The Neutron
A neutron is a hydrogen atom crushed until its electron orbits at close to the speed of light, inside a shell of trapped Aether. Its magnetic moment, spin, mass, size and lifetime all follow from that one picture.
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
- The electron must orbit outside the proton, at more than 0.990 fm. This follows from two measured magnetic moments and the speed of light alone — no force law, no lattice, no model.
- The orbit cannot be the source of the neutron’s spin. Its angular momentum is short by a factor of 65.
- A perpendicular spin axis removes the electron’s own magnetic moment exactly, by symmetry, not by cancellation.
- The configuration cannot exist without an external inward force. Coulomb and centrifugal already cancel, and the ring’s self-field is unopposed.
The rest of the memo — the orbit radius, the shell mass, the tilt angle — is derivation rather than proof: it follows given the assumptions in the ledger.
In plain terms
Squeeze a hydrogen atom hard enough and the electron, which normally orbits a long way out, is driven down onto the proton until it is circling at nearly the speed of light, roughly fifty thousand times closer than it started. At that point the two are locked together and the object is no longer hydrogen — it is a neutron.
The electron racing round in that tiny orbit is an electric current, and a current makes a magnetic field. That is where the neutron's magnetism comes from, even though the neutron has no overall charge: the positive and negative charges cancel, but the motion does not.
The trouble is that a loop of current tries to burst itself open, the way a spinning hoop wants to fly apart. Something has to hold it shut. In this model that something is a shell of Aether, drawn in and packed around the outside by the very field that is trying to tear it open. The neutron builds its own container.
And the container eventually fails. Free neutrons fall apart after about fifteen minutes — but a neutron inside an atomic nucleus lasts forever, because there it has support. That is the difference between a neutron on its own and one that is part of something.
1. The claim, and why it is not new
That a neutron might be a proton and an electron bound together was the standard view before 1932. It was abandoned for good reasons, and those reasons have to be met rather than ignored. They are addressed in sections 7 and 8 and listed in the ledger.
What is proposed here is narrower than the old model: not that a neutron contains a loose proton and a loose electron, but that it is a hydrogen atom driven into a particular compressed configuration and held there by a shell of the surrounding medium. The configuration is what the rest of this memo calculates.
2. Where the magnetic moment comes from
The neutron has no net charge but it does have a magnetic moment, measured as −9.6624 × 10−27 J/T, or −1.913 nuclear magnetons. The minus sign means it points opposite to the neutron's spin.
If the neutron contains a proton, that proton brings its own moment of +2.793 nuclear magnetons with it. So the electron must supply the whole of the difference:
A charge e going round a loop of radius r at speed v produces a magnetic moment μ = evr/2. Setting that equal to (1):
What equation (2) already tells you
Nothing can travel faster than light. So if the product of speed and radius is fixed at 2.967 × 10−7, and the speed cannot exceed 3 × 108 m/s, then the radius cannot be smaller than about 0.99 femtometres.
That is a hard floor, and it needed no theory at all — just two measured magnetic moments and the speed limit. And it says something surprising: the electron has to orbit outside the proton, which is 0.84 femtometres across. It is not buried inside it.
ProofThe electron orbits outside the proton
The neutron’s magnetic moment is measured. The proton’s magnetic moment is measured. If the neutron contains a proton, the electron must supply the difference, which is −4.706 μN.
A circulating charge produces μ = evr/2, so the product vr is fixed at 2.967 × 10−7 m2/s. Since v cannot exceed c, r cannot be less than 0.990 fm. The proton’s charge radius is 0.8414 fm.
Nothing else is used. No force law, no lattice, no property of the Aether — two measured moments, one classical formula for a current loop, and the speed limit. The conclusion is that the electron cannot be buried inside the proton, which is the opposite of what the pre-1932 composite model assumed.
It is also independently supported: electron-scattering form factors show the neutron carries positive charge at its centre and negative charge further out. That was not an input here.
Chain: measured μn and μp → equation (1) → equation (2) → equation (3). Premise: the neutron contains a proton retaining its free moment.
3. Closing the orbit with force balance
Equation (2) fixes the product of speed and radius but not either separately. A second condition is needed, and the obvious one is that the orbit must actually balance: the electrostatic attraction pulling the electron in must equal the centrifugal effect throwing it out.
The γ is the relativistic factor, necessary because the electron turns out to be moving at nearly light speed. Solving (2) and (4) together gives a unique answer:
| Quantity | Value |
|---|---|
| Orbit radius | 1.049 fm |
| Orbital speed | 0.9435 c |
| Relativistic factor γ | 3.018 |
| Ring current | 6,876 A |
Two equations, two unknowns, no free parameters. The electron sits just outside the proton's surface, circling it 4.3 × 1022 times a second.
