Glossary: Real Space, Real Waves
Space and longitudinal waves
| Term | Meaning in WSM |
|---|---|
| Space | P1’s one nearly rigid, slightly elastic wave medium. Its primitive motion is longitudinal plane-wave vibration. Infinite, eternal and continuous follow immediately from its being the one substance; they are deductions, not added postulates. |
| Region of Space | A local part of continuous Space identified for description. It remains joined to its neighbouring regions and never becomes a separate object or parcel that flows through Space. |
| Solid continuity | Enduring neighbourhood relations within Space. “Solid” names continuous connection and nonflowing adjacency, not an atomistic material solid made from e-spheres. |
| Vibration of Space | The bounded back-and-forth displacement, compression and extension of neighbouring regions of Space. |
| Longitudinal compression plane wave | A flat equal-phase compression–extension disturbance travelling through Space. At every point, Space vibrates backwards and forwards in the same direction that the wave travels. |
| Compression | The part of a longitudinal vibration in which neighbouring regions of Space move slightly closer together. |
| Extension or stretching | The opposite part of the vibration, in which neighbouring regions move slightly farther apart than their balanced positions. |
| Plane wave | A longitudinal wave whose equal-phase positions form planes. Each plane advances in the wave’s direction while Space vibrates backwards and forwards in that same direction. |
| Plane of equal phase | The complete plane whose regions are at the same place in the vibration cycle. The wave travels at right angles to this plane. |
| Wavefront | A surface on which a wave has the same phase. A background wavefront can be flat, while an e-sphere can write a half-sphere curve into the passing plane. |
| Amplitude | The size of the displacement, compression or extension of Space during a vibration. |
| Phase | A wave’s place within its repeating compression–extension cycle. |
| Frequency \(f\) | The number of complete vibrations per unit time; angular frequency is \(\omega=2\pi f\). |
| Wavelength \(\lambda\) | The simultaneous spacing between successive equal-phase crests. With speed and frequency measured in the same coordinates, \(\lambda'=c'/f_{\rm crest}\). The distance \(\ell=c' T_0\) travelled during the rest-reference interval \(T_0=1/f_0\) is that wavelength only when \(f_{\rm crest}=f_0\). |
| Directional wave-energy density \(E_d(\hat{\mathbf n})\) | The local wave energy associated with longitudinal waves travelling in direction \(\hat{\mathbf n}\). It is not a material-fluid density. |
| \(E_{d0}\), \(c_0\) | The reference directional energy density and wave speed of the balanced background. |
| \(c'(\hat{\mathbf n})\) | The local propagation speed of longitudinal waves travelling in direction \(\hat{\mathbf n}\). |
| The One Law | P2 gives \(c'/c_0=E_d/E_{d0}\): changed directional wave-energy density changes propagation speed. A wavelength follows as \(\lambda'=c'/f_{\rm crest}\) when speed and crest frequency use the same coordinates. The universal intrinsic frequency supplies the reference scale; its mapping to a moving component’s crest frequency must be specified. |
| Directional moments | \(U=\int E_d d\Omega\), \(\mathbf J=\int\hat{\mathbf n}E_d d\Omega\), and \(\Pi_{ij}=\int\hat n_i\hat n_jE_d d\Omega\) summarize the all-direction distribution. They are readings of \(E_d\), not extra factors in the One Law. |
| Background wave sea | The generally disordered longitudinal plane waves travelling through Space in every direction. “Sea” names their abundance, not fluid flow. |
| Wave overlap | Several longitudinal waves occupying the same region of Space. Their displacements, compressions, extensions and phases jointly determine that region’s vibration. |
| Sideways propagation | A longitudinal wave travelling sideways relative to a chosen reference axis. Space still vibrates in that wave’s own direction of travel; sideways travel is not transverse vibration. |
The e-sphere and matter
| Term | Meaning in WSM |
|---|---|
| Huygens sphere | The spherical all-direction wave relation through which the out-waves of other matter combine as the chosen e-sphere’s in-waves. Every e-sphere stands at the centre of its own finite observable relation. The spheres overlap; matter and organised structure continue beyond each one. The boundary is neither a material shell nor an edge of matter or Space. |
