Olbers' Paradox | Hacker News Reader

Olbers' Paradox

en.wikipedia.org

75 pointsluu50 comments

Constant speed of light is the main problem…

More infos: https://en.m.wikipedia.org/wiki/Variable_speed_of_light

Paper: http://www.januscosmologicalmodel.com/pdf/1988-ModPhysLettA-...

Is there a good explanation as to why this paradox isn't explained by universal expansion? From wikipedia: "To any observer in the universe, it appears that all of space is expanding, and that all but the nearest galaxies (which are bound by gravity) recede at speeds that are proportional to their distance from the observer.";

Wouldn't this imply that, there was probably a time in the distant past when the night sky was saturated brilliantly with light, but as things expand apart, we simply see less-and-less because those infinitely distant galaxies are so far away that their light cannot ever reach us?

Additionally, and maybe related; we can only see 13 odd billion or so lightyears away. The universe could be infinite; there could be a point of light at every "pixel" of the night sky, twenty billion light years away; we simply cannot see that far, as their light cannot travel faster than the rate they're expanding away from us. Is that accurate?

Additionally; space is pretty empty, but not empty. Even ignoring all this, its not unreasonable to think that, over truly universal distances, this matters. We look at the night sky and see nothing; we point a powerful telescope at that same place and see millions of objects, but still darkness between them. Is there an argument against the notion that, maybe, the light from objects even further away was just absorbed naturally before it could get here? Or maybe our telescopes are not sensitive enough?

Additionally; the paradox makes an assumption that space is uniform, but even our naïve observations of the universe prove this to be inaccurate. Its tremendously non uniform; mostly thanks to gravity. Stellar matter is not distributed uniformly; it coalesces into galaxies. Galaxies are not distributed uniformly; they coalesce into galactic neighborhoods, fibers which stretch across the cosmos. There are many regions like the Bootes Void, which contain magnitudes fewer galaxies as we'd expect. There's the Great Attractor, an abnormally massive area which affects the placement of galaxies around it. Maybe on an absolutely, truly, insanely large scale, trillions of lightyears, infinite lightyears, that non-uniformity averages out, but again it comes down to; the universe may be infinitely large, but it doesn't seem to be infinitely old.

> Is there a good explanation as to why this paradox isn't explained by universal expansion?

It is - as described in the second paragraph of the linked article.

> we can only see 13 odd billion or so lightyears away

The radius of the observable universe is ~45 billion light years, not 13.

> but even our naïve observations of the universe prove this to be inaccurate.

On the contrary; at a cosmic scale it is very uniform. Galaxies are just blips: https://en.wikipedia.org/wiki/Cosmological_principle

Expansion does fix this problem, as does a "young" universe. We actually have both, which would be nice if it wasn't terrible. There was a time that the universe was saturated with light, which we now see as the cosmic background radiation, but it wasn't from stars. The universe was basically very hot, and thus glowed brightly (it's more complicated than that, physics was weird before things cooled down, but still).

I don't know how all of the factors you bring up interact, but as far as the last point: the universe is indeed uniform and isotropic at a large enough scale (~300 million ly), called, nicely enough, the End of Greatness ( https://en.wikipedia.org/wiki/Observable_universe#End_of_Gre... ).

Its confusing to me that this would be the case, when the Bootes Void alone is ~330M ly in diameter; and that's small. The Canes Venatici Supervoid is upward of 1300M ly in diameter; the LOWZ North 13788 void is potentially as large as 3000M ly; the list goes on. We've detected over 100 of these supervoids larger than the "End of Greatness"; and that's just what we've seen so far.

Obviously, supervoids are a part of universal uniformity, at a large enough scale, but I'm having a hard time rectifying that the scale we're talking about is ~300M ly, and not significantly larger, with the fact that there are, trivially, a large number of "300M ly windows" one could pick, anywhere in the universe, and see extremely different things. In some cases, an extreme density of billions of galaxies, and in others a number that is dwarfed by even the number of large bodies in our own solar system. Is this a situation where we just didn't know about these 300M+ ly superstructures when that scale was calculated, and it needs to be revised? Or we knew about them, the math would naturally allow for a level of deviation, and to this day they're still rare and small enough that the deviation is low? Or is there something about the math I'm missing whereby discovering any number of these, into the future, still allows that ~300Mly number to work?

More to read, I do believe.

> In some cases, an extreme density of billions of galaxies

I think you might be overestimating how dense a galaxy is, in the grand scheme of things. You may think it's a long way down the road to the chemist's, but it's still almost entirely empty space.

Assuming an infinite amount of anything seems to be a good way to end up with a paradox.