4. The energy budget, and the shell
A neutron is measurably heavier than a hydrogen atom — by 0.782 MeV. In this model that excess must be accounted for. The electron's motion contributes kinetic energy; its position in the proton's electric field contributes negative potential energy.
| Contribution | Energy |
|---|---|
| Electron kinetic energy | +1.031 MeV |
| Electrostatic potential energy | −1.373 MeV |
| Net from the orbit | −0.342 MeV |
| Measured neutron excess over p + e | +0.782 MeV |
| Therefore the shell must supply | +1.124 MeV |
The orbit is a bound configuration — the pair together weighs 0.342 MeV less than a free proton and a free electron. The neutron is nonetheless heavier, which means something else is present and carrying mass. In this framework that is trapped Aether: 1.124 MeV of it, held in a shell around the pair.
Why there must be something else
If a neutron were only a proton and an electron stuck together, it would weigh slightly less than the two apart — that is what binding means, and it is why a hydrogen atom weighs less than its parts. But a neutron weighs more.
So the sum does not close. Something with mass has been added, and in this model the only thing available is the medium itself, drawn in and held. The amount needed is not a free choice: it is whatever makes the books balance, and that comes to 1.124 MeV.
5. Why the shell is not optional
In the balance of section 3, Coulomb attraction and centrifugal effect cancel exactly — both are 209.7 N. But a current loop also pushes itself open. The outward hoop force on a 6,876 A ring depends logarithmically on the thickness of the ring, which is not well known, so it is bracketed:
| Ring thickness | Hoop force (outward) | As a fraction of the binding |
|---|---|---|
| R/10 | 108 N | 52% |
| R/100 | 176 N | 84% |
| R/1000 | 245 N | 117% |
ProofThe shell is required, not optional
Section 3 fixes the orbit by setting Coulomb attraction equal to the centrifugal effect. At the solution both are 209.7 N, so they cancel completely and nothing is left over.
But the orbiting electron is a 6,876 A current ring, and a current ring exerts an outward hoop force on itself — between 108 and 245 N depending on the ring’s thickness.
That force has nothing to oppose it. The configuration as described in section 3 is therefore not in equilibrium and would fly apart. Some inward force external to the pair is required, and its magnitude is set: it must equal the hoop force.
Chain: the section 3 force balance → the self-inductance hoop force of a current ring → no remaining opposing term.
Whichever value is right, the self-field is a large fraction of the electrostatic binding and it points outward. With the other two forces already cancelling, nothing is left to oppose it. The configuration cannot exist without an external inward force, and the Aether shell is the only candidate in the model.
The shell is therefore not decoration. It is load-bearing, it has a required magnitude, and the field that demands it is the same field that gathers it — the ring's own magnetic field, at 3.8 × 1012 T, draws magnetised Aetherons up its gradient.
6. Spin comes from somewhere else
The electron's orbital angular momentum works out at 0.00773 ℏ. The neutron's spin is 0.5 ℏ — sixty-five times larger. The orbit cannot be the spin.
ProofThe orbit is not the spin
From the solve in section 3, the electron’s orbital angular momentum is L = γmevr = 0.00773 ℏ. The neutron’s spin is measured at 0.5 ℏ.
The shortfall is a factor of 65. No adjustment to the orbit can close it, because the orbit is already fixed by the magnetic moment — raising L means raising vr, which raises μ above its measured value.
So the moment and the spin cannot both come from the electron’s circulation. They must have different origins, which is the structural reason the neutron’s gyromagnetic ratio is anomalous.
Chain: the section 3 solve → L = γmevr → comparison with measured spin.
The alternative is bulk rotation of the whole object. Treating the neutron as a thin shell of its own mass at 0.84 fm, carrying 0.5 ℏ requires an angular velocity of 6.69 × 1022 rad/s, which is 0.188c at the equator. Comfortably sub-luminal, so it works.
So the two properties have two different origins: the magnetic moment from the electron's orbital current, the spin from the rotation of the body as a whole. That is not a contrivance — it is why the neutron's gyromagnetic ratio is anomalous in the first place.
7. The electron's own magnetism, and the one free parameter
This is the objection that has sunk every previous proton-plus-electron model. An electron carries its own magnetic moment of one Bohr magneton, 9.274 × 10−24 J/T. That is 960 times the neutron's entire moment. If a real electron sits inside a neutron, its magnetism should swamp everything.
