The Three Waves
The Aether carries a compression wave, a twist wave and a shear wave. Nothing in nature can excite the first two, and the third is light.
Draft. This memo is a working draft, published for scrutiny rather than as a settled result. Figures, derivations and conclusions are open to revision, and the ledger at the foot records what is derived, what is measured, what is assumed and what remains unanswered. Where a number is carried from a secondary source and not verified against the original, the sources section says so.
The TOE series supersedes the earlier A Classical Aether Model and Governor Atom Model white papers one memo at a time. Where this memo and those papers disagree, this memo is the later position.
Proven in this memo
- A superluminal longitudinal mode is unavoidable in any stable solid once light is identified with the transverse wave. It cannot be tuned away by any choice of elastic constants.
- That mode has no source: conservation of mass removes monopole radiation and conservation of momentum removes dipole radiation, leaving quadrupole, which is transverse.
The twist-branch cutoff in section 5 is a calculation, not a proof, and it depends on a lattice spacing that has not been determined. The ledger states the range over which it holds.
In plain terms
Hit the end of a steel rail and you send a squeeze down it — the metal moves the same way the wave goes. Shake it sideways and you send a side-to-side wave. Twist one end and you send a twist wave. Three different disturbances, all in the same rail, and which one you get depends entirely on what you do to it.
The Aether has all three. Only one of them is ever seen, and that one is light. The other two are not missing — they are barred, and each is barred for a different reason.
The squeeze wave would need someone to create or destroy matter in one place, rapidly. Nothing can, because matter is conserved. So the wave exists and is permanently silent.
The twist wave needs a minimum pitch before it will sound at all, like an organ pipe that will not speak below a certain note. That minimum sits about a million billion times higher in energy than the most violent gamma rays ever detected.
The side-to-side wave has no threshold and nothing blocking it. Anything that shakes an electric charge makes one. That is why everything we see is light.
1. The numbers
- Wave types an elastic solid carries: three.
- Wave types ever observed: one.
- Longitudinal speed: √3 c — 5.193 × 108 m/s.
- Minimum ratio of longitudinal to transverse speed in any stable solid: 1.155.
- Twist-branch cutoff: ~1019 GeV, against 106 GeV for the most energetic photon ever detected.
2. The three modes
A micropolar elastic solid — one whose particles carry independent rotation as well as position — supports three kinds of wave.
| Mode | Motion | Speed |
|---|---|---|
| Longitudinal | Along the direction of travel | √((K + 4G/3)/ρ) |
| Transverse acoustic | Across the direction of travel | √(G/ρ) |
| Transverse optical | Particle rotation, coupled to displacement | gapped — see section 5 |
The first two exist in any ordinary solid. The third appears only where the medium resists being turned as well as being sheared, which the Aether does because its particles carry aligned magnetic moments.
3. The longitudinal wave is faster than light
Using the elastic constants from memo 1.3, with K/G = 5/3:
So the compression wave travels at 5.193 × 108 m/s, or 1.73 times the speed of light. This is not an artefact of the particular value of K/G.
ProofEvery stable solid carries a superluminal mode, given this identification
For an isotropic solid, cL/cT = √(K/G + 4/3). Mechanical stability requires K ≥ 0 — a material with negative bulk modulus collapses on itself, since compressing it would make further compression easier.
Therefore cL/cT ≥ √(4/3) = 1.155, with equality only in the limiting case of zero bulk modulus.
Once the transverse wave is identified with light, as memo 1.4 requires, the longitudinal wave is necessarily faster than light. There is no choice of elastic constants that avoids this. It cannot be tuned away, and a model of this kind that claims otherwise has made an error.
Chain: the standard isotropic wave speeds → K ≥ 0 for stability → ratio ≥ √(4/3). Premise: light is the transverse mode (memo 1.4).
4. Why nothing makes a longitudinal wave
A compression wave is created by changing the amount of material in a region — by putting more in or taking some out. In field terms it couples to the mass monopole.
Mass is conserved. No process adds or removes it, so the monopole cannot change and no monopole radiation is produced. The next term is the mass dipole, which is the centre of mass; it does not accelerate, by conservation of momentum, so there is no dipole radiation either. The leading surviving term is the quadrupole — and quadrupole radiation is transverse.
ProofThe longitudinal mode has no source
Longitudinal radiation requires a time-varying mass monopole. Conservation of mass forbids one.
Dipole radiation requires a time-varying mass dipole, which is the centre of mass. Conservation of momentum means the centre of mass of an isolated system does not accelerate, so this vanishes too.
The first non-vanishing multipole is the quadrupole, and quadrupole radiation in an elastic medium is transverse. Therefore no isolated system can emit a longitudinal wave, whatever it does internally.
This is the same argument that gives general relativity no monopole and no dipole gravitational radiation. It is a conservation result, not a property of the Aether.
Chain: multipole expansion → conservation of mass kills the monopole → conservation of momentum kills the dipole → quadrupole is transverse.
So the superluminal mode is real, permitted, and permanently unexcited. It cannot carry a signal because nothing can make one.