True sometimes perhaps, but not in this case. There's really no "paradox", just an interesting observation. An infinitely old, infinitely large, non-expanding universe is incompatible with the stellar density we see. As it turns out, not only is our universe not infinitely old but it is expanding. So-called paradox resolved, a conclusion easily reached the minute it was formulated, which was of course the point.

What about time?

One cannot even assume time is infinite- there are theories postulating infinite time and finite time, as well as theories postulating that time may not really exist at all.

I mean yeah, but not in a "will cause contradiction" kind of way. You can totally think about infinite time without paradox, as well as infinite space, infinite most things really. You can also think about finite things obviously, if you're into that kind of thing.

When I first encountered this idea it quickly jumped to me that the universe does not appear to be "static", or at least our observation of it is constantly changing. This also plays into homogeneity, and the last assumption of being "infinite" is somewhat irrelevant, because if the first 2 aspects don't hold, being infinite still won't make the sky appear 'filled', at least past the point of our observation.

Of course there's still the theory of an imploding universe which could shrink back together all matter and thus maybe achieve this effect, but even then we still don't have a static characteristic, it only makes an argument for an 'infinitely occurring universe', maybe something akin of the theory proposed by Penrose.(which however still has a lot of unanswered questions, imo)

A more concise explanation can be found in the Usenet Physics FAQ:

https://math.ucr.edu/home/baez/physics/Relativity/GR/olbers....

> too. It does act like a radiation shield, exponentially damping the distant starlight.

This is wrong, damping is not exponential but to the fourth root.

A root is a fractional exponent; I can see that as a valid description.

Exponentially means that it grows like exp(x).

Also it's an important distinction, because an exponential will always eventually grow (or shrink, depending on sign) faster than a polynomial, no matter how high order.

Cool concept, but doesn't consider planets, or nebulae, or other space objects that can block light. I have no expertise to speak with authority on this, so please, weigh in on this consideration. But wouldn't this break the "homogeneity" assumption?

EDIT: Thinking about this further, could you make approximation rules about the things that block light, too? e.g. By the nature of a star's mass, you can assume that some opaque object is likely between Earth and any given star with some likelihood?

EDIT2: Thanks to everybody for the replies - this really helps clarify! Cheers!

Blocking light means absorbing energy. In an eternal universe, you have to reach thermal equilibrium eventually, so you have to shed that energy somehow, and for a constant amount of matter just hanging around in empty space radiation is the only logical possibility. At the end of the day, your absorber will reach the same temperature as the emitter and emit the same amounts of light that it absorbs on frequencies where it does absorb, though perhaps in different directions. This is the insight behind Kirchhoff’s law and blackbody radiation.

There's no "blocking light": anything that "blocks light" would get hot from absorbing that light and, then, reradiate. By this time (some point along the curve of "infinitely old universe") everything should be radiating a lot.

Or the energy may get captured and stored as chemical for example.

If you read the section on "The Paradox" in the article, it's basically using a simplifying geometric assumption to divide the universe into concentric shells, each of which contributes the same intensity of light to the observer. If space is sparse enough that any light reaches us from shell N+1, then you'll get the same amount of light from every shell, and so you'd have a fully-saturated bright sky.

So there are possible infinite/steady-state universes universes (very dense, lots of dust) where you don't see shell N+1. But since we can see stars from shell N+1 and other shells, we know that we don't live in that universe. Therefore our universe isn't a steady-state / infinite time one.

> but doesn't consider planets, or nebulae, or other space objects that can block light

This is addressed in the article. ctrl+f cloud

If you imagine a curve of the light from a star, the dip in the curve from a planet passing in between us and the star is actually relatively small. They don't block that much light (and what they do block heats the planet, which in turn will radiate lower energy light)

From a mathmatical perspective: does the assumption that "any line of sight from Earth must end at the surface of a star" hold? There are countable infinite number of stars, and uncountable number of places in the night sky (I think?). Can a sphere be covered by a countable infinite number of points?

Reminds me of the classic Barrington J Bayley short story "the Knights of the Limits"...

> ‘No, she’s quite a way off,’ Corngold said, taking a look at a meter. ‘Roughly a googol olbers.’

> ‘Your gadget can see that far? But good God – how do you find a single object at that distance?’

So basically, we don't exactly know why the night sky is mostly dark? (At least, that's what I got out of this)

> The darkness of the night sky is one of the pieces of evidence for a dynamic universe, such as the Big Bang model. That model explains the observed non-uniformity of brightness by invoking spacetime's expansion, which lengthens the light originating from the Big Bang to microwave levels via a process known as redshift; this microwave radiation background has wavelengths much longer than those of visible light, and so appears dark to the naked eye.

