This paper develops a mass-free radial periodic-state model within Habitat Information Physics (HIP) and examines its relation to the Planck relation, electronic transitions, photoionization thresholds, and cross-scale experimental records. Two processes are kept separate. In a source-side bound–bound transition, the electron remains within the atomic internal habitat and the source releases an outward light signal. In a receiver-side bound–continuum transition, an absorbed signal opens an ionization channel and the electron enters an unbound state. A threshold wavelength specifies the minimum signal condition for escape, not a finite “completed-escape radius”; at threshold, the asymptotic excess speed approaches zero. For a system with an identifiable core construct, operational radius r, radial amplitude ratio ηr, characteristic period T, and angular frequency ω=2π/T, the paper assigns a radial amplitude Ar=ηr r. It then defines the mass-free oscillator invariant εH=(1/2)ω²Ar², with dimension m² s⁻², and the closed-cycle kinematic action jH=πωAr², with dimension m² s⁻¹. These quantities satisfy the identity εH=jHν, where ν=1/T. They are specific, or response-normalized, quantities; they are not joules and joule seconds. Consequently, jH cannot be identified directly with h. The conventional relation E=hν is represented as a calibrated total-quantity layer, E=μcalεH and h=μcaljH, where μcal is an empirically testable response scale rather than an assumed primitive in the mass-free layer. The framework is audited against double-slit interference, the Na I D2 line and first ionization threshold, 57Fe Mössbauer resonance and lifetime data, the Pound–Rebka shift, nuclear-resonant phase interferometry, radial Rydberg wave packets, photoionization microscopy, atomic recoil measurements, Josephson voltage–frequency universality, and a Penning-trap frequency ratio. Each case is separated into object state, propagating signal, instrument record, observable combination, model inversion, and ontological interpretation. Existing data repeatedly constrain frequency, wavelength, phase, count, timing, and dimensionless ratios, but operational radii and mass parameters are often model-assisted. No published single-system dataset yet provides independent r, T, η_r, and angular collection fraction f_Ω without importing h- or mass-derived scales. The paper therefore establishes dimensional closure, explicit numerical benchmarks, a mass-free agreement statistic, and falsification protocols; the proposed cross-system minimum j₀ remains an E5 candidate hypothesis.
This paper develops a mass-free radial periodic-state model within Habitat Information Physics (HIP) and examines its relation to the Planck relation, electronic transitions, photoionization thresholds, and cross-scale experimental records. Two processes are kept separate. In a source-side bound–bound transition, the electron remains within the atomic internal habitat and the source releases an outward light signal. In a receiver-side bound–continuum transition, an absorbed signal opens an ionization channel and the electron enters an unbound state. A threshold wavelength specifies the minimum signal condition for escape, not a finite “completed-escape radius”; at threshold, the asymptotic excess speed approaches zero. For a system with an identifiable core construct, operational radius r, radial amplitude ratio ηr, characteristic period T, and angular frequency ω=2π/T, the paper assigns a radial amplitude Ar=ηr r. It then defines the mass-free oscillator invariant εH=(1/2)ω²Ar², with dimension m² s⁻², and the closed-cycle kinematic action jH=πωAr², with dimension m² s⁻¹. These quantities satisfy the identity εH=jHν, where ν=1/T. They are specific, or response-normalized, quantities; they are not joules and joule seconds. Consequently, jH cannot be identified directly with h. The conventional relation E=hν is represented as a calibrated total-quantity layer, E=μcalεH and h=μcaljH, where μcal is an empirically testable response scale rather than an assumed primitive in the mass-free layer. The framework is audited against double-slit interference, the Na I D2 line and first ionization threshold, 57Fe Mössbauer resonance and lifetime data, the Pound–Rebka shift, nuclear-resonant phase interferometry, radial Rydberg wave packets, photoionization microscopy, atomic recoil measurements, Josephson voltage–frequency universality, and a Penning-trap frequency ratio. Each case is separated into object state, propagating signal, instrument record, observable combination, model inversion, and ontological interpretation. Existing data repeatedly constrain frequency, wavelength, phase, count, timing, and dimensionless ratios, but operational radii and mass parameters are often model-assisted. No published single-system dataset yet provides independent r, T, η_r, and angular collection fraction f_Ω without importing h- or mass-derived scales. The paper therefore establishes dimensional closure, explicit numerical benchmarks, a mass-free agreement statistic, and falsification protocols; the proposed cross-system minimum j₀ remains an E5 candidate hypothesis.