| e-sphere | The finite, wavelength-scale central wave-centre core of an electron or positron. It circumscribes a cube of side \(\lambda_0\), so \(R=\sqrt3\lambda_0/2\). Huygens-combined longitudinal plane waves cross this core and continue outward; the complete spherical standing-wave relation extends beyond it, and no shell reflects the waves. |
| Open recurrence | A stable organisation continually rebuilt by through-passing waves. No material shell reflects or traps them. |
| Wave centre | The repeatedly reconstructed centre where the all-direction waves cross and form the central spherical compression and extension. |
| Spherical reclosure | The return of the complete all-direction phase relation to the same e-sphere organisation. As the incoming waves cross it, the e-sphere’s own directional \(E_d\) changes their \(c'\), wavelength, curve and phase so the spherical vibration continually reconstructs. |
| Normalized cube–sphere geometry | The e-sphere circumscribes a cube of side \(\lambda_0=1\), giving \(R=\sqrt3/2\) and \(V=\pi\sqrt3/2\). The absolute dimensional scale is an output. |
| \(j_0\) compression pattern | The spherical compression–extension distribution \(j_0(kr)=\sin(kr)/(kr)\) formed by the equal-phase sum of waves from every direction. |
| \(j_1\) radial-motion pattern | The radial motion of Space one quarter-cycle from the \(j_0\) compression maximum. It is the motion phase of the same spherical vibration. |
| Real quadratures | The compression pattern and radial-motion pattern separated by one quarter-cycle. They are successive aspects of one vibration, not extra electron states. |
| Radial phase | The background-relative timing of the e-sphere’s compression and extension. |
| Electron \(e^-\) | One background-relative radial phase of the stable e-sphere recurrence. |
| Positron \(e^+\) | The opposite radial phase: when the electron pattern compresses, the positron pattern stretches. |
| Antimatter | The opposite background-relative radial phase of the same kind of e-sphere, not another substance. In the WSM proton recurrence \((++-)_{\mu}\), positron-phase roles are bound inside ordinary matter rather than appearing as free positrons. |
| Charge sign | The opposite forward/rear curve orientation written onto passing plane waves by the electron and positron’s opposite background-relative radial phases: constructive same-phase and opposite-phase interference change \(E_d\), \(c'\), wavelength and phase in opposite ways while the plane crosses the e-sphere. |
| Universal cosmic clock | WSM requires electron and positron to remain opposite radial-phase organisations relative to the common background wave sea, including under motion. Each e-sphere’s changes to its incoming plane waves must maintain this cosmic phase relation. The universal intrinsic frequency standard, fixed-position Fourier frequencies and phase rate along a moving centre are distinct readings; their physical connection must preserve this requirement. |
| Stationary e-sphere | A spherical e-sphere with the same \(E_d\), \(c'\), wavelength and frequency in every direction. Its equal all-direction timing repeatedly rebuilds one centre. |
| Free e-sphere | A stable e-sphere not changing between bound modes. Uniform free motion does not itself write a discrete light train. |
| Bound standing-wave organisation | Two or more e-spheres held in a phase-related recurrent pattern with a discrete set of stable modes. |
| WSM proton phase structure | The proposed inseparable muonic-scale three-lobed recurrence \((++-)_\mu\). Its two positive and one negative radial-phase roles supply the proton’s charge bookkeeping; the collective conserved current determines the physical charge. These roles are not independently stored free muons. |
| Neutral-hydrogen phase inventory | Within the proposed proton construction, \((++-)_\mu+(-)_e=++--\) gives two positive and two negative radial-phase roles in neutral hydrogen. Extending that count to nuclei requires the neutron’s collective phase structure; internal roles are not a count of free antimatter particles. |
Curves, charge, force, inertia and gravity
| Term | Meaning in WSM |
|---|---|
| Curve on a plane wave | A half-sphere displacement and phase profile written by an e-sphere onto a passing longitudinal plane wave. Two physical stages must be kept distinct. While the plane crosses the e-sphere, its interference with the radial standing wave changes directional \(E_d\), \(c'\), wavelength and phase according to the radial-phase relation. After the curved portion leaves the e-sphere, it spreads over greater area; its ordered wave energy is then diluted, so its \(E_d\) and \(c'\) fall below those of the flatter carrying plane wave and it widens, flattens and lags. |
