What State Of Matter Is It?
Two earlier memos reached conclusions that disagree. Resolving them picks out one specific state of matter, predicted fifty years ago and produced in 2019.
The fluid option fails badly. A frictionless fluid has no sideways grip by definition, and liquid helium is the case in point: ninety years of work has found four kinds of sound in it, every one travelling lengthways. No fluid carries a sideways wave, so no fluid can carry light. The solid option fails the other way — it would have ended the Earth’s orbit within weeks.
There is a third state that has both properties at once: crystalline order, and a component that flows without friction. It was predicted independently by three physicists between 1969 and 1970, and made in a laboratory by three groups in 2019. Nothing about it is proposed here; only its application.
One thing has not been checked, and it decides everything: whether such a state can grip sideways as firmly as light requires. In the ones that have been made, the grip is weak.
Proven in this memo
- A frictionless fluid cannot carry a sideways wave, and therefore cannot be the medium light travels in. A sideways wave needs a restoring shear stress; a fluid has none.
- Neither of the two familiar states of matter satisfies both requirements — one carries light and stops the planets, the other lets the planets through and cannot carry light.
That a supersolid is the answer is a proposal, not a proof. It has both properties, and it is a real state of matter — but whether it can be as stiff as this framework requires has not been calculated, and section 7 says so.
Draft. A working draft, published for scrutiny rather than as a settled result. The ledger at the foot records what is derived, what is measured, what is assumed and what remains unanswered.
This memo resolves a contradiction between two earlier ones. Memo 1.4 concluded the Aether is a solid. Memo 1.10 concluded it flows without resistance. Both cannot be true of the states of matter most people have heard of.
1. Two Jobs, And They Look Incompatible
Two earlier memos each reached a firm conclusion, and the conclusions disagree.
Memo 1.4: light waggles sideways, a sideways wave needs a material that grips sideways, therefore the Aether grips sideways. That is what makes something a solid.
Memo 1.10: if the Aether resisted matter moving through it, the Earth would have spiralled into the Sun within weeks. It does not resist. That is what makes something a fluid — and a very particular sort of fluid, one with no friction at all.
| Requirement | Where it comes from | What it means |
|---|---|---|
| Grips sideways | Light is polarised | It is a solid |
| No resistance to matter | The planets still orbit | It is a frictionless fluid |
A thing cannot be a solid and a fluid. So either one of the two memos is wrong, or there is a state of matter that is not on the usual list.
2. A Frictionless Fluid Cannot Carry Light
It is worth being clear how badly the fluid option fails, because it is the one that first looks attractive.
Liquid helium below about two degrees above absolute zero becomes a superfluid. It has no friction whatever. It flows through cracks too fine for any ordinary liquid, climbs the walls of its container, and lets objects move through it with no resistance. This is the substance memo 1.10 pointed at, and it is exactly what the drag problem needs.
But it cannot carry a sideways wave. Superfluid helium carries four distinct kinds of sound, and physicists have numbered them:
| Mode | What waves | Direction of motion |
|---|---|---|
| First sound | Pressure and density | Along the travel direction |
| Second sound | Temperature | Along the travel direction |
| Third sound | The surface of a thin film | Along the travel direction |
| Fourth sound | Density, in a porous solid | Along the travel direction |
ProofA frictionless fluid cannot be the medium of light
A sideways wave exists only where the material resists being sheared. That resistance is the restoring force: displace a layer sideways, and what pulls it back is the shear stress.
A fluid, by definition, has no shear resistance. Slide one layer over another and nothing pulls it back — which is why fluids flow. A frictionless fluid has even less: not merely weak resistance but none at all.
So no fluid carries a sideways wave, and superfluid helium is the case in point. Four sound modes have been found in it over ninety years of work, and every one moves along the direction of travel.
Light is a sideways wave. A frictionless fluid therefore cannot be what light travels in. This is not a difficulty to be worked around; it is a straight contradiction.
Chain: a sideways wave needs a restoring shear stress → fluids have none → no fluid carries one. Premise: light is transverse, established in memo 1.4 from polarisation.
3. And An Ordinary Solid Cannot Let Matter Through
The other option fails just as cleanly. A solid grips sideways, so it carries light — but it also resists anything moving through it, and the resistance is not small. Work out what the Earth would experience ploughing through a medium of this density at orbital speed and the answer is a force that would have ended its orbit within weeks of the solar system forming.
So neither of the two familiar states will do. One carries light and stops the planets; the other lets the planets through and cannot carry light.
4. The State That Does Both
There is a third option, and it is not a compromise between the two — it genuinely has both properties at once. It is called a supersolid.
