What we observe and what we infer

A number on a screen has a history

Suppose an observing programme reports a galaxy's redshift as 0.10. The instrument did not receive the number 0.10 from space. Photons produced signals at different detector locations. A calibration related locations to wavelengths. Astronomers identified a pattern of spectral features, compared it with laboratory wavelengths, and estimated a common shift with an uncertainty.

These steps are part of measurement. They rely on knowledge of detectors, atomic spectra and noise. Calling a quantity 'observed' does not mean it arrived without interpretation. A useful distinction is how far the conclusion is from the detector record and which assumptions each step requires.

An inference is a conclusion drawn from records together with reasoning or a model. Some inferences are tightly constrained and repeatedly checked; others depend strongly on untested assumptions. We should inspect the chain instead of sorting everything into the misleading extremes 'pure fact' and 'mere guess'.

A wavelength ratio before a distance

Let λₑ be the laboratory wavelength assigned to an emitted spectral feature and λₒ the corresponding observed wavelength. The Greek letter λ, pronounced lambda, denotes wavelength: the spatial separation between successive wave crests. With both lengths in the same units, redshift is z = (λₒ − λₑ)/λₑ = λₒ/λₑ − 1. The number z is dimensionless.

Use a synthetic example: λₑ = 500 nm and λₒ = 550 nm. Then z = (550 − 500)/500 = 0.10. A second identified feature at 600 nm would be expected at 660 nm for the same shift. Checking a whole pattern helps distinguish a genuine spectral shift from a mistaken identification of one line.

A physical explanation comes next. Cosmic expansion can produce redshift; motion relative to the large-scale cosmic flow and gravitational effects can contribute too. For a nearby galaxy, its local motion may be important compared with the expansion contribution. An interpretation should say which effects were included or corrected.

Under the ideal expansion interpretation, 1 + z = aₒ/aₑ, where aₒ and aₑ are scale factors at observation and emission. A scale factor tracks relative large-scale separations in a homogeneous cosmological model. Setting aₒ = 1 is a normalization convention, not a measurement of an absolute cosmic size. At z = 0.10 this gives aₑ ≈ 0.909. To infer a distance or travel time, we need the intervening expansion history and must choose the kind of distance.

A microwave spectrum before a cosmic history

The FIRAS instrument on the COBE satellite measured radiation across frequencies. Its analysis separated contributions including an all-sky average component, a directional dipole and Galactic emission. The published spectrum includes a thermal, or blackbody, curve together with residuals and uncertainties. Residuals are the differences between the observed spectrum and a fitted prediction.

That processed spectrum is much closer to an instrument's record than a statement about the Universe's age. A near-blackbody background supports the hot early-Universe account because thermal physics predicts such radiation from an earlier dense, hot state, with expansion shifting its wavelengths. The conclusion gains strength when combined with other evidence, including light-element abundances.

The CMB is not a picture of the moment when everything began. Its photons existed in the early plasma. As neutral atoms formed and free-electron scattering became less frequent, much of the radiation began to travel relatively freely. Later scattering and gravitational effects also modify the sky we observe. A coloured CMB map commonly shows departures from an average temperature; those colours are a visualization choice, not visible colours of the ancient sky.

A precise age inferred from CMB patterns goes further still. It requires a physical model, parameter estimates and an expansion history. A sentence about that age should identify its dataset and model. The existence of the microwave signal is not conditional on adopting one particular numerical age.

A dimmer supernova before an accelerating model

A supernova observation supplies a light curve, meaning brightness as a function of time, along with colours and spectral information. Astronomers compare suitable supernovae after accounting for correlations in their properties. The result is a calibrated relation that can be used to estimate relative distances, with uncertainty and possible systematic effects.

A more distant source is generally fainter for a given intrinsic luminosity, but dust, source differences and selection can also alter the observed sample. Luminosity is emitted power; flux is received power per area. Distinguishing them matters because the instrument measures the arriving light, not the source's total emitted power.

The landmark supernova studies compared inferred distances at measured redshifts with predictions from expansion models. Acceleration was a conclusion from that comparison, supported by later tests, rather than a direct movie of a galaxy increasing its speed. Those studies also examined possible effects such as extinction by dust, population evolution, sample selection and local motions.

An inference can be strong even though several stages separate it from detector counts. Strength comes from successful checks, clear assumptions and agreement among complementary probes. It does not come from pretending that calibration and modelling were absent.

Carry uncertainty through the chain

Random noise causes measurements to vary between repeated observations. A systematic effect can shift many results together, such as a common calibration offset. A model limitation concerns whether the physical account includes the relevant effects. A quoted error bar may describe only some of these sources of uncertainty; read what the analysis actually includes.

For the synthetic 500 nm feature, suppose the observed wavelength has uncertainty ±1 nm and the laboratory value is treated as exact for this exercise. Since z = λₒ/500 nm − 1, the propagated wavelength contribution is ±1/500 = ±0.002. The result is z = 0.100 ± 0.002 under those assumptions. Uncertainty in line identity, laboratory calibration or wavelength calibration would need separate treatment.

This exercise also shows why added decimal places do not create knowledge. Writing 0.100000 would not remove the ±0.002 uncertainty. Conversely, stating uncertainty does not mean the redshift could be anything. It describes the range supported under a specified measurement model.

Read a claim backwards

When you meet a striking statement, trace it back: what fitted quantity produced it, what model connected that quantity to the sky, and which records anchored the fit? Then ask which part would change if an assumption changed. A new distance calibration might alter an inferred expansion parameter while leaving the measured wavelengths intact.

The goal is to preserve distinctions without dismissing inference. Almost all deep knowledge of the Universe requires it. A transparent chain tells us how to improve a result, how to compare two studies, and what new evidence could settle a disagreement.

Worked reasoning

Try the reasoning

1. A laboratory feature at 400 nm is observed at 480 nm. Find z. If all the shift is cosmological and today's scale factor is 1, what emission scale factor follows?

   Show the answer and reasoning

   z = 0.20 and aₑ = 1/1.20 ≈ 0.833.

   The wavelengths have the same unit, so the ratio is dimensionless. The scale-factor answer adds the ideal homogeneous-expansion interpretation; it is not an independent observation.

2. A wavelength-calibration correction changes the measured spectral positions. A new dark-energy model changes the interpretation of distance at fixed z. Are these the same kind of change?

   Show the answer and reasoning

   No. The first changes the measured wavelength estimate; the second changes a model-dependent inference from it.

   Both can matter, but locating them at different stages helps explain which other conclusions must be revisited.

3. Does a red patch on a CMB temperature-fluctuation map mean ancient space literally glowed visible red there?

   Show the answer and reasoning

   No. The displayed colour encodes a numerical temperature departure using a chosen colour scale.

   Read the legend, units, map processing and foreground treatment. The radiation is observed mainly at microwave wavelengths today.

What to carry forward

• Measurements have calibration and processing histories; cosmological conclusions add further physical reasoning.
• Redshift is a dimensionless spectral ratio. Distance, age and scale-factor interpretations require additional assumptions.
• Model dependence should be made explicit and tested; it does not make every inference equally uncertain.
• Keep random uncertainty, shared systematic effects and physical-model limitations visible.