5. Why nothing makes a twist wave either
In a micropolar medium the displacement and the particle rotation couple, and the two transverse branches that result behave differently. The acoustic branch propagates at all frequencies. The optical branch is gapped: below a cutoff frequency it does not propagate at all, the way a waveguide passes nothing below its cutoff.
The cutoff sits near the lattice frequency, c divided by the lattice spacing. At Planck spacing that is 1.85 × 1043 rad/s, which corresponds to a photon energy of about 1019 GeV.
| Energy | Source |
|---|---|
| 10−3 GeV | Visible light |
| 1 GeV | Fermi-LAT, routine |
| 106 GeV | LHAASO, most energetic photons observed |
| 1019 GeV | Twist-branch cutoff |
Thirteen orders of magnitude between the most violent photon ever recorded and the threshold. Nothing in the observed universe comes near it.
6. What is left is light
The transverse acoustic branch has no threshold and no conservation law standing in its way. Anything that accelerates a charge excites it. That is light, and it is also gravitational radiation — the same mode in the same medium, which is why they travel at the same speed.
One door of three
One door is bricked up: the squeeze wave would need matter created or destroyed, and nothing can do that. One needs a key nobody has: the twist wave will not start below an energy a million billion times beyond the most violent thing ever detected. The third is wide open.
So a universe with three possible waves shows us one, and it is not because the other two were left out of the design. They are there. Nothing can reach them.
7. What would falsify this
- Detection of a longitudinal gravitational-wave polarisation. LIGO and Virgo can distinguish polarisation content with three or more detectors; GW170814 was consistent with pure tensor. A scalar or longitudinal component would falsify the argument of section 4.
- Any signal travelling faster than light. The model says the channel exists but cannot be opened. If it could be opened, causality goes with it — this is the framework's most dangerous commitment and it should be stated as such.
- Binary pulsar timing. Extra radiation channels would accelerate orbital decay. The Hulse–Taylor system matches general relativity to 0.2%, which caps any additional channel at that level.
8. Sources
Reference codes read source.work.passage and resolve on the Master Source Register, which carries every source used across this series.
- L. D. Landau & E. M. Lifshitz. Theory of Elasticity, Course of Theoretical Physics Vol. 7. The longitudinal and transverse wave speeds, and the stability requirement K ≥ 0 used in section 3. 75
- A. C. Eringen. Microcontinuum Field Theories I: Foundations and Solids, Springer (1999). The micropolar wave branches, the coupling constant, and the gapped optical mode of section 5. 78
- B. P. Abbott et al. (LIGO and Virgo). GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence, Physical Review Letters 119 (2017) 141101. Polarisation content consistent with pure tensor. Cited as reported; not verified against the original.
- J. M. Weisberg & Y. Huang. Relativistic measurements from timing the binary pulsar PSR B1913+16, Astrophysical Journal 829 (2016) 55. Orbital decay agreeing with general relativity, used as the cap on extra radiation channels. Cited as reported; not verified.
- LHAASO Collaboration. Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 gamma-ray Galactic sources, Nature 594 (2021) 33–36. The most energetic photons observed, used in section 5. Cited as reported; not verified.
Verification register: the LIGO, pulsar-timing and LHAASO citations are carried as reported and have not been checked against the originals. The cutoff energy in section 5 depends on the lattice spacing, which is not determined — see memo 1.7.
Ledger — memo 1.5
- Derived
- cL/cT = √3 exactly, from K/G = 5/3
- That any stable solid has cL/cT ≥ 1.155, so a superluminal mode is unavoidable once light is the transverse wave
- That conservation of mass and momentum leave the longitudinal mode with no source
- That the twist branch is gapped at roughly 1019 GeV and cannot be excited by anything observed
- Measured
- Most energetic photons observed, ~1.4 PeV
- Gravitational-wave polarisation content, consistent with pure tensor
- Binary pulsar orbital decay matching general relativity to 0.2%
- Assumed
- K/G = 5/3 from memo 1.3. Sets the √3 exactly; the general result cL/cT ≥ 1.155 does not depend on it.
- The lattice spacing. The cutoff in section 5 scales as c/d, and d is bounded but not determined (memo 1.7). At the upper bound of 6 × 10−22 m the cutoff falls to about 106 GeV — the PeV range, where photons have been observed. The twist-branch argument is therefore only safe at the smaller end of the permitted range.
- That the medium is micropolar, which requires the Aetherons to carry aligned magnetic moments. Without that there is no third branch and no gap to argue about.
- Open
- The superluminal mode is a standing hazard. The argument that nothing can source it is a conservation result and looks sound, but a medium containing a faster-than-light channel is a serious commitment, and the series should not pretend otherwise
- The micropolar coupling κ has not been computed. If it is not small, the identification of the shear modulus with μ alone in memo 1.3 needs revisiting, and the branch speeds change
- Whether a third polarisation could be excited in an extreme astrophysical environment, rather than in a laboratory, has not been examined
- Prior art
- E. and F. Cosserat, 1909 — micropolar continua, media whose points carry orientation as well as position
- A. C. Eringen — the modern formulation, including the gapped optical branch used in section 5
- The conservation argument in section 4 is standard multipole radiation theory and is not original here