Astronomy & Celestial Mechanics
the sky, computed
Cosmology

The most perfect blackbody ever measured

The whole sky glows at 2.7255 kelvin, and its spectrum matches the Planck curve to fifty parts in a million. Nothing else in astronomy is thermal to a part in twenty thousand, and a spectrum that exact is not a description of the radiation — it is a constraint on the history of everything that could have disturbed it.

Assumes Stellar colour and Expansion.

18 min read 8 figures Light is the only messengerMeasuring the unreachable

Point a radio receiver anywhere in the sky, away from the Galactic plane, and it detects a signal. Point it somewhere else and it detects the same signal, to one part in a hundred thousand. The signal is not from anything in particular; it is a floor, present in every direction, and it has the spectrum of a body at 2.7255 kelvin.

The temperature is not the finding. The shape is.

A blackbody at 2.7255 kelvin, filling the sky. The Planck function at 2.7255 K in the units the measurement is reported in, with the peak marked where Wien's law in frequency puts it: x = hν/kT = 2.8214, so ν = 160.2 GHz and the intensity there is 384 MJy per steradian. The points are drawn at the twenty-one frequencies across the FIRAS band, displaced from the curve by a Gaussian of 50 parts per million of the peak, which is the root-mean-square deviation the instrument actually reported. At the scale of this plot that displacement is a fifth of a pixel and the points sit on the line — which is the entire finding. Nothing else in astronomy is a blackbody to a part in twenty thousand: a stellar spectrum is a blackbody with absorption lines cut into it and a continuum that is the wrong shape at both ends. A thermal spectrum this exact requires that the radiation was once in equilibrium with matter, which requires that the universe was once opaque, which requires that it was once hot and dense.
Fig. 1 The Planck function at 2.7255 K in the units the measurement is reported in, with its peak where Wien’s law in frequency puts it: x=hν/kT=2.8214x = h\nu/kT = 2.8214, so ν=160.2\nu = 160.2 GHz and the intensity there is 384 megajanskys per steradian. The points are drawn at twenty-one frequencies across the band the FIRAS instrument covered, displaced from the curve by a Gaussian of fifty parts per million of the peak, which is the root-mean-square deviation the instrument actually reported. At the scale of this plot that displacement is a fifth of a pixel, and the points sit on the line. That is the entire result, and it is why the error bars in the published figure had to be drawn four hundred times too large to be visible at all.

Nothing else in the sky does this

Colour is a thermometer because a hot dense body radiates a spectrum whose shape depends on nothing but its temperature. That is a theorem about matter and radiation in equilibrium, and it is the foundation of half the measurements in this collection. What is easy to lose is how badly real objects approximate it. A spectrum this thermal is a statement about history rather than about the source. Perfect thermal equilibrium between radiation and matter requires many scatterings, which requires opacity, which requires that the radiation was once confined in a hot, dense, ionised medium. There is no way to produce a Planck spectrum by adding up emission from a collection of transparent objects, because each object contributes its own shape and the sum is not thermal. The 2.7 K spectrum therefore says, on its own and before any other observation, that the universe was once opaque.

A blackbody at 2.7255 kelvin, filling the sky. The Planck function at 2.7255 K in the units the measurement is reported in, with the peak marked where Wien's law in frequency puts it: x = hν/kT = 2.8214, so ν = 160.2 GHz and the intensity there is 384 MJy per steradian. The points are drawn at the twenty-one frequencies across the FIRAS band, displaced from the curve by a Gaussian of 50 parts per million of the peak, which is the root-mean-square deviation the instrument actually reported. At the scale of this plot that displacement is a fifth of a pixel and the points sit on the line — which is the entire finding. Nothing else in astronomy is a blackbody to a part in twenty thousand: a stellar spectrum is a blackbody with absorption lines cut into it and a continuum that is the wrong shape at both ends. A thermal spectrum this exact requires that the radiation was once in equilibrium with matter, which requires that the universe was once opaque, which requires that it was once hot and dense.
Fig. 2 The same curve out to three terahertz, five times past the band FIRAS covered. The Wien tail falls exponentially and the measurement stops long before it becomes small — which is the practical reason the high-frequency end of the published spectrum is where the Galactic dust foreground is comparable to the signal, and the reason the useful band ends where it does. The shape is the finding and the shape is verified over a decade in frequency rather than over the whole curve, because past that decade the sky in front of the background is brighter than the background.

