Near-Linear Quantum Transition Modes: A Toy Framework for Quantum Excitation, Tunneling, Local Jacobian Evolution, and Tests of Superluminal Dispersion
This speculative theoretical note develops a toy framework linking quantum tunneling (QT), quantum excitation (QE), local Jacobian/state-space evolution, and a proposed near-linear QT/QE mode. It derives epsilon_Q = A_Q k_Q, reviews the standard near-threshold tunneling limit kappa -> 0, and shows that coherent QT/QE dynamics can be continuous under Schrodinger evolution. The nonstandard FTL step is isolated as a separate requirement: a physically justified dispersion relation and an operational signaling test. No experimental evidence for faster-than-light signaling is claimed. ChatGPT (OpenAI) assisted with exposition, checking, organization, figures, and document preparation; Chaman Prakash Kanth is the author and is responsible for the final content. Recommended notes field:Version 0.1.0. Speculative research note. This deposit is intended to document the mathematical formulation and priority of a testable hypothesis, not to claim experimental confirmation. Future versions should be deposited as linked Zenodo versions if the equations, numerical tests, or experiments change substantially. AI assistance statement:ChatGPT (OpenAI) was used as a research-writing and mathematical-assistance tool. It helped translate the author's verbal/conceptual ideas into equations, distinguish standard physics from speculative assumptions, check elementary algebra and derivatives, organize the manuscript, and prepare figures and formatting. The central QT/QE near-linearity hypothesis and the decision to publish this speculative framework are attributed to Chaman Prakash Kanth. The author assumes responsibility for the final content. Sarvam AI was also extensively used like Chatgpt.
This speculative theoretical note develops a toy framework linking quantum tunneling (QT), quantum excitation (QE), local Jacobian/state-space evolution, and a proposed near-linear QT/QE mode. It derives epsilon_Q = A_Q k_Q, reviews the standard near-threshold tunneling limit kappa -> 0, and shows that coherent QT/QE dynamics can be continuous under Schrodinger evolution. The nonstandard FTL step is isolated as a separate requirement: a physically justified dispersion relation and an operational signaling test. No experimental evidence for faster-than-light signaling is claimed. ChatGPT (OpenAI) assisted with exposition, checking, organization, figures, and document preparation; Chaman Prakash Kanth is the author and is responsible for the final content. Recommended notes field:Version 0.1.0. Speculative research note. This deposit is intended to document the mathematical formulation and priority of a testable hypothesis, not to claim experimental confirmation. Future versions should be deposited as linked Zenodo versions if the equations, numerical tests, or experiments change substantially. AI assistance statement:ChatGPT (OpenAI) was used as a research-writing and mathematical-assistance tool. It helped translate the author's verbal/conceptual ideas into equations, distinguish standard physics from speculative assumptions, check elementary algebra and derivatives, organize the manuscript, and prepare figures and formatting. The central QT/QE near-linearity hypothesis and the decision to publish this speculative framework are attributed to Chaman Prakash Kanth. The author assumes responsibility for the final content. Sarvam AI was also extensively used like Chatgpt.
This non-peer-reviewed exploratory preprint tests whether a coupled quantum Hamiltonian with one additional spatial coordinate can produce barrier transmission distinct from ordinary one-dimensional quantum mechanics when both calculations share exactly the same observable slice V(x,0). A prescribed self-similar Gaussian barrier is compared using three calculations: fixed-width 1D, shrinking identical-slice 1D, and full coupled (x,w) scattering with harmonic confinement. The shrinking 1D slice is itself non-monotonic, so an upward turn is not uniquely extra-dimensional. The full model nevertheless gives a quantitatively different curve, with a sampled minimum near V0=18 and T=9.87e-3 at V0=64 versus 6.09e-9 for the identical slice. This is a reproducible coupled-channel result within a mathematical toy Hamiltonian, not evidence that nature has an accessible fourth spatial dimension. The barrier family is prescribed rather than derived from a constitutive field law. The record includes the manuscript and a supplement containing code, complete numerical results, metadata, and convergence checks. ChatGPT and Sarvam AI assisted with brainstorming and language development. ChatGPT also assisted with literature triage, control design, numerical implementation and auditing, and drafting. AI systems are not authors. Chaman Prakash Kanth remains responsible for the manuscript, assumptions, metadata, and publication decision.
