The Most Astounding Fact

Neil de Grasse Tyson describes the most astounding fact as being that the elements in your body were created in the white heat of long-dead giant stars.

Though why he feels the need to talk like William Shatner

I have no idea.

It's a pretty neat thing, no doubt about it. But before you get all misty-eyed or swoon from sheer misplaced romanticism, it's worth stating this in another way.

Yeah I've used this before, but whatcha gonna do ?

Even so, it's a great quotable fact. What could I possibly offer to trump this ? Simple.

The sky is dark at night.

If astronomy is the oldest profession (hint : it isn't), then this is surely the oldest observation. It's also, perhaps, one of the most profound. Its consequences are - quite literally - infinitely more significant than knowing where our atoms come from.

Olber's Paradox is breathtakingly simple. If the Universe is infinite in size, eternal, and full of stars, then every line of sight should end with a star. The night sky would be as bright as the surface of the Sun.

From wikipedia.

It would be quite wrong of me to omit this astonishingly good video by MinutePhysics which explains (almost) all the relevant issues in less than 4 minutes. The only downside is that it is, perhaps, a bit of a blitzkrieg of information on some pretty complicated issues.

Let's take a more sedate look at possible solutions to the paradox.


1) The stars are very far away. Duuuh !

This does seem like a good solution at first, because obviously the further away a star is, the dimmer it appears. Right ? Wrong. Well, sort-of wrong. It's true we receive less of the star's energy output, because obviously most of its light never reaches us but just carries on out into the void, so it appears dimmer. That's just simple geometry.

A planet near a star receives a greater fraction of the star's energy than one further away. The energy from the star is spread out over larger areas at larger distances.

But there's another quantity which is more relevant here : surface brightness, or the brightness per unit area. That, it turns out, does not vary with distance at all.

Imagine that you have two large, equally powerful floodlights. One is 10m away and the other is 1000m away. Obviously, the 10m floodlight will be painful to stare at while the the 1000m floodlight won't cause you any problems. But suppose that you hide behind a wooden fence in which there is a very small hole - small enough that you can only see a small part of even the distant floodlight through it. If you look at both lights through the hole, you won't be able to tell which is which. Bizarre, but true*.

* A simplified truth, actually. I'll get back to that later.

Or, to put it another way, the stars we see only appear dim because they also look small. If you made them so large that they would appear as large as the Sun does, they'd also appear as bright as the Sun.

So unfortunately we can't use sheer distance to resolve Olber's Paradox. Booo.


2) There's something in the way.

The Universe is full of gas and dust, and those aren't bright at visible wavelengths. The problem is that given enough time, all of this gas and dust should heat up and become just as hot as the surface of a star. At which point they will also look as bright as the surface of a star. I say "a star" rather than "the Sun" because of course not all stars have the same brightness - but they all, to our eyes, have a high surface brightness. Anyway the same thing applies to dim stars as it does to dust - they'll get heated up by the infinite number of other bright stars.

Dark clouds like this one obscure stars in our Universe, but this doesn't work if the Universe is infinite and eternal. Everything should have reached the same temperature.

One might wonder about black holes, which do not let light escape. If there was a black hole along every line of sight, would it not prevent us from seeing all of the starlight ? Well, perhaps. But this is going to mean having all the black holes set up just right so as to prevent us from seeing stars beyond a certain distance. And the mass infalling into the holes is going to have to be absolutely perfectly balanced to counter their shrinking due to Hawking radiation - otherwise they'll either grow to infinite size and consume everything, or vanish. Which is preposterous given how varied the Universe is on small scales.


3) We're looking at the wrong wavelength.

I myself have made great efforts to point out that the dark night sky we see...

... is only because visible light is not the whole story. If we could see hydrogen gas, it'd look a whole lot different.

But this is missing the point. Although there's a lot of hydrogen gas in the way, it doesn't obscure our view of the stars, so we should see with our eyes a bright sky.

A much more sophisticated argument is that maybe light changes wavelength over great distances, eventually becoming something we can't see. This "tired light" is a discredited alternative idea to explain why distant galaxies look redder. Conventional contemporary astronomy says this is because the Universe is expanding; tired light has it that light loses energy as it travels. Just where that energy is supposed to go I'm not sure.

People sometimes try to use the Cosmic Microwave Background to explain the parodox. The CMB is microwave radiation in the... cosmos... and it's in the background... well we'll get back to that. The point is that this radiation occurs across the whole sky and it's not coming from gas in our own galaxy. When analysed in detail however, whatever it is it simply cannot be from redshifted stars. So that doesn't help us explain the paradox after all.

You can actually see part of the CMB yourself if you don't tune in your TV correctly -  a few percent of the static comes from this. At least it did back in the era of analogue telly. Not sure about this new digital era.

4) Stars don't last forever.

True. We see them exploding all the time. But we also know that new stars are born as well. So if the Universe is infinite, that should still mean that there are an infinite number of stars along every line of sight.

