A complete degrees-of-freedom inventory for photons and phonons — what each one can carry, what only one of them can carry, how they couple, and which of it we are currently leaving on the table.
| part | what it is | what it holds or does |
|---|---|---|
| Store | phase-change holographic medium | pattern files — chords, transforms, the library. Non-volatile, rewritable, associative |
| Compute core | optical cavity (EML toroid) + written transforms | the live holographic state; the bridge in both directions between chamber and store |
| Chamber | a boundary-controlled volume | where photonic and phononic fields are created, controlled and measured, and where they act on matter |
That is the whole machine; everything else in the paper set is detail of how one of the three is built. Since the chamber's entire job is field control, the machine's capability ceiling is set by how many independent handles the two carriers offer, and how many we actually use.
Grouped by kind, not by convenience. Every entry is an independently addressable property of a light field.
| # | degree of freedom | what it is | range / quantum |
|---|---|---|---|
| Scalar, per mode | |||
| 1 | Amplitude | field magnitude |E|; intensity ∝ |E|² | continuous |
| 2 | Phase | arg(E) — absolute and, more usefully, relative between ports | continuous, mod 2π |
| 3 | Frequency | ω; and its time-derivative, chirp | continuous |
| Internal (vector) — the "spin" family | |||
| 4 | Polarisation = spin angular momentum (SAM) | the E-vector's orientation/handedness. This is photon spin | exactly 2 states, ±ħ per photon |
| 5 | Longitudinal field component | absent in a free plane wave; present in tightly-focused, evanescent and structured fields — including our toroidal pulses | continuous |
| External (spatial) | |||
| 6 | Wavevector direction k | propagation direction; in a cavity, the mode index | discrete in a cavity |
| 7 | Orbital angular momentum (OAM) | azimuthal phase winding eilφ — a vortex | unbounded integer l, lħ per photon |
| 8 | Transverse spatial mode | the full field profile — Hermite–Gauss, Laguerre–Gauss, Bessel | a complete basis |
| Temporal, and mixed | |||
| 9 | Temporal envelope / pulse shape | the mode in time, dual to the spectrum | continuous |
| 10 | Space–time nonseparability | fields that cannot be written as (space)×(time) — toroidal and toroidal-helical pulses live here | a structural property, not a number |
| 11 | Space–polarisation nonseparability | vector beams: polarisation varies across the beam. Poincaré beams, optical skyrmions | a structural property |
| Statistical and quantum | |||
| 12 | Coherence | temporal (linewidth) and spatial (mutual coherence) — how well phases hold across time and aperture | continuous |
| 13 | Photon number / quantum state | Fock, coherent, thermal; squeezing; entanglement | quantum |
The same grouping, and one enormous difference at entry 4 that governs much of the machine's design.
| # | degree of freedom | what it is | range / note |
|---|---|---|---|
| Scalar, per mode | |||
| 1 | Amplitude | pressure, or particle displacement / velocity | continuous |
| 2 | Phase | as for light — the holographic handle | continuous |
| 3 | Frequency | Ω; strongly dispersive in structured media, unlike light in free space | continuous, band-limited |
| Internal (vector) — where phonons differ radically | |||
| 4 | Polarisation | In a fluid (air, melt): longitudinal only — fluids carry no shear. In a solid: three branches — 1 longitudinal + 2 transverse (shear) | 1 in fluid, 3 in solid |
| 5 | Surface / guided modes | Rayleigh (elliptical, retrograde), Lamb (plate: symmetric + antisymmetric), Love (shear-horizontal), Stoneley (interface) | a family with no optical analogue this rich |
| 6 | Acoustic spin | local elliptical trajectory of the velocity field. Long thought impossible for longitudinal waves; established for structured sound (evanescent, interfering) since ~2019 | real, and easy to overlook |
| External (spatial) | |||
| 7 | Wavevector direction q | direction; cavity mode index | discrete in a cavity |
| 8 | Acoustic OAM | acoustic vortex beams, eilφ — carries torque, spins trapped particles | unbounded integer l |
| 9 | Transverse mode structure | full pressure-field profile; the holographic handle for shaping | a complete basis |
| Temporal, nonlinear, and material | |||
| 10 | Temporal envelope | pulse shape; time-of-flight is the ranging observable | continuous |
| 11 | Nonlinear products | harmonics, and difference-frequency — the parametric array: two ultrasonic beams generate a low-frequency beam along their overlap | strong; sound is far more nonlinear than light |
