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I've had this question for a while. I understand the universe is full of "dust". I am also aware of the fact that there is an average measure of particle density in the universe.

I am assuming for this question that these are actually separate, meaning where there is dust, there is dust, everywhere else, there is the background "1 proton per cubic meter" (or whatever, not important to be exact here). It could be that this is a false dichotomy and therefore the question falls away.

If not, I ask on the latter: this "1 proton per cubic meter", on the scale of billions of light years - does it produce a dimming/colouring of what we see that we have to take into account? In the same way distant mountains become blue because air isn't 100% transparent?

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One way of thinking about this is in terms of the physics of the cosmic microwave background. The cosmic microwave background occurs as a phenomenon when a nearly homogeneous universe transitions between being hot and ionised and opaque to electromagnetic radiation to being slightly cooler, mainly neutral and transparent to visible and longer wavelength light.

Given that the universe has expanded and become rarefied (on average) by a factor of $(1100)^3$ since then, it should be obvious that absorption by atomic hydrogen at most wavelengths must be negligible. The exception to that is short wavelength radiation which may be absorbed by atomic transitions in hydrogen and at observed wavelengths that depend on the redshift of the absorbing gas. This leads to phenomena like Damped Lyman Alpha systems, which are broad absorption lines caused by discrete clouds of neutral hydrogen along the line of sight. The amount of absorption at wavelengths corresponding to wavelengths shortward of the rest wavelength of the Lyman Alpha transition ($121.6$ nm) can be 50% or more at redshifts of $>3$ (Thomas et al. 2020).

In terms of ionised hydrogen, we could think about Thomson scattering from electrons, which has a cross-section of $\sigma = 6.6\times 10^{-29}$ m$^2$ and is wavelength-independent. A reasonable fraction of the Universe's hydrogen is ionised and given that the ionised early universe was opaque it requires a calculation to see what the opacity of those electrons might be now. This does require an estimate of the density, and the number $n$ of a few (say 3) electrons per cubic metre is not a bad estimate. The mean free path of a photon before it is scattered is given by $(n\sigma)^{-1} = 5\times 10^{27}$ m, or 500 billion light years. This is a lot bigger than the observable universe and so can be neglected.

In terms of dust, this requires heavy elements (carbon, silicon, oxygen) and these are produced inside stars. Most star formation in the universe occurs at redshifts of around 3-5 or less. Some of that dust is expelled from galaxies and pollutes the intergalactic medium. This should produce a small extinction/reddening effect which is bigger for shorter wavelength light. There have been estimates of this - Thomas et al. (2020) look at various datasets and review various work which seems to suggest a reddening parameter of just $E(B-V) \sim 0.1$ out to redshifts of 3 or 4, which equates to an extinction of just 20-30% at visible wavelengths.

So what effects does this have? In the case of absorption shortward of Lyman alpha it means there are dramatic changes in the colours of the galaxies at wavelengths corresponding to redshifted Lyman alpha. i.e., the extinction is very wavelength-dependent;the galaxies' light can be completely absorbed at shorter wavelengths. The effects of dust are much more subtle. The extinction occurs across a broad range of wavelengths and there is a small reddening effect; but it is so small that it has been very difficult to measure with any precision.

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    $\begingroup$ Thank you for getting right into my head and giving me a perfect answer. $\endgroup$
    – Rabbi Kaii
    Commented Nov 24, 2022 at 12:28
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    $\begingroup$ "This is a lot bigger than the observable universe and so can be neglected." Its radius is about a tenth of that, so a few percent of photons will eventually scatter, but the most distant observable galaxies are probably subject to about as much obscuration as a tenth of the mean free path in a more familiar air-based example. That's about 10 nm, so you're right that the obscuration effect is negligible. (The per-scatter obscuration effect could be different in the two cases, but not enough to matter.) $\endgroup$
    – J.G.
    Commented Nov 25, 2022 at 17:09
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In a sense yes - there is interstellar (i.e. intra-galactic) absorption of Lyman-$\alpha$ photons by neutral hydrogen.
This plays a role e.g. when trying to determine how much hydrogen is lost from hot exoplanets via 'planetary winds' into space - one observes the Ly-$\alpha$ line, but it is obscured at the center, so only the broad line wings are left to study.