Why expansion leaves the shape alone

An objection presents itself immediately. If the radiation was thermalised long ago at high temperature, and has been redshifting ever since, why is it still thermal? Redshifting is not a thermalising process — nothing is scattering any more — so why has the spectrum not been distorted out of shape?

The one spectrum expansion leaves alone. The same radiation at three epochs, drawn on logarithmic axes. Each curve is a Planck function at T = 2.7255(1+z) K, and nothing else has been done to it: the point is that expansion, which stretches every photon's wavelength by (1+z) and dilutes their number by (1+z)³, takes a blackbody to another blackbody rather than to some redder non-thermal thing. The peak moves by (1+z) in frequency and the peak intensity by (1+z)³, so between z = 0 and z = 3 the curve rises by a factor of 64 and slides right by 4, and its shape is unchanged. That invariance is what makes the microwave background usable as a thermometer of the past. It also means the observed 2.7 K spectrum cannot by itself date the epoch it came from — the temperature does that, and the temperature at high redshift has been measured independently, from the excitation of carbon and carbon-monoxide lines in absorption against distant quasars, and it follows the (1+z) law.
Fig. 3 Because the stretching is proportional. Each curve is a Planck function at T=2.7255(1+z)T = 2.7255(1+z), and the three are the same curve moved: expansion multiplies every photon’s frequency by 1/(1+z)1/(1+z) and dilutes their number density by (1+z)−3(1+z)^{-3}, and a Planck distribution transformed that way is exactly a Planck distribution at a temperature lower by (1+z)(1+z). The peak moves by (1+z)(1+z) and the peak intensity by (1+z)3(1+z)^3, and the shape does not move at all.

The reason is worth stating properly, because “the photons all redshift the same amount” is not sufficient — that would preserve the shape as a function of frequency but not the normalisation. What actually happens is that both the occupation number of each mode and the frequency of each mode transform in exactly the way that leaves the Bose–Einstein form invariant with T∝1/aT \propto 1/a. A blackbody stays a blackbody under free expansion, and no other spectrum has that property.

The one spectrum expansion leaves alone. The same radiation at three epochs, drawn on logarithmic axes. Each curve is a Planck function at T = 2.7255(1+z) K, and nothing else has been done to it: the point is that expansion, which stretches every photon's wavelength by (1+z) and dilutes their number by (1+z)³, takes a blackbody to another blackbody rather than to some redder non-thermal thing. The peak moves by (1+z) in frequency and the peak intensity by (1+z)³, so between z = 0 and z = 1100 the curve rises by a factor of 1334633301 and slides right by 1101, and its shape is unchanged. That invariance is what makes the microwave background usable as a thermometer of the past. It also means the observed 2.7 K spectrum cannot by itself date the epoch it came from — the temperature does that, and the temperature at high redshift has been measured independently, from the excitation of carbon and carbon-monoxide lines in absorption against distant quasars, and it follows the (1+z) law.
Fig. 4 The same three-curve construction run out to the surface of last scattering. At z=1100z = 1100 the radiation is at three thousand kelvin and its peak is in the near infrared, which is where the universe was when it became transparent — and the curve is the same curve, moved by a factor of eleven hundred in both axes’ natural units. What the figure asserts is that no distortion accumulated over that entire journey, and the residual measurement in the next section is the bound on how much did.

This has a consequence that is directly testable. If the radiation is cosmological, its temperature at redshift zz must have been 2.7255(1+z)2.7255(1+z). That has been measured, from the excitation of carbon and carbon-monoxide levels seen in absorption against distant quasars, out to z=6.3z = 6.3. The measured temperatures follow the linear law, and the constraint on any departure is a few per cent. A local radiation field from some nearby source would not do that, and the test is the reason the last serious alternatives were abandoned.

The measurement itself is worth a sentence, because it is a good example of this subject’s habit of reading a number off something that was not built to carry it. A cold interstellar cloud sitting in a bath of radiation has its atomic and molecular levels populated according to the bath’s temperature, provided the levels are separated by energies comparable to kTkT and provided nothing else is exciting them. Carbon’s ground-state fine-structure levels are separated by about 0.0079 electronvolts, which is kTkT at 92 kelvin — close to the background temperature at z=2.4z = 2.4 — so the ratio of two absorption lines in a quasar spectrum is a thermometer for the radiation at that redshift. It is the same trick as reading composition out of absorption, applied to the excitation rather than to the identity of the lines.

