The eighteen pages of the front page, six topics at three reading levels, on one plain page with their drawings: for reading without JavaScript, for search, and for anyone who wants to quote or check a line. Every figure is computed from the published VMS documents; each page is exactly the one the front page shows, and each is also served on its own. Also as a PDF.
A photon is the smallest piece of light. Light always goes straight, as fast as anything can go, and it hides the space behind it.
If a photon gets curled into a loop it goes around and around, and it keeps hiding the space inside. That trapped light is what we call mass. Everything you can touch is made of trapped light.
Inside (left): the photon runs around and around and hides the space in the middle.
Outside (right): you cannot see the hidden space at all, only a dot. But all the lines of space around it lean in toward it. That leaning is how you can tell something is there, and it is what makes things fall (next page).
A photon is the smallest piece of light; this page follows one photon closed into a loop, the electron, and the space it hides. Light runs at c and hides the space behind it. Close its path into a loop and it hides a fixed amount of space every cycle; that hidden total is the inertial measure, mass. Seen from inside (panel 0) the loop is a path at c around a missing disk. Seen from outside (panels I to IV) the missing space cannot be seen at all: there is only a point, and every line of space that passes it leans in, the lines that would have crossed the missing disk meeting at the point and continuing. The electron sets the scale, ฦโ = ฤง/(mโc) = 386.16 fm, the frameworkโs single calibration.
0 ยท the closed path, inside view. The electron: one photon on a closed path at c, hiding the space inside it. The grid is drawn straight; this view sets the object and the scale. Sโ = ฤง on this loop is the single calibration; m = (ฯs/cยฒ)ยทLฮ, Lฮ = 2ฯฦโ.
I ยท the merge point, outside view. The same electron seen from outside: the grid lines of space under the map. Lines that crossed the missing disk merge at the point and continue; passing lines bend inward. Two lines are annotated with their computed closest pass and their curvature there, where it is largest.
II ยท vertex detail, 2ร closer. Every line that crossed the missing disk passes through this one vertex: formerly parallel lines meeting, the geometry of an interaction. The tangent line touches and continues. Two dashed traces (computed, not part of the grid) show how fast the closest pass collapses just outside tangency.
III ยท zoom out ร2. Same law, half the magnification. The arc radii grow fast with distance: one grid step farther out bends on a circle several times larger.
IV ยท zoom out ร100. At this distance no line shows a visible bend; the numbers carry the physics. For each annotated line, the share of space missing at its closest pass, ฮด, is printed next to the pure inverse square (ฦโ/R)ยฒ at the same seen radius. On the farthest line they agree to five decimals: from here outward a single particleโs missing space and the Newton form cannot be told apart, shown as arithmetic, not assertion.
Reading order. 0, the object itself in flat space, scale set. I, the object seen from outside, with measured bends. II, the vertex where every crossing line merges and continues. III, one zoom out, the bending dying as the square of the distance. IV, one hundred times out, nothing visibly bends and the printed arithmetic shows the missing-space profile and the pure inverse square agreeing to five decimals on the far line. No inverse-square law is used to draw any line; it appears in IV only as a printed number beside the computed value.
Nothing about the loop changes and the light still runs at c. Seen from a laboratory it is moving past, its cycle takes ฮณ times longer, the photonโs path opens into the curve drawn, and the loopโs outline is squeezed to R/ฮณ along the motion. In the loopโs own frame the path is the closed circle and head meets tail at the same place every cycle; from the laboratory the point where head meets tail is itself moving, so the path never rejoins where it started (the small pinch marks). The mass seen is ฮณ times the rest mass. In the textbookโs letters this is E = ฮณmcยฒ, and the first two terms of that are the rest energy mcยฒ and the kinetic energy ยฝmvยฒ.
1 ยท at rest. The photonโs path is the circle; the loop hides one disk of space per cycle. Mass seen: m.
