities Descending from dx4/dt = ic Dr. Elliot McGuckenLight, Time, Dimension Theory — elliotmcguckenphysics.comApril 2026 “A theory is…
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McGucken Quantum Formalism: The Novel Mathematical Structure of Dual-Channel Quantum Theory underlying the Physical McGucken Principle of a Fourth Expanding Dimension dx₄/dt = ic: A Comprehensive Survey of Prior Art in Quantum Theory and Identification of the Novel Categorical Claim — Companion Paper to McGucken Geometry
McGucken Quantum Formalism: The Novel Mathematical Structure of Dual-Channel Quantum Theory underlying the Physical McGucken Principle of a Fourth Expanding Dimension dx₄/dt = ic A Comprehensive Survey of Prior Art in Quantum Theory and Identification of the Novel Categorical Claim — Companion Paper to McGucken Geometry Dr. Elliot McGucken Light, Time, Dimension Theory — elliotmcguckenphysics.com…
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McGucken Geometry: The Novel Mathematical Structure of Moving-Dimension Geometry underlying the Physical McGucken Principle of a Fourth Expanding Dimension dx₄/dt = ic
McGucken Geometry: The Novel Mathematical Structure of Moving-Dimension Geometry underlying the Physical McGucken Principle of a Fourth Expanding Dimension dx₄/dt = ic A Comprehensive Survey of Prior Art and Identification of the Novel Geometric Claim Dr. Elliot McGucken Light, Time, Dimension Theory — elliotmcguckenphysics.com April 26, 2026 “More intellectual curiosity, versatility and yen for physics…
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A Unique, Simple, and Complete Derivation of Thermodynamics as a Chain of Theorems of the McGucken Principle of a Fourth Expanding Dimension dx₄/dt = ic : Closing Einstein’s Three Gaps in the Boltzmann-Gibbs Programme — The Probability Measure as Haar Measure on ISO(3), Ergodicity as Huygens-Wavefront Identity, and the Second Law as the Strict Theorem dS/dt > 0 from a Single Geometric Principle
Dr. Elliot McGucken Light, Time, Dimension Theory — elliotmcguckenphysics.com April 26, 2026 “More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet.” — John Archibald Wheeler, Joseph Henry…
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A Unique, Simple, and Complete Derivation of Quantum Mechanics as a Chain of Theorems of the McGucken Principle of a Fourth Expanding Dimension dx₄/dt = ic A Formal Derivation from First Geometric Principle to the Schrödinger and Dirac Equations, the Born Rule, and Quantum Nonlocality
Dr. Elliot McGucken Light, Time, Dimension Theory — elliotmcguckenphysics.com April 26, 2026 “More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet for graduate school in physics.” —…
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A Unique, Simple, and Complete Derivation of General Relativity as a Chain of Theorems of the McGucken Principle of a Fourth Expanding Dimension dx₄/dt = ic
A Formal Derivation from McGucken’s Physical Principle to the Einstein Field Equations and Their Canonical Solutions Dr. Elliot McGucken Light, Time, Dimension Theory — elliotmcguckenphysics.com April 26, 2026 “More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. Originality, powerful motivation, and a can-do…
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The McGucken–Kleinian Programme as the Geometric Foundation of Constructor Theory: A Categorical Formalization
The McGucken–Kleinian Programme as the Geometric Foundation of Constructor Theory: A Categorical Formalization Dr. Elliot McGucken — Light Time Dimension Theory — elliotmcguckenphysics.com — April 2026 “More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. Originality, powerful motivation, and a can-do spirit make me think that McGucken…
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The McGucken Lagrangian as Unique, Simplest, and Most Complete: A Multi-Field Mathematical Proof (McGucken vs. Newton, Maxwell, Einstein-Hilbert, Dirac, Yang-Mills, Standard Model, and String Theory)
The McGucken Lagrangian as Unique, Simplest, and Most Complete: A Multi-Field Mathematical Proof Drawing on the Calculus of Variations, Lovelock’s Theorem, Stone–von Neumann, Wigner Classification, Wess–Zumino Consistency, Coleman–Mandula, Wilsonian RG, Atiyah–Singer, Ostrogradsky Stability, Kolmogorov Complexity, and Category-Theoretic Universality to Establish that ℒ_McG = ℒ_kin + ℒ_Dirac + ℒ_YM + ℒ_EH Is the Unique Solution Under…
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Deriving Thermodynamics as a Theorem of the McGucken Principle dx₄/dt = ic: Resolving Einstein’s Unease — The Probability Measure as Haar Measure, Ergodicity as Huygens-Wavefront Identity, and the Second Law as Strict dS/dt > 0
Dr. Elliot McGucken — Light Time Dimension Theory — elliotmcguckenphysics.com — April 2026 “More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet…” — John Archibald Wheeler, Joseph Henry Professor of Physics, Princeton…
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The McGucken Principle as the Unique Physical Kleinian Foundation: How dx₄/dt = ic Uniquely Generates the Seven McGucken Dualities of Physics — (1) Hamiltonian/Lagrangian, (2) Noether Conservation Laws / Second Law of Thermodynamics, (3) Heisenberg/Schrödinger, (4) Wave/Particle, (5) Locality/Nonlocality, (6) Rest Mass / Energy of Spatial Motion, and (7) Time/Space — as Theorems of the Kleinian Correspondence Between Algebra and Geometry, and Why It Is Unique
Dr. Elliot McGucken — Light Time Dimension Theory — elliotmcguckenphysics.com — April 2026 “More intellectual curiosity, versatility and yen for physics than Elliot McGucken’s I have never seen in any senior or graduate student. Originality, powerful motivation, and a can-do spirit make me think that McGucken is a top bet…” — John Archibald Wheeler, Joseph Henry Professor of Physics, Princeton…
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How the McGucken Principle of a Fourth Expanding Dimension Generates and Unifies the Dual A-B Channel Structure of Physics: (A: Hamiltonian Operator Formulation & B: Lagrangian Path Integral) and (A: Noether Conservation Laws & B: Second Law of Thermodynamics) and (A: Heisenberg PicturHow the McGucken Principle of a Fourth Expanding Dimension Generates and Unifies the Dual A-B Channel Structure of Physics: (A: Hamiltonian Operator Formulation & B: Lagrangian Path Integral) and (A: Noether Conservation Laws & B: Second Law of Thermodynamics) and (A: Heisenberg Picture & B: Schrödinger Picture) and (A: Particle Aspect & B: Wave Aspect) and (A: Local Microcausality & B: Nonlocal Bell Correlations) and (A: Rest Mass & B: Energy of Spatial Motion) and (A: Time & B: Space) via dx₄/dt = ic
How the McGucken Principle of a Fourth Expanding Dimension Generates and Unifies the Dual A-B Channel Structure of Physics: (A: Hamiltonian Operator Formulation & B: Lagrangian Path Integral) and (A: Noether Conservation Laws & B: Second Law of Thermodynamics) and (A: Heisenberg Picture & B: Schrödinger Picture) and (A: Particle Aspect & B: Wave Aspect)…