The one spectrum expansion leaves alone. The same radiation at three epochs, drawn on logarithmic axes. Each curve is a Planck function at T = 2.7255(1+z) K, and nothing else has been done to it: the point is that expansion, which stretches every photon's wavelength by (1+z) and dilutes their number by (1+z)³, takes a blackbody to another blackbody rather than to some redder non-thermal thing. The peak moves by (1+z) in frequency and the peak intensity by (1+z)³, so between z = 0 and z = 10 the curve rises by a factor of 1331 and slides right by 11, and its shape is unchanged. That invariance is what makes the microwave background usable as a thermometer of the past. It also means the observed 2.7 K spectrum cannot by itself date the epoch it came from — the temperature does that, and the temperature at high redshift has been measured independently, from the excitation of carbon and carbon-monoxide lines in absorption against distant quasars, and it follows the (1+z) law.
Fig. 5 The temperatures that measurement reaches. At z=3z = 3 the background is at eleven kelvin and its peak has moved to 640 gigahertz; at z=10z = 10 it is thirty kelvin and 1.8 terahertz. Neither is observable directly from here — the radiation arriving now is the z=0z = 0 curve, whatever redshift it is looked at from — so the quasar-absorption thermometer is measuring the local bath at that epoch through its effect on a cloud, which is the only way any of these curves is checked. Three of the plot’s curves are the past and one of them is a spectrum.

What the residual excludes

The flatness of the residual is not a null result; it is one of the strongest constraints in cosmology, and it is a constraint on things that did not happen.

What a spectrum with no features rules out. The deviation from a pure blackbody, in parts per million of the peak intensity, at the scale FIRAS measured it. The shaded band is the ± 50 ppm the instrument achieved and the points are a realisation of that noise; the curve is what a Compton-y distortion of y = 1e-4 would look like, computed from ΔT/T = y(x coth(x/2) − 4). Its distinctive shape — a deficit below 227 GHz and a surplus above, crossing zero where x coth(x/2) = 4 — is the signature of photons being scattered up in energy by hot electrons after the universe became transparent. It is drawn an order of magnitude above the bound and it is still barely outside the band, which gives the sense of scale: the measured limit is y < 1.5 × 10⁻⁵, and that single number bounds every process that could have injected energy into the radiation over more than a decade of cosmic history. A spectrum with no features is not a null result. It is a constraint on everything that did not happen.
Fig. 6 Deviations from a pure blackbody, in parts per million of the peak, at the scale FIRAS measured them. The shaded band is the ±50\pm 50 ppm the instrument achieved and the points are a realisation of that noise. The curve is what a Compton-yy distortion of 10−410^{-4} would look like — the shape produced when hot electrons scatter background photons up in energy after the universe has become transparent, computed from ΔT/T=y(xcoth⁡(x/2)−4)\Delta T/T = y(x\coth(x/2) - 4), with its deficit below 217 GHz and its surplus above. It is drawn an order of magnitude above the measured bound and is still barely outside the band.

The published limits are ∣y∣<1.5×10−5|y| < 1.5\times10^{-5} and ∣μ∣<9×10−5|\mu| < 9\times10^{-5}, and each bounds a different epoch. A μ\mu-distortion — a chemical potential, meaning photons whose number is wrong for their energy — can only be erased while double Compton scattering is fast, which stops at about z=2×106z = 2\times10^6; so a μ\mu limit constrains energy injection between then and recombination. A yy-distortion cannot be erased at all once scattering stops, so a yy limit constrains everything since.

Between them those two numbers say that no process anywhere in cosmic history added as much as one part in ten thousand to the energy of the radiation. Decaying particles, evaporating primordial black holes, dissipating acoustic waves, an early generation of stars: all are bounded by a single measurement of a spectrum with no features in it.

What a spectrum with no features rules out. The deviation from a pure blackbody, in parts per million of the peak intensity, at the scale FIRAS measured it. The shaded band is the ± 50 ppm the instrument achieved and the points are a realisation of that noise; the curve is what a Compton-y distortion of y = 5e-5 would look like, computed from ΔT/T = y(x coth(x/2) − 4). Its distinctive shape — a deficit below 227 GHz and a surplus above, crossing zero where x coth(x/2) = 4 — is the signature of photons being scattered up in energy by hot electrons after the universe became transparent. It is drawn an order of magnitude above the bound and it is still barely outside the band, which gives the sense of scale: the measured limit is y < 1.5 × 10⁻⁵, and that single number bounds every process that could have injected energy into the radiation over more than a decade of cosmic history. A spectrum with no features is not a null result. It is a constraint on everything that did not happen.
Fig. 7 The same comparison with the distortion halved, to y=5×10−5y = 5\times10^{-5}. It is now only just distinguishable from the noise band by eye, which is a fair picture of where the published bound of 1.5×10−51.5\times10^{-5} actually sits — a factor of three below anything a drawing at this scale can show. That is the awkward property of a null result: the constraint tightens as the curve becomes invisible, so the figure that best conveys the strength of the limit is the one that shows a distortion the data already excluded.