| Chord-effective \(2c_0\) | If a straight ray must cross the full chord \(2x_b\) before the outside carrier reaches the sphere’s centre plane, its transit time must be \(x_b/c_0\): \(\int_{\rm chord}ds/c'=x_b/c_0\). The harmonic chord-average speed is then \(2c_0\). This is the timing condition for the hemispherical exit-front construction, not every local speed and not H-M1’s effective reconstruction rate. |
| Forward and rear curves | When a plane wave crosses an e-sphere in the same radial phase, constructive wave interference raises directional \(E_d\) and \(c'\) while crossing and writes the forward curve. Crossing an e-sphere in the opposite radial phase gives the opposite interference change and writes the oppositely oriented rear curve. These are the two charge-like curve orientations. After either curved portion has left its e-sphere, both spread over greater area, both have lower \(E_d\) and lower \(c'\) than the flatter carrying plane wave, and both widen, flatten and lag. These curve orientations are not the same distinction as the leading and rear spatial sectors of a moving wave egg. |
| Charge | The opposite radial phase of electron and positron expressed in the opposite curves they write onto the real plane waves connecting e-spheres. |
| Charge interaction | A curve arriving on a plane wave changes the directional reconstruction of another e-sphere. The curve’s orientation and the receiver’s radial phase determine whether the centres reconstruct toward one another or apart. |
| Force | The change in an e-sphere’s motion caused when an incoming curve reshapes its all-direction standing wave. The arriving side is flattened, the opposite departing side is elongated, and the centre next reconstructs toward the elongated end. |
| Mass | The energy and recurrent wave organisation whose complete three-dimensional shape must be changed to change an e-sphere’s motion. |
| Inertia | The persistence of the existing e-sphere shape and its resistance to being reshaped. A stationary sphere remains spherical; a uniformly moving wave egg continually rewrites and rebuilds its asymmetry. Acceleration requires incoming curves to change that whole shape, giving the physical content represented by \(F=ma\). |
| Coulomb curve \(\zeta(R)\) | The shallow longitudinal displacement curve whose radial slope changes an e-sphere’s reconstruction. The declared small-slope response ansatz identifies that slope with the per-cycle velocity change, \(|d\zeta/dR|=\Delta v/c_0=2\pi\alpha\bar\lambda_e^2/R^2\), giving \(|\zeta(R)|=2\pi\alpha\bar\lambda_e^2/R\). WSM Action must derive this response relation. |
| Gravity | The common phase-even delay remaining when neutral matter’s opposite charge-like curve effects cancel. In the curve-spreading model, fixed wave-layer energy and thickness give lower \(E_d\) over greater area, hence lower \(c'\) by P2; both curve orientations can then lag. A delayed source-side front meets the opposing front closer to the source, biasing repeated e-sphere reconstruction toward it. This establishes the stated geometry of attraction; its magnitude, universality and conservation follow from the complete wave response. A stationary e-sphere does not continuously donate energy merely by writing a curve. |
Motion, spin and Dirac structure
| Term | Meaning in WSM |
|---|---|
| Motion of an e-sphere | Repeated reconstruction of its wave centre at successive positions after the all-direction geometry becomes asymmetric. |
| Moving wave egg | The complete three-dimensional deformation of a moving e-sphere: an elongated lower-\(E_d\) front and flattened higher-\(E_d\) rear joined by one continuous phase envelope. Axial reconstruction fixes \(c_0\pm v\); the all-direction \(\hat{\mathbf n}\!\cdot\!\mathbf v\) projection gives the leading interpolation. The full side-sector \(E_d\), \(c'\), wavelength and \(O(\beta^2)\) shape are quantitative outputs of WSM Action. |
| Leading sector | The elongated front of the wave egg: lower representative \(E_d\) and \(c'\), and a shorter crest travel distance in a fixed reference interval. Its internal wavelength is shorter when the same-coordinate crest frequency is held fixed. |
| Rear sector | The flattened rear of the wave egg: higher representative \(E_d\) and \(c'\), and a longer crest travel distance in a fixed reference interval. Its internal wavelength is longer when the same-coordinate crest frequency is held fixed. |
