A Ladder With No Ground Floor But One

Nothing about astronomical distance is directly observable. You cannot lay a ruler against a star, and the only information arriving is light. Everything we know about how far away anything is comes from a chain of inferences, each calibrated against the previous one.

The first rung is the only one that requires no assumption about the object.

Hold a finger at arm's length and close each eye alternately. It jumps against the background, and the size of the jump depends on how far away it is. Observe a star in January and again in July, and the Earth has moved 300 million kilometres, which gives a very long baseline. The star's apparent position shifts against more distant stars, and trigonometry does the rest.

The shifts are extremely small. The nearest star's parallax is less than one arcsecond (roughly the angle subtended by a coin two miles away) and the first successful measurement was not made until 1838, three centuries after Copernicus. Ancient astronomers had used the absence of measurable parallax as an argument that the Earth does not move, which was a perfectly sound inference from the data they could get.

Parallax works out to a few thousand light years with modern satellites. Everything beyond that requires a different approach: find something whose true brightness you know independently, measure how bright it appears, and use the fact that light dims with the square of distance.

Such an object is called a standard candle, and the first useful one was found by a woman employed to count dots on photographic plates.

Henrietta Swan Leavitt worked at Harvard College Observatory as a computer, cataloguing variable stars. Studying Cepheid variables in the Magellanic Clouds, she noticed that the brighter ones pulsated more slowly, and because everything in a Magellanic Cloud is at roughly the same distance from us, apparent brightness could be compared directly.

The period-luminosity relation means a Cepheid's pulsation period tells you its true brightness. Find one in another galaxy, time its pulsations, measure how bright it looks, and you have the galaxy's distance. It is the rung that took astronomy beyond the Milky Way, and Hubble used it in 1924 to establish that Andromeda is a separate galaxy rather than a nebula within our own.

Beyond Cepheids, the ladder uses type Ia supernovae. A white dwarf accreting matter from a companion detonates at a characteristic mass, and therefore with a characteristic brightness, and it is bright enough to be seen across billions of light years. Calibrating them requires Cepheids in the same galaxies, so the rung rests on the one below.

Which is the ladder's structural weakness, and it matters right now.

Each rung is calibrated against the previous one, so a systematic error anywhere propagates outward to everything above it. Overlapping regions where two methods both work allow cross-checking, and the whole structure is only as sound as its foundation.

This is where the sharpest open problem in physics currently sits.

The expansion rate of the universe (the Hubble constant) can be measured two ways. Climb the distance ladder and you get a value around 73 kilometres per second per megaparsec. Alternatively, take the cosmic microwave background, apply the standard cosmological model, and infer what the expansion rate must be now: around 67.

Both numbers have small and shrinking uncertainties. They disagree by far more than either admits. This is the Hubble tension, and it has survived years of attempts to find the mistake.

Either one of the two measurements carries an unidentified systematic error (the Cepheid calibration is the most-suspected candidate, which is partly why the Gaia satellite's dramatically improved parallaxes mattered so much) or the standard cosmological model is missing something between the early universe and now.

Nobody knows which, and the possibility that the model is incomplete is taken seriously by people who would much prefer it not to be. That is worth noticing as an example of how a field behaves when two good measurements disagree: not by picking the convenient one, but by taking both seriously enough to be uncomfortable for as long as it takes.