The Actions of the Aether
Put two masses together and each shadows the other. The shadow raises the dent between them. That gives two pushes on each body: inward, from the other body’s dent, and outward, from its own dent made lopsided. Nothing pulls. Everything is pushed.
The answer is the same at every scale. Two Aetherons, two protons, two red giants — at four radii apart the outward push is 6.351 % of the inward push for every one of them. Mass cancels, size cancels, and only geometry, distance and mass remain.
What this memo does and does not do
Section 1 separates the measured law from the proposed mechanism. Sections 3 to 9 are arithmetic on the measured law of gravity and can be checked directly.
Sections 10 to 19 set out shadowing, a proposed mechanism, not an established result. Every assumption it makes is numbered in section 12. Nothing in it is fitted. Section 20 states what it does not yet settle.
Published for scrutiny rather than as a settled result.
The model behind the figures — dents in three dimensions, cross-sections, gradients and orbits — is built as an interactive tool, and the gravity figures reproduce in it.
1. Gravity: The Measurement And The Mechanism
Two questions are easy to run together. How strong is gravity? That is a measurement. What does the pushing? That is a mechanism. This memo accepts the first answer as it stands and proposes a different answer to the second.
SettledNewton’s law is correct
In 1687 Newton published the law: the force between two masses is GMm/r². Every figure in this memo is calculated with it, unchanged. It gives the Moon’s acceleration from its measured period to within 0.008 %. This memo does not challenge Newton’s calculations. It reproduces them.
Newton did not say what causes it. In 1713 he wrote that he would frame no hypotheses about the cause. In a 1693 letter to Richard Bentley he went further: one body acting on another across empty space, with nothing between them to carry the action, he called an absurdity. Newton left the mechanism open and thought a medium was needed.
In 1717 he proposed one. In Query 21 of his Opticks he asked whether the medium filling space is thinner inside and near the Sun and planets, growing denser with distance — so that every body is pushed from the denser parts toward the thinner. That is the dent this memo sets out. Newton put it as a question and never ruled it out.
The people and their breakthroughs
| Year | Who | Breakthrough |
|---|---|---|
| c. 330 BC | Aristotle | Heavy things fall to their natural place, the centre of the world. |
| 1543 | Copernicus | The Sun, not the Earth, at the centre of the planets. |
| 1609–1619 | Kepler | From Tycho Brahe’s observations: planets move in ellipses, by three fixed laws. |
| 1638 | Galileo | Falling bodies speed up alike, whatever their weight. |
| 1644 | Descartes | Planets carried round by vortices in a fluid filling space. |
| 1679 | Hooke | Suggests to Newton an attraction falling as the inverse square of distance. |
| 1687 | Newton | The law of universal gravitation, GMm/r². Cause left open. |
| 1717 | Newton | Opticks, Query 21: a medium thinner near the Sun and planets, denser with distance, pushing bodies toward the thinner parts. |
| 1748 | Le Sage | Bodies pushed by particles arriving from every direction, each shadowing the other. |
| 1798 | Cavendish | Weighs the Earth with a torsion balance — the first laboratory measurement of the force between masses. |
| 1801 | Soldner | Newton’s law applied to light: starlight should bend 0.87 arcseconds at the Sun’s edge. |
| 1846 | Le Verrier, Adams | From the wobble of Uranus, predict an unseen planet. Neptune is found where predicted. |
| 1859 | Le Verrier | Mercury’s orbit turns faster than the other planets explain. Proposes a planet, Vulcan. Never found. |
| 1865 | Maxwell | Light as a wave of the electromagnetic field, taken to travel in an aether. |
| 1887 | Michelson, Morley | Look for the Earth’s motion through the aether. Find none. |
| 1905 | Einstein | Special relativity: light explained with no aether. |
| 1915 | Einstein | General relativity: gravity as the curvature of spacetime by mass. Gives Mercury’s extra turning exactly. |
| 1916 | Schwarzschild | The first exact solution: the field around a single round mass. |
| 1919 | Eddington, Dyson | Eclipse measurement of starlight bending at the Sun: 1.75 arcseconds, twice Soldner’s figure. |
| 1920 | Einstein | At Leiden: space in general relativity has physical properties, and in that sense an aether exists. |
| 1959 | Pound, Rebka | Clocks lower in a dent run slower — measured up a 22.5 m tower. |
| 1974 | Hulse, Taylor | A pair of neutron stars losing orbit exactly as gravitational waves predict. |
| 2015 | LIGO | Gravitational waves detected directly. |
| 2019 | Event Horizon Telescope | An image of the dark centre of the black hole in the galaxy M87. |
| 2026 | This series | The dent and the flow of the Aether. Bodies pushed down its gradient. Space does not curve. |
Mapping every body — what it already gives
Summing the force from every body is Le Verrier’s method, and the method this memo reproduces. It found Neptune. Applied to Mercury, the forces from all the planets turn its orbit about 531 arcseconds a century. The measured turning is about 574. 43 arcseconds a century are left over. A map of every body’s dent gives the 531. The author proposes the 43 come from the flow of the Aether — motion of the medium itself, beyond the static sum of dents. Mercury’s orbit is the most stretched of the planets (eccentricity 0.21) and the most tilted (7° to the Earth’s orbit). A full model of every body, and the flow between them, is the test.