| Orthogonal and oblique directions | The first-order continuation is \(c'(\hat{\mathbf n})/c_0=1+\hat{\mathbf n}\cdot\mathbf v/c_0+O(\beta^2)\). Orthogonal directions have no first-order change. Neither their second-order speed nor the transverse radius is fixed by this approximation. Wavelength also requires the corresponding crest frequency. |
| Common intrinsic recurrence | Every direction forming one stationary or moving e-sphere participates in one resonantly locked intrinsic recurrence, maintaining its radial-phase relation to the background wave sea. This does not assign the same fixed-position frequency to every Fourier component. The reciprocal axial model’s common encountered phase rate is \(\omega_0/\gamma\); identifying that modulation with the globally locked radial phase is a separate physical question. |
| Axial reconstruction pair \(c_0\pm v\) | H-M1 assigns effective inward reconstruction rates \(c'_r=c_0+v\), \(c'_f=c_0-v\). During the same chosen interval \(T\), opposed fronts cover \((c_0+v)T\) and \((c_0-v)T\); their signed mean velocity is \(v\), and their closing rate is \(2c_0\). This specifies an axial timing rule, not the entire local speed profile or a clock period. |
| Raw egg factors \(1\pm\beta\) | The axial speed and representative density ratios \(1\pm\beta\) in H-M1 and P2. They also give reference-interval travel distances \(\ell_{r,f}=\lambda_0(1\pm\beta)\). They give internal wavelength ratios if the corresponding crest frequency is held fixed in the same coordinates; they are not the wavelengths of the calm-Space Fourier pair. |
| Reciprocal Doppler factors \(e^{\pm s}\) | For a stable one-to-one opposed-wave recurrence, phase matching fixes the frequency ratio. The additional geometric-mean closure \(\sqrt{\omega_+\omega_-}=\omega_0\) fixes \(D_\pm=\omega_\pm/\omega_0=\gamma(1\pm\beta)=e^{\pm s}\). The two real Fourier waves propagate at \(c_0\), with \(\lambda_\pm=\lambda_0/D_\pm\); these factors do not replace the internal reconstruction rates \(c_0\pm v\). |
| De Broglie phase wave | The phase modulation of the reciprocal opposed real-wave pair, with \(\Omega=\gamma\omega_0\), \(K=\gamma\beta k_0\) and \(\lambda_{\rm dB}=2\pi/K\). Its unequal fixed-position component frequencies arrive phase-matched at the moving centre, where \(\Omega-Kv=\omega_0/\gamma\). The beat is a relation between the real waves, not another substance. |
| Lorentz factor \(\gamma\) | The exact factor \(\gamma=(1-\beta^2)^{-1/2}\) obtained from the phase-matching ratio together with geometric-mean frequency preservation. The separate cap-area model gives \(S/S_0=\gamma^2\) from the same \(1\pm\beta\) kernel; this is not an independent derivation of the frequency closure. |
| Electron Compton cycle | The rest-reference wavelength and period \(\lambda_e=h/(m_ec_0)\), \(T_e=\lambda_e/c_0=h/(m_ec_0^2)\), using the measured rest calibration. The reciprocal free-motion modulation completes one centre-phase cycle in \(\gamma T_e\) of background time. |
| Fine-structure displacement | For the ideal Bohr ground-state relation \(v=\alpha c_0\), the centre advances \(\Delta X_{\rm ref}=vT_e=\alpha\lambda_e\) in one rest-reference interval. Hence \(\alpha=\Delta X_{\rm ref}/\lambda_e\). This interval is not automatically a complete moving-centre or bound-state phase period. |
| Spherical phase wave | The real moving equal-phase relation made by the ordered intersections of longitudinal waves arriving from different directions. Its two hands and \(4\pi\) closure give WSM’s physical meaning for spin; WSM Action must complete the stable quantitative dynamics. |
| Superluminal phase speed | The speed of successive equal-phase positions. Different intersecting waves create those positions; no region of Space or energy is carried at that phase speed. |
| Spherical phase rotation | Rotation of the phase relation over the complete sphere, not circular bodily rotation around an axis. |
| Spin hand \(h=\pm1\) | The two opposite directions of spherical phase rotation. These become the two spin channels relative to an analyser. |
| \(4\pi\) recurrence | Two \(2\pi\) turns are required before the complete directional phase relation returns to its original background-relative condition. |
| Four WSM/Dirac configurations | \((e^-,+1),(e^-,-1),(e^+,+1),(e^+,-1)\): two radial phases multiplied by two spherical phase-rotation hands define four WSM configurations. Their identification with physical Dirac states requires independent modes, their coupling and the conserved current to be established. |
| Dirac spinor | The four-component mathematical representation used for the intended radial-phase and spherical-hand sectors. Their physical identification depends on the derived dynamics. Its entries are state coordinates, not four pieces of an electron. |