The gyroscope answer
A spinning top does not fall over. Tip its axis and it does not simply topple — it precesses, sweeping its axis round in a cone. Anything attached to the top that points sideways gets swept round with it, and averages out to nothing over a full circuit.
The electron is spinning. If its spin axis sits crosswise to the neutron's own axis, its magnetism sweeps round in exactly that way, and the sideways part averages to precisely zero — not nearly zero, exactly zero, by symmetry. Nothing has to be finely balanced.
ProofPerpendicular precession cancels exactly
A spinning body in a field precesses: its axis sweeps out a cone at constant angle. Any vector fixed to that body traces the same cone.
Decompose the electron’s moment into a component along the precession axis and a component perpendicular to it. The parallel component is constant. The perpendicular component rotates through a full circle each precession period, so its time-average is zero — the integral of cos over a full period vanishes identically.
At θ = 90° the parallel component is μecos 90° = 0, so the entire moment averages away. This is exact, and it is why no fine-tuning to one part in 960 is required: the cancellation is a symmetry of the motion, not a balance of two large numbers.
Chain: rigid-body precession → time-averaging over one period. Independent of the moment’s magnitude.
Precession about a tilted axis removes the perpendicular component entirely. Only the component along the neutron's axis, μe cosθ, survives the averaging. At exactly 90 degrees it contributes nothing at all.
It is not exactly 90 degrees, and the reason is a third measurement. The neutron's mean-square charge radius is measured at −0.1155 fm2 — negative, because negative charge sits further out than positive. With the proton's charge at 0.8414 fm, that puts the electron at 0.9074 fm.
But section 2 gave a floor of 0.990 fm from the moment alone. The two constraints disagree by 9 per cent, and at 0.9074 fm the orbit can supply only 4.315 μN even at light speed, against the 4.706 required.
That residual is 2.13 × 10−4 of a Bohr magneton, which corresponds to a tilt of 0.0122 degrees from perpendicular. Allow the precession to leave that much of the electron's own moment uncancelled and both measurements are satisfied at once.
This is the one free parameter in the construction. It is not fitted to the moment — it is forced by requiring the moment and the charge radius to agree.
8. The lifetime
A free neutron lasts 878.4 seconds on average. A neutron inside a stable nucleus never decays at all. Any mechanical account has to explain both, and also the shape of the decay.
Neutron decay is exponential, which means the chance of decaying in the next second is the same whether the neutron is one second old or one hour old. It does not age. That rules out progressive wear: a structure that gradually degrades would produce a peak at a characteristic age, and none is seen.
Exponential decay is the signature of random barrier escape. Expressed per orbit rather than per second, the electron completes 3.8 × 1025 circuits in a mean lifetime, so the chance of the lock slipping is 2.7 × 10−26 per orbit — a constant small probability each time round, which produces exponential statistics automatically.
When it does slip, the event is fast: at the 782 keV endpoint the electron leaves at 0.92c and clears the proton in 3.1 × 10−24 s. So the neutron waits, motionless in structural terms, for 1026 characteristic times, and then comes apart in one.
A consistency check that goes the right way
If the neutron's lifetime depends on an electron circling inside it, you might expect a strong magnet to change it. It does not — no laboratory field has ever shifted the neutron lifetime.
The model explains why. The ring's own internal field is 3.8 × 1012 tesla. The strongest steady field ever produced in a laboratory is 45 tesla, about one part in 1011 of it. There is nothing on Earth that could perturb the orbit.
It also makes a prediction. Magnetar surfaces reach about 1011 tesla, which is 2.7 per cent of the internal field — no longer negligible. Free neutron decay rates should differ measurably in that environment.
9. What the whole thing rests on
Five measured numbers went in: two magnetic moments, the charge radius, the mass excess, and the lifetime. One parameter came out free, the tilt angle. Everything else — orbit radius, speed, shell mass, rotation rate, escape probability — is determined.
| Quantity | Value | Fixed by |
|---|---|---|
| Electron orbit radius | 0.907 – 1.049 fm | moment and charge radius |
| Orbital speed | 0.94 c | force balance |
| Trapped Aether shell | 1.124 MeV | mass excess |
| Bulk rotation | 6.69 × 1022 rad/s | spin of ½ℏ |
| Escape probability | 2.7 × 10−26 per orbit | 878 s lifetime |
| Spin-axis tilt | 0.0122° from perpendicular | the one free parameter |
The compression involved is worth stating plainly. A hydrogen atom's electron orbits at 52,918 fm. Here it orbits at about 1 fm — a factor of 50,448 in radius, and 1.3 × 1014 in volume. And the configuration sits 6.0 per cent above the angular momentum at which a relativistic orbit spirals into the centre. There is nowhere further to compress.