How the ephemerides are calculated today
NASA’s Jet Propulsion Laboratory computes the positions of the planets (the DE440 ephemeris) by integrating every planet, the Moon, hundreds of asteroids and a ring of outer bodies, with each body’s field mapped from its shape. That part is the dent and its gradient — the method of this memo. The equations of motion also carry relativistic correction terms, and the quantity used is energy per kilogram. No pressure appears in the calculation.
ProposedA dent in the Aether
This series proposes a different mechanism from Einstein’s. Space is filled with the Aether at a deep-space pressure. A mass lowers that pressure around itself — the dent — and bodies are pushed down its gradient. Nothing pulls. The arithmetic of the dent is Newton’s arithmetic, which is why sections 3 to 9 reproduce his law exactly.
The author’s position: space does not curve. Gravity is the pressure of the Aether — its dents and its flow. This is the premise of the Aether model: an alternative explanation to the curvature of space. The full case is set out in T.1 — Space Is the Void.
What the mechanism still has to answer
General relativity has passed measurements that Newton’s law alone does not explain. A mechanism offered in its place must account for each:
- Mercury’s orbit turning 43 arcseconds a century beyond the 531 that the sum of every planet gives. The author proposes Aether flow accounts for it. Response: E.4 Mercury’s Perihelion (planned); the flow of the Aether in T.7 Whirlpools All the Way Down, and Up.
- Starlight bending 1.75 arcseconds at the Sun’s edge — twice the 0.87 that Newton’s law gives. The series proposes Aether density gradients bend it; that has to come out at 1.75. Response: E.2 Eddington 1919 (planned); T.1, Bent Starlight Cannot Settle This; T.3 Light Needs a Medium.
- Clocks running slower lower in a dent — measured in 1959, and corrected for daily in GPS satellites. Response: E.6 Clocks and GPS (planned); T.2.2 The Theory of Relative Time.
- Radio signals delayed passing the Sun, measured to high precision by the Cassini probe in 2003. Response: E.3 VLBI and Cassini (planned); 1.6 The Speed of Light.
- Gyroscopes in orbit turning as Gravity Probe B measured in 2011. Response: E.5 Gravity Probe B (planned).
- Gravitational waves, detected in 2015. Response: 4.9 The Self-Propagating Wave.
The dent as set out in this memo gives Newton’s results. Each measurement above has its response in the series, listed with it. The Experiments set, E.1 to E.15, examines each on its own terms — what was measured, what was assumed in reducing it, and whether the same data reduce differently under the Aether model.
2. The Rules
Everything that follows rests on these. Rules 1, 2 and 4 to 7 are the measured law of gravity in this series’ terms. Rule 3 is the series’ reading of it, set out in T.5.1. Rule 8 belongs to the proposal that starts in section 10.
Rule 1A mass makes a dent
depth = −GM/r. Deepest at the mass, rising toward the deep-space level, never reaching it.
Rule 2A dent does not push. A gradient does.
Depth on its own does nothing. The centre of the Earth is the deepest point and has no force at it.
Rule 3Nothing pulls
Every force is a push. A body moves toward another because its outside face is pushed harder than its inside face.
Rule 4The gradient acts on the whole mass
It acts on every Aetheron in the volume, not on the surface. force = M × gradient.
Rule 5A body is moved only by another body’s dent
Its own dent is the same all round and cancels — unless something makes it lopsided.
Rule 6At a distance, only mass and distance count
Outside a body the gradient is GM/r². Its radius and its density do not enter.
