Plate IX · the clearing
The wall in the infrared
We do not stand in colour. We stand in the microwave — a bath peaking at 1.06 millimetres, two-point-seven degrees above absolute zero. To look into the past is to climb the spectrum: shorter wavelengths, hotter light, slower light. The climb runs 2.8 decades and then stops, and where it stops is not red. It is the infrared, and every colour there has ever been lies on the far side of it.
01 · you are here
The bottom rung is a microwave
Take the bath we actually receive and find where it peaks: λ = 1.0632 mm, T = 2.7255 K. That is the ground floor of the ladder, and it is the only rung anyone has ever stood on. Every other rung on this page is reached by going up.
Going up means going back. Higher on the spectrum is denser, hotter, more compressed — and light itself is slower there, because the medium it hands off through is packed tighter.
02 · the climb
One rung, one wavelength, everything else forced
Name a wavelength and the rest follows with nothing left to choose. The temperature is Wien's law. The rung number is that temperature over ours. The speed of light on that rung is c divided by the rung, and the radiation pressure is the rung to the fourth.
T = b/λ · N = T/T₀ · v = c/N · P = N⁴P₀
Nothing is fitted. Two measured numbers go in — the temperature of the bath we sit in, and how many baryons there are per photon — and the ladder comes out.
03 · the obstacles
Matter is what the light jams around
Light does not travel through emptiness here. It is handed spation to spation, and matter sits in that traffic as pinned obstacles. The ratio that matters is how much of the medium's inertia the obstacles carry against how much the radiation carries — the loading, R.
Far up the ladder the radiation carries nearly all of it and the relay is jammed on itself: light cannot find a clear corridor. Coming down, the obstacles grow in share. The jam breaks when the two are equal.
R = 676.6 / N → R = 1 at N = 677
04 · the wall
1571 nanometres, and no further
That is the whole climb. Loading unity falls at rung 677, a bath peaking at 1571 nm and 1844 K, where light crawls at 4.43 × 10⁵ m/s — one part in a thousand of the speed we measure — under a radiation pressure of 2.92 × 10⁻³ Pa.
Above that rung the medium is jammed and nothing gets out. It is not a surface anyone placed there. It is where the traffic clears.
05 · what you never saw
Red is on the other side
The visible spectrum begins at 750 nm — rung 1418. That is past the wall by a factor of 2.1. Climbing from the microwave you meet the jam in the infrared and stop, short of red, with the entire visible range — rungs 1418 through 2798 — behind it.
So there was a moment when the sky was orange, and one when it was green, and one when it was violet. None of them were ever received. The cut in the model beside you is a cheat: it is the only way to look at colour that never arrived.
06 · not a knife edge
The wall has width
The loading runs smoothly, so the clearing is a sweep rather than a line. Between R = 0.6 and R = 1 the bath moves from 943 nm to 1571 nm — rungs 1128 down to 677.
A band in the infrared, opening gradually, entirely short of red. What we receive is whatever found a clear corridor while it opened.
The ladder
Each row is a wavelength; everything to its right is forced by the four relations above. Swatches carry the true hue of a body at that temperature — below about 800 K there is no visible emission at all, and those rows are tinted for legibility only.
| λ peak | band | T [K] | N | v [m/s] | P [Pa] | R | received |
|---|
What it costs
Two measured numbers, no fitted ones
The ladder consumes the temperature of the bath we sit in and the baryon-to-photon ratio from deuterium. Both are measurements taken elsewhere; neither is tuned to the thing being explained. Nothing on this page was adjusted to make a number land.
The wall's position rests on there being no dark matter. Loading unity is the point where matter and radiation carry equal inertia — and with baryons alone that falls in the infrared. Add a cold dark component to the obstacle budget and the same criterion moves the wall to 196 nm, deep in the ultraviolet, nowhere near what we receive. The claim fails cleanly in that direction, which is the only kind worth making.
Scope
The four relations are exact given the ladder; the wall's position is only as good as the loading criterion, and loading unity is a physical argument rather than a proof. The two neighbouring conventions — equality with and without the three-quarters factor — put the wall at 1571 and 1179 nm respectively, and both sit in the infrared.
Three alternative criteria were tested and fail badly: wave delocalisation misses by fourteen orders, rate-matching by a factor of forty-eight, single-scattering by two hundred and fifty-six. That they miss by orders rather than by margins is the reason for trusting the one that lands.
What the ladder does not yet carry is the harmonic structure of the received bath. That remains open, and it is the largest single thing outstanding.
Wien's displacement constant and the bath temperature are measured; the baryon-to-photon
ratio is taken from primordial deuterium rather than from any fit to the microwave sky, so
that the ladder cannot be circular with what it explains. Swatch colours are computed from
Planck's law against the CIE 1931 observer and converted to sRGB; hue is physical, brightness
is normalised so that dim rungs remain legible. Rungs below visible emission are shown in a
conventional warm tint and carry no colour information.
J. C. Harvey, Melbourne.