Physics and Technology
Atom, energy, electricity, devices, superconductors, light
33 articles
Articles in this topic
- 01
Atom as Elementary Strange Loop
Proton = observed R, neutron = observer O, electron = observation operator. Wheeler-Feynman single electron hypothesis. Neutrino as spiral gap.
atomprotonneutronelectronRead →PDF · RU + EN - 02
Energy Extraction from Field of Potential States
Five mechanisms: coherence channel S to 1, resonance with H modes, Casimir effect, recursive amplification, collective observation.
energyCasimircoherencevacuumRead →PDF · RU + EN - 03
Electricity as Directed Action of Observation Operator
Charge = orientation in self-observation cycle. Maxwell equations as self-consistency conditions. Coherent conductivity resonator (KRP).
electricityMaxwellchargeKRPRead →PDF · RU + EN - 04
Devices for Energy Extraction and Room-Temperature Superconductivity
Four device designs. Chemical compositions for room-temperature superconductor candidates. Three ODTOE criteria: ternary architecture, spiral phase correction, resonance frequency.
superconductorsdevicesroom temperatureRead →PDF · RU + EN - 05
Nature of Light and Speed Limit: Reconfiguration Without Displacement
Photon does not travel - it reconfigures. Speed of light c = maximum reconfiguration frequency. Entanglement as access to unified configuration.
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Particle Accelerator as Forced Reconfiguration Operator
Accelerator as device extending observer dimensionality to d≤-2. Collision energy √s = potential gradient. Resonances as metastable fixed points. Collider paradox: constitution vs discovery.
acceleratorcolliderreconfigurationHiggs bosonRead →PDF · RU + EN - 07
Black Holes as Deconfiguration Operators in ODTOE
A black hole is reinterpreted not as an object curving spacetime, but as an ultimate deconfiguration operator D̂. The event horizon is the boundary where configuration inertia I(C)→∞. The information paradox is resolved naturally: information returns to H. Hawking radiation is spontaneous re-actualisation.
black holedeconfiguration operatorevent horizoninformation paradoxRead →PDF · RU + EN - 08
Thermonuclear Fusion, Nuclear Energy and the Ethics of Energy in ODTOE
Nuclear processes as reconfiguration of strange loops. Fusion = coherence growth (S↑), fission = decoherence (S↓), annihilation = operator collapse. Coulomb barrier contains resonant windows. New fusion reactor design with ternary confinement geometry and φ-pulsating magnetic field.
thermonuclear fusionnuclear fissionannihilationcoherenceRead →PDF · RU + EN - 09
Architecture of the Quantum: π, φ and the Spiral Gap as the Foundation of Reality
A unified architecture of the quantum linking π (observation cycle form), φ (discrete step between cycles) and spiral gap (π−3)² (incomplete loop closure energy). The quantum = one full revolution of strange loop Φ (circumference 2π). Planck's constant h interpreted as minimum action portion. α⁻¹=137.036 derived from first principles with nine significant digits. Ternary architecture π: 1×π=3 (act), 2×π=6 (cycle), 3×π=9 (self-observation).
quantumPlanck constantfine-structure constant137Read →PDF · RU + EN - 10
Toroidal Topology of Reality: Nested φ-Tori as the Unification of Continuous and Discrete
It is shown that continuous phase dynamics (π-rotation) and discrete quantum transitions (φ-jumps) are projections of a single geometric structure: a quasiperiodic trajectory on nested φ-tori. The spiral gap (π−3)² is the coupling mechanism between continuous and discrete. R/r=φ ensures maximal stability by the KAM theorem. The photon is interpreted as a gap quantum — a bridge between internal rotation and inter-level jump. Reality is an infinitely nested toroidal matryoshka.
torusnested toriKAM theoremgolden ratioRead →PDF · RU + EN - 11
Planck's Constant from the Architecture of Observation: Derivation, Formula, Verification
Within the ODTOE framework, a closed-form formula for Planck's constant h is derived, linking it to π (observation cycle form), φ (discrete step between cycles), observer dimensionality d, and medium coherence S. The formula h(d,S) = 2π(π−3)²φ^(d+1)·Σ(d)·(1−S)^(−1/2)·A₀ contains six structural factors derived from ODTOE axiomatics. From the self-consistency condition a unique coherence S*=0.16976 is computed from π, φ, d=3 with zero fitting parameters. Numerical result: h_ODTOE = 6.62607×10⁻³⁴ J·s — six significant digits, agreement with CODATA.