Rule 7At the surface and inside, density counts
Two bodies, both of mass 10. One has radius 10, the other radius 100, so the small one is 1,000 times denser. Depth and gradient in units of GM:
| Distance from centre | R = 10 depth | gradient | R = 100 depth | gradient |
|---|---|---|---|---|
| 0 | −0.150 | 0 | −0.015 | 0 |
| 10 | −0.100 | 1.0 × 10−2 | −0.01495 | 1.0 × 10−5 |
| 50 | −0.020 | 4.0 × 10−4 | −0.01375 | 5.0 × 10−5 |
| 100 | −0.010 | 1.0 × 10−4 | −0.010 | 1.0 × 10−4 |
| 200 | −0.005 | 2.5 × 10−5 | −0.005 | 2.5 × 10−5 |
| 1000 | −0.001 | 1.0 × 10−6 | −0.001 | 1.0 × 10−6 |
The dense body’s dent goes ten times deeper at its centre and is a thousand times steeper at radius 10. Outside radius 100 the two dents are identical. Inside a body the gradient is (4/3)πGρ per metre from the centre — density alone.
Two measures of steepness at a surface. The gradient there is (4/3)πGρR — density times size. How fast it changes with distance there is density alone: it rises at (4/3)πGρ per metre just inside, and falls away at (8/3)πGρ per metre just outside. Going to small scales, size shrinks the first and leaves the second untouched. A proton is denser than a neutron star (6.74 × 1017 against 2.75 × 1017 kg/m³), so its gradient falls away faster just outside its surface — 3.77 × 108 against 1.54 × 108 per second squared — though the gradient itself is 1019 times smaller.
The same mass at three densities. One solar mass, packed tighter each time:
| Density ×1 | Density ×8 | Density ×27 | |
|---|---|---|---|
| Radius | 696,340 km | 348,170 km (½) | 232,113 km (⅓) |
| Density, kg/m³ | 1,406 | 11,251 | 37,970 |
| Rate of rise inside, per s² | 3.93 × 10−7 | 3.15 × 10−6 (×8) | 1.06 × 10−5 (×27) |
| Peak gradient at surface | 273.8 | 1,095 (×4) | 2,464 (×9) |
| Dent depth at surface, J/kg | 1.91 × 1011 | 3.81 × 1011 (×2) | 5.72 × 1011 (×3) |
| Dent depth at centre, J/kg | 2.86 × 1011 | 5.72 × 1011 | 8.58 × 1011 |
| Gradient at 1 AU | 0.005931 | 0.005931 | 0.005931 |
At the same mass, raising the density by k raises the rate of rise inside by k, the peak gradient at the surface by k⅔ and the dent depth by k⅓. Far out, nothing changes.
Rule 8The shadow is geometry
How much one body shadows another is set by its size and its distance. A denser body of the same mass is smaller and casts less shadow.
Geometry, distance and mass — and density, where a body’s own surface and interior are concerned. At every scale.
3. What A Mass Does To The Aether
A mass lowers the pressure of the Aether around it. That lowered region is the dent. Its depth at distance r from the centre is
depth = − G M / r
Deepest at the mass, rising back toward the deep-space level with distance, never quite reaching it — which is why gravity has no edge.
One fact. The rest of the memo is what follows from it.
4. A Dent Does Not Push. A Gradient Does.
How fast the depth changes with distance is the gradient:
gradient = G M / r²
At the bottom of a valley nothing moves you. On the side of one you roll. The bottom of a dent is the same: at the centre of the Earth the depth is greatest and there is no difference in any direction, so there is no force at all. All the depth in the world, and nothing pushing.
The depth does not act. The gradient acts.
What the gradient acts on
The gradient acts on every Aetheron in the body — the whole volume of its mass, not its surface. The force is the gradient times the mass it acts on:
force = M × gradient
The body’s radius does not enter. A wider body spans a larger difference in depth, but over a wider width, and the two cancel. The Earth at double its radius and the same mass:
| Earth radius | Difference across it | Gradient | Force |
|---|---|---|---|
| 6,371 km | 75,578 J/kg | 5.931408 × 10−3 | 3.5422 × 1022 N |
| 12,742 km | 151,156 J/kg | 5.931408 × 10−3 | 3.5422 × 1022 N |
Radius enters in two places only: inside a body, where its own dent’s gradient is GMa/R³ (section 13), and in the shadow, where how large one body looks from the other sets q (section 11).
5. A Body Has Two Faces
A body is not a point. It has an inside face, toward the other mass, and an outside face, away from it. The dent has one depth at each, and the pressure difference between them is the force.