The Crab Nebula, formed by a supernova explosion that was actually observed and recorded in 1054 A.D.

5) Stars don't go on forever.

In one sense this is true : our Galaxy has an edge. But of course, beyond that there are more galaxies, full of stars. So far, there's no evidence that there's any sort of "edge" to galaxies. And if there were, everything should have collapsed into a big ugly heap - the Universe would have a centre which everything would slowly fall towards.

Welsh cosmology is the best cosmology.

Besides, infinite space which just has a few galaxies in it is no way of resolving the paradox - it's simply a way of saying that the assumption of infinite stars is wrong.


6) The Universe is a fractal.

Oooh, this one's interesting ! Remarkably, it turns out that it is possible to have an infinite number of stars in an infinite Universe but not have every line of sight end on a star. One really obvious way to do this would be to have all the stars in a really long line. Infinite stars but lots and lots of dark sky !

Worst. Universe. Ever.

Which is of course very silly because that's just not what we see. Or maybe it is. Maybe all the galaxies we see are part of an infinitely long cylinder...naah. That's just stupid*. For one thing the cylinder would collapse radially down to a line, for another, you'd only have dark sky in certain directions. But more complicated fractals can also allow for dark sky in a more interesting pattern.

* Sometimes, just sometimes, this is a legitimate argument.

Man I hate fractals. They make my head hurt.

This is Fournier's fractal, proposed in 1907 as one possible resolution to the paradox. Clearly it allows large parts of the sky to be dark. It can also be rendered in 3D :

You may wonder if that means that along some lines of sight there'd still be infinite stars and so infinite energy. Tricky. The idea here is that the energy density decreases as you go to larger and larger scales, so the total energy when you sum over infinity is still finite. That's actually a perfectly sensible everyday bit of mathematics for describing continuous functions, but doesn't work for discrete objects like stars. If you have a finite amount of energy, you must have a finite number of stars. Which means there's an edge to the stars, and we get back to the collapsing-heap problem again.

In any case, that's definitely not what the Universe looks like. But the concept is there. I was hoping to be able to find out more about fractals that actually do resemble the Universe, but while there's a great deal of alternative (mostly outright bonkers) ideas about the Universe being a fractal on the internet, I couldn't find a single one addressing this point. Well, I did come across one article modelling a fractal distribution of stars (not the large-scale galaxy filaments), but annoyingly I can't find it again. If anyone can provide simple instructions, I'd love to visualise this - though it's not obvious to me if such a structure is even possible (i.e. stable).

Another problem I suspect with the fractal idea is : why would the Universe remain a fractal ? Galaxies move around quite a lot. Occasionally, stars get ripped out of galaxies. Over infinite time, the nice fractal structure is going to get destroyed, and those blank areas will be filled in.

The Universe is a dynamic place. It's tough to see how galaxy motions are compatible with a fractal structure - what stops distant galaxies from moving into the regions we see as dark ?

Finally, observations have demonstrated that the Universe just isn't a fractal, so this can't be the solution either.


7) The Universe isn't infinite.

We've sort of already covered this one with the idea that there aren't infinite stars. But having a finite number of stars in an infinite void of empty space is philosophically unsatisfying, as well as just plain not working. So, maybe the Universe has always existed but has a limited volume ? The nice thing about this is that space wouldn't need to have any kind of edge - curved space would allow you to travel in any direction and eventually get back to where you started.

Specially modified version of the Virgo Cluster.

The problem is that this doesn't avoid the everything-collapsing-to-big-ugly-heap problem. Einstein's equations show that a static Universe is unstable unless you very carefully tweak things - it's not a natural solution at all.

Now, if you'll remember the very first point, I mentioned that saying surface brightness doesn't vary with distance is a simplified truth. It works in a static Universe. It's not true in an expanding Universe - if space is expanding, surface brightness should vary in a very particular way which we can actually test, and from the results it really does seem that the Universe is expanding (there are also other reasons to believe that redshift indicates expansion and not some other effect like tired light; the cosmic microwave background is also very well explained by this).

There's also a slightly simpler argument to believe that the Universe is expanding. As I mentioned, distant galaxies look redder and this is thought to be because space is expanding, giving them the appearance of moving away from us. Of course, it could instead simply mean that every galaxy is terrified of ours and is trying like hell to get as far away from us as possible.

Worst. South Park. Ever.
This is why I'm not a cartoonist.

That only works if you think our Galaxy is somehow an incredibly special place, which most of us don't. There are good reasons for this - the Universe looks pretty similar in every direction, so it would be extremely surprising if the speed measurements didn't match this. So instead we postulate that it if we were in any other galaxy, we would still see all the other galaxies rushing away, which avoids the weirdness of us having a special position. Remarkably, this seems to work. It really is the case that the Universe is expanding. Even more amazingly, it may even be possible - one day - to measure this expansion directly in real time : to watch a galaxy's velocity change over time as the Universe expands.

And of course, if the Universe is expanding but also finite, then it cannot also be eternal.


8) Energy and mass conservation is for hippy losers ! 

