SCIENCE · INVESTIGATE AND EXPLAIN

Connect redshift to expansion ratios without a speed shortcut

Cosmological redshift is the ratio of observed to emitted wavelength minus one. In a homogeneous expanding background with present scale factor one, 1+z=1/a_emit. The scale factor relates large-scale comoving separations; it does not imply that every atom, star or bound galaxy expands with the same rule.

Learning outcome: Close wavelength, energy, time and scale-factor ratios, then identify the additional expansion-history assumptions required for a distance.

Starting recap

Keep galaxy mass, source calibration, expansion history and independent cosmological evidence distinct.

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Try

At z=1 and emitted 600 nm, the scale factor is 0.5, observed wavelength 1200 nm, photon-energy ratio 0.5 and time-stretch factor 2. The supplied adiabatic background temperature is 5.451 K, not the temperature of every emitting object.

Open the experiment

Predict

Does one redshift by itself specify a unique distance or lookback time?

Your prediction and reason

Experiment

Close wavelength, energy, time and scale-factor ratios, then identify the additional expansion-history assumptions required for a distance.

Connect scale factor, photon wavelength and time intervals

Worked teaching model · synthetic values · Original homogeneous expansion with present scale factor 1: a_emit=1/(1+z), lambda_obs=(1+z)lambda_emit, photon energy ratio 1/(1+z), time-stretch 1+z. Reference radiation temperature 2.7255 K scales as 1+z under adiabatic expansion; no peculiar-speed conversion.

Cosmological redshift: 1 z Emitted wavelength: 600 nm

Reset keeps your prediction, captures and practice history.

Cosmological redshift connects expansion ratios, not a universal special-relativistic peculiar speed.

Original homogeneous expansion with present scale factor 1: a_emit=1/(1+z), lambda_obs=(1+z)lambda_emit, photon energy ratio 1/(1+z), time-stretch 1+z. Reference radiation temperature 2.7255 K scales as 1+z under adiabatic expansion; no peculiar-speed conversion.

Original conditional model ledger
Quantity	Value	Unit
Emission scale factor	0.5000000	ratio to present
Observed photon wavelength	1200	nm
Observed/emitted photon energy	0.5000000	ratio
Observed/emitted time interval	2	ratio
Adiabatic radiation temperature at emission	5.451000	K

These supplied models are not current measured cosmological parameters, a new galaxy discovery or independent actual observing evidence.

Cosmological redshift connects expansion ratios, not a universal special-relativistic peculiar speed.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

1. Define the cosmic evidence

2. Connect mechanisms and alternatives

The original calculation supplies an emitted wavelength and redshift. Observed wavelength is(1+z) times the emitted value, photon energy is reduced by the inverse factor and an emitted time interval is stretched by 1+z when observed. These statements concern radiation propagated through the stipulated expanding background.

Under adiabatic expansion of a thermal radiation field, its temperature scales inversely with the scale factor. A supplied present reference 2.7255 K therefore becomes 2.7255(1+z) K at emission. This does not identify a particular source’s effective temperature or supply a full early-universe thermal history.

At large cosmological redshift, applying cz or a special-relativistic isolated-source Doppler conversion as a universal peculiar speed is inappropriate. Distances and lookback times need an expansion history. The redshift of the actual archived QSO used earlier can be discussed in this framework without pretending the course independently remeasured its pipeline value.

3. Work the supplied comparison

4. Predict and investigate

Does one redshift by itself specify a unique distance or lookback time?

Close wavelength, energy, time and scale-factor ratios, then identify the additional expansion-history assumptions required for a distance.

Apply the evidence to a changed case

At z=2 and emitted 400 nm, find observed wavelength, emission scale factor and background reference temperature.

Retain the evidence frame, calculations and assumptions before opening public feedback.

Compare a worked response

Observed wavelength is 1200 nm, emission scale factor 1/3 and reference radiation temperature 8.1765 K. The same observed wavelength can arise from a different emitted wavelength/redshift pair.

Source and boundaries

Primary source. Checked 31 October 2026. Original model records are not new galaxy observations, current parameter measurements or a full cosmological inference pipeline. No physical observing procedure is requested.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

At z=2 and emitted 400 nm, find observed wavelength, emission scale factor and background reference temperature.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Separate a local expansion estimate from velocity offsets Next: Distinguish expansion rate, distance and lookback time

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