The ruleThe difference across a body is the force
The Earth in the Sun’s dent. Radius 6,371 km, distance 149.6 million km.
| Where | Depth of the Sun’s dent, J/kg |
|---|---|
| Earth’s inside face | −887,376,427 |
| Earth’s outside face | −887,300,849 |
| difference across the Earth | 75,578 |
The inside face is deeper, so the pressure there is lower, so the outside face is pushed harder. Divided by the Earth’s width and multiplied by its mass: 3.54 × 1022 N, toward the Sun.
6. Why Its Own Dent Does Nothing
The Earth makes its own dent — 62.6 million J/kg deep at its surface. It is the same depth all round the Earth’s centre. Every push it makes in one direction is matched by an equal push in the opposite direction, and it cancels.
A body is moved only by another body’s dent. Section 12 is about the one thing that changes that.
7. Adding It Up Inside
Nothing is watertight to the Aether. The pressure difference acts on every Aetheron in the body, not on its skin. The force is summed through the whole volume, and that is why mass and not size decides it.
The faces are how the gradient is read, not where the force acts
“Inside face” and “outside face” describe the gradient across the body. The force itself lands throughout the interior. For the outward push in section 13, taking it at the surface instead gives an answer eight times too large.
The check: with no shadowing, summing through the volume reproduces Newton’s law exactly — 1.0000 at 4, 10 and 40 radii.
This is Archimedes in form and Newton in result. A floating body is pushed on its skin because water is kept out. Nothing keeps the Aether out, so there is no displaced volume and no buoyancy — only mass.
8. Same Mass, Any Size
Two bodies of the same mass, one large and thin, one small and dense, placed at the same spot in the Sun’s dent. The large one spans more of the dent, so the difference across its faces is larger — but over a wider width. The gradient comes out the same, and so does the force.
| Earth’s mass at 1 AU, radius | Density, kg/m³ | Difference across faces, J/kg | Force |
|---|---|---|---|
| 637 km | 5.5 × 106 | 7,558 | 3.5422 × 1022 N |
| 6,371 km | 5,513 | 75,578 | 3.5422 × 1022 N |
| 63,710 km | 5.5 | 755,780 | 3.5422 × 1022 N |
| 637,100 km | 0.0055 | 7,557,940 | 3.5422 × 1022 N |
Close in, the two faces stop telling the whole story. Near the Sun the dent curves across a large body: its near side is pushed much harder than its far side. Summed through every Aetheron, the round body comes out at exactly the push at its centre.
| Earth’s mass, 2 Sun radii from its centre, radius | Two-face reading ÷ Newton | Volume sum ÷ Newton |
|---|---|---|
| 6,371 km | 1.00002 | 1.00000 |
| 63,710 km | 1.00210 | 1.00000 |
| 637,100 km | 1.26466 | 1.00000 |
In another body’s dent, force = mass × the gradient at the body’s centre, for any round body, whatever its size or density. The faces read the gradient; the volume carries the force.
9. Two Dents, One Medium
Put a second mass nearby and the two dents add. Between them the two gradients oppose, and at one point they cancel exactly:
| Pair | Gradients cancel at | Share of the separation |
|---|---|---|
| Earth and Moon | 346,000 km from Earth | 90.019 % |
| Sun and Earth | 259,000 km from Earth | 99.827 % |
| two matched bodies | the midpoint | 50.000 % |
Each body still feels only the other body’s dent. The combined curve shows where the gradients cancel. It does not show the force on either body.
10. One Body Shadows The Other
From here the memo sets out a proposal. Everything above is arithmetic on measured gravity. What follows is not.
The dent is held in place by the Aether pressing in from every direction. A second body standing nearby blocks part of that from the side it stands on. That blocking is the shadow, and it raises the dent in the region between the two bodies.
11. What The Shadow Blocks
How much one body blocks is geometry and nothing else. Seen from one body, the other covers an angle θ with
sin θ = R / d · blocked fraction f = (1 − cos θ) / 2 · shadow factor q = 2f
q is the blocked fraction as a share of the inside half — the half facing the other body.
| Separation | θ | f | q |
|---|---|---|---|
| 4 radii | 14.478° | 1.5877 % | 0.031754 |
No mass, no depth, nothing about what the bodies are made of. Only size and distance.
12. The Shadow Working, Step By Step
Assumptions — stated, not yet shown
A1. Something maintains the dent.
A2. Whatever maintains it can be blocked by another body.
A3. The amount blocked scales with the covered fraction, q.
A4. The shadow raises a body’s own dent at its inside face by the fraction q.
A5. A body responds to its own dent once that dent is no longer the same all round.
Two protons, four radii apart. Each shadows the other.