2 ยท v = 0.5c, ฮณ = 1.155. The path over one loop period, the loop advancing 2ฯฮฒฮณ = 3.63 loop radii per cycle; the outline at one instant is contracted to R/ฮณ along the motion. Mass seen: 1.155 m.
3 ยท v = 0.9c, ฮณ = 2.294. The loop advances 12.97 loop radii per cycle and its outline is squeezed to 0.436 R. Mass seen: 2.294 m. The loop can never reach c: a loop at v = c could not close.
Every line computed. Panels 0 to IV: the disk of area ฯฦโยฒ is the space the loop hides (axiom A1); from outside it is not seen, and every point of space at true distance r from the loop centre is seen at R(r) = โ(rยฒ โ ฦโยฒ), points inside the disk all at the centre point. This map is the drawingโs construction of two lines of the Mathematical Bridge, section 3: the loop โremoves a volume of available transverse area from the surrounding space, fixing the missing volumeโ, and โthis deficit propagates outward with profile ฮg(r) ~ 1/rยฒโ; it removes exactly ฯฦโยฒ from every circle around the point, and its missing share ฮด = ฦโยฒ/rยฒ is exactly the inverse square. Every grid line is the image of a straight line under that map; lines that crossed the disk are drawn through the point and out the other side. Annotated values: the closest pass of a line is its seen radius โ(xโยฒ โ ฦโยฒ); the curvature ฮบ is evaluated where the line crosses the centre line, its maximum; Rarc = 1/ฮบ. Panel IV prints ฮด at each lineโs true offset xโ beside (ฦโ/R)ยฒ at its seen radius. Speed panels: the photonโs path is the standard relativistic transformation of the rest-frame circle (Mechanics Math Appendix, section 3): x = ฮณR cos ฮธ + ฮฒฮณRฮธ, y = R sin ฮธ, its speed c at every point (axiom A2), the loop period ฮณ times longer, the outline contracted to R/ฮณ along the motion; ฮณ values and the mass ratio computed, nothing else drawn.
A photon is the smallest piece of light; this page follows one photon closed into a loop and derives what the high school page stated. A region of space is hidden; from outside the missing space is not observable, there is only the point and its effect on every line of space that remains. That is the definition of mass. A: the inside view, the closed path and the sphere it hides. B: the map acting on a flat plane through the centre. C: the identical map on the three mid-planes of a block, where every line stays traceable. D: the full block, every radius at once. In B, C and D the lines that met the hidden boundary merge at the point and continue; the crowding and darkening around it is the interaction zone, and the point is the only near-black. Each numbered circle is a panel below.
Published documents used, and nothing else: the Mathematical Bridge (section 3, Closed Loop โ Inertial Measure and Gravity, recipe steps 1 to 4) and its Math Appendix (Mass and Gravity from Closed Void Loops, sections 1 to 4); the Bridge Narrative, step 3 (mass as missing space); the Treatise on Caustics, Loop Closure (the closed path, head and tail merged, seen as one point); the Particle Mechanics Math Appendix (Sโ = ฤง, ฦโ). Only ratios enter; Sโ = ฤง is the one scale.
