Physical Sciences

Abstract: I propose that both quantum theory and gravitation are emergent low-energy phenomena arising from a deeper pre-quantum, pre-spacetime dynamics formulated on split bioctonionic geometry with symmetry E8 × ωE8. In this framework, Connes time replaces external classical time, trace dynamics replaces quantum kinematics, and spacetime itself emerges when many atoms of spacetime-matter become sufficiently entangled and undergo a quantum-to-classical transition. The program naturally accommodates three fermion generations, left-right structure, gravi-weak unification, and explicit charged-fermion mass relations. I explain these achievements, identify the principal open problems, and compare the program fairly with string theory. The central claim is that unification may require not quantizing classical spacetime, but deriving both spacetime geometry and quantum mechanics from a more primitive octonionic dynamics.

Abstract: We address the paradoxical transformation of a classical-mechanical particle motion when the space and time scales of observation pass down the uncertainty principle threshold. This is analyzed in the language of classical statistical mechanics, considering specifically many-particle systems inhomogeneous along one spatial direction. We employ the density functional formalism in its square-gradient form and find: i) The macroscopic solution is analogous to the classical trajectory of a particle under a potential of force given by (minus) the free energy density. Whereas, ii) fluctuations around the solution in (i) are equal to the quantum-mechanical wave functions of a particle under a potential given by the curvature of the free energy density. We illustrate this situation with three textbook examples: A particle in a box, the harmonic oscillator, and the hydrogen atom. We show that their time-independent Schrödinger equation wave functions describe, respectively, the fluctuations of a fluid interface, of critical point fluctuations, and of a confined ideal gas. At large scales sharp probability distributions make fluctuations irrelevant, the vanishing of the first variation yields the macroscopically observable statistical-mechanical non-uniformity, equivalent to the classical particle trajectory. But at sufficiently small scales, with necessarily very few particles, distributions appear much wider, fluctuations dominate, and one obtains the Schrödinger equation (for the microscopic potential).

Abstract: Inspired by the holographic theory of gravity originating from the microscopic degrees of freedom of black holes, as well as the profound connection between quantum entanglement and space-time revealed by the AdS/CFT correspondence, this paper attempts to establish a connection among quantum measurement, quantum entanglement, and space-time, thereby proposing a "Multi-Space-Time" scheme. Under this scheme, the "problem of the preferred basis" and the "problem of definite outcomes" in quantum measurement can be solved simultaneously. Furthermore, it reveals that classical space-time originates from quantum measurement. However, a derived result of this scheme is that the number of classical space-times in the universe is not unique; rather, there may exist a multitude of them. The "Multi-Space-Time" scheme demotes measuring instruments or observers to a status of parity, establishing an egalitarian relationship between the measured system and the measuring instrument. Nevertheless, the proposal remains largely a conceptual or epistemic framework at present, and its verification relies on the establishment of quantum gravity. Yet, it provides a potential direction for future quantum gravity research when dealing with classical space-time, quantum measurement, and quantum entanglement simultaneously.

Abstract: This research answers the knowledge gap regarding the explanation of the quantum jump of the electron. This scientific paper aims to complete Einstein’s research regarding general relativity and attempt to link general relativity to quantum laws.

Abstract: We propose a generalized definition of rest energy in which mc^2 is interpreted not as an immutable intrinsic quantity, but as a latent kinetic form. Within this framework, any kinetic contribution—Fermi, Coulomb, or relativistic gravitational—that assumes a rest-like structure becomes energetically dormant unless a non-arbitrary infinitesimal deficit is introduced. We show that such a deficit leads naturally to an alternative relativistic solution characterized by extreme excitation and particle-number amplification, while preserving total energy conservation. This mechanism gives rise to a bound, atom-like gravitational configuration at macroscopic scales, referred to here as a giant atom, governed by a precise orbital condition linking de Broglie coherence to gravitational binding. A scalar field condensate is introduced not as a new source of energy, but as a geometrical and dynamical mediator: it traps the configuration, screens the enormous Coulomb self-energy, and enables migration through its gradient structure and intrinsic frequency. Importantly, the model does not rely on a phase transition or energy injection. Instead, the dynamics become effective only when cosmological damping falls below the intrinsic frequencies of the trapped system. We argue that the initial closed configuration can be established at very early times (∼〖10〗^(-5) s before BB) and remain dynamically frozen, protected by the scalar field, until plasma dilution around T∼0.1MeV allows the latent kinetic structure to express a minute energetic imbalance. This marks the onset of gravitational potential deposition and the emergence of large-scale ordered motion. The framework offers a pathway toward the formation of atom-like gravitational systems, with potential implications for early-universe dynamics and the origin of planetary system.