Step 1Proton 2’s dent, across proton 1
| Proton 1’s face | Depth of proton 2’s dent, J/kg | Pressure |
|---|---|---|
| inside | −4.429793 × 10−23 | lower |
| outside | −2.657876 × 10−23 | higher |
Higher pressure on the outside face. Pushed inward.
Step 2Proton 1’s own dent, shadowed by proton 2
| Proton 1’s face | Depth of its own dent, J/kg | Pressure |
|---|---|---|
| inside — raised by q | −1.286739 × 10−22 | higher |
| outside — unshadowed | −1.328938 × 10−22 | lower |
Before proton 2 arrived these two were equal. Now the inside face is higher. Pushed outward.
Step 3The dent between them
The region between the pair is raised 3.175 % at the midpoint and 0.794 % two radii outside it.
The shadow raises the depth at the inside face, which changes the difference across the body, which changes the push. Both pushes come from shadowing.
13. How Big The Outward Push Is
Inside a body its own dent has gradient GMa/R³ at distance a from the centre. The unshadowed part cancels by symmetry. What remains, summed over the inside half, is πR⁴/6. Divided through the volume:
outward push = G M² q / (8 R²)
Far apart, q approaches R²/2d², so for two matched bodies
outward push = G M² / 16 d² · inward push = G M² / d²
Both fall as 1/d². Their ratio never changes with distance.
14. Two Pushes, Opposite Ways
Nothing pulls. Each body is pushed twice: inward by the other body’s dent, outward by its own. For the two protons:
| At 4 radii | |
|---|---|
| inward push | 1.6539 × 10−35 N |
| outward push | 1.0503 × 10−36 N |
| outward ÷ inward | 6.351 % |
What repulsion would require
Between two matched bodies, with q as geometry gives it, the inward push is larger at every distance. For them to be pushed apart, the outward push must exceed the inward one, which requires the shadow to be 16 times the geometric value — q = 0.5 at four radii. q cannot exceed 1, so closer than 2.83 radii no shadow of any strength reaches it. And because the ratio is the same at every scale (section 15), the factor that separated two protons would separate the Earth and the Moon by the same share. Between unequal bodies one of the two can be pushed away — section 19. Where repulsion comes from is set out as open in section 20.
15. The Same Answer At Every Size
Outward ÷ inward is q·d²/(8R²), and q depends only on R/d. The mass cancels and the size cancels.
| Separation, radii | q | Outward ÷ inward |
|---|---|---|
| 2 (touching) | 0.1339746 | 6.6987 % |
| 4 | 0.0317542 | 6.3508 % |
| 100 | 5.0001 × 10−5 | 6.2502 % |
Two protons and two 1,000 kg spheres, both at four radii, both give 6.351 %. The forces differ by 1031.
16. Nothing About It Changes With Size
Geometry, distance and mass decide the answer, at every scale. No new force appears as bodies get larger or smaller, and nothing is re-tuned from one scale to the next.
| Pair, four radii apart | Outward ÷ inward |
|---|---|
| two Aetherons | 6.3508 % |
| two protons | 6.3508 % |
| two grains of sand | 6.3508 % |
| two Earths | 6.3508 % |
| two red giants | 6.3508 % |
What does not stay the same
The forces. They span about 1070 N across that table. What holds is the ratio and the form of the law, not its size.
The floor. The Aetheron has one fixed radius. Near that size the blocked region stops being a smooth disc in a continuous medium, and f = (1 − cos θ)/2 no longer applies. “Every scale” means every scale above the Aetheron.
17. Bodies That Match
Two matched bodies see the same blocked fraction and receive the same outward push. Everything is symmetric, and the forces on the pair sum to zero. One curve describes every matched pair in the universe.
18. The Large And The Small
Each body is shadowed by how large the other looks, but feels that shadow through its own dent. For unequal bodies those are different things.
| Pair | Outward ÷ inward, larger body | Outward ÷ inward, smaller body |
|---|---|---|
| Sun and Earth | 174.569 % | 0.224 % |
| Earth and Moon | 37.790 % | 1.034 % |
A large body’s own dent is deep, so shadowing it slightly produces a large outward push. A small body’s own dent is shallow, so the same shadow does little. The matched case is the exception. Every pair doing real work in the universe is unequal.
For a proton and an electron, both are pushed inward only if the electron’s radius lies between 0.583 % and 9.335 % of the proton’s. Outside that window one of the two is pushed away.
19. Dense And Diffuse
Start with the dent itself. Sirius B, a white dwarf, holds about one solar mass in a radius of 5,850 km — 119 times smaller than the Sun and 1.69 million times denser.