| 12 | Mode conversion | L↔T at interfaces and boundaries — no optical equivalent | a boundary phenomenon |
| 13 | Dispersion engineering | phononic-crystal band structure, band gaps, slow sound, negative index | the metamaterial handle |
| property | photon | phonon | consequence for the machine |
|---|---|---|---|
| polarisation states | 2 (transverse only, free space) | 1 in fluid, 3 in solid | the solid plates have a shear channel the air volume simply does not; mode conversion at the plate face is a real, usable handle |
| speed | 3 × 10⁸ m/s | ~343 (air) to ~5000 m/s (solid) | see §5 — this is the single most important number in the architecture |
| momentum per unit energy | tiny (E/c) | ~10⁵–10⁶ × larger (E/v) | sound moves matter; light does not — per watt. At µm-and-below payloads light's direct gradient traps become the precision channel (R1-b, 2026-08-01: sound is the hands, light is the fingertips — The Photons §3b) |
| nonlinearity | weak in ordinary media | strong — harmonics and parametric mixing are easy | acoustic difference-frequency generation is available almost for free |
| dispersion | weak in free space | strong, engineerable via structure | rainbow trapping, band gaps, slow sound — the passive multiplexing of the panels |
| medium required | none | yes — no sound in vacuum | the chamber must contain a medium; the compute cavity need not |
| surface-wave family | plasmons, limited | Rayleigh, Lamb, Love, Stoneley | the plates and panels are wave-guiding structures, not just radiators |
At the same frequency, sound's wavelength is about five orders of magnitude shorter than light's, because the speeds differ by that much:
| frequency | light | sound in air | sound in solid |
|---|---|---|---|
| 1 kHz | 300 km | 343 mm | 5 m |
| 1 MHz | 300 m | 343 µm | 5 mm |
| 1 GHz | 300 mm | 343 nm | 5 µm |
Sound buys fine spatial structure at low frequency; light buys speed and bandwidth at coarse structure. A GHz sound wave in a solid has a 5 µm wavelength — comparable to visible light — which is exactly why an acoustic wave can act as a diffraction grating that light can see. Having both carriers is not redundancy. It is the only way to get fine structure and high bandwidth in the same instrument.
| mechanism | direction | what happens |
|---|---|---|
| Photoelastic / acousto-optic | phonon → photon | strain changes refractive index; sound becomes a moving grating that diffracts light. The workhorse |
| Electrostriction | photon → phonon | the optical field creates strain — the inverse of the above |
| Brillouin scattering | both, resonantly | light scatters off an acoustic wave and shifts by exactly the acoustic frequency. Stimulated Brillouin is the strong version: light generates the sound that scatters it |
| Radiation pressure / optomechanics | photon → phonon | light pushes a boundary; the boundary's motion phase-modulates the light. Weak per watt, but the basis of cavity optomechanics — and of the dynamical Casimir effect at the extreme |
| Thermoelastic (photoacoustic) | photon → phonon | absorbed light heats, thermal expansion launches sound. Inefficient, deposits heat, but works in any absorbing target |
| Piezoelectricity | EM field ↔ phonon | not photon-to-phonon directly, but the machine's actual transducer: field ↔ strain at near-unity coupling in single-crystal relaxors |
| Raman scattering | photon ↔ optical phonon | couples to molecular vibration rather than bulk sound — the machine's composition sensor |
| Phonon-polariton | hybrid | in polar dielectrics, an optical phonon and a photon mix into one quasiparticle. The "mixing angle" element of the transducer roadmap |
the_replicator.html §6.10 and
replicator_field_compiler.html §17.6, and is now the canonical
home for the crossings; the compiler paper keeps its software-facing §17.6
copy until its next revision, then links here.Section 6 lists the coupling mechanisms — the element-level physics (piezo, PMUT, the polaritonic roadmap row). What that leaves unexploited is the crossing in the build volume itself: the two carriers interacting in flight, in air and in melt, because sound is a density wave and density sets the refractive index. The currency of these crossings is not power — photon momentum per watt is ~10⁶× below phonon momentum, the same arithmetic that rejects radiation pressure as a drive (the parametric bound, below). It is addressing, verification, and measurement diversity — exactly the quantities the compiler's scan program identifies as binding.