| Symbol | Meaning | Where it is fixed |
|---|---|---|
| ฮ, W | the closed path of the photon; the worldsheet it sweeps in time | Bridge Math Appendix, Mass and Gravity ยง1 |
| Ad, Sฮ | display area, the space a front obscures; the loop action โฎAd ds | Bridge ยง1 and ยง3; Appendix ยง1 |
| ฯs | surface-action density (a derived constant) | Appendix ยง2 |
| Rโ, r, R | radius of the closed path; a pointโs true distance; its distance seen from outside, Rยฒ = rยฒ โ Rโยฒ | the map (the drawingโs construction of Bridge ยง3) |
| ฮด | the deficit, the missing share of display area at seen radius R | the map; Bridge ยง3, ฮg ~ 1/rยฒ |
| ฦe, Sโ = ฤง | the electron loop radius, 386.16 fm; the single calibration | Particle Mechanics Math Appendix |
Every line computed. All four views use the same boundary Rโ = 2.5 lattice steps and the same extent (ยฑ6 steps). A draws the flat lattice with the closed path (orange, at c) and the sphere it hides; nothing is bent, because from inside the hidden region is simply there. B maps each grid line of the central plane point by point through R(r) = โ(rยฒ โ Rโยฒ); lines that cross the disk are drawn through the point and out the other side. C and D map their lines through the same map along each radius and then through a fixed perspective camera, nearer lines drawn darker; segment darkness and weight follow the local deficit ฮด (declared), so the interaction zone is where the ink itself accumulates; the near-black is reserved for ฮด = 1, the point. The blue line y = 1 in the z = 0 sheet is the same line in B, C and D and is worked in panel 3. Tables in panels 3 and 4 are computed from the map. Sources: Mathematical Bridge, Bridge Math Appendix, Bridge Narrative, Treatise on Caustics, Loop Closure, Particle Mechanics Math Appendix. Generator: gen_mass_proofs3d.py.
A photon is the smallest piece of light. The ring is one photon trapped in a loop, like on the mass page. The black dot is a big trapped-light mass, seen from outside: you cannot see its hidden space, only the lines of space leaning in toward it.
Nothing pulls the little loop. The lines of space lean toward the missing space, and the loop just follows the lines it lives in. There is the same time between every picture, and the jumps get longer on their own. That is gravity.
Each loop wears dark green where space is squeezed shortest, the side by the mass, and yellow where space runs longest, the side far away. The squeezed side always wins, so the loop swings toward its dark green.
Inside the little loop the photon keeps going around at the same speed the whole time. Outside, the mass is only a dot; the little arrows under pictures 1 and 5 show how much space is missing at the loopโs near side and its far side. The near side is always deeper, and the pair grows as the loop falls.
A photon is the smallest piece of light; this page follows one photon closed into a loop, standing in the missing-space profile of another loop, a mass. Nothing pulls it. Around a mass the lines of space lean in, and the space itself is not the same on the loopโs two sides: on the near side more of it is already missing. The loopโs photon still runs at c, but its route โleans slightly toward the region with more space already hidden and pays a tiny time premium to get pastโ (Bridge Narrative, step 4). That lean, every cycle, is gravity: โno pushes or pulls; cleaner route winsโ. Far away and slow, it is Newtonโs law exactly; the four classical tests of general relativity come out of the same route picture with one factor set once.
One loop of light near a mass, drawn on the same mapped space as the Mass page, and drawn where it is seen: through the massโs map its circle appears elongated toward the mass (Bridge Math Appendix, 6A: โits apparent circle elongates toward the curvature sourceโ). The photon runs at c the whole way round (axiom A2). The space under its two halves is not the same: at the near side, r = 2 ฦโ from the mass, 25% of the space is missing; at the back, r = 4 ฦโ, only 6.25%. In the Walk-Throughโs cost map, n(x) = 1 โ 2ฮฆ/cยฒ with ฮฆ = โGM/r, a step near the mass costs more (โhigher n means this step hides a bit more display-area than averageโ): the near edgeโs premium is twice the far edgeโs, and summed round the two halves the near half pays 1.53 times what the far half pays (computed, โซ(n โ 1) ds; G cancels in the ratio). The colour runs by that cost per step: green where each step hides the most space, yellow where it hides the least. Routes turn toward higher n, that is the ray equation d/ds(n t) = โn, and โn at the loop points toward the mass; so every cycle the loop drifts that way. Only the size of the drift rests on G, an acceptance lock. As a seven-year-old put it: just like a Beyblade in a curved bowl, it wants to go toward the centre.
