Figure: The polygonal membranes are real space; the interiors are not part of space.
The Lattice
In Swarm Theory, the fundamental structure of reality is not empty volume but a lattice of zero nodes surrounded by flat, tension-bearing membranes. These membranes intersect like woven planes, enclosing each node as if within a geodesic sphere. The lattice is a tension-weave: real, massless, and continuous.
An important consideration: this physical model is the scaffold from which the mathematics was developed. The same mathematics could, in principle, be derived from any physical structure that obeys the same rules. The model should therefore be read as a platform that supports the math, not as a final claim about what spacetime is made of.
Distances, directions, fields, waves, and matter exist only on the membranes. They do not float in a background void. Where the membrane goes, space goes. Where the membrane does not exist, neither does space.
Why the Interiors Are Not Real Space
Each node’s membranes enclose an interior volume, but this interior is not part of the universe. It is not “empty space” — it is the absence of space. Inside there are no distances to measure, no directions to point, no fields to propagate. Waves cannot enter zero nodes because there is nowhere for them to go. Reality is confined to the membrane itself.
How Large Is the Lattice Spacing?
The membranes of the lattice are separated by a characteristic coherence aperture — the repeating distance that defines the weave of space itself. In Swarm Field Theory this spacing is λ ≈ 8.20 × 10−10 m, less than a nanometer and comparable to atomic scales.
This spacing is understood to be static under ordinary conditions. It anchors the constants we measure in the laboratory. At everyday scales the lattice appears perfectly continuous — like a fabric that looks smooth from a distance — because the “threads” of real space are fine enough that light and matter cannot resolve the gaps.
Click to open➡️ Note on high-energy limits
The fixed macro aperture λ and its implied membrane tension do not by themselves support the highest-energy photons observed in nature. Swarm Field Theory allows for three possible extensions (not mutually exclusive):
- Deeper aperture (λS ≪ λ): an additional, finer scale probed only by extreme-energy photons.
- Stretching under load: the lattice may elastically deform when carrying very high-energy waves.
- Induced tension growth: the effective membrane tension increases dynamically with wave energy.
Each path implies a clear experimental test: push the lattice with high-energy events and watch how it responds.
Other characteristic lengths appear as well, such as the node closure length (~8.9 × 10−9 m), which coincides with observed atomic X-ray lines. Together these scales suggest that the lattice has a measurable geometry — and may reveal new behaviour when pushed to its limits.
Why does light travel helically, and can it go faster than c?
A wave bound to two-dimensional membranes cannot move in a straight line through three-dimensional geometry. To advance, it must wrap around the lattice planes, tracing a helix. The helical path is longer than the straight-line projection, which means the observed speed of light c ≈ 2.998 × 108 m/s is always a projected value of the maximum lattice speed cmax ≈ 3.25 × 108 m/s. Arthur’s Constant κ ≈ 0.922 captures the ratio between the two.
Light is massless, so moving faster than c does not violate relativity — the restriction applies only to massive objects. In principle, the lattice supports propagation at cmax. But the geometry of the helix forces every photon we measure to project down to c. No detector can ever register a photon at cmax, because all real propagation is bound helically.
This also explains why information cannot travel faster than c. The lattice may allow a deeper maximum speed, but the helical geometry guarantees that c is the only measurable signal speed. Phase effects may appear to move faster, but information and measurement are always bound by c.
A simple analogy: a sine wave on a rope has a forward speed, but the crest traces a longer path. The local motion is higher than the forward projection, yet the signal speed is fixed. Swarm Theory uses the same idea at the lattice level.
Consequences
- Boundaries: Membranes define where space exists. Interiors are not “places.”
- Quantization: Helical propagation leads directly to discrete action values, including Planck’s constant.
- Forces as geometry: Gravity, inertia, and electromagnetism emerge from membrane tension and curvature.
- Projection effects: Observed constants arise from the geometry of helical propagation.
Light and Vision: Common Questions
Do we really see in straight lines?
No. We only register the lattice waves that strike the retina. The brain reconstructs the scene as if lines extend outward, but vision is the end-point of a wave that has already travelled on the membrane.
If light travels helically, why does it look straight?
Because we only ever see the projection. The helical motion is wrapped around the lattice but what reaches us is the straight-line projection, so c is the speed we measure.
Why does light seem instantaneous?
It is only fast relative to human timescales. Every arrival is still a finite helical propagation across the lattice.
Can we see inside a zero node?
No. The interior is not part of real space. There is no geometry to carry a wave, so nothing to see.
So what do we really see?
We see lattice events — photon resolutions on a biological screen. The lattice is the hidden carrier, not the thing we observe.
Why we cannot see the lattice
The lattice is the projector, not the picture. It never returns an image of itself. We see only the wave that survives to the retina. That is why the weave of real space is hidden: it supports light but is not light.
How can mirrors or lenses bend light if space is a lattice?
Matter is a coherence swarm that locally reshapes the membrane. A helical wave encountering that region meets new boundary conditions — reflection, refraction, focusing — exactly as in optics, but implemented as lattice geometry.
Is this the holographic principle?
Not quite. Holography is about information on a boundary. Swarm Theory says the membranes themselves are the real space. It looks holographic only because we live on a 2D weave that constructs a 3D experience.
Summary
Real space is the membrane. Waves and matter live only on the lattice weave. The interiors of node enclosures are excluded from reality. Helical propagation is demanded by this structure, and from it arise the constants and the quantization we observe.