> The redshift hypothesised in the Big Bang model [...]

Doesn't sound to me like it's more than a hypothesis, but I could be wrong.

Well redshift alone explains the paradox. You don't even need to accept the big bang theory. You can just say "stars that are further away are more redshifted" and that alone explains this. Which we know is true. That's not a hypothesis, redshift can be observed directly. And that fact alone explains the apparent paradox. The most distant stars are redshifted away.

To quote the above article

>The redshift hypothesised in the Big Bang model would by itself explain the darkness of the night sky even if the universe were infinitely old.

Redshift is what explains this. There could be different explanations for the redshift but redshift is 100% an observed phenomena.

Saying "stars that are further away are more redshifted" is Hubble's law and leads almost directly to the big bang. It alone, however, does not explain the paradox. For example even with red shifting, you could have a bright night sky if there are infinitely many stars and the speed of light is instantaneous.

It doesn't really, no? Physicists were well convinced of the big bang for ages before it popped out that the expansion was speeding up, not slowing down. Also, it's pretty hard to imagine a universe where light travels infinitely fast, but also redshifting still exists.

Both the big bang and the observation that galaxies are moving away from the Earth at speeds proportional to their distance originated from the same physicist, George Lemaitre in 1927. The observation came first and then subsequently Hubble formalized it further into Hubble's law and Hubble's constant in 1929.

It's hard to imagine a lot of things, including that the speed of light is the same for all observers, but that's not particularly relevant. Any discussion of the nature of the universe including the big bang itself is going to involve things that are hard to imagine.

> Both the big bang and the observation that galaxies are moving away from the Earth at speeds proportional to their distance originated from the same physicist, George Lemaitre in 1927. The observation came first and then subsequently Hubble formalized it further into Hubble's law and Hubble's constant in 1929.

Ope, right you are. Got my history a little mixed up there.

> It's hard to imagine a lot of things, including that the speed of light is the same for all observers, but that's not particularly relevant.

I mean, sure, but if light was infinitely fast it would lack every single quality that might make it redshift. Is it possible? Sure, anything is possible, but you'd need something that isn't a wave and doesn't act like a wave to independently behave exactly like a wave in a single specific circumstance. I'm sure someone could try and construct such a theory, but it would need a lot of epicycles to make it work. If light was infinitely fast, it really wouldn't be light anymore, at least not as we understand it.

ed: I guess relativity does kind of account for redshift in a way that looks the largely the same as it would with the standard Doppler effect combined with a classical electromagnetic wave, but for different reasons. Still, infinite speed is a bigger leap

That being said, rereading the original comment I see that yeah, even if redshifting wasn't tied to relative velocity the fact that distant galaxies are more redshifted absolutely solves Olber's paradox. I short circuited from "observe redshift" to "universe is expanding" due to velocities, but as long as the energy of distant light fades out fast enough obviously it doesn't matter why.

Something being a wave does not require a finite velocity and in fact there is nothing in physics inconsistent with an instantaneous velocity of light. We know that the two-way speed of light is finite, but all currently known laws of physics are consistent with an instantaneous one-way speed of light [1]:

https://en.wikipedia.org/wiki/One-way_speed_of_light

I am not suggesting that light is instantaneous, only that there is nothing inconsistent with it being so, and that consequently trying to reason about these matters on the basis of what appeals to our intuitions is not sufficient to come to any solid understanding of this phenomenon.

We have a fairly firm grasp on exactly why. The universe is finitely old (rather, has looked basically the way it does for a finite length of time) and rapidly expanding. Either could handle the issue alone, but both make sure of it. We are independently confident both in the fact that the early universe looked like a hot, roughly uniform soup and that the universe is currently expanding. The whys and hows are less clear on both fronts, but these at least are physical observations we make. My astrophysics friends inform me that there's lots of debate on the exact timeline and if inflation happened the way that it is often described, but my physics knowledge tends smaller so that's about the limits of my knowledge, at least until someone finds a way to slap a nice God-fearing operator over this whole mess.

The paradox itself is that if the universe is both infinite and eternal then we shouldn't have a dark sky. This is 'trivially' solved by demonstrating that either of those conditions aren't true. The article opts to use the explanation given by Edgar Allan Poe to demonstrate this, which is that the universe has a finite age and the speed of light is finite so there's only a finite amount of observable universe, which gives us a universe which was darker in the past and one that will only get brighter in the future as more of the universe becomes observable. This has some problems of course and the model Poe would have been working with would have been one of a cyclic universe of eternal growth and decay. This leads us to the Big Bang theory.

