Lumen⁴'s light survives the lens vacuum. What matter feels of it changes, and so does the sky.
Lumen⁴ worked out light from ordinary 4D Maxwell. The force chapter then put a different vacuum under it, to pin 1/r. Do Lumen⁴'s conclusions still hold? Almost all of them do, and exactly. In the lens vacuum, the fields D/ε₀ and μ₀H obey Maxwell's equations in empty 4D space, with the same charges and currents as sources. So the light that travels is Lumen⁴'s light. What's new is how matter feels it.
light: E′ = D/ε₀, B′ = μ₀H, Maxwell's in 4D · what pushes a charge: E = E′/ℓ|k|, B = B′/ℓ|k|
The second line is a lens: at each instant it blurs the light across all of space with a 1/r³ kernel. A wave of one frequency ω has a single |k| = ω/c, so the lens is just one number for it, c/ℓω. Its pattern isn't changed at all, only its strength. A sudden flash has every k at once, and the lens smears it across space at once.
| Lumen⁴ says | in this universe |
|---|---|
| a point fades as 1/r³; a line as 1/r² | holds. The light is Maxwell's, spreading over a 3-sphere. |
| a laser is a line, a dot in your slice | holds. |
| a flash leaves a negative wake | holds for the light. Matter also feels a flash faintly before its front arrives, because the lens acts across space at once. |
| a round hole's first dark ring at 1.43 λ/D | holds. One wavelength goes through the lens as one number, so every pattern is unchanged. |
| three polarizations; glare polarized in a plane | holds. |
| hot bodies: ν⁴/(eˣ − 1), power as T⁵ | holds. A body in balance with its light fills every mode of it, and the lens doesn't change the modes. |
| the rainbow, and its conic sections | holds as geometry. The 42° is our water's, though. 4D water's refractive index is unknown. |
| (not in Lumen⁴) how hard light pushes | new. Long waves push charges harder, by c/ℓω. Small particles scatter as ω³, where 4D Maxwell gives ω⁵ and ours ω⁴. |
Air scatters short waves more than long ones, which is why our sky is blue: scattering grows as ω⁴. With plain 4D Maxwell it would grow as ω⁵, and 4D sunlight (ν⁴) is bluer to begin with, so the sky would be deeper blue still. Through the lens, a particle both feels the wave and sends its scattered light at c/ℓω, against an incoming flux that carries c/ℓω once. That takes two powers of ω off: ω³. Here are the three skies at noon under a 5800 K sun, computed. Each assumes a polarizability that doesn't depend on frequency, as for our air.
Light travels at c, and Lumen⁴'s relativistic wave optics stand. The force between charges doesn't wait for light: wiggle a charge and every other charge feels a little of it at once, through the lens. So there is an absolute now, and a preferred frame in which the lens is instantaneous. Electromagnetism isn't relativistic here, though its light is. One length, ℓ, sets how strong the pinned force is.
So we don't rebuild Lumen⁴: we annotate it. Lumen⁴ and IRIS⁴ stand as the physics of this universe's light, and Lumen⁴'s page now points here for what matter makes of it.
ATOM⁴: the position · how it works · Lumen⁴ · IRIS⁴ · KATABASIS · Four · the arcade