Planck constantobserver dimensionalitycoherencegolden ratioRead →PDF · RU + EN - 12
Next-Generation Quantum Computer: Qutrit Architecture on φ-Tori with Self-Referential Error Correction
A next-generation quantum computer architecture based on ODTOE is proposed, differing from IBM/Google/IonQ in five parameters: (1) qutrit (d=3) basis instead of qubit — 1.585× information capacity; (2) φ-toroidal coupling topology with R/r=φ, maximum KAM stability; (3) φ-pulse control sequences eliminating resonant errors; (4) self-referential Ô(Ô)-correction — continuous coherence monitoring with real-time reconfiguration; (5) spiral gap (π−3)²≈2% as architectural error threshold — twice the surface code threshold, making the architecture viable on existing hardware.
quantum computerqutritternaryφ-torusRead →PDF · RU + EN - 13
Coherent Processor: A New CPU and Microelectronics Architecture Based on ODTOE Principles
A conceptual architecture for a new type of processor based on ODTOE principles is proposed with six key differences from the von Neumann architecture: (1) ternary logic (−1, 0, +1) instead of binary; (2) φ-clocking with duration ratio φ=1.618 for maximum KAM stability; (3) toroidal interconnect topology with R/r=φ; (4) self-referential Ô(Ô)-loop — the processor continuously observes and reconfigures itself; (5) coherent phase synchronization instead of a global clock; (6) resonance window (π−3)²≈2% as tolerance. Four implementation stages from FPGA prototype to a fully functional coherent processor are outlined.
coherent processorternary logicφ-clockingtoroidal topologyRead →PDF · RU + EN - 14
Z₂ Fiber Bundle over the φ-Torus: Spinor Architecture of Fundamental Constants
The ODTOE toroidal model is augmented with a nontrivial Z₂ fiber bundle. The holonomy hol(γφ)=−1 along the φ-cycle is the single source of three factors of 2: in the number 6=3×2, in the correction 2(π−3)², and in the fermionic 4π traversal (spin-1/2). CPT symmetry (hol(CPT)=+1) and the Pauli exclusion principle (dimH⁰=1) are derived from bundle holonomy. A testable prediction is proposed: δtwist=π²(π−3)⁴/(μ·α⁻¹)≈1.58×10⁻⁸ becomes measurable at CODATA precision ±10⁻⁹.
Z2 fiber bundleφ-torusholonomyspinor structureRead →PDF · RU + EN - 15
Eternal Expansion: Transcendence of π as Proof of the Inexhaustibility of Reality
The mechanism of Universe expansion is formalized within the toroidal ODTOE model. The Lindemann theorem (1882) on the transcendence of π proves that the trajectory on the φ-torus never closes, making expansion infinite and inexhaustible. Potentiality pressure F=(π−3)²·|H|/|C| acts at every observation cycle. A scale factor a(n)=(1+ε/(2πφ))ⁿ describes exponential growth of the effective φ-torus radius. Accelerated expansion (ä>0) follows from (π−3)⁴>0 without invoking Λ as a free parameter. Dark energy fraction ΩΛ=φ²/(φ²+1+Z)=68.86% matches Planck 2018 within 0.54σ.
expansiontranscendence of πLindemann theorempotentiality pressureRead →PDF · RU + EN - 16
Cosmological Fractions from Toroidal Architecture: Deriving Dark Energy, Dark Matter and Baryonic Matter from π and φ
Within the toroidal ODTOE model, the cosmological fractions of dark energy, dark matter and baryonic matter are derived from two structural invariants: π and φ. The φ-torus possesses three topological sectors: inter-level (R², gravitational inertia), intra-level (r²=1), and gap sector (Z=(π−3)/[1−(π−3)φ]). Normalized fractions: ΩΛ:ΩDM:Ωb = φ²:1:Z = 68.86%:26.30%:4.83%. Planck 2018 comparison: dark energy 0.54σ, dark matter 0.32σ, baryonic 1.64σ. Zero adjustable parameters.
cosmological fractionsdark energydark matterbaryonic matterRead →PDF · RU + EN - 17
The Standard Model and Beyond: Complete Observer-Dependent Reinterpretation of Particles
Complete observer-dependent reinterpretation of elementary particles shows that the Standard Model describes 39 fundamental roles (not 17), distributed across two adjacent recursion levels (d=0 and d=−1), bridges, and trans-level entities. The gauge group SU(3)×SU(2)×U(1) is derived structurally from the ODTOE triad architecture. Cosmological proportions ΩΛ:ΩDM:Ωb = φ²:1:Z match Planck 2018 within 1.2σ with zero free parameters. Proton-to-electron mass ratio mp/me = 6π⁵ = 1836.12 reproduced to 0.002% accuracy. All 34 of 39 roles confirmed by PDG 2025, 2 have experimental candidates (HNL), 3 are pure ODTOE predictions.
