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First of all, let me tell you that I'm not a physicist but rather a computer scientist with a mere interest in physics at nowhere near a professional level so feel free to close this question if it doesn't make any sense.

I remember a physicist friend mentioning me about an argument about the finiteness of the universe. I have looked it up and it turned out to be Olbers' Paradox.

We computer scientist like to use astronomical numbers to help us imagine the complexity of an algorithm. One of the most common one is the number of atoms in the Observable Universe (which we take as $10^{80}$) so I have a crude understanding about the observable universe concept.

I had known these two for some time hence I woke up with the dilemma today. So my question is, how come it can be argued that universe is finite just because it is dark if we know that we can only observe a finite portion of it? Can't it be the case that the universe is infinite even if the sky is dark because not all the light from all the stars reach the earth?

I have searched this a little bit but I think I need an explanation in simpler terms (like popular physics). A historical perspective would also be welcomed.

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  • $\begingroup$ Related: physics.stackexchange.com/q/11014/2451 and physics.stackexchange.com/q/26613/2451 $\endgroup$
    – Qmechanic
    Commented Dec 9, 2012 at 12:40
  • $\begingroup$ People answering here, please remember, when stating the paradox, that light from distant sources goes down as the square of distance. $\endgroup$
    – arivero
    Commented Dec 9, 2012 at 22:19
  • $\begingroup$ All the answers are based on the limits of our minds to grasp the concept of infinity; so, we do what we can by utilizing the concept of the observable universe, which is reasonable, for now. What lies beyond? You and I will never know. Perhaps some distant future relative will. $\endgroup$ Commented Jan 5 at 19:14
  • $\begingroup$ See en.wikipedia.org/wiki/Extinction_(astronomy) $\endgroup$
    – pygosceles
    Commented Mar 6 at 18:45

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So my question is, how come it can be argued that universe is finite just because it is dark if we know that we can only observe a finite portion of it?

You are mixing two theories here. Olbers paradox has as a basic theory a static infinite in space and time universe. The dark night sky means that either the universe is not static, or has a beginning, or has a finite extent in space. Or all three.

Can't it be the case that the universe is infinite even if the sky is dark because not all the light from all the stars reach the earth?

A different model than a static infinite in space and time universe is needed in this case, an infinite universe that appeared at a time t=0, for example, so that the light of distant stars would not have reached us by now. But there are more data than the dark night sky to be fitted by a cosmological model and the available data fit the Big Bang model quite well:

the Big Bang occurred approximately 13.75 billion years ago, which is thus considered the age of the Universe. After its initial expansion from a singularity, the Universe cooled sufficiently to allow energy to be converted into various subatomic particles, including protons, neutrons, and electrons.

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Here is an analogy for you:

You find yourself in a forest. A forest ranger stand next to you. He tells you the forest goes on and on and has no boundary. You look around. There is tree trunks all around you, yet you do see gaps between the trunks. How do you react to the forest ranger's remark? You tell him he is wrong. If the forest was infinite in extent, wherever you look, your line of sight would ultimately hit a tree trunk. The forest ranger thinks for a while and responds: "the forest stretches without limits, but you only see part of the forest. This is because the ground is not flat, and distant trees disappear behind the horizon."

As any analogy, this is not a full representation of 'the real thing'. It does not provide an analogy for all aspects of the commonly accepted solution to Olbers' paradox. Still it might help explaining how concepts like "observable universe" contribute to the resolution of the paradox.

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Olber's paradox just states that if the universe is infinite and static (and flat) then any line of sight to the sky will invariably hit a star/source of light, and therefore our sky should be bright all the time.

The observable universe is a concept that arises from the expansion of the universe. Because the universe is expanding in such a way that points farther away from us are moving away faster than points closer to us (i.e, the further something is from us, the faster it's moving away) there is a definite point beyond which light will never reach us, since that point is moving away faster than the speed of light.

Now to come to your question - You're absolutely right. We don't actually know whether then whole (observable + the rest) universe is finite or not. There are theories which hypothesize the lower limit on the size of the entire universe (not just the observable universe) but in literature people mostly restrict themselves to speaking about the observable universe since we cannot (by definition) observe anything outside the observable universe, so no hypothesis can be tested.

This isn't necessarily a contradiction of Olber's paradox, since he was talking about an infinite and static universe. So his paradox can be seen as favouring an expanding universe model rather than a static one to explain what we see.