Double-slit interference, weak-light interference, nominal single-photon counting, which-path experiments, Mössbauer resonance, the Pound–Rebka frequency shift, and EUV/BEUV multilayer reflection are reconstructed as record-generation problems involving a propagating signal, external habitat, boundary construct, receiver internal habitat, and threshold conditions. The popular statement that light is a wave when unobserved and becomes a particle when observed is replaced by a testable physical hierarchy: human awareness is absent from the apparatus dynamics; path markers, detectors, polarizers, scattering constructs, absorbing layers, and environmental coupling alter the experimental habitat and therefore the record [3–8]. A complete light signal packet SP_gamma is introduced. “Complete” means that the propagating variables are fully specified within a chosen optical channel, direction, mode, bandwidth, and time window; it does not mean that the signal reproduces the complete internal state of the source. Source-side bound-state transition, propagating signal, and receiver-side excitation, ionization, or click are kept distinct. The cross-internal-habitat equation defines R_x as a thresholded feedback record. Wave-like records are reclassified as coherent-feedback records, particle-like clicks as local threshold records, and quantum erasure as path-information reclassification rather than information destruction. Mössbauer, Pound–Rebka, and EUV/BEUV data further show that records are jointly generated by signals, material electronic structure, boundaries, and thresholds [9–24].
Habitat Information Physics, Volume I establishes a unified physical framework for describing objects, boundaries, fields, signals, interactions, and measurement records across multiple scales. The book introduces the habitaton and the habitaton field as foundational physical concepts. It explains light as a continuous signal wave propagating through the habitaton field, interprets discrete optical counts as detector-threshold records, defines the electron as a bounded habitaton cluster, and reconstructs long-range celestial constraints without treating mass as their primary ontological source. Across twenty chapters and four technical appendices, the framework is applied to double-slit interference, beam-splitter experiments, atomic and nuclear transitions, photoionization, Mössbauer spectroscopy, the Pound–Rebka experiment, Josephson relations, slow and stopped light, vacuum birefringence, neutrino experiments, and Solar-System orbital dynamics. This volume presents a systematic and testable research program for understanding how physical states are generated, transmitted, reorganized at boundaries, and converted into observable records. It offers a new foundation for field theory, foundational physics, complex systems, and cross-scale physical organization.
This paper gives a first-principles structural derivation of Planck’s constant within the completion-locked closure framework. The derivation begins from a completion-locked phase–time–energy structure in which admissible phase-frequency comparisons are fixed before energy observables are compared. It does not assume the numerical value of Planck’s constant, the Planck–Einstein energy–frequency law, the standard Hamiltonian phase convention, or canonical commutator normalization. Instead, the action scale is derived from a projective phase carrier, a strongly continuous time-translation representation with Stone angular-frequency generator, an admissible class of energy observables for the same deformation, a sector-rich and spectrally exhaustive comparison structure, and, for dimensional reporting only, a unit convention. The main representation theorem proves that any admissible energy observable satisfying spectral affiliation, direct-sum naturality, tensor-product additivity, zero normalization, continuity, positivity orientation, spectral exhaustivity, and common-source descent must be linear in the Stone generator. This yields a unique reduced action scale, from which the full-cycle quantum of action follows by circle normalization. The Planck–Einstein energy–frequency law is then derived as a consequence of the same structure rather than assumed as an input. The paper also establishes conditional action-unit closure pathways. A certified electromagnetic response branch supplies one action-unit closure path, while a certified curvature–vacuum branch supplies a second through an independently derived source vacuum invariant. A single certified dimensional branch determines the action unit within its unit convention; two same-source certified branches overdetermine the same action unit and therefore must agree. Since Planck’s constant is dimensional, its decimal value becomes meaningful only after an action-unit convention or certified dimensional branch has been specified. Under the post-2019 SI convention, the numerical value of Planck’s constant is exact by definition. The structural contribution of the paper is to identify Planck’s constant not as an empirical insertion into quantum dynamics, but as the derived action-conversion invariant relating phase-frequency generation to physical energy observables, with independent electromagnetic and curvature–vacuum closure paths for the same action unit. License note: Distributed under CC BY-NC-ND 4.0.
De Broglie’s “phase harmony” suggests that quantization can be understood as a requirement of global phase consistency after completing the fundamental cycles of a bound orbit. We show that the Einstein–Brillouin–Keller (EBK) quantization rules for planar Coulomb orbits can arise without introducing a matter wave, from a long-lived localized internal clock whose phase advances in proper time at a fixed rest-frame angular frequency. In the slow–fast regime, special-relativistic time dilation makes the clock accumulate a small phase lag relative to laboratory time. After subtracting the trivial rapid ticking at the carrier frequency, the remaining drift defines two independent loop phases on the Kepler torus: one around the azimuthal cycle and one around the radial cycle (the torus generators). To leading order these generator phases are proportional to the corresponding Kepler actions, with a single action scale set by the reduced mass, the speed of light, and the clock frequency. Requiring the clock factor to return to itself after each generator loop—its holonomy, meaning the accumulated loop phase—yields closure conditions identical in form to EBK quantization, including the universal turning-point and Coulomb-origin phase slips known as the Maslov and Langer shifts. Because the Coulomb energy depends only on the principal action given by the sum of the radial and azimuthal actions, these closure conditions reproduce the familiar hydrogenic inverse-square bound-state ladder with the expected reduced-mass scaling. We also show how closure can carry an energetic bias in a frequency-local sealed-clock regime: if electric-type dipole radiation is cancelled exactly at the carrier frequency but nearby detuned sidebands radiate, then a holonomy mismatch shifts spectral weight into detuned lines and increases near-carrier leakage quadratically near closure. The identification of the action scale with Planck’s constant is treated as an external calibration.