Five equal-time snapshots of one loop released from rest, drawn where each is seen. The small arrows under pictures 1 and 5 print the share of space missing at the loopโs near and far edge: at picture 1, ฮด = 0.00592 against 0.00444; by picture 5, 0.0969 against 0.0368. Both arrows of a pair point toward the mass, since gravity has no handedness to flip a side, only depth. The near side is always deeper, and the pair grows as the loop falls. Each loop is painted by the cost map along its rim, n โ 1 โ 1/r at each rim pointโs distance from the mass: darkest green where each step hides the most space (the near side, drawn heavier), darkest yellow where it hides the least (the far side), pale between. The loop always swings toward its dark green.
The point on the right is an electron; its missing space is what bends the grid. The five shapes are a second electron at five distances and five speeds, five separate situations. At rest (1) it hides exactly the same space as the first, ฯฦโยฒ each. Moving, its outline is contracted to R/ฮณ along the motion and the mass seen is ฮณmโ (the Mass page). Under each, the acceleration between them in the Newtonian limit, a = Gmโ/rยฒ: about 10โปยนโธ m/sยฒ, which is why gravity between two electrons is never felt, yet the geometry drawn here is the same machinery that runs planets.
Three descriptions, one ladder. Far and slow, everyone tells the same story. Where light bends, is delayed, and clocks drift, Newton falls behind and VMS lands on the tested numbers with general relativity, from one route picture and one factor set once. At the core of a single particle GR runs to infinity where VMS stops, because you cannot hide more space than there is.
Solid: ฮด(R) = ฦโยฒ/(Rยฒ + ฦโยฒ), the quantity every line above is drawn from. Dashed: the pure inverse square (ฦโ/R)ยฒ, the point-mass form Newtonโs gravity and weak-field GR require, normalised in the far field. Near the core they disagree, VMS keeps the scale ฦโ, a point mass has none. The gap closes as the square of the distance: by 10 ฦโ it is 1%; by the Bohr radius, 5 ร 10โปยณ %. For a single particle the two are indistinguishable from there outward.
Every line computed. Grids: the map R(r) = โ(rยฒ โ ฦโยฒ) about the mass, the Mass pageโs construction of the Bridgeโs fixed missing volume and ฮg ~ 1/rยฒ. Loops: radius ฦโ, their rims pushed through the same map, so each is drawn where it is seen, elongated toward the mass. Positions in sections 2 and 4A: equal-time snapshots of infall from rest under a = โGM/rยฒ (GM a visibility choice; the spacing pattern is scale free). Gauges: ฮด = ฦโยฒ/rยฒ at each edgeโs true distance, arrow lengths โฮด on one common scale (declared for visibility), values printed exact. Hue: the Walk-Throughโs cost per step along the rim, n โ 1 = 2GM/(rcยฒ) โ 1/r at each rim pointโs true distance, normalised per loop; the near-to-far premium ratio printed in section 1 is โซ(n โ 1) ds over the two halves, G cancelling. The lean arrow in section 1 is the direction of โn at the loop centre, computed; its length is drawn. Section 3: outlines contracted to R/ฮณ along the motion (Mechanics Math Appendix, section 3), then mapped; accelerations Gmโ/rยฒ with CODATA G, mโ, ฦโ. Section 4B: the four numbers are the Mechanics Math Appendixโs own worked examples (1.75 arcsec, 123.6 ฮผs, 2.455 ร 10โปยนโต, 43.0 arcsec per century). 4C: rph = 3GM/cยฒ and bc = 3โ3 GM/cยฒ from Walk-Through 1A, drawn to scale in units of GM/cยฒ. 4D: ฮด(R) from the map against (ฦโ/R)ยฒ; rs = 2Gmโ/cยฒ computed. The probeโs own dent in space is omitted for clarity. โVMS lands with GRโ means: through the Bridgeโs coupling Gฮผฮฝ = ฮบTฮผฮฝ and the Walk-Throughโs matched kernels, as published.
