Two ways of measuring one universe, and clear air between the answers

mainstream · published, sourced, re-read on import

The universe has an expansion rate. There is one of it.

km s⁻¹ Mpc⁻¹ · 1σ

Measure it from the infant cosmos and you get one number; measure it from the present-day sky and you get another, and the two do not overlap. Both methods have been checked for a decade by people trying hard to find their own mistakes. The gap has only got harder to explain away.

Planck 67.40 ± 0.50 — the infant cosmos — the microwave afterglow, read through our best model of physics. CCHP 70.39 ± 1.94 — the tip of the red-giant branch — a different rung, climbed independently. SH0ES 73.04 ± 1.04 — the present-day universe — a ladder of Cepheid stars and exploding suns.

Planck and SH0ES do not touch at one sigma. Every figure here is computed from its published source rather than written into the sentence — the last time this page typed its numbers, two of them were out of date and one was misread.

held · ours, and re-runnable

It is not a coincidence.

the arithmetic

Two careful measurements can land apart by luck. Not this far apart. Taking the separation and dividing by the two uncertainties added in quadrature gives 4.89σ, and the odds of a gap that wide arising by chance are about 1.0×10⁻6 — one in 979,501.

The teams themselves quote the tension at 5σ, comparing the measurement against the standard model’s prediction with a fuller error treatment than two headline numbers in quadrature. Both figures are correct calculations of slightly different questions, and the interesting part is how little it matters which you take: the gap is wide enough that how you measure the measuring barely moves it.

Five sigma is the bar physics sets for calling something a discovery. By that standard the disagreement is the discovery.

mainstream

The tension is not between two instruments.

two ages of one light

Both rulers read the same medium. One reads the oldest light there is — the afterglow of the first transparent moment, stretched cold by the whole age of the universe, arriving with no clock of its own. The other reads the newest: Cepheids and supernovae shining now.

It is between the universe’s earliest light and its latest — and neither can be talked into agreeing with the other, because light does not renegotiate what it carried.

held · computed so it can be shown, not described

So it averages, and produces a number no instrument measured.

the crowned mean

Almost every system that stores this has one slot for the answer. Weight each reading by its own precision, combine, and out comes 68.56 — a single confident number sitting in the clear air where the data specifically is not.

The average is not a mistake of arithmetic. It is the honest output of a container with one slot. The mistake is upstream, in choosing a container that cannot hold a disagreement — and then reading its output as though the disagreement had been resolved rather than flattened.

held · a property of the substrate, checkable in the code

Hue is identity and it is fixed at birth.

the three channels

In our index a concept is a colour, and each of its three channels moves in exactly one direction. This is not a convention we follow carefully. It is the shape of the type.

Two measurements of the expansion rate are two identities, not two samples of one. There is no operation that merges them into a third, because there is no way to write one — the field has no setter. Saturation is how completely the looking has been accounted for, and it only ever drains: every direction a reading opened and left open costs it, and so does every place two readings part. It cannot be talked back up — not by agreement, and not by combining two things you would like to see agree. Lightness is how much the collective has looked, and it fills toward one without ever arriving, so nothing in the index is ever finished.

held · the refusal is mechanical

Hand it two rulers and it will hold two rulers.

the seam

The centre that these readings would meet in refuses a crisp bond outright — a clean 0 or 1 is treated as a crown and declined at the seam — and its live meter returns named numbers with, deliberately, no single score.

That is not restraint applied by a careful operator. It is the only thing the substrate can do.

A five-sigma disagreement between two of the best instruments ever built is not a problem to be smoothed over until it fits the container. It is the most informative thing in the room, and it deserves a substrate that can carry it at full width.