Several fundamental physical relations share a mathematical structure in which the product of two conjugate quantities equals an invariant constant. Representative examples include the energy-period relation ET = h (where T = 1/f is the oscillation period and h is Planck’s constant), the momentum-wavelength relation pλ = h (the de Broglie relation), and the frequency-wavelength dispersion relation fλ = c. Although these expressions originate from quantum mechanics, wave mechanics, and electromagnetism respectively, each belongs to the generalized class XY = K, where K is an invariant constant. Their shared algebraic form raises the question of whether a common organizational principle underlies physical representation. This paper proposes the Foundational Principle of Closure Representation as an interpretational framework. Within this framework, action is adopted as the foundational quantity, and closure is introduced as a representation-independent measure of cyclic completion, defined by the condition Δθ = 2π. Planck’s constant h is interpreted as the action associated with one completed closure—consistent with the Bohr–Sommerfeld quantization condition ∮p dq = nh. The Planck relation E = hf is accordingly understood as the product of action per closure and closure rate per unit time. A representation-transfer relation (RX)(Y/R) = XY is introduced, where R is a dimensionless representation coordinate. A measurable realization is given by R = λC/λdB = p/(mc), coinciding with the standard relativistic quantity γβ. This relation is a mathematical identity; its physical significance lies in the proposed interpretation of R as a representation coordinate characterizing the distribution of closure action between conjugate observables. The proposed framework does not introduce new physical laws, modify established equations, or claim to supersede existing theories. It provides a unified interpretational architecture within which several established reciprocal relations—connecting action, closure, wavelength, frequency, momentum, and propagation—may be understood as instances of a common closure-action structure.
Boltzmann's combinatorial entropy S = kB ln W on continuous phase space requires a cell scale ω of action dimension to render the microstate count finite, and the placeholder is exposed at differing strengths by absolute entropies, the third law, the Gibbs paradox once paired with indistinguishability, and specific-heat freeze-out. Five quantitative regimes then converge on the same numerical value ω = h per canonical pair, namely the Sackur-Tetrode absolute entropies, the Planck spectrum derived from cell-counting by Bose 1924, the Fermi-Dirac and Sommerfeld free-electron metals, the Davisson-Germer matter-wave wavelength, and the harmonic-oscillator specific-heat threshold. This paper offers a structural reading of where that cell scale comes from, locating its origin in matter-wave Fourier content. On a matter wave whose wavelength satisfies the de Broglie relation λ = h/p, confirmed for electrons by Davisson and Germer 1927 and subsequently established for neutrons, atoms, fullerenes, and molecules beyond 25 kDa, the Heisenberg-Kennard variance bound of Kennard 1927 and Weyl 1928 reads σx σp ≥ ℏ/2, while the Weyl symplectic measure dq dp/h assigns one orthogonal state per phase-space cell of volume h per canonical pair. The two facts are distinct but consistent, both involve the same action constant h, and Boltzmann's cell scale ω = h emerges as the in-phase-space manifestation of matter's wave nature. Four converging experimental anchors then constrain the matter wave's mathematical form. Davisson and Germer 1927 measured the de Broglie wavelength directly through electron diffraction from a nickel crystal, while Stern and Gerlach 1922 observed splitting of silver atoms into two discrete magnetic-moment components along the field axis, with the angular-momentum interpretation, the universality across orientations, and the assignment of the value ±ℏ/2 supplied by Goudsmit and Uhlenbeck 1925 and the subsequent development of spin theory. Rauch et al. 1975 and Werner et al. 1975 then measured a 4π rotation period for neutron spin in interferometry experiments distinct from the gravitational interferometry of Colella, Overhauser, and Werner the same year, and Pauli's 1925 exclusion principle was reformulated by Heisenberg and Dirac in 1926 as antisymmetric exchange of multi-particle wave functions. Taken together these four anchors, some direct and some theory-mediated, constrain the candidate matter-wave object to be wave-valued, spinor-valued under spatial rotations with 4π period, and antisymmetric under particle exchange. With this much structural content empirically constrained, the matter wave is naturally read as physically real in the same sense the electromagnetic four-potential is naturally read as real after Aharonov and Bohm 1959. That reading is an interpretive position rather than an operational theorem, and an epistemic interpretation remains formally available, as does the parallel debate over Aμ realism. The standard pedagogical narrative dates ℏ's entry into physics to Planck's 1900 fit of the blackbody spectrum, whereas the structural reading offered here dates the placeholder for ℏ to Boltzmann's 1877 combinatorial entropy formula and treats the 1900-1928 quantum revolution as the period in which a value already presupposed by classical statistical mechanics was empirically pinned. The Dirac equation, curved-spacetime quantum mechanics, the configuration-space versus spacetime locus, the measurement problem, the Born rule, the spin-statistics theorem, and second quantisation lie outside the present scope.