A photon is the smallest piece of light; this page follows one photon closed into a loop, the probe, standing in the space another loop has shaped, and derives what the high school page stated. A closed Void path removes a fixed transverse area, the deficit that is its inertial mass. That deficit does not stay local: it propagates outward as an inverse-square curvature of the surrounding space. A second loop, its action computed in that geometry, has its path deflected toward the first; in the weak-field, large-distance limit this is exactly Newtonโs law. Gravity is an emergent property of the geometric deficits carried by the loops, not an imposed field. Left, the probe from inside: its hidden region and the path its photon runs. Right, the source from outside: the missing space, with the lattice drawn into it. The orange curve is the probeโs centre, computed, deflected toward the source. Each numbered circle is a panel below.
Published documents used, and nothing else: the Mathematical Bridge (section 3, steps 1 to 6) and its Math Appendix (Mass and Gravity from Closed Void Loops, sections 3 to 7 and 6A, both framings of the Newtonian limit); the Bridge Narrative, step 4; the Mechanics Narrative and Math Walk-Through (the cost map n(x), the ray equation, the bending, delay and clock-drift kernels, periapsis, the photon sphere and capture); the Mechanics Math Appendix (sections 4 to 8, the worked numbers). Only ratios enter; Sโ = ฤง is the one scale; c and G are acceptance locks.
| Symbol | Meaning | Where it is fixed |
|---|---|---|
| ฮ, ฮโฒ | the source loop; the probe loop (both closed Void paths) | Bridge ยง3 |
| Ad, Sฮ, Sฮโฒ | display area; the loop actions โฎAd ds (source, probe) | Bridge ยง1, ยง3; Appendix ยง1 |
| Tฮผฮฝ, Gฮผฮฝ, ฮบ | the loopโs stressโenergy; the Einstein tensor; ฮบ = 8ฯG/cโด, fixed by comparison | Appendix ยง3, ยง5, ยง7 |
| ฮฆ, hฮผฮฝ | the Newtonian potential, โGm/r; the metric perturbation, hโโ = โ2ฮฆ/cยฒ | Appendix ยง7 |
| n(x), ฮทโ | the cost map, 1 + ฮทโฮฆ/cยฒ; |ฮทโ| = 2 set once by the deflection | Mechanics Walk-Through, conventions and ยง1 |
| Rโ, r, R, ฮด | loop radius; true distance; seen distance Rยฒ = rยฒ โ Rโยฒ; the missing share | the map (the drawingโs construction of Bridge ยง3) |
| G, c, Sโ = ฤง | acceptance locks; the single scale | Mechanics Narrative, language and locks |
Every line computed. The lattice is drawn through the map R(r) = โ(rยฒ โ Rโยฒ) about the source, Rโ = 2.5 lattice steps, the same map and scale as the Mass page; ink darkens with the local deficit ฮด (declared). The source loop removes a fixed transverse area ฯRโยฒ from every circle about it on the central plane (the Mass page, panel 4) and its deficit falls as 1/rยฒ (panel 6 table), the seed of the Newtonian potential. The probe loop is drawn from inside: its hidden sphere and its photonโs path, the great circle in the loopโs plane (front half solid, back half dashed), its lattice lines clipped at the sphere. The probeโs centre (orange) is integrated under a = โGM rฬ/rยฒ from a start off the axis with a transverse velocity, GM a visibility choice, then pushed through the map; the arrowheads sit at equal-time positions; the dashed line is the same start with no source. All relations are from the published Mathematical Bridge, section 3, its Math Appendix and the Mechanics documents; G is an acceptance lock and is not fit. Sources: Mathematical Bridge, Bridge Math Appendix, Bridge Narrative, Mechanics Math Walk-Through, Mechanics Math Appendix. Generator: gen_gravity_proofs3d.py.
A photon is the smallest piece of light. This is one photon trapped, one particle, seen from the inside like before. You saw before how it hides space and makes gravity. The direction it goes makes charge.
Where the head meets the tail you can see how it hides the space around it, strongest up close, fading at the speed of light as it moves away. As it spins, it swooshes a bright ribbon through the grey, the swoosh always curls the same way it spins.