There is one distortion that is guaranteed to exist and has not been detected. Hot gas in galaxy clusters produces a yy-distortion along lines of sight through them — the Sunyaev–Zel’dovich effect — and that is observed, cluster by cluster, and is one of the three independent routes by which a cluster gets weighed. What has not been observed is the average over the whole sky, which standard structure formation predicts at y≈2×10−6y \approx 2\times10^{-6}, a factor of seven below the FIRAS bound.

What a spectrum with no features rules out. The deviation from a pure blackbody, in parts per million of the peak intensity, at the scale FIRAS measured it. The shaded band is the ± 5 ppm the instrument achieved and the points are a realisation of that noise; the curve is what a Compton-y distortion of y = 1e-4 would look like, computed from ΔT/T = y(x coth(x/2) − 4). Its distinctive shape — a deficit below 227 GHz and a surplus above, crossing zero where x coth(x/2) = 4 — is the signature of photons being scattered up in energy by hot electrons after the universe became transparent. It is drawn an order of magnitude above the bound and it is still barely outside the band, which gives the sense of scale: the measured limit is y < 1.5 × 10⁻⁵, and that single number bounds every process that could have injected energy into the radiation over more than a decade of cosmic history. A spectrum with no features is not a null result. It is a constraint on everything that did not happen.
Fig. 8 What an instrument ten times more sensitive would see. The noise band has shrunk to five parts per million and the same distortion now stands well outside it — and so would one a tenth its size. That is the case for a successor mission stated as a picture: the predicted all-sky signal is a factor of seven below the present bound and a factor of a few above this band, so it is not an ambitious target but an arithmetic one. The measurement has not been made because the instrument has not been flown, rather than because the signal is hard to compute.

The cluster effect has a property that makes it unlike every other way of finding distant objects, and it follows directly from the shape drawn above. The distortion is a fixed fractional change in a background whose surface brightness does not fall with distance, so a cluster’s signal is independent of how far away it is. A survey that finds clusters by their microwave shadow finds them equally well at z=0.1z = 0.1 and z=1.5z = 1.5, which no optical or X-ray survey can do — and that redshift-independence is why cluster counts became a cosmological probe rather than a catalogue.

What was actually measured

The measurement is unusual in this field for being a laboratory measurement carried out in orbit. FIRAS, on the COBE satellite, was a differential instrument: it compared the sky against an internal blackbody calibrator whose temperature could be tuned, and reported the difference. When the calibrator was set to match the sky, the difference went to zero, and what was measured was the calibrator’s temperature with a platinum resistance thermometer.

That design is the whole reason for the precision. An absolute radiometer has to know its own gain, its own emissivity and its own losses at every frequency, and getting any of those to a part in ten thousand across a decade of frequency is not possible. A null instrument has to know none of them — it only has to be stable while the calibrator is moved in and out, and it has to have a calibrator whose emissivity is genuinely 0.9999, which was achieved with a re-entrant cone of iron-loaded epoxy.

The published spectrum has 43 points and error bars smaller than the thickness of the line. The dominant remaining uncertainty is not statistical and not instrumental: it is the subtraction of foreground emission from Galactic dust, which at the high-frequency end of the band is comparable to the signal.

The one number the spectrum hands over

A blackbody has one parameter, so the measurement returns one number — and 2.7255 kelvin is not, by itself, of much interest. What makes it consequential is that a temperature fixes the number density of photons, and the number density of photons compared against the number density of baryons is the quantity the early universe is actually described by.

The Planck distribution gives nγ=411n_\gamma = 411 photons per cubic centimetre at this temperature, with no assumptions in the arithmetic beyond the temperature itself. The baryon density comes from elsewhere — from the primordial abundances, or from the anisotropies — and the ratio is

η=nbnγ≈6×10−10.\eta = \frac{n_b}{n_\gamma} \approx 6\times10^{-10}.

There are about two billion photons in the universe for every proton, and that ratio has not changed since the first minutes, because expansion dilutes both alike and nothing since has created or destroyed either in appreciable numbers.