Outside the Sun’s surface the two dents are one curve. Inside it they separate: the Sun’s flattens into a shallow bowl, and Sirius B’s keeps following the same curve down into a narrow, deep hole. Sirius B is the Sun’s mass packed inward. Where that mass went, the dent deepened. Beyond the Sun’s radius no mass moved, so nothing changed.
Density makes the dent deeper. The same two dents drawn to true scale:
| Depth, J/kg | Bottom of the dent | At the surface | At 1 AU |
|---|---|---|---|
| Sun | −2.86 × 1011 | −1.91 × 1011 | −8.87 × 108 |
| Sirius B | −3.40 × 1013 | −2.27 × 1013 | −8.87 × 108 |
| Neutron star | −1.66 × 1016 | −1.11 × 1016 | −8.87 × 108 |
Same mass, same depth far out. At the surface the depth is GM/R, so packing the mass into a smaller radius deepens it: 119 times for Sirius B, 58,000 times for a neutron star. The bottom, at the centre, is one and a half times the surface depth.
| Distance from centre | Sun, N/kg | Sirius B, N/kg | Neutron star, N/kg |
|---|---|---|---|
| 6 km | 0.0024 inside | 3,978 inside | 4.61 × 1011 inside |
| 12 km | 0.0047 inside | 7,957 inside | 9.22 × 1011 surface |
| 1,000 km | 0.39 inside | 663,100 inside | 1.33 × 108 |
| 5,850 km | 2.30 inside | 3,879,000 surface | 3,879,000 |
| 100,000 km | 39.3 inside | 13,270 | 13,270 |
| 696,340 km | 273.8 surface | 273.8 | 273.8 |
| 1 AU | 0.0059 | 0.0059 | 0.0059 |
One solar mass each. Densities 1,406, 2.37 × 109 and 2.75 × 1017 kg/m³, taken as uniform. The neutron-star column carries −GM/r to its limit; measurements near a neutron star’s surface depart from it.
Apply the face rule to a 1 kg object 2 km wide. Close in, its two faces sit at nearly the same depth in the Sun’s bowl and at very different depths on Sirius B’s wall. Far out they sit at the same two depths whichever body made the dent.
The ruleDensity decides how deep and how close
A denser body of the same mass has a deeper dent. It also lets you stand, outside it, nearer its centre, and the gradient keeps climbing as 1/r² all the way down to that surface. Surface gradient is (4/3)πGρR — density times size. Beyond the less dense body’s radius the dents even out: mass and distance alone, which is why an orbit weighs a star without telling its size.
The same density that deepens the dent carries into the outward push.
Mass alone does not decide how a body is treated. Rule 7 showed that at the same mass a denser body has a deeper, steeper dent at and inside its surface. Its outward push comes from that dent, so density carries straight into the push. Far apart, for body i facing body j:
outward ÷ inward = (Mi / Mj) × (Rj / Ri)² ÷ 16
The same two bodies as rule 7, both of mass 10:
| Pair | Outward ÷ inward |
|---|---|
| both radius 10 — dense and dense | 6.251 % |
| both radius 100 — diffuse and diffuse | 6.351 % |
| radius 10 facing radius 100 — the dense body | 626.6 % |
| radius 10 facing radius 100 — the diffuse body | 0.0625 % |
Matched pairs give the same small share whatever their density. Put a dense body beside a diffuse one of the same mass and the dense one is pushed away: its own dent is deep, and the diffuse body is wide enough to shadow a large share of it.
| Other body’s radius ÷ own radius, equal mass | Outward ÷ inward |
|---|---|
| 2 | 25.00 % |
| 3 | 56.25 % |
| 4 | 100.00 % |
| 10 | 625.00 % |
This is repulsion, and it comes from density, not a stronger shadow. It acts on one body of the pair. The diffuse body is still pushed inward, so the pair is not driven apart and the forces on it do not balance — section 20.
20. Where The Argument Stops
OpenThe third law
Matched pairs are balanced. Unequal pairs are not, because each body’s outward push goes with its own M²/R². Earth and Moon: 7.279 × 1019 N left over, 1.204 × 10−5 m/s² of self-acceleration on the pair — 0.2 % of Earth’s acceleration about the Sun, 5.931 × 10−3 m/s². The fault lies in the M²/R² scaling of the outward push, not in the dent.
OpenWhat maintains the dent
A1 and A2 are assumed. A standing field can be shadowed — a Faraday cage does it — but the series has not yet said what maintains the dent.