| Dirac equation | The relativistic first-order equation that couples the four Dirac sectors. WSM associates its components with two opposite radial phases and two spherical \(4\pi\) phase-rotation hands. Recovering the equation requires their coupled relativistic dynamics and conserved current to follow from the same wave recurrence. |
| Pauli and Dirac matrices | The mathematical rules for how changes of direction, motion and interaction mix the two spherical rotation hands and the two radial phases while preserving the spinor’s \(4\pi\) structure and relativistic factorisation. |
| Complex \(i\) | Notation for a real quarter-cycle phase relation, such as compression and radial motion. It is not an imaginary substance and does not add physical states. |
Light and quantum interaction
| Term | Meaning in WSM |
|---|---|
| Stable mode | A bound standing-wave arrangement that repeatedly reconstructs the same complete phase relation. |
| Half-sphere curve | The curved displacement and phase profile an e-sphere imprints on a background plane wave as that plane passes through it. |
| Bound transition | The continuous reconstruction of a bound organisation from one stable standing-wave mode into another. |
| Source-written curve train | The finite ordered succession of changed half-sphere curves written onto successive passing plane waves during a bound transition. |
| Photon | A finite source-written curve train carried by real longitudinal background waves and capable of resonantly rebuilding a receiver into a new stable mode. |
| Quantum | The wave action associated with one allowed change between stable bound modes. The stable source and receiver modes make exchange discrete. |
| Resonance | Frequency and phase compatibility between a source-written curve train and an allowed standing-wave mode of a receiver. |
| Absorption | Successive incoming curves progressively reshape a receiver until it settles into a new stable standing-wave mode. |
| Receiver reclosure | The physical re-formation of a receiver as one stable mode after the incoming train has crossed the nonlinear threshold. |
| Measurement | A wave interaction in which apparatus geometry defines possible stable receiver modes and one mode becomes a persistent physical record. |
| Huygens ring | The circle of wave directions perpendicular to a light train’s direction. Its collective phase ordering carries two photon hands; it is distinct from the e-sphere’s Huygens sphere. |
| Photon helicity | The two opposite phase orders around the Huygens ring. Every contributing Space wave remains longitudinal. |
| Wave action \(J\) | The action associated with a complete wave recurrence. On the harmonic or linear-action branch, \(J=E/\omega\) measures ordered wave content. For a general periodic family, canonical cycle action obeys \(\omega=\partial E/\partial J\); the stronger \(E=J\omega\) relation requires the stated branch condition. |
| \(\hbar\) | The universal wave-action scale associated with one complete elementary mode change, giving \(E=\hbar\omega\). |
| Born probability | The normalized receiver-channel weight \(P_j=J_j/\sum_kJ_k=|\psi_j|^2\), once the action metric and receiver dynamics supply \(J_j\propto|\psi_j|^2\). |
| Pauli exclusion | Two identical electron patterns cannot both reclose as the same complete bound mode because their joint all-direction phases cannot reproduce that one recurrence twice. |
| Entanglement | A pair-specific phase and curve relation written by one source across two outgoing wave organisations and resolved through one joint receiver-channel calculation. |
| Bell nonfactorisability | The joint probabilities cannot be made from two independent lists of local prewritten answers; they belong to the complete source-created relation. |
| Annihilation | Destructive interference of opposite-phase electron and positron e-spheres. Their repeated curve patterns disappear; the changing cancellation writes outgoing gamma-ray curve trains. |
| Pair creation | The reciprocal formation of two stable e-spheres locked into opposite background-relative radial phases. |
| WSM Action | The one-substance dynamical equation named in the opening status statement. It must produce stable e-spheres and their quantitative quantum, relativistic, gravitational and cosmological behaviour. |
Relativity, clocks and measurement
| Term | Meaning in WSM |
|---|---|
| Physical wave speed \(c'\) | The actual local and directional speed at which a longitudinal compression plane wave travels through Space. The One Law changes \(c'\) when \(E_d\) changes. |
