Lesson 1 of 6 · Redshift, scale factor & distance
Read expansion in a spectrum
10 minute lesson · 3 checks along the way
Your goal for this lessonCalculate a cosmological redshift from identified spectral lines and explain what additional assumptions connect it to distance or time.
Words with a dotted underline open a short definition right here in the lesson.
Identify a pattern before assigning a shift
A spectrum separates received light by wavelength. Atoms leave recognizable combinations of emission or absorption lines, which laboratory measurements place at known . describes how expansion increases the wavelengths of traveling light. A red-looking object alone is insufficient evidence: dust and a cool emitting surface can also change color without moving every spectral feature by one common factor.
Define redshift as z = (observed wavelength − rest wavelength) / rest wavelength. The numerator and denominator must use the same units, so z is dimensionless. A positive value means the identified feature is observed at a longer wavelength. Checking several features guards against mistaking one atomic transition for another, a detector artifact, or light from an unrelated foreground source.
Check 1 of 3
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Work through a decision
Use the same multiplier for different lines
In an invented spectrum, two securely identified lines with rest wavelengths 400 and 500 nanometers appear at 800 and 1,000 nanometers. The first gives z = (800−400)/400 = 1. The second gives (1,000−500)/500 = 1. Both wavelengths doubled, despite increasing by different numbers of nanometers. A proposal that adds the same 400 nanometers to every line would predict the second at 900, contradicting the measurement.
For light whose shift is entirely cosmological, 1+z = a(now)/a(emission), where a is the of the expanding universe. Conventionally set a(now)=1. Here 1+z=2, so a(emission)=0.5. This describes a ratio of large-scale separations at two times; it does not state that the universe was half its current age. Expansion can proceed at different rates during different eras.
Match a multiplier, not an offset
Original instructional spectrum with invented features, not an observed source. Horizontal positions use the same linear nanometer scale; line heights carry no physical flux information.
Open full-size diagram in a new tab: Match a multiplier, not an offsetCheck 2 of 3
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Expansion has no marked central address
The standard large-scale model treats the universe as approximately and : statistically similar from place to place and direction to direction on sufficiently large scales. Unbound locations following the average cosmic flow separate as the scale factor grows. An observer elsewhere would also find distant systems generally receding. This pattern does not identify our galaxy as the center of an explosion into surrounding empty space.
Local forces still matter. Stars, planets, and gravitationally bound galaxies do not simply expand in proportion to the cosmic scale factor. A galaxy can also have a relative to the average flow, adding a local Doppler contribution to its measured redshift. For a nearby object, that contribution may be important compared with the small shift associated with expansion.
Choose the relation appropriate to the evidence
At sufficiently small cosmological redshift, recession speed is approximately cz and the local distance relation is v≈H₀d. Those approximations are useful when their errors and peculiar motions are controlled. Applying v=cz at z=1 as though it measured ordinary motion through a static room ignores the cosmological geometry. At large redshift, distance also has several distinct definitions, depending on what is being measured.
To turn the toy z=1 result into a , supply an expansion history and its parameters. To infer a distance, specify the distance convention too. A responsible report therefore keeps the measured line positions separate from the adopted cosmological model. Another team can then test the same spectrum with a revised model without pretending that the photons or laboratory wavelengths have changed.
Check 3 of 3
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Put it together
Your lesson progress
Each check connects to a part of the story. Complete all 3 to earn your 25-point lesson bonus.
Go to the source
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