Abstract: This manuscript develops a timelike-boundary reading of locality and reality within the established Lorentzian causal structure of special relativity and the standard record language of quantum measurement. The central object is a timelike boundary equipped with a boundary observer field and observer-adapted cuts. Such a cut is treated as the local comparison surface on which selected quantities are read relative to a coarse-grained reference structure. A local record appears when a boundary-relative deviation becomes resolvable on that cut. The framework separates two roles that are often compressed into one event statement. Lorentzian geometry supplies causal admissibility: it determines which prior data or contextual contributions may be relevant for a candidate event. The boundary comparison supplies record content: it identifies the deviation that becomes locally manifest. Thus the causal cone constrains the admissible domain, but it does not by itself provide a microscopic route or a measurement record. The proposed reading therefore assigns locality to cut-local record formation under Lorentzian causal admissibility. Reality is associated with stable, record-accessible deviations rather than with direct exposure of the underlying reference structure. The result is a compact assignment framework in which causal structure, reference structure, resolved deviation, and local record formation are organized on the same timelike boundary without replacing the established mathematical content of special relativity or quantum mechanics.

Abstract: A relativistic stress-energy configuration is identified in which halo-like scaling in galaxies can arise from the rotational sector of matter without modifying the Einstein equations. In stationary axisymmetric systems, the mixed stress-energy components associated with vorticity define a conserved Killing current describing angular-momentum transport. The corresponding stream potential admits a multipole structure in which the dominant odd mode controls the radial flux and fixes its asymptotic amplitude. If this transport channel approaches a finite large-radius flux, the leading mode scales as r^-2. With the Alena Tensor closure, the same rotational sector that carries this transport mode contributes to the active weak-field source through the rotational part of the stress-energy tensor, giving an effective density with the same radial scaling and therefore approximately flat rotation curves. The baryonic Tully-Fisher relation is treated here as a constraint on the asymptotic transport amplitude, not as a first-principles derivation. The resulting framework gives testable predictions for disk-aligned lensing anisotropy, residual correlations with baryonic angular momentum, and suppressed halo-like scaling in systems without coherent rotation.

Abstract: Timelike boundaries provide a natural setting for organizing geometric, quasilocal, and coarse-grained information in general relativity. This work develops a cut-level reference framework for finite-radius timelike interfaces in Lorentzian spacetime. Starting from a timelike boundary, a tangent observer field, and observer-adapted spatial cuts, the construction assigns selected boundary quantities, coarse-grained reference structures, channel-specific comparison values, resolved deviations, local event closure, and cut-level response terms to the same geometric surface. The framework is local in its physical reading. The coarse-grained reference structure is not treated as a single resolved boundary record, but as the macroscopic comparison structure relative to which local deviations are defined. A local boundary event is represented by a boundary-relative deviation that becomes resolvable at the candidate event. The causal condition fixes the Lorentzian admissibility domain; it does not by itself define a resolved trajectory or microscopic propagation history between spacetime points. In the classical realization developed here, the selected variables are supplied by the Brown--York cut-level dictionary. Observer-adapted projections of the boundary stress tensor define surface energy density, momentum density, spatial cut stress, and isotropic pressure. A coarse-grained boundary reference package specifies which variables are resolved, on which cut they are evaluated, and which reference structure serves as their comparison level. The corresponding deviation map and channel-dependent resolution norms identify the locally resolved boundary content. The same cut-level variables also enter a classical balance structure in which cut-energy variation separates into normal exchange and tangential mechanical response. In isotropic spherical symmetry, this response reduces to the pressure--area form, linking cut-level stress to the area-response channel of a timelike shell. Timelike thin-shell dynamics and macroscopic shell-balance laws then appear as concrete realizations of the general reference-cut structure. The resulting formulation provides a classical boundary-reference language for finite-radius timelike systems, relating local Lorentzian geometry, quasilocal stress, coarse-grained reference structure, resolved deviations, causal admissibility, and area response within one common cut-level framework.

