Picking up where Hubble left off
From the first guide in this rung you carry one firm fact: almost every distant galaxy has its light shifted toward longer wavelengths, and the farther the galaxy, the larger the shift — the proportion we named [[hubbles-law|Hubble's law]]. You also know it is tempting, and wrong, to read this as every galaxy flying away through space with us at the center of the fleeing crowd. This guide is about what the redshift truly is. The short answer is that it is not motion through space at all; it is space itself doing the stretching. Getting that distinction right is the hinge on which all of cosmology turns.
Recall too the rule that lets us measure any redshift at all. Stamped across a galaxy's light is a barcode of spectral lines sitting at fixed, laboratory-known wavelengths. To find a galaxy's redshift you locate that barcode and measure how far the whole pattern has slid toward the red — moving as one rigid unit, every line stretched by the same fraction. That fraction is the redshift, written z. A galaxy whose lines all arrive ten percent longer than their rest wavelengths has z equal to 0.1; one whose lines arrive at twice their rest wavelength has z equal to 1. The number is just a ratio of wavelengths, and that simplicity is about to pay off.
What is actually stretching
Here is the heart of it. When a galaxy launches its light toward us, the light wave sets out crossing the space between us — and over the millions or billions of years of its journey, that space is not standing still. It is expanding: every region of empty space is gradually growing larger, a feature we call the [[expansion-of-space|expansion of space]]. The light wave is carried along inside that growing space, and as the space swells, the wave swells with it. Its crests are drawn farther apart. By the time the light reaches your telescope, its wavelength is longer than it was at launch — not because the galaxy outran it, but because the road underneath it lengthened while it traveled. That stretch is the [[cosmological-redshift|cosmological redshift]].
Why insist that this is not the ordinary Doppler shift you met earlier in this rung? Because the cause is genuinely different. The [[doppler-shift-of-light|Doppler shift]] comes from a source moving through space relative to you, and its size depends on how fast the source travels along your line of sight. The cosmological redshift comes from the space between you and the source expanding, and its size depends on nothing more than how much that space grew during the light's trip. Nearby — within our galaxy, between two stars in a binary — there is no meaningful expansion to speak of, so what you measure there is a true Doppler shift. On cosmic scales the stretch of space takes over, and the Doppler formula quietly stops being the right tool.
The scale factor: one number for the whole universe
To make this precise we need a way to say how big the universe is — not in kilometers, since there may be no edge to measure, but in relative terms. That is the job of the [[scale-factor|scale factor]], written a. Think of it as a ruler for the universe itself. We set its value today to exactly 1, and then a tells you the relative size of every distance between far-apart galaxies at other times. When a was one half, every such cosmic distance was half what it is now; when a was one tenth, every cosmic distance was a tenth of today's. The galaxies do not move to make this happen — they ride along, roughly fixed in the grid, while the grid itself rescales. The scale factor is the single number that captures, for the whole cosmos at once, how much it has grown.
Now the payoff, and it is beautifully clean. The light wave is stretched by exactly the same factor as space. So the wavelength you receive, divided by the wavelength at which it was emitted, equals the size of the universe now divided by its size back when the light set out. Written with the scale factor and the redshift z, that is the relation below. Read it once and a great deal clicks into place: the redshift is not really a velocity at all — it is a direct, honest measurement of how much the universe has expanded since that ancient light began its journey.
1 + z = lambda(observed) / lambda(emitted) = a(now) / a(then) z = 0 -> 1 + z = 1 -> universe same size as now (light from next door) z = 1 -> 1 + z = 2 -> universe was HALF its present size z = 9 -> 1 + z = 10 -> universe was 1/10 its present size z ~ 1100 -> the cosmic microwave background: universe ~1/1100 its size
This reframing is worth pausing on. A galaxy's redshift is no longer mainly a speed; it is a kind of timestamp. A redshift of 1 means its light left when the universe was half its present size — and, working through how fast the universe grew, several billion years ago. The faint glow of the [[cmb-relic-radiation|cosmic microwave background]], the oldest light we can see, carries a redshift near 1100: its wavelength has been stretched roughly a thousandfold, which is why light that was once a fierce orange-hot glow now arrives as cool microwaves at about 2.7 kelvin. The redshift quietly doubles as a clock, telling you not just where a galaxy is but when its light was born.
Misconceptions this clears up
The stretched-space picture is not just tidier — it quietly resolves a whole cluster of puzzles that the naive moving-galaxy picture creates. The first is the question of a center. If galaxies were truly flying outward through space, surely they fly from somewhere, and we could trace the explosion back to its origin. But there is no such point. Because it is space everywhere that grows, an observer on any galaxy sees exactly what we see — all the others receding, in the same tidy proportion. Every vantage point looks central and none is. This is not luck; it is the [[cosmological-principle|cosmological principle]], the well-tested assumption that on the largest scales the universe looks the same from everywhere.
The second puzzle is faster-than-light speed. If you wrongly treat a large redshift as a velocity through space, the most distant galaxies seem to recede faster than light — an apparent violation of relativity that troubles many newcomers. The resolution is simply that the redshift is not a velocity. Nothing is moving through space at those speeds; space is expanding, and the rate at which the distance between two faraway points grows can exceed the speed of light without anything traveling through space at all. Relativity forbids matter from racing past light through space; it sets no such limit on how fast space itself may stretch. The galaxies sit nearly still in their patch of space while the gulf between widens.
Reading the universe's history in a redshift
Once you see redshift as a record of expansion, it becomes a way to read history. Because light travels at a finite speed, looking far out is looking far back: a galaxy at z = 2 shows you not how it is today but how it was when the universe was a third of its present size, its light spending most of the universe's age in transit. This marriage of distance and time is the [[look-back-time|look-back time]] you met earlier. Sorting galaxies by redshift sorts them by epoch, letting us watch the cosmos as a movie — galaxies young and clumpy at high z, mature and settled nearby — rather than a single frozen snapshot.
Be honest about what redshift alone does and does not pin down. The bare relation 1 + z = a(now)/a(then) tells you how much smaller the universe was when the light left — that is exact. But turning that into an actual distance in light-years, or an actual age in years, requires knowing the full history of how fast the scale factor grew, which depends on what the universe is made of and how it pulls on itself. That extra machinery — the contents of the cosmos and the equations governing the scale factor — is precisely what the rest of this rung builds. Redshift hands you the stretch cleanly; converting stretch into a calendar and a map is the work still ahead.
Step back and feel how far this one idea reaches. The same simple stretch that reddens a faraway galaxy's light, run backward in your imagination, tells you the whole universe was once smaller, denser, and hotter — and pushed back far enough, that is the seed of the Big Bang story you will meet next. The scale factor is the thread running through all of it: a single number whose history is the history of the cosmos. Master cosmological redshift and you hold the key that lets starlight, by nothing more than how stretched its waves arrive, report on the size and age of the universe itself.