>> The redshift hypothesised in the Big Bang model [...]

>Doesn't sound to me like it's more than a hypothesis, but I could be wrong.

The way the Big Bang theory resolves the paradox is similar to that of how Poe resolved it, with a finite cap on the age of the universe there's only a finite amount of observable universe, and similar to Poe's explanation it presents a problem in that a younger universe would have been immensely bright. However this new issue is resolved through the explanation of the expansion of space which can be observed through the redshift of distant galaxies.

As we do observe a dark sky we know the hypothesis that led to the paradox can't be true, namely that the universe is both infinite and eternal, so the question is less about why we have a dark sky and more about what possible alternate hypotheses resolve the paradox. While the Big Bang theory is just a theory it's important to remember that proof is reserved for maths, a theory is a hypothesis backed up by observational data. General relativity led to the hypothesis of an expanding universe and this was something that was later observed from redshift measurements and from it we derive the Hubble–Lemaître law, that galaxies are moving away from earth with speeds proportional to their distance, in some cases faster than the speed of light, this alone fully resolves the paradox and crucially the Big Bang theory is not incompatible with this observation.

>The paradox itself is that if the universe is both infinite and eternal then we shouldn't have a dark sky

I've never really felt like I understood the paradox, since the way people explain it, it sounds to me like they're just denying the idea that an infinite sum can have a finite value.

Like, why couldn't the brightness of the sky in an infinite universe be any value at all, depending on the density?

The argument against an infinite universe that makes sense to me is that it would collapse on itself. But as a thought experiment, the stars could be massless and/or fixed in place.

I mean, it's not like some abstract denial of convergent sums. You can work out the sum yourself, it doesn't converge. The density doesn't matter if it's consistent through the universe (which is one of the possible outs, but our universe is indeed consistent on the very large scale). The article explains it pretty well, and it's not hard to formalize:

> To show this, we divide the universe into a series of concentric shells, 1 light year thick. A certain number of stars will be in the shell 1,000,000,000 to 1,000,000,001 light years away. If the universe is homogeneous at a large scale, then there would be four times as many stars in a second shell, which is between 2,000,000,000 and 2,000,000,001 light years away. However, the second shell is twice as far away, so each star in it would appear one quarter as bright as the stars in the first shell. Thus the total light received from the second shell is the same as the total light received from the first shell.

The argument that the universe would collapse in on itself is made using similar math (gravity decreasing with the square of the distance is by no accident the same as brightness) so if you buy one you sorta have to buy the other. Of course, the universe probably is infinite and isn't collapsing in on itself, but that's because of dark energy (OK yes, there are all sorts of universes that obey relativity, and some of them are infinite and not collapsing, but if we live in one of those no one's found the solution that fits our observations. The dominant thinking was that the universe would eventually collapse until we discovered it's actually expanding).

I read that, I just reflexively feel like it must be the wrong math problem to be solving.

Doesn't it imply the observer has existed forever? Which doesn't seem to me like an obvious assumption.

What we know is that an infinitly old and large universe is not possible given our understanding of physics and the sky being dark at night.

That's all.

An infinitely large observable universe is not possible, however an infinitely large and infinitely old universe is still possible with dark sky at night.

Howso?

If the universe is infinitely large and old, and light works as well believe it does, then light should come from all directions. That's the entire point of this paradox.

Light as we know it moves without limit. If anything is blocked by it, the blocking object would heat up until it glowed just as brightly.

Rapid expansion looks the same as infinitely large and finitely old, in this case. Our universe, as it turns out, also seems to be expanding in addition to being finitely old. If it were not, the sky would slowly be getting brighter, but it will in fact only get darker from here on out. The space beyond the edge of the observable universe will be forever out of reach, even to light.

'Infinitely large' isn't a prerequisite to the paradox. Rather, it's an infinite number of stars.

Or, more precisely, an infinite number of stars spread out rather uniformly.

It's not possible to have an infinite number of stars in a finite region. However, you could have a finite number of stars that form a cover over some point.

I agree.

I was just pointing out that the thread keeps referring to ‘infinitely large’ universe. Perhaps it’s just shorthand for ‘infinite number of stars’. No big deal. Obviously, if you had 10 stars in an infinitely large universe, there is no ‘paradox.’

> Light as we know it moves without limit.

Black holes say no.

Considering gravity decreases at the same rate as brightness, that's a cure that would be significantly worse than the disease. Black holes would need to significantly outnumber stars, and we really don't see that.

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