This educational technical note derives the leading semiclassical tunneling exponent for a one-dimensional particle in a static electrostatic potential from the local Dirac dispersion relation, and shows how the Schrödinger WKB result follows in the low-energy limit. It also introduces a hypothetical parameter lambda multiplying the quadratic relativistic term and compares the corresponding exponents for a defined rectangular barrier. The standard Dirac-WKB derivation reproduces established relativistic quantum mechanics; it is not presented as a new physical law. The lambda modification is exploratory and has no independent theoretical derivation or experimental support in this note. The numerical comparison is a sensitivity calculation for an illustrative 10 fm rectangular barrier with constant Delta = 0.1 MeV and mu*c^2 = 1118 MeV. It is not a realistic D-T interaction model or a prediction of a fusion reaction rate. The note does not claim cold fusion, anomalous fusion enhancement, or reactor-relevant performance. A one-particle Dirac equation does not describe the complete D-T nuclear collision, which involves composite nuclei, strong-interaction channels, spin, and plasma/environment effects. The cited 2026 D-D metallic-hydride study concerns ion-beam and electrochemical loading conditions and does not validate the hypothetical lambda model or establish self-sustaining fusion. AI assistance: ChatGPT assisted with literature triage, numerical calculations, equation review, and drafting. Chaman Prakash Kanth is responsible for the scientific assumptions, calculations, manuscript, and metadata.
This pedagogical technical note derives a connected model from a one-dimensional monoatomic lattice through acoustic phonons, strain, photoelastic refractive-index modulation, Stokes and anti-Stokes optical sidebands, and a conditional spin-population response. It explains why a realistic optical-to-spin step requires a platform-specific intermediate state or Raman pathway, and treats direct spin–phonon coupling as a separate route. Under a fixed-amplitude ideal two-level model, the note analytically derives spin responsivity to a phonon-frequency perturbation, checks a π-pulse numerical example, and identifies the first detuning-dependent term in the short-pulse expansion. The deposit includes the PDF, LaTeX source, numbered references and BibTeX bibliography, figures, and reproducibility scripts. This is a pedagogical synthesis and quantitative illustration; no new experiment or novelty claim is made. AI contribution statement: This manuscript was developed with AI assistance from ChatGPT and Sarvam AI. ChatGPT assisted with conceptual development, step-by-step mathematical derivation, technical organization, mathematical checking, manuscript drafting and editing, and visualization planning. Sarvam AI additionally assisted with quantitative evaluation of the phonon-frequency-shift to optical-sideband-detuning to spin-response chain, numerical exploration of Rabi-response curves, and calculation and visualization of spin responsivity versus detuning. The AI systems are not authors. Chaman Prakash Kanth is responsible for scientific interpretation, verification, final claims, and the final manuscript. Version 0.2.0 adds the four-page companion note, How light and sound change each other (light_sound_reciprocal_coupling.pdf). The companion explains reciprocal optical-acoustic coupling, derives a linear anti-Stokes model with optical backaction, and illustrates how shifting an acoustic resonance changes optical sideband field amplitude and intensity under fixed-drive assumptions. It connects the amplitude derivative to a conditional Raman spin-response chain rule, distinguishes fixed-drive and frequency-tracking configurations, and states the model's limitations. These are illustrative calculations of established physics; no experimental validation, threshold, hysteresis, or novelty claim is made. The original manuscript and version 0.1.0 source archive are retained as the base documents. Companion AI disclosure: ChatGPT substantially assisted with explanation, model selection, algebra, numerical illustration, figure generation, and document preparation. The named human creator did not produce the companion alone; it has not undergone independent scientific review.
FINDING: Quantum tunneling and macroscopic entanglement are being experimentally probed, but the search results are pedagogical/overview-level, not new mathematical breakthroughs. | MATH: No new equations or constants extracted; standard quantum tunneling transmission coefficient T≈e−2κd (with κ=2m(V0−E)/ℏ) and entanglement tomography of macroscopic mechanical oscillators (Gaussian state covariance matrices) are implied. | CONNECTION: The tunneling exponential decay rate κ has no direct golden-ratio link; however, the macroscopic entanglement tomography (NIST) involves phonon modes whose frequency ratios in coupled oscillators can yield 2 or harmonic ratios, but no explicit 0.618/1.618 evidence in the provided text. | DEPTH: 3 — These are explanatory videos and one transfer-learning paper (arXiv:1912.08278), not primary derivations. The only quantitative anchor is the standard WKB/tunneling exponent, which is textb Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
FINDING: Quantum tunneling is a wave-mechanical penetration of finite potential barriers, with a transmission coefficient governed by exponential decay of the wavefunction inside the barrier; "impossible" relativistic measurements are shown to be possible but non-ideal, revealing a fundamental tension between QFT and measurement theory. MATH: - Transmission coefficient T≈e−2κL, where κ=2m(V0−E)/ℏ (rectangular barrier, E<V0). - For a general barrier V(x): T≈exp[−ℏ2∫x1x22m(V(x)−E)dx] (WKB approximation). - Reflection coefficient R=1−T (unitarity). - In QFT impossibility: signaling between spacelike-separated regions is avoided only if measurement operators commute — the paper (arXiv:2311.13644) shows nonlocal joint measurements in non-relativistic QM produce the same paradox, implying a constraint on measurement algebra: \( [\hat{O}_A, \hat{O}_ Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com