A supersolid has crystalline order: its particles sit in a regular arrangement, which is what gives it something to grip sideways with. And it simultaneously has a component that flows with no friction, the way a superfluid does. Both at the same time, in the same material.
| Requirement | Ordinary solid | Frictionless fluid | Supersolid |
|---|---|---|---|
| Carries sideways waves | Yes | No | Yes |
| No resistance to matter | No | Yes | Yes |
| Circulation in exact units | No | Yes | Yes |
How something can be both
It sounds like a contradiction and it is not. The trick is that the material has two things going on in the same place at once — an ordered arrangement that holds its shape, and a portion of it free to move through that arrangement without rubbing on it.
The nearest everyday comparison is poor but useful: imagine a scaffold with water running through it. The scaffold gives the structure its rigidity; the water passes through without the scaffold resisting. In a supersolid both are made of the same particles, which is what makes it strange — but the effect is that one material does two jobs that normally require two.
5. It Was Predicted, Then Made
This is not a state invented for the purpose. It has a fifty-year history.
1969 to 1970. Andreev and Lifshitz, then Chester, then Leggett, each independently argued that a solid could in principle have a frictionless component. It was a theoretical prediction with no known example.
2004. Kim and Chan reported evidence for it in solid helium-4. The result was later reinterpreted as a change in the helium's stiffness rather than supersolidity, and the helium case remains unsettled.[4,5]
2019. Three groups independently produced supersolids in ultracold gases of dysprosium and erbium, and published within months of each other.[1,2,3] That case is not contested.
Why the history matters
If this memo had invented a state of matter with exactly the two properties needed, that would be a fair thing to object to. It did not. The state was proposed on theoretical grounds five decades ago by people with no interest in the Aether, and it was made in a laboratory before this framework needed it.
That does not make the Aether a supersolid. It makes the proposal an ordinary one rather than a special plea.
6. It Answers A Third Question Unasked
The same property delivers something the framework needed elsewhere.
Circulation round a vortex in a frictionless material comes in exact units — never a half unit, never one and a third. It is not a matter of how carefully the vortex is made; the amount is fixed by the geometry of going round a loop and coming back to the same place. This was measured in liquid helium in the 1960s.
Electric charge behaves the same way. Every electron carries the same charge as every other, to one part in 1021. Not approximately the same — identically, with no spread to measure.
So the state of matter chosen to answer the light-and-drag problem also supplies the reason charge comes in exact units. One assumption, three results. That is developed in memo 4.3.
7. What Has Not Been Checked
One thing, and it is the thing that decides whether any of this works.
The grip has to be enormous. Memo 1.3 requires a sideways stiffness of 8.1 × 1016 pascals — some hundred and fifty thousand times that of diamond. That is what carrying light at its measured speed demands, and it is not negotiable.
In the supersolids that have been made, the ordered part is a small fraction of the whole and the grip is correspondingly weak. Whether a supersolid can be arranged with a grip of that magnitude has not been calculated, and nothing in this series has shown that it can.
Nobody has made one like this
The supersolids that exist are dilute and grip weakly, and those two facts go together. The Aether is proposed to be dilute by weight — 0.9 kilograms per cubic metre, lighter than air — but packed by count in a way nothing else is.
Count the particles rather than weighing them and a laboratory supersolid holds about 1020 per cubic metre. Air holds 1025. The Aether would hold at least 1063, and possibly 10104. Each particle unimaginably light, and unimaginably many of them.
That regime has never been made. Which is why the stiffness question is open rather than answered: the weak grip of the laboratory examples may be a fact about being dilute in number, and this proposal is not.
The honest position
Two requirements that looked incompatible turn out to pick out one specific state of matter, which was predicted independently fifty years ago and has since been produced. That is a good deal better than a contradiction.
But it is not a solution yet. The question has moved from is there such a state? — yes, there is — to can such a state be this stiff? That has not been answered, and until it is, this memo has relocated the problem rather than removed it.
8. What Would Prove This Wrong
- A calculation showing a supersolid cannot reach the required stiffness would break it. Both earlier memos would then stand in contradiction with no resolution available, and one of them would have to be wrong.
- A sideways sound wave found in a frictionless fluid would remove the need for this memo entirely. Ninety years of work on liquid helium has found four sound modes and no such wave.
- Measurable drag on a planet or spacecraft, beyond what known effects account for, would falsify memo 1.10 and with it the reason this memo exists.
- Supersolidity turning out to be an artefact would remove the third option. The 2019 ultracold results would have to fail replication, having been produced independently by three groups.
9. The Numbers
In summary, the figures behind the argument:
- Jobs the medium has to do at once: two.
- Familiar states of matter that do both: none.
- Sound modes found in a frictionless fluid, all of them lengthways: four.
- Years between the supersolid being predicted and being made: fifty.
- Independent groups that made one in 2019: three.
- Sideways stiffness the Aether requires: 8.1 × 1016 Pa, and whether a supersolid can reach it is unknown.