| Constant measured \(c\) | Every signal, ruler and clock is made from the same waves and e-spheres. When \(E_d\) changes \(c'\), it also changes local wavelength, wave-egg geometry, bound rulers and phase-clock comparisons. Since \(\lambda'=c'/f_e\), these linked changes make observers locally measure the same value \(c\), while the physical variations of \(c'\) produce interactions. |
| Spacetime | The measured geometry of a moving plane wave. Space supplies physical extension; the plane wave’s advancing phase supplies the ordered change measured as time. Spacetime coordinates describe this real wave motion rather than forming another substance. |
| Time | A measure of ordered wave change. Physical clocks compare the repeating phase of e-spheres and bound standing-wave organisations. |
| Proper time | The phase count accumulated by the e-spheres forming a particular clock along its motion through Space. |
| Lorentz transformation | The reciprocal axial wave sum has the phase-coordinate form \(x'=\gamma(x-vt)\), \(t'=\gamma(t-vx/c_0^2)\). Connecting these exact phase relations to all measured bound rulers and clocks is the corresponding physical construction. Space remains the vibrating medium; the coordinates describe its wave relations. |
| Matter-energy curves spacetime | Matter’s e-spheres write real curves onto passing plane waves. Those curves change directional \(E_d\), hence \(c'\), wavelength, phase, clock rates, reconstructed centres and light paths. The geometrical statement that matter-energy curves spacetime describes these physical changes of the moving plane waves. |
Cosmology
| Term | Meaning in WSM |
|---|---|
| Infinite eternal Space | The immediate deduction from P1: as the one substance, Space cannot be bounded, created or interrupted by another substance. Matter and all wave motion exist within it. |
| Unbounded matter network | Matter and organised structure continue beyond every finite Huygens sphere. If matter ended, boundary e-spheres would lose equal all-direction support and an isolated finite domain would collapse. Local structures are finite; the connected matter network has no edge. |
| Observable Huygens sphere | The finite, observer-centred domain whose ordered waves can participate in one e-sphere’s present physical record. Every e-sphere is the centre of its own sphere; the spheres overlap, and their boundary is neither an edge of Space nor an edge of matter. The exact profile and radius are WSM Action outputs. |
| Mach–Huygens principle | Each e-sphere’s local recurrence and inertia are physically sustained by Huygens-combined in-waves supplied by surrounding matter. Overlapping spheres connect the local domain to external matter, so local physics contains the action of the wider matter distribution. |
| External Huygens support | The reciprocal waves supplied by matter beyond any one observable Huygens sphere. They sustain its e-spheres and make the domain physically connected to the wider matter network. WSM identifies this support as the candidate source of the large-scale non-collapsing response called dark energy; that bulk response is distinct from the all-direction support requirement. |
| Common Huygens overlap | The part of the source’s and receiver’s effective Huygens support shared by both. Its decrease with separation joins curve decay to the smaller completed receiver transformation and therefore contributes directly to WSM redshift. |
| Source curve train | The finite ordered sequence of changed displacement, phase, curvature and conjugate motion written onto successive longitudinal plane waves by a bound transition. |
| Carrier, modulation and event envelope | Three time scales in one physical history: the fundamental plane-wave recurrence, the transition’s changing pattern and the macroscopic luminosity record. A cosmological redshift law must map all relevant scales consistently. |
| Redshift factor \(K(D)\) | The common source-to-receiver factor required by \(K=1/(1+z)\). WSM’s proposed mechanism combines source-written curve spreading, diminishing Huygens overlap and smaller-gap receiver reclosure. It must produce the same factor for spectral periods and complete event histories while the travelling background planes retain their spacing. |
| Statistical stationarity | The cosmological working assumption that, after environment and observational selection are accounted for, the distribution of developmental stages repeats statistically across sampled times and transfer depths. Eternal Space has no universal creation time; eternity alone does not require an unchanging population distribution. |