It's true that the collapse-to-a-heap problem of a finite Universe or finite number of stars can be solved, if you provide some force to keep the galaxies moving outward (or to keep the Universe expanding). The trouble is that you could solve pretty much anything by allowing energy to be created - it would be basically saying "because magic". You'd have to have some incredibly good reason why this only happens to keep the Universe balanced, otherwise you may as well throw the laws of thermodynamics out of the window, shout "ALACKAZAM !" and watch them plummet to a firey doom.

All that said, however, the accelerating expansion of the Universe can be explained without violating the conservation of energy. So maybe something similar could stop the Universe collapsing and keep it nicely balanced - if things were set up perfectly. There would be literally zero margin for error, since over infinite time a non-static Universe would either expand to infinity (in which case we wouldn't see any other stars at all) or collapse to a point (in which case we wouldn't see anything at all).

Worse, a Universe in a truly steady state - with star birth and death precisely balanced so the Universe always appears much as it does now - requires violation of conservation of energy.


9) The Universe isn't eternal.

First, let's recap.

• The paradox can't be resolved by the sheer distances to the stars because brightness doesn't work like that.
• There can't be a barrier blocking our view because it would heat up to the same temperature as the stars.
• The sky is bright everywhere at other wavelengths, but the details show that this cannot possibly be due to starlight.
• The finite lifetime of stars doesn't work because stars are also born.
• If the stars only span a finite part of an infinite Universe, they would have all collapsed.
• A fractal Universe might not remain a fractal, and observations show that the Universe isn't a fractal.
• A finite Universe doesn't work because the evidence that the Universe is expanding is very strong, and therefore the Universe cannot also be eternal.

The only thing left is to question the premise of the paradox itself. Maybe the Universe just isn't infinite and eternal after all.

You could, I suppose, argue that maybe the Universe is infinite and eternal but simply doesn't always look the way it does now. After all, we know galaxies looked different in the past to how they do today - not to mention that quasars are only found in the distant (early) Universe - so clearly things have changed :

The "spiderweb" galaxy seen by Hubble, about 10 billion light years away - a chaotic series of galaxy mergers.

The Andromeda galaxy M31, just two million light years away - a stable, rotating disc.

A totally steady state is out. But maybe there's a quasi-steady state of multiple Big Bangs - as the Universe expands and all the stars disperse and die, new material is suddenly created. Well, maybe. The question to ask is whether you prefer the Universe to be infinite and eternal or finite and mortal.

A mortal Universe (finite in time) solves Olber's Paradox at a stroke - or rather, it's more like cutting the Gordian Knot since it effectively declares the paradox invalid. If there hasn't been infinite time, and the Universe has been changing, there's no reason to expect a bright night sky. There was once a time when there weren't any stars, and since then stars have formed so far away that there hasn't been time for their light to reach us yet.

Strictly speaking, a mortal universe doesn't preclude it from being infinite in space. Personally I'd rather it was finite in space as well. I see infinities as problems to be avoided, not solutions to be invoked. They're a useful mathematical trick - but they also let you get away with murder. In an infinite Universe, you can explain any anomaly as being a statistical fluke, no matter how unlikely something is, it will happen somewhere. Which means there's no way of knowing if your observations are telling you something about the underlying physics at work, or if you're just in a really weird part of the Universe. And, of course, this.


Conclusion

Olber's Paradox implicitly assumes that an infinite eternal Universe is preferable. Why, I'm not sure. I suppose it might be nice to think that the Universe will go on and on forever, but personally I prefer the exact opposite. As for whether a Universe that once didn't exist will eventually cease to exist, I've no idea.

Interestingly, those people who are still convinced the Universe must be eternal (google "steady state" and "fractal cosmology") tend to do so because they see Big Bang cosmology as too religious. Seriously. Even the great Fred Hoyle (and he was great, no matter how wrong he was), one of the original proponents of Steady State theory, thought that the idea of a creation was irrational. There are many others on the internet stating things more directly : that the Big Bang is pseudoscientific idea that justifies Christianity.

I wonder what six-day Creationists have to say about that.

Of course, this is not a sensible reason to reject the theory. Things do get created and destroyed all the time, albeit from things which already exist. Most scientists accept the idea of creation from absolute nothingness without believing in a deity as the cause of it. And while religious texts are indeed full of gibberish, the idea that things got created is no more nonsensical than the idea that humans exist - which religious texts also state, but no-one is trying to debunk that.

Debunking the Big Bang because you think it's too religious is a "nuke the whales" policy - it might be fun (those cetacean jerks would do the same to us if they could), but it isn't sensible.

You nuke those whales, Fred. You nuke 'em good.

But whether you believe the Universe is eternal or mortal, finite or infinite (and I'm glad there are people still examining all the options, even if I do think most of them are loony), consider this. The lifetime of stars, the expansion of space, fractal geometry, the very nature of reality itself - all of these are important in understanding why the sky is dark at night. And that's why for me, it's tough to think of a more astounding fact.