Abstract: We develop a unified first-order framework for relativistic fields of different spin, in which the dynamics are governed by a common operator-based equation. This formulation provides a coherent description of scalar, spinor, vector, and tensor fields within a single structure and reproduces the corresponding second-order wave equations in appropriate limits. A central result is the emergence of a consistent spin-2 sector from the same underlying dynamics. By constructing the tensor field as a bilinear combination of internal spacetime degrees of freedom, we obtain a symmetric rank-2 field with the correct number of independent components. In the massless limit, the resulting equation matches the structure of linearized gravity, while source-like terms arise naturally from quadratic combinations of field derivatives, providing an intrinsic origin for an effective energy–momentum tensor. The Lagrangian formulation yields conserved quantities via Noether’s theorem and reproduces derivative structures consistent with the weak-field Einstein–Hilbert action. These results suggest that gravitational dynamics may emerge from a more fundamental first-order field theory.

Abstract: The gauge-hierarchy problem — the fourteen-order-of-magnitude chasm between the Planck and electroweak scales — and the cosmological-constant problem collectively constitute the deepest structural wounds in the standard model of gravitation. Existing remedies, whether anthropic selection [1], large extra dimensions [2], or warped compactification [3,4], each purchase conceptual economy at the expense of either predictive sterility or geometric fine-tuning. This framework develops upon effective-field that welds three architecturally cohesive structures: an F(R) = R + αR^2/M_∗² − 2Λ₅ bulk action in five dimensions, a circular Kaluza–Klein (KK) compactification whose radius RKK is fixed by a light stabilised radion of mass m_φ ∼ H₀, and the Hartle–Hawking no-boundary wave functional as the cosmological boundary condition. Within this architecture the KK tower generates an analytically controlled repulsive correction to the Newtonian potential above a comoving threshold λ ∼ c/H₀ ≈ 1 Gpc, the effective cosmological constant receives a geometrically negative KK contribution that partially cancels the vacuum energy without anthropic invocation, and the scale-dependent effective Newton constant G_eff(k, a) offers a possible resolution the σ8 tension — predicting σ₈ = 0.769 against the lensing-derived 0.766 ± 0.020 — with no additional free parameter beyond the two that define the bulk geometry.

Abstract: We investigate the astrophysical implications of Sedenionic Quantum Gravity (SQG), a theoretical framework derived from the non-associative structure of sedenion algebra. In this approach, the antisymmetric sector of the sedenionic field generates an effective Yukawa-type correction to the gravitational interaction, introducing a finite interaction range that modifies gravitational dynamics on galactic and cluster scales. In the weak-field limit, the antisymmetric sector produces a massive field equation whose solution yields a Yukawa-type modification to the gravitational potential. We test the phenomenological consequences of this framework using rotation curves of three well-studied spiral galaxies—NGC 2403, NGC 3198, and NGC 5055—and hydrostatic mass profiles of two relaxed galaxy clusters, Abell 2029 and Abell 478, derived from X-ray observations of the intracluster medium. Using a stretched-exponential baryonic density distribution and least-squares fitting, the SQG model successfully reproduces the rapid inner rise and extended quasi-flat behavior observed in galaxy rotation curves as well as the circular-velocity profiles of galaxy clusters, without invoking dark matter halos or MOND-like prescriptions. The model is also consistent with the baryonic Tully–Fisher relation as an emergent scaling behavior of the Yukawa-modified gravitational interaction and may provide a plausible explanation for cluster-merger phenomena such as the Bullet Cluster through the antisymmetric, nonlocal gravitational sector. These results suggest that the non-associative algebraic structure underlying SQG may provide a unified explanation for gravitational phenomena traditionally attributed to dark matter across multiple astrophysical scales.