OpenRepulsion
Between matched bodies (section 14) the inward push wins at every distance and every scale. Repulsion there needs a shadow 16 times the geometric value, unreachable closer than 2.83 radii, and by scale invariance it would apply to every matched pair at once.
Between unequal bodies (section 19) a body is pushed away when (Mi/Mj)(Rj/Ri)² exceeds 16. The other body is still pushed in, so the pair is not driven apart as a pair.
TestThe laboratory
If the shadow is real, a measurement of G depends on the apparatus. For two spheres of equal density the correction on the test mass is Rtest/(16 Rsource).
| Rtest / Rsource | G measured low by |
|---|---|
| 0.05 | 3,581 ppm |
| 0.20 | 13,095 ppm |
| 0.33 | 21,741 ppm |
| 0.75 | 48,255 ppm |
CODATA 2022: G = 6.67430(15) × 10−11 m³ kg−1 s−2, relative uncertainty 22 ppm. Experiments disagree with each other by about 550 ppm, and that disagreement has not been shown to follow apparatus geometry. The predicted effect is 6.5 to 88 times the whole spread. This is where the mechanism is tested first. Response: E.1 Measuring G (planned).
ClosedIt is not charge
| Two protons | N·m² |
|---|---|
| electric, k e² | 2.3071 × 10−28 |
| gravity, G mp² | 1.8672 × 10−64 |
| outward push, G mp²/16 | 1.1670 × 10−65 |
Short by 1.977 × 1037 — sixteen times the gravity-to-electricity gap of 1.2356 × 1036. Held by the dent alone, a hydrogen atom would be 1.20 × 1029 m across. Charge has two signs, is the same on bodies of different mass, cancels in a neutral atom, and comes in one fixed unit; a shadow does none of these. Electromagnetism is T.5.2.
21. Why The Apple Falls
In 1726 Newton told William Stukeley that the idea of gravity first came to him when an apple fell, at his mother’s farm at Woolsthorpe in the plague years of 1665–66. He asked why it went straight down — not sideways, not up, but always toward the centre of the Earth.
In the Aether model the answer is the rules of this memo, applied to an apple. The Earth’s mass lowers the pressure of the Aether around it: at the ground the dent is 62.6 million J/kg deep, deeper below and shallower above. An apple 8 cm across has its top face 0.79 J/kg shallower than its bottom face. The top is pushed harder than the bottom. While the stem holds, the stem takes the push. When it lets go, nothing does, and the apple falls — one metre in 0.45 seconds.
The same is happening to you now. Standing 1.8 m tall, your feet sit 17.7 J/kg deeper in the Earth’s dent than the top of your head — three ten-millionths of the depth. That difference, acting on every Aetheron in a 70 kg body, is 687 N, pushing you toward the Earth’s centre.
What you feel is the floor. The push acts through the whole body at once, on every part alike, so it cannot be felt on its own. What you feel is the floor stopping you, pressing back on your feet with 687 N. Take the floor away and the feeling goes. On the space station, 400 km up, the gradient is still 89 % of what it is at the ground; the crew feel nothing because nothing stops them — they are falling around the Earth.
And the same dent holds the Moon. This was Newton’s next step. The Moon is about 60 Earth radii away, so by 1/r² the gradient there is 60 × 60 = 3,600 times weaker:
| Distance from Earth’s centre | Gradient, m/s² | |
|---|---|---|
| The apple | 1 Earth radius | 9.82 |
| The Moon, by 1/r² | 60 Earth radii | 9.82 ÷ 3,600 = 0.00273 |
| The Moon, measured from its orbit | 60.4 Earth radii | 0.00273 |
The apple and the Moon are pushed by the same dent. One falls to the ground; the other is moving sideways fast enough that it keeps falling around the Earth instead.
The weight you feel sitting here is the Aether of deep space pressing on every part of you — a little harder on the side away from the Earth than on the side toward it.
22. The Numbers
- Sun’s dent at Earth’s orbit: −8.873 × 108 J/kg. Difference across the Earth: 75,578 J/kg.
- Earth’s own dent at its surface: −6.256 × 107 J/kg, cancelling entirely.
- Volume sum against Newton, no shadow: 1.0000.
- Earth–Moon gradients cancel at 346,000 km from Earth, 90.019 % of the way.
- Shadow factor, four radii: q = 0.031754.
- Two protons at four radii: inward push 1.6539 × 10−35 N, outward push 1.0503 × 10−36 N.