On a cosmological scale (i.e. very much extra-galactic), this effect continues to exist: as we look back to ever-increasing redshift, the Ly-$\alpha$ line coming to us will have been (partially) absorbed by blobs of neutral hydrogen at any redshift. But because throughout the universe, hydrogen exists everywhere, just not very uniformly, this creates a continuous spectral absorption effect known as the Ly-$\alpha$-forest.

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    $\begingroup$ Thank you for your answer, bringing me right to where I wanted to go. If I could expand a bit on my question now, is this effect something that is merely a technical thing that our complicated instruments need to take account of, or would this even be a visual effect in say, a visual-spectrum hubble image of deep sky? Are those galaxies a different colour than they would be if they were closer? (having accounted for doppler shift of course - I don't want to confuse that with this question). If we say, "air is blue", what colour is "universe"? $\endgroup$
    – Rabbi Kaii
    Commented Nov 24, 2022 at 12:04
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    $\begingroup$ @RabbiKaii The Universe radiates mostly in the non-visible - no sensible colours can be assigned to those wavelengths. Ly-a is already in the ultraviolet. $\endgroup$ Commented Nov 24, 2022 at 13:34
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    $\begingroup$ ok thank you! That clears things up (pun unintended but I wish I had intended it when I wrote it) $\endgroup$
    – Rabbi Kaii
    Commented Nov 24, 2022 at 13:57
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    $\begingroup$ @AtmosphericPrisonEscape but redshifted Lyman alpha can be in the visible as can damped Lyman alpha systems. $\endgroup$
    – ProfRob
    Commented Nov 24, 2022 at 13:57
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“ hydrogen in the universe create an obscuration effect similar to the way air does at great distances?”

Ask the one who looked, not the one who didn’t.

Ultraviolet astronomy was (effectively) unfunded, at least by mega-funders, because enough people suspected the interstellar medium (galactic gas, overwhelmingly hydrogen) would just result in a “fog” at those wavelengths- certain hydrogen lines, which are largely in the UV. (This did not stop solar and planetary UV astronomy, since solar illumination is good, and distances are irrelevant for the interstellar medium.)

At some point, someone with decent enough resources did a UV program, and found… no fog, really. The interstellar medium, as embodied as hydrogen gas, forms a “cirrus”- patchy and wispy. Plenty of things are visible, even in the UV, where the hydrogen just so happens to be thinner, not thicker. Even in some arbitrarily-dense regions of hydrogen, a fine enough spatial resolution (“high magnification”) decreases the background level, but does not decrease point sources (e. g., stars). A well-planned observing program then experiences a worse signal-to-noise ratio, but may be able to continue anyway, depending.

And of course, this is in UV- hydrogen has no strong lines in vis. If you want to get pedantic, you can even do UV astronomy by exploiting wavelengths between the H wavelengths, though in some spectral regions this will mean seriously expensive filters, with serious discrimination.

We can repeat this exercise for dust. Dust is primarily an issue in infrared, both due to self-emission (thermal) and the inherent size of particles. Depending on the details of your observation, the dust will be relevant or irrelevant. This includes those looking at the dust itself .

Vague, ill-posed questions get vague, inconclusive answers. What is your target, what is your hypothesis/null hypothesis, what is your observing plan, and your (baseline) instrument? For a given line of investigation, a better question is whether your instrument will answer that particular question, or whether you need more funding to produce a significant result (including any non-vague answer). The notion that things are “invisible/visible” presumes a particular eye, observer, etc. Not a telescope technology, a program with a given resource level, or possibly an observer with a new approach.

The history of astronomy is littered with people who “saw the light” after they tried a new way (though, more and more these days, that means trying to win more funding). The notion of “invisible” (and thanks for saying “obscuration” instead) is vague and ill-posed, based on arbitrary human sensory and perceptive ability.

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