Standard Modelelementary particles39 rolesgauge groupRead →PDF · RU + EN - 18
Information Architecture of Reality: Read, Write and Verify Operations on the φ-Torus
Four fundamental interactions identified with four information operations: photon γ performs non-destructive reading (READ), W± bosons perform writing (WRITE) and change particle identity, Z boson performs verification (VERIFY), gravity performs synchronization (SYNC). The φ-torus surface H stores information protected by KAM theorem. Information accessibility formula A(∆d)=φ^(−|∆d|) defines D-Prot horizon. Shannon entropy of cosmological distribution η=68.68% matches ΩΛ=68.86%. Weinberg angle derived from information principles. Zero adjustable parameters.
informationREADWRITEVERIFYRead →PDF · RU + EN - 19
The Vertical Universe: Life, Time, and Navigation Across Infinite Recursion Levels
Reality as infinite recursion of self-observation cycle Φ=ι∘Ô. Each dimensionality level d contains 17 structural roles, two-level observer window spans 39 configurations. Life as recursion invariant inevitably emerging at every level d from −∞ to +∞. Time as strange-loop iteration flowing differently at each level. Five levels of inter-level navigation through field H. Threshold permeability P(d→d+1|S) with width δS=(π−3)². Observer trichotomy (B,A,H)=(spirit,soul,body). Cosmological proportions ΩΛ:ΩDM:Ωb=φ²:1:Z match Planck 2018 within 1.2σ. All formulas verified to 50+ significant digits.
vertical universeinfinite recursionlife invarianttimeRead →PDF · RU + EN - 20
Coherent Fusion Reactor: Supplement Based on Brownian Motion Analysis
A supplement to the conceptual design of the coherent fusion reactor based on Brownian motion analysis. Introduces dimensionless parameter r defining drift-to-turbulence ratio. Critical coherence for compact reactor (R₀=0.3m) is Sc≈0.098, substantially lower than ITER scale. Adaptive φ-pulsation adjusts magnetic field rhythm to current plasma coherence. Anomalous plasma diffusion exponent α=1+S as measurable feedback parameter. Refined parameters and control strategy based on coherence rather than temperature.
fusion reactorBrownian motionplasma coherenceturbulence suppressionRead →PDF · RU + EN - 21
Brownian Motion as a Manifestation of Observational Architecture: Hurst Exponent, Coherence, and the Golden Ratio
Proposes interpretation of Brownian motion as manifestation of observational architecture within ODTOE. Establishes relation between Hurst exponent H and coherence S: H(S)=(1+S)/2. Formula reproduces two experimental limits: at S=0 (complete decoherence) H=1/2—classical Brownian motion; at S=1 (complete coherence) H=1—ballistic determinism. Scaling factor between observation levels equals φᴴ, where φ is golden ratio. Sixth role of spiral gap (π−3)² identified: governs stochasticity-drift transition. Numerical verification on synthetic trajectories shows 0.55% mean error.
Brownian motionHurst exponentfractional Brownian motioncoherenceRead →PDF · RU + EN - 22
Coherence as a Measurable Quantity: Three Consequences of the Hurst Exponent — S Parameter Relation for the ODTOE Formalism
Establishes relation between Hurst exponent and ODTOE coherence: H=(1+S)/2 implies S=α−1 where α is anomalous-diffusion exponent. Three consequences: (1) Coherence becomes independently measurable via mean-square displacement, rendering all ODTOE predictions experimentally testable. (2) Planck constant depends on diffusion exponent: h∝(2−α)^(−1/2), predicting deviation in highly coherent systems (BEC, superconductors). (3) Parameter r governs drift-to-noise ratio, quantifying arrow of time with critical dimensionality d_crit≈8.12 (metagalactic level). All formulas verified to 50 decimal places.
