The Universe as a Propagation Channel

Intuition

The journey is part of the experiment

A telescope does not receive a distant galaxy, supernova or early cosmic state. It receives electromagnetic radiation after that radiation has crossed a physical path.

In communications engineering, a received waveform is not automatically identified with the waveform that left the transmitter. The path between them is treated as a channel because it may attenuate, delay, filter, disperse, rotate polarisation, mix modes or otherwise reshape what reaches the receiver.

The claim here is not that the cosmic path must strongly transform every observable. It is that this is a physical question that has to be answered rather than silently removed from the reconstruction.

Why this matters

If propagation is effectively neutral for a particular observable, that should follow from the physics of propagation. If it is not neutral, then part of what is attributed to the source or to cosmic history may instead belong to the journey.

The Argument

Start with the whole communication chain

The most general useful schematic form is an operator chain:

Here \(S\) represents the emitted electromagnetic signal, \(\mathcal H_L\) the physical action of the propagation path over length \(L\), \(\mathcal W\) the receiver and measurement operation, and \(N\) noise and other contributions.

The telescope gives direct access to \(Y\), not independently to \(S\). Writing the channel as an operator keeps open the possibility of transformations more general than ordinary filtering, including a remapping of frequency or time scale.

The receiver can be calibrated; the path is harder

Instrument response can often be tested locally. The propagation history cannot normally be inspected continuously along an astronomical path. Its contribution therefore has to be modelled and constrained from the received evidence.

A channel model has strict obligations

Treating propagation as physical does not permit arbitrary alternatives. A proposed channel must preserve everything observations show to be preserved and transform only what observations show to be transformed.

Depending on the observation, that can include spectral line structure, relative frequency spacing, pulse and light-curve shape, polarisation, phase coherence, image sharpness, angular information and intensity relations.

The useful question

The useful question is not whether propagation can alter a signal. It can.

The useful question is whether one physically specified propagation process can produce the particular transformations astronomy observes while keeping the rest of the record consistent with observation.

That question belongs before those transformations are used as unique evidence about source history or cosmic geometry.

Deep Notes

The simplified source–channel–receiver picture is useful because it separates physical stages that are often compressed into a single act of observation. But once the channel is taken seriously, the problem becomes more demanding. It is not enough to say that light travelled a long distance, or that something may have happened to it along the way. A physical channel has to be described by rules: what properties of the signal it can change, what environmental quantities those changes depend on, how the effect accumulates with distance, and what parts of the original information survive the journey.

This is also where the telecommunications analogy has to become precise. A terrestrial communications engineer normally knows a great deal about the transmitter, the channel conditions and the receiver. In astronomy the situation is reversed. The received field is available locally, the detector can be calibrated, but the source is remote and the propagation history cannot be inspected continuously along the path. Much of that history therefore has to be reconstructed from the same signal whose transformation is being investigated.

That makes the channel part of the inverse problem rather than a correction added after the source has already been reconstructed.

A general channel description

A convenient schematic description is

The source signal \(S\) is acted on by a propagation operator \(\mathcal H_L\), the result is acted on by the receiving and measurement operation \(\mathcal W\), and the observation also contains noise and other contributions \(N\).

The notation is deliberately general. It does not assume that the channel is linear, time invariant or unable to move information between frequencies. The telescope gives access to \(Y\). Recovering \(S\) requires a physically adequate account of \(\mathcal H_L\) and \(\mathcal W\).

The central question of this path is therefore whether the propagation operator assumed in the reconstruction is physically complete enough for the inference being attempted.

The familiar linear channel is only a special case

For an ordinary linear time-invariant system, the operator reduces in the frequency domain to a multiplicative transfer function:

This form is extremely useful for attenuation, phase response and conventional filtering. It is not general enough to represent every conceivable channel transformation.

The channel is not an excuse for arbitrary alternatives

Introducing a propagation operator does not show that redshift, the cosmic microwave background, or any other observation is caused by the journey. It does something more limited but important: it prevents the journey from disappearing from the reasoning.

A proposed channel explanation must specify a physical process. It must say what changes, how that change accumulates, what controls it, and what other observable consequences follow. Only then can it compete with an existing cosmological interpretation.

Ordinary filtering is not enough

In the simplest linear time-invariant case,

Such a filter may change the amplitude and phase of existing frequency components. But multiplying a spectrum by \(H(f)\) does not, by itself, translate every spectral feature from one frequency to another.

A coherent mapping such as

is therefore a stronger requirement than ordinary attenuation or filtering. Any propagation explanation of a systematic redshift must provide a physical process capable of producing that mapping while preserving the observed structure of the spectrum.

Calling the universe a channel does not make redshift easy to explain. It makes the required explanation more precise.

A signal contains more than frequency

An electromagnetic transmission can carry information in several linked structures. Its spectrum is one. Its temporal envelope is another. Polarisation, phase relations and spatial structure may carry additional information.

A proposed propagation process must therefore be tested against the whole received record, not just one number extracted from it.

For example, a mechanism that changes characteristic frequencies but predicts no corresponding transformation of a signal's temporal structure may be distinguishable from a mechanism that coherently rescales the entire waveform.

This is why supernova duration becomes useful later in this path. It is not merely another cosmological observation. It is a test of what kind of channel transformation is being proposed.

Distance changes the problem

Suppose a small transformation accumulates according to

where the evolution of some signal property \(X\) depends on distance and on physical properties of the environment. The accumulated effect is

Even if \(F\) is locally small, the integrated result need not be small when \(L\) is astronomical. This does not establish that such an effect exists. It shows why the actual path length belongs in the physical model.

What is directly measured?

The detector can measure quantities associated with the arriving field, such as observed frequency, intensity, polarisation, arrival-time structure and angular structure, depending on the instrument.

It does not directly measure the emitted frequency at the moment of emission, nor does it inspect every physical state through which the field passed. Those quantities are reconstructed through a model.

The standard cosmological interpretation remains a physical model

In the standard cosmological description, cosmological redshift is connected to the evolution of the scale factor:

This description is not based on redshift alone. It belongs to a much larger network of observations and successful predictions.

A propagation alternative therefore cannot compete with it merely by producing a frequency shift. It would have to reproduce the wider observational structure that the cosmological model explains.

The purpose of this path is narrower: to keep the propagation law explicit and ask whether it is physically complete enough for the inverse reconstruction being attempted.

What would distinguish the possibilities?

A useful propagation model should eventually make predictions that differ from a pure expansion interpretation. Those discriminators have to emerge from the mechanism itself.

They might involve dependence on path properties in addition to distance, frequency-dependent residuals, polarisation signatures, cumulative spectral distortions, correlations with intervening matter or fields, or a specific relation between spectral and temporal transformations.

The exact tests cannot be chosen before the mechanism is specified. That is the burden of the channel hypothesis: it must eventually do more than reinterpret existing observations.

The point of the path

Before the received signal is used to reconstruct source history or cosmic evolution, the physical properties of that journey deserve their own model.

The next question is then unavoidable: could such a channel produce the systematic frequency shift that we call redshift?