Cosmology · Cosmic scale, time and looking into the past

Looking back in time and estimating age

A signal can be seven billion years old while showing an object that was only three billion years old. Learn to keep travel time, object age and cosmic age on separate clocks.

Preparation: ratios, powers of ten and ordinary arithmetic. Physical quantities and notation are introduced as they are needed.

Back to the chapter

After reading, you can

Distinguish lookback time, cosmic age at emission and the age of an observed object.
Calculate these intervals from a labelled synthetic timeline.
Explain why converting redshift into a time requires an expansion history.

Which clock does the number describe?

Suppose an image brings us light that travelled for a long time. That travel interval does not tell us how old the emitting star was when it shone. A newly formed star in a distant galaxy and an old star in that galaxy can have nearly the same light-travel time while having very different ages.

Lookback time is the interval between the cosmic time assigned to an emission event and that assigned to reception in a chosen cosmological model. Cosmic age at emission is the time since the model's chosen early-time origin up to that emission event. The object's age at emission is the interval between its own formation and emission. The three intervals use different endpoints.

The phrase 'age of the light' often refers informally to lookback time. It should not be read as an ordinary clock carried by a photon. A photon has no rest frame in which we can attach such a clock. Use named emission and reception events and a specified time coordinate instead.

Put the events on one labelled timeline

Use a deliberately synthetic history, expressed in billions of years, abbreviated Gyr. The model's reference early time is t = 0. An object forms at t = 2 Gyr, emits the observed light at t = 5 Gyr, and that light is received at t₀ = 12 Gyr. These values are chosen to teach intervals; they are not estimates for the real Universe or a particular object.

The lookback time is t₀ − tₑ = 12 − 5 = 7 Gyr, where tₑ is the emission time. The cosmic age at emission is 5 Gyr relative to the chosen origin. The object was 5 − 2 = 3 Gyr old when the light left. All three statements can be true together.

If the same object survives to t₀ in this simplified history, its age then would be 12 − 2 = 10 Gyr. We do not directly observe that later state in the arriving light. Survival and evolution are additional physical questions. A distant object may have changed or ceased to exist after the event we see.

Synthetic events and intervals: one cosmic-time convention, not measured cosmic history
Quantity	Calculation	Meaning
Cosmic age at reception	12 Gyr	Reception time since the model's origin
Cosmic age at emission	5 Gyr	Emission time since that origin
Lookback time	12 − 5 = 7 Gyr	Interval from emission to reception
Object age when seen	5 − 2 = 3 Gyr	Interval from formation to emission
Object age at reception, if it survives	12 − 2 = 10 Gyr	An inferred later age, not the observed earlier state

Synthetic linear cosmic-time axis, not measured cosmic history. Formation at 2 Gyr, emission at 5 Gyr and reception at 12 Gyr give an object age of 3 Gyr at emission, lookback time of 7 Gyr, and a possible age of 10 Gyr at reception only if the object survives. The received light directly shows its earlier state. Coloured intervals also have explicit labels. Original Ark teaching diagram.

Redshift is not a clock without a history

In the ideal homogeneous expansion interpretation, cosmological redshift gives the ratio 1 + z = a₀/aₑ. With today's scale factor normalized to a₀ = 1, redshift z = 1 corresponds to aₑ = 0.5. This tells us a relative scale factor. To assign a time, we need to know how a changed with cosmic time.

Two hypothetical histories can reach a = 0.5 at different cosmic ages. A model that expands more rapidly during an interval can pass through the same scale-factor change in less time. A measured redshift ratio alone therefore cannot choose a unique lookback time.

The expansion history depends on physical assumptions and parameters. Cosmological time estimates integrate that history. Distance, background-radiation and other observations constrain the model; the model then relates redshift to cosmic time. Changing the allowed model can change the inferred age or interval without changing the measured spectral ratio.

This is why a plot of redshift against cosmic age should identify its cosmology. A second age axis placed above a redshift axis is a model-based conversion, not a universal relabelling independent of assumptions.

An object's age uses a different physical model

A star's spectrum and brightness can be compared with models of stellar evolution. A galaxy's light combines populations formed at different times, with effects from composition, dust and star-formation history. Estimating an age from such light is a physical inference; it is not obtained by subtracting a distance from today's date.

Be clear about what an age means. The age of the oldest stars, an average age weighted by emitted light, and the time since a galaxy assembled much of its mass need not be the same. A small young population can contribute substantial light without representing most of a galaxy's stellar mass.

A consistency check compares an inferred object age at emission with the cosmic age available at that emission event in the chosen cosmology. If the object appears older than the permitted cosmic time, something in the estimates, definitions or assumptions requires examination. The discrepancy does not automatically identify whether stellar modelling, observational calibration or cosmology is responsible.

A model's time origin has a domain of validity

The age assigned by a cosmological model is usually a cosmic-time interval traced back through the adopted expansion history. Extrapolation toward an extreme early regime can reach a boundary where known physics is insufficient. A fitted age does not by itself describe an ultimate creation event or establish that no earlier phase existed.

Distinguish the question the data answer from a broader interpretation. A model can supply a useful time since a specified early boundary while leaving the physical origin of that boundary open. More speculative early scenarios require additional definitions and evidence rather than a casual change of the word 'beginning'.

For ordinary reading, carry a short set of questions: age of what, at which event, measured or inferred how, and within which history? Those questions prevent many apparently paradoxical statements about ancient light and young objects.

Worked reasoning

A young object in an old image

In another synthetic timeline, an object forms at t = 3 Gyr and emits at t = 4 Gyr; reception is at t₀ = 10 Gyr. A report calls it a 'six-billion-year-old object'. What should the report say?

Calculate the lookback interval: 10 − 4 = 6 Gyr.
Calculate the object's age at emission: 4 − 3 = 1 Gyr.
Distinguish the endpoints: the signal's lookback interval is six Gyr, while the object was one Gyr old in the observed state.

Say: 'We observe the object at a lookback time of six Gyr in the stated model; it was one Gyr old at emission in the assumed formation history.'

Try the reasoning

In the 12-Gyr synthetic history, an object forms at t = 4 Gyr and emits at t = 8 Gyr. Give its observed age and lookback time.
Show the answer and reasoning
It was 4 Gyr old at emission, and the lookback time is also 4 Gyr.
The equal numerical values are a coincidence: 8 − 4 and 12 − 8 use different pairs of endpoints.
Does z = 1 alone establish that an object's light has travelled for half the current cosmic age?
Show the answer and reasoning
No. It establishes a scale-factor ratio of two only under the ideal cosmological-redshift interpretation.
The relationship between scale factor and time depends on expansion history. A factor of two in scale does not imply a factor of two in age.
An inferred stellar age at emission exceeds the inferred cosmic age then. What is the first responsible response?
Show the answer and reasoning
Check the age definitions, data, uncertainties and physical assumptions in both estimates.
The mismatch is a consistency problem to investigate. Its existence alone does not identify a particular new physical explanation.

What to carry forward

Lookback time, cosmic age and object age have different endpoints.
The arriving light shows an earlier state, not the source's directly observed present state.
Redshift becomes a clock only after an expansion history is specified.
Age comparisons are useful tests when their definitions, models and uncertainties are aligned.

References

Sources supporting the explanations, physical distinctions and examples in this lesson.