| High-redshift structure | With statistical stationarity and redshift interpreted as transfer depth, mature galaxies, heavy elements and massive black holes continue to occur at large redshift without a cosmic-age ceiling. The qualitative consequence follows under these premises; the selected population distribution is the quantitative test. |
| Luminosity distance \(D_L\) | The distance inferred from received flux after source luminosity, energy transfer, arrival-rate transfer and geometric spreading are specified. Its WSM relation is an output of the complete transport calculation. |
| Angular-diameter distance \(D_A\) | The relation between a source’s physical transverse size and its observed angle. Raw Euclidean propagation and reciprocity-weighted propagation are distinct candidate branches until the wave-bundle action selects one. |
| Distance reciprocity | The observed relation among source area, receiver area, frequency, arrival rate and solid angle. Naming reciprocity does not derive it; the WSM transverse phase-space map must reproduce it or predict a measured alternative. |
| CMB equilibrium state | The proposed microwave statistical equilibrium organisation of the same Vibrating Space, distinct from the matter-sustaining background carrier. Its Planck spectrum, absolute temperature and distortions must be derived through resonant exchange with matter. |
| \(T(z)\) | The temperature sampled locally by matter at the source relation corresponding to observed redshift \(z\). Redshifting the spectrum received here does not by itself derive the temperature experienced there. |
| Visibility kernel | The distance-, direction- and frequency-dependent weighting that determines which source-written structures survive coherently into the received sky. One kernel must connect CMB anisotropy, polarisation, damping, lensing and BAO rather than fitting each independently. |
| Expansion of Space | An interpretation assigned to redshift and distance relations in FLRW cosmology, not an observed local motion and not a physical process in WSM. WSM describes the observations through real waves propagating and being reconstructed in non-expanding Space. |
Reality, causality and knowledge
| Term | Meaning in WSM |
|---|---|
| Causal connection | A continuous physical wave relation in which a changed curve or \(E_d\) changes \(c'\), wavelength, arrival phase and the later reconstruction of another e-sphere. |
| Necessary connection | The One Law makes the causal sequence necessary: changed directional \(E_d\) entails changed \(c'\); changed \(c'\) entails changed wavelength and arrival phase; changed phase entails changed spherical reclosure and motion. |
| Hume’s problem of causation | Repeated observation alone shows succession but not why one event must follow another. WSM locates that necessity in the continuous wave connection and the One Law joining each physical change to the next. |
| Kant’s thing-in-itself | The observer, observed object and signals between them are organisations and motions of the same Space. The reality behind appearances is therefore not a separate unknowable realm: it is the common vibrating Space causally producing both the object and its representation. |
| Truth | A representation that corresponds to the physical reality causing it. |
| Absolute truth | The one infinite, eternal, continuous Space and its real wave motion as the common cause against which every finite representation can be tested. |
Ontology and language guardrail
- Space does not flow, stream or circulate through itself.
- Space is not an ordinary material solid made from atoms and has no primitive transverse shear waves.
- A longitudinal wave means Space vibrates in the same direction that the wave travels.
- Spin is not a rigid electron surface or circular path rotating around an axis.
- The e-sphere has no reflecting material shell.
- \(j_0\) and \(j_1\) quadratures do not multiply the number of Dirac states.
- There are no invented reciprocal reconstruction grades in the Dirac state count.
- Complex numbers, spinors, fields and probabilities are mathematical representations, not extra substances.
- A photon is not a pellet travelling through empty space.
- Collective transverse geometry may be formed by longitudinal waves travelling in different directions; no individual Space wave vibrates sideways.
- Do not call an interaction merely a “completed event”; name the source transition, curve train, receiver deformation and new stable standing-wave mode.