The idea that gravity could arise from particle occlusion was first proposed by Nicolas Fatio de Duillier (1690) and later independently by Georges-Louis Le Sage (1748). In Le Sage's model, space is filled with ultra-fast corpuscles (ultramundane particles) moving in all directions. An isolated body intercepts these corpuscles equally from all sides and experiences no net force. When a second body is present, each body shields the other from a fraction of the incoming flux, producing a net push toward the other body.
The classical objection to Le Sage gravity was that the corpuscles would heat the bodies and slow over time, violating energy conservation. The simulation presented here sidesteps this by treating the particle field as a thermodynamic bath maintained at constant temperature — the particles are continuously re-emitted at full speed after absorption, representing the nucleus re-emitting absorbed vacuum energy.
In the modern era we have evidence of the Higgs Field, as well as the nucleus of atoms. Combined they explain the gravitational force as a pressure difference between the nucleus and the vacuum, plus an absorbtion coefficient. Instead of prticles made from matter, a working model would have particles made from the Higgs field itself. My work is a proof of concept that the mechanism of gravity as particle occlusion is physically consistent and numerically verifiable, even if the actual particles in our universe are not the same as those in the simulation. Currently this is the only known mechanism that can reproduce the inverse-square law of gravity without invoking action at a distance, and it is directly observable in the simulation by watching two absorbing bodies drift together over time. The simulation is a proof of concept that the mechanism of gravity as particle occlusion is physically consistent and numerically verifiable.
The simulation maintains a uniform sea of $N$ particles distributed randomly across the domain $\Omega$, each with speed drawn from a uniform distribution:
The particles move in straight lines, collide elastically with boundaries, and are redistributed isotropically after absorption. The mean free path is long compared to the body radii, so the field approximates an ideal gas in the continuum limit. The radiation pressure on any surface element $dA$ from an isotropic particle bath is:
with $n$ the local number density, $k$ Boltzmann's constant, and $T$ the effective temperature of the particle bath.
Consider two spherical bodies $A$ and $B$ of radii $r_A$, $r_B$ separated by distance $d$ (centre to centre), with $d \gg r_A, r_B$.
A single body in an isotropic field receives equal flux from all directions. The net force is zero by symmetry:
Body $B$ intercepts a cone of solid angle
as seen from body $A$. This cone is partially depleted of incoming particles. The shadow deficit on the face of $A$ pointing toward $B$ is:
where $P_0$ is the ambient bath pressure and $\eta \in [0,1]$ is the opacity of $B$. The net force on $A$ directed toward $B$ is then:
Noting that $P_0 = nkT$ and that the cross-sectional areas $\sigma_A = \pi r_A^2$, $\sigma_B = \pi r_B^2$ scale with mass for uniform-density bodies ($m \propto r^3$, so $\sigma \propto m^{2/3}$), we recover an inverse-square force:
For point-like, fully absorbing nuclei the cross-section saturates and the dependence approaches $F \propto m_A m_B / d^2$, recovering Newton exactly.
The simulation implements this mechanism directly. Each frame, for every particle that enters an absorbing body:
for each particle i:
move particle by velocity × dt
for each absorbing body B:
if particle is inside B:
// Transfer momentum to body
B.vx += particle.vx / B.mass
B.vy += particle.vy / B.mass
// Teleport particle to random location outside all bodies
// Assign fresh isotropic velocity
Key parameters of the Gravity preset:
| Parameter | Value | Effect |
|---|---|---|
| Particles | 75,000 | Sets bath density $n$ |
| Speed multiplier | 0.3 | Sets effective temperature $T$ |
| Damping | 0.98 | Near-elastic boundary collisions |
| Particle collisions | off | Reduces inter-particle scattering noise |
| Wrap edges | on | Maintains constant $n$ (periodic boundary) |
| Body radius | 120 px | Sets cross-section $\sigma$ |
| Body mass | 100 | Sets inertia for momentum integration |
The momentum transferred per absorbed particle is:
Summed over all absorbed particles per unit time, this gives a continuous force directed toward the net incoming flux — which is reduced on the side facing the other body, producing attraction.
The force field visualisation (enable Show Force Field) displays the local kinetic energy density of the particle bath:
The shadow between the two bodies is clearly visible as a low-energy (cool, dark) corridor. The pressure differential across each body — higher on the outer face, lower on the inner face — is the direct cause of the attractive force. No action at a distance is required.
The full radiative transport equation for the force density on an absorbing medium is:
where $\kappa$ is the opacity, $f_0$ is the isotropic bath flux, and the exponential is the Beer-Lambert attenuation along ray direction $\boldsymbol{\Omega}$. In the optically thin limit ($\kappa \to 0$ everywhere except at the body surfaces) this reduces to the geometric shadow formula derived in Section 3.
This model makes several testable predictions within the simulation:
1. Force scales as $d^{-2}$ — doubling the separation should quarter the attractive force, as the solid angle of the shadow scales as $d^{-2}$.
2. Force scales with cross-section — larger bodies attract more strongly, independent of their mass. Mass dependence enters only through opacity.
3. Three-body shielding — placing a third body between two others should reduce the pairwise attraction, because the intermediate body re-emits particles isotropically, partially filling the shadow.
4. Retarded propagation — perturbations in the particle bath propagate at the mean particle speed, not instantaneously. Gravitational "signals" are therefore retarded, analogous to the finite speed of gravity in general relativity.
5. Inertia–gravity equivalence — the same particle bath that produces attraction also carries momentum, so a body accelerated through the bath experiences drag proportional to its cross-section, connecting inertial mass and gravitational cross-section.
A common intuition is that being hit by particles from all sides should push bodies apart. This is incorrect. An isolated body is in equilibrium — equal pressure from all directions. It is the deficit of pressure on the facing surfaces that produces attraction. The net force is always directed toward any nearby absorbing body, not away from it.
Classical Le Sage gravity requires the corpuscles to slow down (losing kinetic energy to heat), eventually dissipating. In the present model the absorbed particles are immediately re-emitted at full speed from a random location, maintaining constant $T$. This represents the body acting as a quantum absorber-emitter — absorbing a vacuum fluctuation and re-emitting it in a random direction, consistent with the zero-point field interpretation.
The pressure-shadow model is Lorentz-covariant in the limit where the particle bath moves at the speed of light. In this limit the shadow geometry reproduces the geodesic deviation of general relativity to first order. The effective metric perturbation is:
reproducing the Schwarzschild weak-field result.
Gravity as particle occlusion is a physically consistent, numerically verifiable mechanism that:
— Requires no action at a distance
— Emerges from a single postulate: space is filled with an isotropic particle bath
— Reproduces the inverse-square law geometrically
— Connects gravitational and inertial mass through cross-sectional area
— Is directly observable in the simulation by watching two absorbing bodies drift together
Karl Lilje, 2016 · Particle Lab — Interactive Physics Simulation · ← Return to Simulation