Abstract: When applying the geometric quantization ansatz that focuses on quantizing the fundamental metric tensor to the reformulation of general relativity, eigencurvatures emerge at low (quantum) scales. They are distinct from the standard curvatures that manifest gravitational sources in conventional general relativity. The analytical and numerical evolution of timelike geodesic congruence expansion in the spacetime surrounding rotating, massive, non-charged, and axially symmetric Kerr black hole is introduced. This facilitates the assessment of whether the space singularity continues to exist or diminishes at low (quantum) scales. Furthermore, the characteristics of the quantum-conditioned curvatures can be defined by means of the Kretschmann invariant scalar. We conclude that the space singularity can be regulated by the proposed quantization approach. Moreover, the quantum-conditioned curvatures that arise in Kerr spacetime are genuinely real, essential, and intrinsic. They cannot be classified as artifacts in any coordinate systems, whether known or yet to be found.

Abstract: We develop a theoretical framework in which spacetime geometry and gravitational dynamics emerge from a non-associative spinor algebra defined on the sixteen-dimensional sedenion structure. In this approach, the spacetime metric is constructed from bilinear combinations of fundamental spinor fields, leading naturally to an effective four-dimensional geometry despite the higher-dimensional algebraic foundation. A central role is played by the associator, which measures the failure of associativity and introduces additional geometric degrees of freedom. Incorporation of the associator into the gravitational action yields modified Einstein equations with an effective geometric stress–energy contribution. In the weak-field limit, this leads to a Yukawa-type correction to the Newtonian potential, providing a geometric origin for phenomena commonly attributed to dark matter. The framework also suggests a natural interpretation of dark energy through associator vacuum contributions and establishes a connection between galactic dynamics and cosmological expansion scales. Furthermore, the model offers a pathway toward understanding early-universe coherence and the emergence of large-scale structure. These results indicate that non-associative spinor geometry may provide a unified algebraic foundation for quantum gravity and cosmology.

Abstract: We present a framework for gravity in which the effective interaction is described by a dynamically generated Yukawa-type potential arising from nonlinear field self-interactions. In this approach, the characteristic scale is not imposed but emerges directly from the field equations, leading to a scale-dependent gravitational interaction. The resulting potential is intrinsically non-perturbative and reduces to standard General Relativity in high-density regimes. We show that this framework naturally reproduces flat galaxy rotation curves and the Tully–Fisher relation, while also providing enhanced gravitational lensing consistent with cluster observations. Using representative fits to dwarf and spiral galaxies, as well as cluster convergence profiles, we demonstrate that a single dynamical mechanism can account for both kinematic and lensing phenomena without invoking dark matter or empirical acceleration scales. These results suggest that gravity may be fundamentally a self-interacting field with an emergent, environment-dependent range.

Abstract: A covariant operator equation with one arbitrary constant in the space of Dirac bi-spinors, equivalent to the classical Einstein equations, is obtained. This constant is an invariant of general covariant transformations. As a first integral of the Einstein equations, this constant has the meaning of the proper mass (energy) of the universe, not reducible to any material forms of energy. A covariant quantization procedure for general relativity is proposed, distinct from the canonical one with a distinct time parameter. The physical interpretation of the new formalism is formulated as a dynamical problem with specified boundary conditions.

Abstract: Quantum relativistic solutions for a particle in a one-dimensional Morse potential are presented using methods previously proposed and applied to a particle in a harmonic oscillator. The methods lead to both numerical and analytical solutions, with the latter allowing smooth variation of the system parameters from non-relativistic to ultrarelativistic limits. Analytical expressions for the energy levels and wavefunctions are obtained, as solutions to a Schrödinger-type equation, including relativistic effects through a state dependent rescaled mass. The eigenstates of the Morse potential exhibit suitable and smooth behavior, and approach the corresponding harmonic oscillator solutions as the depth of the Morse potential well increases, as expected. A comparison is also presented between the relativistic harmonic oscillator obtained with this method, and the so-called Klein-Gordon oscillator.