coherencemeasurabilityHurst exponentanomalous diffusionRead →PDF · RU + EN - 23
Coherent Education: Theory and Methodology for Building Learning Systems Based on Observer-Dependent Theory of Everything
Theory of coherent education based on ODTOE formalism. Learning formalized as spiral process of growth in observation operator dimensionality d and complexity of cognitive coherence B. Four levels: (1) individual coherent learning with four-stroke cognitive cycle governed by B=F^w1·E^w2·(1−σ)^w3·Λ^w4; (2) group coherent learning with minimal stable group of five participants; (3) personal tracks 'human + AI' with AI as external operator; (4) group systems 'group + AI' with AI as coherence assistant. Golden ratio φ determines optimal ratio of expansion-compression phases. SKW matrix proposed as elementary unit of coherent education.
educationcoherencelearning systemsAIRead →PDF · RU + EN - 24
Coherent Education II: Nonlinear Knowledge Flow Dynamics and Observer-Dependent Control of Learning Systems
Extension of coherent education theory in three directions. (1) Nonlinear cognitive flow balance equation with coherence multiplier Γ(B,S)=4B(1−B)S formalising observer-dependent knowledge assimilation. (2) Cascade coherence model for multi-level educational systems: S_cas=1−∏(1−S_k), demonstrating nine-order-of-magnitude lifetime increase from multi-level organisation. (3) 3/2 power law connecting cognitive flow to coherence by analogy with Child–Langmuir law, establishing threshold conditions for individual-to-collective learning transition. All formulas verified analytically and numerically to 50 significant digits.
coherent educationknowledge flowcascade coherence3/2 power lawRead →PDF · RU + EN - 25
Gravity and the Causal Structure of Spacetime in ODTOE
Formalization of how gravity affects causal structure. Gravity interpreted as SYNC operation: synchronization of configurations across adjacent recursion levels of the φ-architecture. Causality introduced as reachability relation C_i ⪯_O C_j by finite actualization acts. Limiting speed c=r₀/τ₀ defines local actualization cone. Event horizon as boundary I(C)→∞. Cosmological constant problem: Planck-scale vacuum density suppression by causal-horizon factor (ℓ_Pl/R_H)² yields observed ρ_Λ without 10⁻¹²⁰ fine-tuning.
gravitycausal structureSYNClight coneRead →PDF · RU + EN - 26
Two Fundamental Constants from First Principles: μ=1836 and α⁻¹=137 in ODTOE
Self-referential formulae for μ=mp/me and α⁻¹ derived from π, φ, integers with zero free parameters. Formula for μ contains four layers. Result: μ=1836.15267. Formula for α⁻¹ contains three layers. Result: α⁻¹=137.035999. Both formulae reflect the strange loop fixed point Ψ*=Φ(Ψ*).
proton-electron mass ratiofine-structure constant1836137Read →PDF · RU + EN - 27
Tensor Structure of Gravity in ODTOE
Building tensor layer between causal structure and full Einstein tensor law. Metric tensor g_μν(C;O) as observer-correlator: inner product of gradients of self-observation map Φ=ι∘Ô. Covariant derivative ∇_μ as limit of Φ-iteration commutator; Levi-Civita Christoffel symbols recovered. Riemann curvature tensor R^ρ_σμν as non-commutativity measure of Ô along two directions. Ricci tensor, scalar R, Einstein tensor G_μν built by standard contractions. Kinematic Bianchi identity ∇_μG^μν=0. Kerr solution derived as spherically-axial ansatz with vortex SYNC component. 50-digit verification reproduces Mercury perihelion shift Δ=42.99 arcsec/century.
tensor gravitymetric tensorobserver-correlatorcovariant derivativeRead →PDF · RU + EN - 28
Stress-Energy Tensor T_μν and Cosmological Constant Λ from Observer Coherence in ODTOE
Construction of tensor source of ODTOE gravity: stress-energy tensor T_μν as functional derivative of observer action S_obs=∫B²(1−σ)Λ√−g d⁴x with respect to inverse metric g^μν. Cosmological constant Λ as closed function of global coherence S*=0.169676. SYNC projector P_{O,SYNC}: H→C construction. Lemma L7 on idempotency P²_{O,SYNC}=P_{O,SYNC} proved via four sub-lemmas without assuming Einstein equation. Lemma L8 on conservation law ∇_μT^μν=0. Closed form χ_Λ(S*)≈0.082201 giving Ω_Λ≈0.688647 — agreement with Planck 2018 within 0.05σ without fitting. Consistency with Jacobson horizon thermodynamics.