Terms Used Here
| Word | What it means |
|---|---|
| Aether | The substance filling all space. One kind of particle, packed everywhere, which light travels through and which matter is built from. |
| Aetheron | The single particle the Aether is made of. One mass, one size, one magnetic strength — every one identical to every other. |
| Lattice | The regular three-dimensional arrangement the Aetherons settle into, like atoms in a crystal. Its spacing is the one number in this framework still unknown. |
| Shear stiffness | How hard a material resists being pushed sideways, one layer sliding over another. Fluids have none. |
| Sideways wave | A wave where the material moves across the direction of travel, like a shaken rope. Light is one. |
| Squeeze wave | A wave where the material moves the same way the wave goes, like sound in air. |
| Polarisation | The orientation of a sideways wave. Polarised sunglasses block one and pass the other. A squeeze wave cannot have it. |
| Deep space | The Aether far from any matter, at its natural density of about 0.9 kg per cubic metre. |
| Magnetic moment | How strong a magnet something is. A circulating charge produces one. |
Every term used across the series is on the terms page.
10. Sources
Reference codes read source.work.passage and resolve on the Master Source Register, which carries every source used across this series.
- L. Tanzi et al. Observation of a Dipolar Quantum Gas with Metastable Supersolid Properties, Physical Review Letters 122 (2019) 130405. Carried as reported; not verified against the original.
- F. Böttcher et al. Transient Supersolid Properties in an Array of Dipolar Quantum Droplets, Physical Review X 9 (2019) 011051. Carried as reported; not verified.
- L. Chomaz et al. Long-Lived and Transient Supersolid Behaviors in Dipolar Quantum Gases, Physical Review X 9 (2019) 021012. Carried as reported; not verified.
- E. Kim & M. H. W. Chan. Probable observation of a supersolid helium phase, Nature 427 (2004) 225–227. The claim in solid helium-4. Carried as reported; not verified.
- J. Day & J. Beamish. Low-temperature shear modulus changes in solid 4He and connection to supersolidity, Nature 450 (2007) 853–856. The reinterpretation that unsettled the helium case. Carried as reported; not verified.
- A. F. Andreev & I. M. Lifshitz (1969); G. V. Chester (1970); A. J. Leggett (1970). The independent theoretical predictions. Carried as reported from secondary sources; volume and page details not verified.
- W. F. Vinen. The detection of single quanta of circulation in liquid helium II, Proceedings of the Royal Society A 260 (1961) 218. Circulation measured in exact units. Carried as reported; not verified.
- L. D. Landau & E. M. Lifshitz. Theory of Elasticity, Course of Theoretical Physics Vol. 7. Why a sideways wave requires shear resistance. 75
Verification register: references 1 to 7 are carried as reported from secondary sources and have not been checked against the originals. The 2019 results are cited here as the basis for a load-bearing claim and should be read before publication. The four sound modes in section 2 are standard textbook material and are not individually sourced.
Ledger — memo 1.11
- Derived
- That a frictionless fluid cannot carry a sideways wave, and therefore cannot be the medium of light
- That neither of the two familiar states of matter satisfies both requirements
- That a supersolid satisfies both, and additionally supplies circulation in exact units
- Measured
- Four sound modes in superfluid helium, all lengthways — ninety years of work, no sideways wave found
- Supersolidity in ultracold dipolar gases, three independent groups, 2019
- Circulation in exact units in liquid helium (Vinen, 1961)
- Charge identical between electrons to one part in 1021
- Assumed
- That light is a sideways wave, from memo 1.4. If light is not transverse, the whole argument is unnecessary — but polarisation has been observed since 1669.
- That matter moving through the medium would otherwise be slowed, from memo 1.10. If there is some other reason for no drag, a supersolid is not required.
- That the Aether is a single substance in a single state throughout. A mixture, or different states in different regions, would change the argument and is not considered here.
- Open
- Whether a supersolid can be as stiff sideways as light requires. Memo 1.3 needs 8.1 × 1016 Pa. In the supersolids that have been made, the ordered fraction is small and the grip weak. This has not been calculated and it decides everything
- The density regime is unlike anything made. Laboratory supersolids hold about 1020 particles per cubic metre and grip weakly. The Aether would be lighter than air by weight while holding at least 1063 particles per cubic metre — dilute in mass, packed in number. Whether the weak grip of the laboratory examples is a consequence of being dilute in number, which this is not, has not been examined
- The helium-4 case remains unsettled, so the only firm evidence is from ultracold gases at temperatures and densities nothing like those proposed here
- Prior art
- Andreev & Lifshitz (1969), Chester (1970), Leggett (1970) — the supersolid was predicted by them, independently, on theoretical grounds. Nothing about the state is proposed here
- Tanzi, Böttcher and Chomaz groups (2019) — the observations
- Vinen (1961) — quantised circulation, which section 6 borrows
- The application to the Aether is the only part not taken from the existing literature