Abstract: We present a limited static-sector construction for the low-energy fine-structure constant within Recursive Interval Geometry (RIG). The recursive substrate itself is not reaxiomatized here; the inherited input is only the canonical principal/structural splitting together with the Ω-weighted norm. The paper introduces four principles: minimal closure with nonempty-state counting, a link–triangle–octahedral carrier hierarchy in one to three dimensions, a display-level readout principle, and a dimension-filtered expansion of the raw structural term. From these assumptions one obtains \( D_1=3,\;D_2=7,\;D_3=127 \), interpreted as nonempty boundary-state counts on minimal one-, two-, and three-dimensional carriers, hence the additive skeleton \( N_{\mathrm{sk}}=137 \) and the multiplicative resolution Ω=2667, together with the display-level form \( \alpha^{-1}=\sqrt{N_{\textup{sk}}^2+\Omega^2\ell_{\textup{raw}}^2} \) . What is not yet absorbed into deeper internal structure is reduced to three residual bridge coefficients in \( \ell_{\textup{raw}}=a_1/\Omega+a_2/\Omega^2+a_3/\Omega^3 \), which are taken in the working model to be \( a_1=\pi \), \( a_2=-2 \), and \( a_3=137+127/2 \). Their strongest current geometric readings are, respectively, the metric normalization of the minimal closed loop, the endpoint subtraction produced when an open interval is closed into a loop, and the sum of the full static skeleton with a third-level shared skeletal load. This yields \( \alpha^{-1}_{\mathrm{RIG}}=137.035999176253147\cdots \), differing from the 2022 CODATA recommended value by \( 7.47\times10^{-10} \) in \( \alpha^{-1} \), or \( 5.45\times10^{-3} \) ppb. The claim is therefore not that quantum electrodynamics has been derived, but that a logically explicit substrate model can be tested as a falsifiable interface proposal.

Abstract: We develop a comprehensive quantum-mechanical and field-theoretic framework for a complex scalar field whose modulus encodes a local time density and whose internal phase carries a U(1) structure. This field, which we call the timeon, admits a potential with two thermodynamically distinct minima: a null-stress vacuum phase and a deeper condensed, highly stable atomic phase. We show that localised, finite-energy atomic-phase domains embedded within the vacuum couple naturally to a conventional matter wavefunction ψ(x,t), giving rise to a new class of composite eigenstates — Baryon Partner States (BPS). These states are elements of the composite Hilbert space H_ψ ⊗ H_Φ and function as the fundamental excitations of the theory. We derive the complete Lagrangian and Hamiltonian governing the timeon field, obtain the coupled Euler–Lagrange equations for the composite system, and construct static, spherically symmetric BPS configurations satisfying regularity and finite-energy boundary conditions. Each BPS exhibits a topologically constrained core, a nontrivial radial profile, and a quantised U(1) phase winding. These structures endow the states with emergent mass, charge, and confinement properties. Baryonic mass arises entirely from spatial gradients and potential energy of the field configuration; charge originates from the internal phase winding; and confinement emerges as an energetic and geometric necessity — continuous unwinding of the phase is forbidden without traversal of configurations carrying arbitrarily large energy cost, preventing fractional excitations from existing in isolation. Vacuum-to-atomic tunnelling and atomic-phase nucleation processes are analysed in detail, including energy barriers, critical radii, and transition amplitudes for metastable decay. The local matter density |ψ|² acts as a compression parameter that dynamically lowers nucleation thresholds and drives the formation of atomic-phase regions. Linearization about both homogeneous phases and static BPS configurations yields the complete small-oscillation spectrum of the theory; these internal modes form a predictive excitation tower and correspond directly to resonances in scattering processes. By promoting the translational degree of freedom of a BPS to a dynamical modulus, we derive its effective nonrelativistic Lagrangian and identify a renormalized inertial mass. Pairwise interactions between BPSs generate an effective potential consisting of strong short-range repulsion, an intermediate-range attractive well, and Yukawa-like long-range decay. This structure supports two-body bound states, determines low-energy scattering phase shifts, and produces resonances when collision energies match internal excitation frequencies. Extending to many-body systems, we show that BPSs form stable clusters analogous to small nuclei. A systematic low-energy effective field theory is obtained by integrating out internal BPS modes. Together, these results demonstrate that mass, charge, confinement, excitation spectra, scattering behaviour, and nuclear-like structure can emerge from the dynamics of a single complex field coupled to a matter wavefunction.