| crossing | mechanism | machine verb | register |
|---|---|---|---|
| sound steers light | photoelastic Δn: the acoustic hologram is a volumetric, reprogrammable GRIN optic, refreshed at microsecond rate | in air, deflection stays ~10⁻⁴ rad — a fine-trim and modulation channel on the axial sightline, not steering; genuine beam shaping belongs to the melt or coupling fluid (correction below), where the acoustic field focuses the optical channel onto the workpiece | commodity acousto-optic modulator art MEASURED |
| light reads sound | the same Δn, run as metrology: schlieren / refracto-vibrometry through the volume | full-field optical tomography of the drive field, a calibration path physically independent of the RX microphone chain. Attacks the Green's-function trust problem head on: the drive field stops being inferred and becomes photographed — a second witness | schlieren imaging of ultrasound; laser refracto-vibrometry MEASURED |
| light writes sound | photoacoustic launch: a modulated/pulsed beam absorbed at a surface radiates ultrasound from that spot | a programmable acoustic source aperture on any optically visible surface, including the workpiece — position diversity for the scan (new rows in the measurement operator, nothing moving, no added transducers), and an optically-placed tap for call-and-response: tap with light, listen with the whole screen. Per ruling R2, spot-scanning is merely this operator's delta basis and the worst one — patterned (Hadamard-class) bases carry the multiplex SNR advantage | laser-ultrasonics, NDT art; structured-illumination photoacoustics MEASURED |
| sound bridges µW↔optical | piezo-optomechanical transduction: a phonon mode coherently coupled to both bands | the polaritonic element's end state; carrier hand-off inside one device | quantum-transduction literature MEASURED; in-machine use OPEN |
155 dB → p = 1,125 Pa Δn = 2.3e-6 1.38 optical waves over 300 mm θ 1.6e-4 rad 165 dB → p = 3,557 Pa Δn = 7.3e-6 4.37 optical waves over 300 mm θ 5.1e-4 rad 175 dB → p = 11,247 Pa Δn = 2.3e-5 13.8 optical waves over 300 mm θ 1.6e-3 radSo Δn ~ 10⁻⁵ and "several optical wavelengths of accumulated phase" are both correct at the kPa class the muscle channel reaches.
REPLICATOR_CAP_STACK_RULINGS_2026-07-30.md, R1. Coherent
phonon↔photon amplification (Brillouin gain in the melt) is real
physics but belongs on the roadmap shelf beside the polaritonic element,
not in the baseline OPEN.
(ii) Corrected 2026-07-27: the claim that photoelastic
coupling makes sound-steers-light "orders stronger" in the melt needs care —
at equal pressure a liquid is worse, not better: water gives
Δn ~ 5×10⁻⁷ against air's 7×10⁻⁶ at the same 3.5 kPa, because ρc² is
~10³× larger, so the same pressure buys far less density change. The real
advantage in melt or coupling fluid is that it admits far higher drive
pressures and a different acousto-optic figure of merit
(M₂ = n⁶p²/ρv³, where the lower sound speed helps), not a larger response
per pascal. State it that way or the number will propagate wrong.
Why this is the same doctrine, not a new one: each crossing is holographic synthesis extended from the boundary into the volume — one carrier plays the reference wave, and the other carrier's modulation of the medium is the recording. The boundary surfaces are computed holograms in a fixed medium; the volume crossings are computed holograms in each other's medium.