That number is the single parameter of big-bang nucleosynthesis. Everything about the primordial abundances — the quarter of the mass that is helium, the deuterium at a few parts in 10510^5, the lithium that does not quite work — follows from η\eta and from nuclear physics measured in laboratories. It is also, up to a constant, the entropy per baryon, and it is enormous: ordinary matter in the universe is a trace contaminant in a bath of radiation, by number if not by energy.

And it is not explained. A universe with equal matter and antimatter would have annihilated to η=0\eta = 0; a universe with a slight excess of matter annihilates down to η\eta equal to that excess. So the measured value says that for every billion antiquarks in the early universe there were a billion and one quarks, and the whole of the material world is the remainder. The number is measured to two per cent and derived from nothing, which is among the sharper open problems in physics.

Why the universe stayed opaque so long

That ratio also settles a question the spectrum raises and does not answer: at what temperature the radiation stopped scattering.

The naive figure is wrong by a factor of fifty, and the reason it is wrong is instructive. Hydrogen’s ionisation energy is 13.6 electronvolts, which corresponds to kTkT at 158,000 kelvin, so the obvious guess is that hydrogen recombines and the universe clears at around that temperature. The measured figure is close to 3,000 kelvin.

The discrepancy is η\eta doing its work. Ionisation does not require the typical photon to carry 13.6 eV; it requires only that there be enough photons in the high-energy tail of the Planck distribution to keep the atoms apart, and the tail falls off exponentially while the number of photons available is two billion per atom. A distribution whose typical photon carries a fiftieth of the ionisation energy still has, out of two billion, enough above the threshold to keep hydrogen ionised.

So the universe stayed opaque until the exponential tail had been driven down by a factor comparable to η\eta itself — which is to say until kTkT was roughly 13.6 eV/ln⁡(1/η)13.6\ \text{eV}/\ln(1/\eta), and ln⁡(1/η)\ln(1/\eta) is about 21. The temperature of last scattering is set by the logarithm of the photon-to-baryon ratio, which is why it is a few thousand kelvin rather than a hundred and fifty thousand, and why the surface of last scattering sits at redshift 1,100 rather than at 12,000.

The same argument runs earlier and gives the same kind of answer: deuterium, bound by 2.2 MeV, does not survive until the temperature has fallen well below that, for exactly the reason above, and the resulting delay — the deuterium bottleneck — is what postpones nucleosynthesis to three minutes and fixes the helium fraction at a quarter. One measured ratio, arrived at by counting photons in a spectrum with no features in it, sets the clock on both.

What the pictures cannot show

The hero figure draws points scattered at the measured deviation and they are not the measured points. The real FIRAS residuals are a specific set of forty-three numbers with a specific correlated structure from the calibration; what is drawn is a Gaussian realisation at the published root-mean-square. The figure’s claim is about the scale of the agreement, not about the shape of the residual, and the caption says so.

Nothing here shows the anisotropies, which are the part of the microwave background that most of the science comes from. They are one part in a hundred thousand, and on the vertical axis of the hero figure they are four hundred times smaller than the line width. The spectrum and the anisotropy are two different measurements of the same radiation, made by different instruments on the same satellite, and they answer different questions.

And the temperature is not uniform even at zeroth order. The largest anisotropy on the sky is a dipole of 3.36 millikelvin — a part in a thousand, twenty times the fluctuations — and it is not cosmological: it is an ordinary Doppler shift from the Solar System’s motion at 370 km/s with respect to the frame in which the radiation is isotropic. Every map subtracts it. That subtraction is also a measurement, and it is as close as physics gets to a determination of absolute velocity — not because the frame is privileged in any dynamical sense, but because there is at last a frame every observer can agree on how to find, which is a convenience relativity does not otherwise supply.

How it was found, twice

The radiation was predicted in 1948 by Ralph Alpher and Robert Herman as a corollary of hot big-bang nucleosynthesis, at “about 5 K”, and the prediction was not pursued. It was rediscovered theoretically in the early 1960s at Princeton, where Robert Dicke’s group was building a radiometer to look for it.

They were beaten by two engineers who were not looking for it. Arno Penzias and Robert Wilson, at Bell Labs, had a horn antenna intended for satellite communications and an excess noise temperature of about 3 K that they could not remove. They checked the receiver, they checked the joints, they evicted a pair of pigeons and cleaned the horn. The noise was isotropic, unpolarised, and unchanged over a year, which ruled out the Earth, the Solar System and the Galaxy in turn. The elimination of every alternative was the measurement; the detection itself had been sitting in the noise budget of radio astronomy for years.