10. Sources
Reference codes read source.work.passage and resolve on the Master Source Register, which carries every source used across this series.
- E. Tiesinga, P. J. Mohr, D. B. Newell & B. N. Taylor. CODATA recommended values of the fundamental physical constants: 2018, Reviews of Modern Physics, 93 (2021) 025010. Neutron and proton magnetic moments, masses, and the neutron mean-square charge radius. 70
- Particle Data Group. Review of Particle Physics, current edition. Neutron mean lifetime and the beta-decay endpoint energy. 71
- J. Chadwick. Possible Existence of a Neutron, Nature, 129 (1932) 312. The discovery, and the end of the proton-plus-electron nuclear model. 85
- S. Galster et al. Elastic electron-deuteron scattering and the electric neutron form factor, Nuclear Physics B, 32 (1971) 221–237. The neutron charge distribution: positive core, negative outer region. 86
- F. E. Wietfeldt & G. L. Greene. Colloquium: The neutron lifetime, Reviews of Modern Physics, 83 (2011) 1173. The beam-versus-bottle discrepancy referred to in the ledger. 87
- W. Pauli, letter to the Tubingen conference, 4 December 1930. The neutrino proposed to account for the continuous beta spectrum. 88
Volume and page details should be checked against the originals before formal publication.
Ledger — memo 2.3
- Derived
-
- The electron must orbit outside the proton, r > 0.990 fm, from the two measured moments and the speed of light alone — no force law required
- Orbit radius 1.049 fm and speed 0.9435c, from the moment plus force balance
- Trapped Aether shell of 1.124 MeV, from the mass excess
- Bulk rotation of 6.69 × 1022 rad/s, from spin ½ℏ
- Escape probability 2.7 × 10−26 per orbit, from the 878 s lifetime
- Spin-axis tilt 0.0122°, forced by reconciling the moment with the charge radius
- That the shell is required, not optional: the hoop force is 52–117% of the binding and points outward, with nothing else to oppose it
- Measured
-
- Neutron magnetic moment, −9.6624 × 10−27 J/T (CODATA 2018)
- Proton magnetic moment, +1.4106 × 10−26 J/T (CODATA 2018)
- Neutron mean-square charge radius, −0.1155 fm2
- Neutron mass excess over proton plus electron, 0.782 MeV
- Neutron mean lifetime, 878.4 s; beta endpoint 782 keV
- Proton charge radius, 0.8414 fm
- Assumed
-
- That the neutron contains a proton and an electron as identifiable structures. This is the whole proposal. It was the standard view before 1932 and was abandoned; the objections are addressed in sections 6 and 7, but not all of them (see Open).
- That the proton inside a neutron keeps its free-particle magnetic moment. Equation (1) assumes this. A compressed proton might not, and if it does not the whole solve shifts.
- That the electron's charge circulates as a thin ring. The hoop force in section 5 depends logarithmically on ring thickness, which is why it is bracketed rather than stated.
- That the moment is purely orbital, μ = evr/2. The classical expression for a circulating point charge, applied to a relativistic electron.
- That spin comes from bulk rotation of the whole body. Section 6 shows this is possible — it does not show it is what happens.
- That the trapped Aether carries mass in the ordinary way. The 1.124 MeV shell is inferred from a mass balance, not observed.
- Open
-
- Nitrogen-14. The proton-electron model was killed in 1929 because 14N would contain an odd number of spin-½ constituents and must have half-integer spin, where its measured spin is 1. This model inherits the arithmetic and has no answer yet. It is the most serious outstanding objection.
- What locks the tilt at 0.0122°. The angle is forced by the measurements but nothing in the model explains why the configuration settles there.
- What triggers the slip. A constant probability per orbit is established; the mechanism producing that number is not. A phase slip between two incommensurate rotations is the candidate.
- The beam-bottle anomaly. Bottle experiments give about 877.8 s, beam experiments about 888 s — a nine-second gap at roughly four sigma, unresolved for over a decade. If this mechanism predicted why counting survivors and counting products differ, that would be a contribution to a live problem.
- The shell radius and thickness are not derived here; see memo 2.6.
- Prior art
-
- Rutherford, 1920 — proposed a proton-electron composite neutron
- Chadwick, 1932 — the discovery of the neutron as a distinct particle, which ended the composite model
- Galster et al., 1971 — the neutron's charge distribution, positive core with negative charge further out. The arrangement derived in section 2 matches it, which was not put in
- M. E. Yousif, 2021 — independently proposes the neutron as proton plus electron bound by the interaction of their rotating fields, with a comparable architecture