Last scattering is not the first moment of existence

The photon existed before its final encounter

Follow a background photon through an ionized plasma. It travels between interactions, encounters a free electron, and scatters into a new direction. It can repeat this process. Its final scattering before arrival at a particular observer is called its last scattering.

The word last looks backward from that arrival. It does not mean the photon began to exist at that encounter. In the Thomson limit relevant to the basic picture, scattering mainly redirects existing photons, with negligible energy exchange at leading order. It does not create a fresh photon population every time a path changes.

When free electrons are abundant, such encounters are frequent. The scattering rate per photon is n_e σ_T c: n_e is free-electron number per volume, σ_T is the Thomson cross-sectional area and c is light speed. Their units multiply to inverse seconds, as required for a rate. The relation describes this scattering process, not every possible interaction of light.

As the Universe expanded and cooled, electrons and nuclei increasingly formed neutral atoms during recombination. This reduced the free-electron density and made long journeys without another Thomson scattering much more likely. Neutral gas is not transparent to every wavelength or every process; the statement concerns the background photons and interaction being described.

Optical depth measures the remaining scattering opportunity

A local scattering rate alone is not the whole escape question. A photon can travel through regions whose electron density changes along its path. Optical depth, written τ, accumulates the scattering opportunity along the remaining journey. It is dimensionless.

In the simple independent-scattering description, the probability of no further scattering is P = exp(−τ). The exponential function exp(x) means e raised to the power x, with e about 2.718. A large optical depth makes an unscattered journey unlikely; a small optical depth makes it likely.

For τ = 1, the no-further-scattering probability is about 0.368, rather than zero. For τ = 0.1 it is about 0.905. There is no hard wall at τ = 1 that every photon crosses at the same instant. The probabilities change continuously.

This is an ensemble statement. It predicts proportions for many comparable photon paths, rather than a promise about the next individual photon. The chosen optical depths in the table illustrate attenuation; they do not assign a real cosmic age or redshift to any row.

A broad window replaces a single universal instant

Very early in a dense plasma, encounters are common but a photon that scatters is unlikely to avoid further encounters. Much later, another encounter is unlikely in the first place. Between these extremes there is a range of stages in which an encounter is likely to be the final one. A visibility function describes the resulting distribution of last scattering.

For a concrete synthetic example, define a dimensionless stage s that increases forward. Choose the remaining optical depth τ(s) = exp(−s). This deliberately supplied law becomes smaller at later stages. Its last-scattering density is g(s) = exp(−s − exp(−s)), a weight per unit s. The equation specifies the curve; it is not a fitted recombination history.

The curve is broad and peaks at s = 0, with height about 0.368 per stage unit. At s = −1 the height is about 0.179; at s = 1 it is about 0.255. Both sides contribute. A probability over a stage interval is the area under the curve over that interval, not its height at one point.

No years or redshifts have been assigned to s. The example explains why a last-scattering surface has a finite thickness in its time history; it supplies no actual width or date for our Universe. Detailed models must calculate the changing ionization, expansion and scattering conditions and compare their predictions with data.

Four different physical questions

Photon production asks which processes create or absorb photons. Thermalization asks how interactions establish a thermal spectral distribution. Scattering that merely redistributes energy while preserving photon number is not, by itself, the whole mechanism needed to establish a blackbody distribution from arbitrary initial conditions.

Recombination asks how electrons become bound in neutral atoms. Last scattering asks about the final encounter along an observed photon’s path. The near-blackbody CMB spectrum was established much earlier than the recombination-era last-scattering window. The four questions should not be compressed into one flash of first light.

There is a further qualification in the real history: later reionization freed electrons again, and some background photons scattered later. A discussion of the primary recombination-era background is not a claim that every photon arriving today has avoided every later encounter. The chosen single-window model omits that additional history.

These distinctions also prevent a misleading timeline. The oldest electromagnetic view that travels nearly freely from a particular epoch is not necessarily the oldest physical information of any kind, nor an observation of a first instant. Inferring earlier history requires models and other evidence.

The surface is part of our observational geometry

Looking in different directions, we receive photons whose paths sample the last-scattering region on our past light cone. That is why a sky map can be described as a view of a surface. It is not an opaque shell centred on a privileged location in space, with nothing beyond it.

Another observer elsewhere would have a different past light cone. The smooth background picture does not select our location as the centre of the Universe. Foreground light and later scattering also lie along our sightlines, which is why a measured sky map needs more than the simple escape story.

For a first reading, keep the photon’s history straight: it existed, it interacted, and it later travelled to us. The distribution of final encounters carries information about conditions at that stage. Neither the word last nor the visible surface establishes when existence began.

Worked reasoning

Try the reasoning

1. Was a background photon necessarily created at its last scattering?

   Show the answer and reasoning

   No. An already existing photon can be redirected by an electron.

   Photon production and final scattering describe different processes.

2. The toy visibility density has height 0.368 at s = 0. Does that mean 36.8 percent of photons scatter at that exact stage?

   Show the answer and reasoning

   No. A density’s height is a weight per stage unit, not a point probability.

   An interval probability comes from the area under the curve across that interval.

3. Does the primary recombination-era window prove that no CMB photon scattered later?

   Show the answer and reasoning

   No. Later reionization caused some photons to rescatter.

   The simple single-window model omits that later history and cannot establish its absence.

What to carry forward

• A photon’s last scattering is the final encounter on its observed path, not necessarily its creation.
• Changing scattering opportunities produce a finite window rather than a universal instantaneous boundary.
• Thermalization, recombination and last scattering are distinct stages; none by itself observes an ultimate beginning.