The 1965 announcement was two papers side by side: one reporting the excess temperature and carefully declining to interpret it, the other, from the Princeton group, explaining what it was.

FIRAS came twenty-five years later and did something quite different. By then the existence of the radiation was settled and the question was whether it was thermal — because the steady-state alternatives that survived 1965 explained the radiation as starlight thermalised by dust, and a dust-thermalised spectrum is not a perfect Planck curve. The measurement took nine minutes of data to exclude them.

The generalisation

The habit this essay turns on appears throughout physics and is under-taught: an agreement can be a stronger measurement than a discrepancy, provided the agreement is with a shape that has no free parameters.

A Planck curve has one parameter, the temperature, and it fixes the value at every frequency. Matching it at forty-three frequencies is therefore forty-two independent tests, and each of them is a bound on something that could have gone wrong. Compare that with fitting a straight line to forty-three points, where two parameters absorb most of the freedom and the residual scatter measures the noise rather than the physics.

The same structure appears wherever a rigid functional form is available. The equal-area law fixes the timing at every point of an orbit once one is given, so measuring sixteen of them is fifteen tests of angular-momentum conservation. The Fraunhofer wavelengths are fixed by atomic physics, so a shift measured on twenty lines at once is twenty checks that the shift is a shift. The 2\sqrt{2} between circular and escape speed holds at every radius without exception, which is why a figure that draws it at one radius has demonstrated much less than one that draws it across a range.

The corollary is the one worth carrying into the rest of this field: a measurement that agrees with a parameter-free prediction to five digits is not a confirmation, it is a set of exclusions, and the interesting question is always what has been excluded.

Where the ladder goes next

The spectrum says the universe was once opaque and says nothing about what was in it. The information about the contents is in the part of the signal this essay set aside — the one part in a hundred thousand by which the temperature varies across the sky — and the next rung takes it up.

Later rungs on this anchor: the surface of last scattering itself, and why it happened at three thousand kelvin; the dipole, and what it means to measure a velocity with respect to the universe; polarisation, and the second, independent map the same photons carry; spectral distortions as a future observable rather than a bound; the Sunyaev–Zel’dovich effect as a way of finding clusters at any redshift; and the neutrino background, which is the same argument run with a different particle and has never been detected directly.

Where this goes next

Blackbody curves at 3000, 5800, 10000 K. Thermal emission against wavelength, each curve scaled to its own peak so the shift can be seen on one plot. The peak moves to shorter wavelengths as the temperature rises, which is why colour is a thermometer. Colour is a thermometer, and it reads across the galaxy A star's colour gives its surface temperature, from two brightness measurements and no other information. It is the cheapest useful measurement in astronomy. An absorption spectrum at 5772 K. A blackbody continuum at 5772 K with absorption lines cut out of it, each line's depth computed from how much of the gas is in a state that can absorb it. 8 of the 8 lines are strong enough to see at this temperature, which is the whole reason the spectral sequence is a temperature sequence. Composition, read from what is missing The dark lines in a stellar spectrum are wavelengths that never arrived. Which ones are absent names the elements present — and the strength of a line says more about temperature than about abundance. The same recession law from two different galaxies. Twenty galaxies at fixed comoving positions after the whole picture has been multiplied by 1.34, with each galaxy's displacement drawn from where it was to where it is. Every arrow's tail sits at the old separation and its tip at the new one, so the arrow is exactly 0.34 times its tail's distance from the highlighted galaxy — proportional to separation for one reason and no other: a uniform scaling moves everything in proportion to its distance from whatever point the scaling is measured about. The right-hand panel measures from a different galaxy and gets the identical law with the identical constant. That is the content of a linear velocity–distance relation. It is the signature of an expansion with no centre, and the observation that every galaxy recedes is therefore not evidence that this one is the centre — it is evidence that none of them is. The shift that is not a Doppler shift Every galaxy beyond the Local Group has its lines shifted to the red, by an amount proportional to its distance. Read as a velocity that looks like a confession that everything is fleeing from here; read as a change of scale it says the opposite, because a uniform expansion produces exactly the same law measured from any galaxy in it.

What this makes readable

Essays that name this one as a prerequisite.

About the same objects

Not linked from either essay — found by the objects both name.

What links here

The 8 of 22 essays linking to this one that name the most of the same objects.

The objects this essay names

Each one links to every other essay that touches it.

Blackbody spectrumCompton y parameterCosmic microwave backgroundEntropy per baryonLast scatteringPhoton to baryon ratioPlanck functionRadiation densitySpectral distortionThermal equilibrium