The point of the inventory. USED is in the design today; PARTIAL is named but not exploited; UNUSED is a handle we have not spent at all.
| degree of freedom | status | where it is, or what it would buy |
|---|---|---|
| amplitude, phase, frequency (both carriers) | USED | the chord alphabet is exactly these three |
| optical polarisation / SAM | USED | handedness of the toroidal-helical launch; anisotropic holography makes it an aperture property. (rev 2026-08-01, per R4: chirality is now doctrine, not incident — driven structures are chiral and separately addressable, passive structures achiral and neutral; handedness is a drive-side knob on both carriers) |
| space–time nonseparability | USED | the toroidal pulses; the super-resolution positioning signature depends on it |
| transverse mode structure (both) | USED | holographic shaping is mode-basis synthesis |
| acoustic dispersion engineering | USED | the graded hex screen; rainbow trapping |
| optical OAM | PARTIAL | implicit in the helical pulses, never used as an independent addressing channel — an unbounded integer index we currently spend as a single bit of handedness. (rev 2026-08-01, per R2-b/R13: the bore optical stem is now a full TX/RX holographic port — toroidal-pulse chords out, density-matrix tomography back — and skyrmion-class topological structure is a named register; the unbounded integer l as a per-channel address is still unspent) |
| acoustic OAM | USED (was PARTIAL) | discussed as vortex trapping; not in the chord format. It carries torque — the natural way to rotate a workpiece without touching it. (rev 2026-08-01, per R3/R4: the cap front end's 3-PZT throat ring synthesizes acoustic OAM m = ±1 by phasing alone — drive-side chirality, no geometric doubling — so acoustic OAM is now in the drive architecture, not merely discussed) |
| shear / transverse phonons in the plates | PARTIAL | the solid has 3 polarisations and we drive essentially one. Mode conversion at the face is free and unexploited |
| surface-wave family (Rayleigh/Lamb) | PARTIAL | the panels are plates — Lamb modes exist whether or not we design for them. Designing for them turns the panel into a waveguide, not just a radiator |
| acoustic nonlinearity / parametric array | UNUSED | two ultrasonic beams generate a difference-frequency beam along their overlap only — a way to place low-frequency energy at a point without a low-frequency aperture. Directly attacks the long-wavelength addressing problem |
| acoustic spin | UNUSED | a local, independently-addressable vector property of structured sound fields |
| angular-momentum transfer sound → light (and topology as a register) | PARTIAL (was UNUSED) | the conservation law says it is available; it would let the acoustic field write topology into the optical readout. (rev 2026-08-01, per R13: topology is now a deliberate register on both carriers — the topological alphabet adopts a measured skyrmion-number extraction toolkit explicitly applicable to acoustic and elastic waves, plus programmable topological TX; the specific sound→light transfer verb itself remains undemonstrated in-machine) |
| optical squeezing / quantum state | UNUSED | sub-shot-noise sensing. Relevant only once the readout is shot-noise-limited — not yet, and worth knowing why not |
| longitudinal optical field component | PARTIAL | present in the toroidal pulses by construction, never treated as a separate handle |
The audit's finding: the machine currently spends amplitude, phase and frequency well, spatial structure adequately, and angular momentum hardly at all. The largest untouched handles are acoustic OAM (torque without contact), the parametric array (low-frequency placement without a low-frequency aperture), and the shear channel in the solid plates. None of these require new physics — they require putting a column in the chord format.
Amendment 2026-08-01 (per R1–R14,REPLICATOR_CAP_STACK_RULINGS_2026-07-30.md): the angular-momentum verdict has partly aged, exactly as this audit predicted it would. Acoustic OAM is now spent (R3/R4 drive-side phasing), chirality is doctrine (R4), and topology is a named register on both carriers (R13). Still on the table: optical OAM as a per-channel integer address, the parametric array, acoustic spin, and the shear channel in the plates.