Abstract: This paper presents a unified theoretical framework based on three fundamental axioms: the Covariance Principle, the Invariance Principle, and the Shielding Principle. Spacetime is not a continuous manifold but a discrete graph G = (V, E) of Planck-scale units, each characterized by a complex field Φ_i = √ρ_i e^{iθ_i}.Rigorously derived results (no experimental input):This paper rigorously derives from first principles: genus g = 3, spin j = 1/2, the Barbero-Immirzi parameter γ = 1/(4√3π), the Planck-scale Weinberg angle sin²θ_W(M_P) = 1/4, the color number N_c = 3, charge quantization, the lightest neutrino mass m_{ν₁} = 0, topological prohibition of fourth-generation fermions, the universal scaling ρ₀a² = 1/(2π), the Wilson coefficient r = a/4, and the gravitational wave echo structure Δt.Cross-sector validation and new discoveries in galactic dynamics (tested with observational data):(i) Using the Milky Way rotation curve (Gaia+VERA 2024) to calibrate the geometric residual parameters: r_c = 6.6 kpc, ρ₀ = 35195 km²/s², reduced χ²_ν = 1.2, perfectly replacing dark matter halos.(ii) Independent prediction of the M31 (Andromeda) rotation curve using the same parameters, in perfect agreement with observations (Carignan et al. 2006), requiring no additional adjustments.(iii) Application of the model to four dwarf galaxies (LMC, SMC, Fornax, Draco), all with reduced χ²_ν < 2.0, leading to the discovery of a new scaling relation r_c ∝ R_half (power-law exponent b = 1.02 ± 0.08, R² = 0.99), unifying the description from dwarf galaxies (R_half ∼ 0.2 kpc) to giant spirals (R_half ∼ 4.5 kpc). Dark matter theory (ΛCDM) requires independent halo parameter fitting for each galaxy and cannot explain this universal scaling law.Unified origin of dark matter and dark energy:The uniform residual of spatial unit proliferation (geometric residual) drives cosmic acceleration (dark energy), while non-uniform cascade transfer produces density gradients and density fluctuation spectra, manifesting as gravity and dark matter effects. The vacuum catastrophe is naturally resolved — uniform zero-point energy has zero gradient and does not couple to gravity. Black hole singularities are eliminated by discrete geometry.Testable predictions:No fourth-generation leptons; gravitational wave echoes (10⁻² s for stellar-mass black holes, 10³ s for supermassive black holes); neutrinoless double-beta decay m_{ββ} ≈ 0.0037 eV; rotation curve oscillations (amplitude 2-3 km/s, period 5 kpc); δ_{CP} = e/2; α_s(m_Z) = 1/(πe); superconducting phase transition radiation ν = 2Δ/h.Core conclusions:The dimensionless constants of the Standard Model are not free parameters but topologically invariant geometric lockings. Dark matter and dark energy are not independent entities but macroscopic manifestations of geometric residual effects. The scaling relation r_c ∝ R_half is the geometric fingerprint of emergent gravity.

Abstract: A macroscopic boundary-balance framework for gravitational collapse is developed for a timelike thin shell separating an effective interior vacuum reference sector from an exterior Schwarzschild or Schwarzschild–de Sitter region. The interior sector is represented by a coarse-grained reference density ρref(χ) and the associated reference energy Eref=(4π/3)R3ρref. Along the shell history, reference-energy descent occurs when the decrease of ρref dominates the geometric increase of the enclosed volume. This condition defines the effective quasilocal input Φeff=−AΣ−1E˙ref, which is positive precisely on the descending-reference branch. The timelike shell converts this input into a finite boundary response. The central balance law, E˙Σ=AΣ(Φeff−Φout)−PA˙Σ, partitions reference-sector input into quasilocal shell storage, exterior release, and pressure–area work. A trajectory-dependent response coefficient Ceff=dEref/dTΣ parametrizes the local boundary-temperature response; on a negative-response branch, reference-energy descent increases the shell temperature. Local shell temperatures and near-boundary mode frequencies are mapped to exterior static observers by the exterior lapse, with spatial infinity recovered only in the asymptotically Schwarzschild limit. The resulting timelike thin shell is a finite-radius quasilocal boundary that organizes reference-state change through surface stress, flux balance, area response, and redshifted observables. The entropy-like variable SΣ=αAΣ records the macroscopic area response and enters the same balance through the pressure–area work term. The framework identifies the classical boundary variables and closure conditions required for perturbative stability analyses, finite-thickness response models, and microscopic boundary descriptions.