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Olbers posed the supposed paradox in 1823.

It wasn't until more than a century later that interstellar extinction, or the attenuation of light due to non-luminous matter absorbing photons, was formally documented.

Olbers's Paradox consequently actually fails to demonstrate a finite or nonuniform universe, by failing to account for a now-known phenomenon of light extinction. Matter is known to attenuate light according to an exponential decay law (see the Beer-Lambert attenuation law). The law of optical attenuation had in fact been known, studied and published on by 1729 and before. What had not been as well studied is the role of interstellar matter in obscuring stars.

The paradox is ripe to be updated in view of this additional component of the model for interstellar transmission of light, but to my knowledge, the 200-year-old 1823 version is to this day still used as though it were evidence for currently popular theoretical physics models, even though we have had nearly a century to catch up with subsequent observational physics. Let's unpack with some math and some computer science too.

Visible effects of interstellar absorptive matter

I have written a basic simulation to validate the effects of non-luminous matter quantitatively and qualitatively. Code here. It directly applies the exponential decay law by assuming a uniform random density of stars and a uniform density of non-luminous matter throughout space. The simulation even cheats massively in favor of Olbers's Paradox by modeling the infinite backdrop of stars at varying distances as a purely luminous wall of light at a fixed, finite and even shortest possible distance beyond the foreground model of direct sampling. This means we have a strict theoretical upper bound on the total light emanating from distant stars. The density of non-luminous matter is controllable as a parameter p. The simulation shows that for even very small values of p, a purely luminous wall would be practically invisible, or be indistinguishable from cosmic microwave background radiation (interstellar attenuation not only decreases apparent intensity, it also induces reddening. The observation that microwaves predominate at such distances is therefore a natural consequence of known laws of optics, and is therefore not evidence for a different nature of the universe so far back in time or at such a distance).

If one sets p=0, the entire field of view is indeed saturated by pure, contiguous starlight under this simulation. But for any non-infinitesimal density p of attenuating matter, the visualization -- and the mathematical solution for expected light intensity over all points in space--converges sharply towards a model that closely resembles what we see in our night sky, regardless of all other parameter settings.

In the following two images, the absorption value is increased only slightly, very close to zero at first: Very low absorption parameter

Low absorption parameter

In both images, there is a perfectly bright wall of simulated stars a short, fixed distance away from the observer. Radiation from that wall leaks and is visible as a uniform grey background when the simulated wall is very close and the density of attenuating matter approaches zero, but if the wall of light is slightly more distant or the density of attenuating matter is only slightly increased, the background very rapidly approaches pitch black, despite there still being an infinite number of perfectly bright stars intersecting every possible line of sight.

You can bump up the stellar density, radii and luminosity as high as you want, and even a tiny percentage of non-luminous matter still overwhelms the resultant apparent brightness calculations with the exponential decay induced by material attenuation.

Of course arguments about thermodynamics I often see cropping up around this subject are just begging the question. How nonluminous matter is able to be there and coexist with stars is a separate matter of discussion. (How stars got there is too, come to think of it). The fact that it is there and that we know it is there, even at great distances, disproves the idea that Olbers's paradox is a paradox at all, as it completely fails to falsify an infinite and uniform universe given what we know.

In case someone thinks this idea is absurd, that even a small amount of matter between stars can block nearly all of the light from them, remember that despite how brightly the Sun shines at noonday and how close it is to the Earth, you can block almost all of that light using a thin cardboard cereal box or a parasol consisting of cloth a couple millimeters thick. This gives you an idea of how effective exponential attenuation is. Can there not be the equivalent matter of one millimeter of cardboard between you and a star 3 billion light years away, among the dust, the stellar remnants, the comets, the hypothesized Oort-like clouds, the planets, the gas clouds, etc.? If not, then what are stars (and their systems) made of?

So in fact it can be the case that the universe is infinite and uniformly occupied with stars per the observed universe, if we will only update our thinking to match the scientific discoveries of the early twentieth century, and reconcile it with theoretical and mathematical understandings of the early eighteenth century, which are still the uncontradicted foundations of the field of optics.

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  • $\begingroup$ This idea is well established ("tired light"), but see that link for the history and why it is not accepted. $\endgroup$
    – Sten
    Commented Mar 6 at 22:11

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