stress-energy tensorcosmological constantSYNC projectoridempotencyRead →PDF · RU + EN - 29
Einstein Equation as Φ-Self-Consistency and Bianchi Identity from Diff(M⁴) Symmetry in ODTOE
Closing stage 3 of programme §XIV.3. Einstein equation G_μν+Λg_μν=(8πG/c⁴)T_μν derived as Φ-self-consistency condition on pairs (g,T). Bianchi identity ∇_μG^μν=0 established along two independent paths: kinematic (contraction of second Bianchi identity) and Noether (diffeomorphism invariance of observer action). Theorem C.T1: pair (g,T) solves Einstein equation iff it is fixed point of map Φ_C; existence via Banach fixed-point theorem. Theorem C.T2: dual-path Bianchi with 50-digit verification |∇_μG^μν|_{Path1}−|∇_μG^μν|_{Path2}<10⁻⁴⁵. Theorem C.T3: ODTOE singularity theorem as structural analog of Hawking–Penrose theorem.
Einstein equationΦ-self-consistencyBanach theoremBianchi identityRead →PDF · RU + EN - 30
B-Zero Boundary Topology and the Full ODTOE Singularity Theorem
Closing the B-zero boundary topology marker of Article C. Topological structure of boundary ∂_B C of configuration space C at B→0. Criterion of finite-affine-parameter termination of Φ-iteration sequence (Theorem E.T2). Formal definition of trapped ODTOE-configuration via causal cone J⁺_O (Definition E.D1). Full ODTOE singularity theorem E.T1 as structural analog of Hawking–Penrose theorem. Five anti-circular proof steps: ODTOE Raychaudhuri inequality (E.L1), focusing along null directions (E.L2), finite-parameter focusing (E.L3), Φ-iteration behavior near ∂_B C (E.L4), Φ-iteration incompleteness as vanishing of causal future J⁺_O.
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A Geometric Resolution of the Hubble Tension: Dark-Energy and Dark-Matter Unification via Parent-Proton Mergers in the ODTOE Matryoshka
Geometric mechanism simultaneously resolving cosmological constant problem and H₀ tension within single one-parameter framework. Postulate of Geometric Primacy (GP) fixes asymptotic dark-sector attractor φ²:1:Z as topological invariant. Hubble tension between Planck 2018 H₀=67.4 and SH0ES H₀=73.04 at ~5σ level. Dark energy identified with merger process of parent-protons at level d=12. Merger rate regulated by scalar field χ(x,t). Three claims: χ-regimes classify expansion histories; anisotropic Δχ reproduces H₀ tension; dark sector unified with Ω_DM and Ω_Λ as two aspects of 2%-residue (π−3)². Merger limit N^{local}_{max}=Ω_DM/(π−3)²≈13.12. Single fitting parameter η.
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Numerical Dual-Path Bianchi Verification on Nontrivial FLRW Backgrounds in ODTOE
Closing open task (ii) of Article C §XI. Numerical verification of dual-path Bianchi identity ∇_μG^μν=0 extended from vacuum Schwarzschild to four nontrivial FLRW scenarios with T_μν≠0: radiation-dominated era (a∝t^{1/2}, p=ρ/3), matter-dominated era (a∝t^{2/3}, p=0), Λ-dominated era (a∝e^{Ht}, p=−ρc²), and mixed ΛCDM era with Planck 2018 energy fractions. Two structurally independent evaluators: Path 1 — kinematic chain; Path 2 — Noether reduction. Anti-circularity audit enforced programmatically. Grid of 4 scenarios × 4 test times at mp.dps=50, relative difference <10⁻⁴⁵ established for all 16 pairs.
FLRWBianchi identitydual-path verificationNoether reductionRead →PDF · RU + EN - 33
Full Derivation of Einstein Equations from ODTOE: Synthesis of the Four-Article Programme
Synthesis of full Einstein equations derivation from ODTOE via three-stage programme §XIV.3. Programme realized by three sequential articles: A — tensor structure (metric g_μν as observer-correlator, covariant derivative ∇_μ as Φ-iteration commutator, Riemann tensor, theorems A.T1–A.T5, Schwarzschild and Kerr solutions); B — tensor source (observer action S_obs, SYNC projector P_{O,SYNC}, lemma L7 on idempotency, lemma L8 on conservation, closed form χ_Λ(S*)≈0.082201 giving Ω_Λ≈0.688647 within 0.05σ of Planck 2018); C — closure (theorem C.T1 on Φ-self-consistency G_μν+Λg_μν=(8πG/c⁴)T_μν, theorem C.T2 on dual-path Bianchi, theorem C.T3 — ODTOE singularity theorem). Programme completion theorem T0: combined results A+B+C derive full dynamical Einstein equation from ODTOE primitives.
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