- Outward ÷ inward: 6.6987 % touching, 6.3508 % at four radii, 6.2502 % at a hundred — every scale.
- Equal masses, radii 10 and 100: the dense body’s outward push is 626.6 % of its inward push.
- Earth–Moon self-acceleration from the third-law imbalance: 1.204 × 10−5 m/s².
- Spread between laboratory values of G: about 550 ppm.
Terms Used Here
| Word | What it means |
|---|---|
| Aether | The proposed substance filling all space, made of one kind of particle. |
| Aetheron | The proposed single particle the Aether is made of. One size, one mass. |
| Dent | The lowered pressure a mass makes in the Aether around it. |
| Depth | How far down the dent goes at a point, in J/kg. |
| Gradient | How fast depth changes with distance. |
| Difference | The gap in depth between a body’s two faces. |
| Inside face / outside face | The side of a body toward the other mass, and the side away from it. |
| Inward push | The push from the other body’s dent, toward the other body. |
| Outward push | The push from a body’s own dent once shadowing makes it lopsided. |
| Near zone | The region outside a dense body but inside the radius a less dense body of the same mass would have. Where density shows. |
| Shadow | The proposed blocking of what maintains a dent, by a second body. |
| Blocked fraction, f | The share of all directions one body covers, seen from another. |
| Shadow factor, q | The blocked fraction as a share of the inside half. q = 2f. |
Every term used across the series is on the terms page.
Sources
Reference codes read source.work.passage and resolve on the Master Source Register.
- I. Newton. Philosophiæ Naturalis Principia Mathematica (1687). The inverse-square law and the shell theorem. Carried as reported; the original has not been consulted.
- G.-L. Le Sage. Lucrèce Newtonien (1784). The earliest shadowing account of gravity. Carried as reported; not verified.
- I. Newton. Opticks, 2nd edition (1717), Query 21. Carried as reported; to be checked against the original text before publication.
- I. Newton. General Scholium, Principia, 2nd edition (1713), and letter to R. Bentley (25 February 1692/3). Carried as reported; not consulted in the original.
- A. A. Michelson and E. W. Morley (1887); A. Einstein (1905, 1915); A. Einstein, “Ether and the Theory of Relativity”, Leiden (1920). Carried as reported.
- Tests of general relativity: Mercury’s perihelion; the 1919 eclipse; Pound and Rebka (1959); Cassini (2003); LIGO (2015). Standard results, carried as reported; figures to be checked against the original papers before publication.
- U. Le Verrier (1859); S. Newcomb (1882, 1895): Mercury’s perihelion and the 43 arcsecond residual. C. M. Will, “The Confrontation between General Relativity and Experiment”, Living Reviews in Relativity. Residual and planetary sum checked against published summaries 21 September 2026.
- R. S. Park et al., “The JPL Planetary and Lunar Ephemerides DE440 and DE441”, Astronomical Journal 161 (2021). Method description checked 21 September 2026.
- J. G. von Soldner (1801); Aristotle; Copernicus (1543); Kepler (1609, 1619); Galileo (1638); Descartes (1644); Hooke to Newton (1679); Cavendish (1798); Maxwell (1865); Schwarzschild (1916); Dyson, Eddington and Davidson (1920); Hulse and Taylor (1975); LIGO (2016); Event Horizon Telescope (2019). Standard history, carried as reported.
- W. Stukeley, Memoirs of Sir Isaac Newton’s Life (1752): the 1726 conversation and the apple. Carried as reported.
- CODATA 2022 recommended values of the fundamental physical constants: G = 6.67430(15) × 10−11 m³ kg−1 s−2, relative standard uncertainty 22 ppm; disagreement between input measurements about 550 ppm; expansion factor 3.9 applied. Verified against published summaries 21 September 2026.
- Masses, radii and distances for the Sun, Earth and Moon; proton and electron masses; elementary charge; Coulomb constant; Bohr radius. Standard reference figures; not individually sourced.
Verification register: sections 3 to 9 are arithmetic on standard figures. Sections 10 to 19 are a proposed mechanism, its assumptions listed in section 12. The laboratory comparison in section 20 is load-bearing as a test.
Where this sits in the series
What the Aether does when there is more than one mass in it — and the proposal that each mass shadows the other.
- T.1 — Space Is the Void — Why space cannot curve: the premise.
- T.5.1 — Gravity — One mass on its own: the dent, the gradient, the push.
- T.4 — Aether Is the Universal Medium — What is being dented.
- T.7 — Whirlpools All the Way Down, and Up — The same medium, circulating.