3D Quantum Field Theory: Mediator Field Lattice

Mediator Field

Coupling strength g 1.00

Mediator mass m 0.00

Live Readouts

Separation r

—

Force |F(r)|

—

Potential V(r)

—

Range 1/m

∞

Lattice cells lit

Elapsed time

0.0 s

How it works

Instead of drawing a single force arrow between the two particles, this scene renders the mediator field itself: a lattice of sample points fills 3D space, and each one is lit to the local value of the Yukawa field sourced by both particles, φ(x) = g·e^(−m·r₁)/r₁ + g·e^(−m·r₂)/r₂. Blue-tinted cells sit closer to particle A, orange-tinted cells closer to particle B.

The particles themselves never use a canned force formula — each frame the force on a particle is measured by numerically sampling the field's gradient at its own position (finite differences of the other particle's potential, F = −∇V) exactly as a real field theory computes the force a field exerts on a source sitting inside it:

V(r) = −g·e^(−m·r) / r
F  =  −∇V   (measured from the sampled lattice, not a closed force law)

A massless mediator (m = 0) floods the whole lattice — the field bubble has no edge, matching the infinite-range 1/r² Coulomb force. Raising m visibly shrinks the lit region to a tight shell hugging each particle, the same exponential screening that confines the weak nuclear force to sub-nuclear distances.

Coupling g — brightens and thickens the field lattice at every distance; scales the sampled force.
Mediator mass m — shrinks the visible field bubble's radius toward 1/m; watch the lattice contract as you raise it.
Charge relation — opposite charges follow the sampled gradient inward (attractive); like charges follow it outward (repulsive).
Drag to orbit the lattice and see the field bubble is a genuine 3D shell, not a flat 2D silhouette.

Particle A / field near A Particle B / field near B

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