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Irregular Podcast! #4

2007-02-10: Irregular Podcast! #4 - "Decorating the Infinite Featureless Plane of Death." (9:18, 2.13 MB)


WARNING: Taking this podcast into a physics exam may be grounds for expulsion from your academic institution.

(opening jingle)

Irregular Podcast!

Welcome to another Irregular Podcast!

Today, I want to take you on a speculative journey. Close your eyes. Yes, close them.

Well, okay, not if you're driving.

Anyway, imagine yourself floating away, far from the cares and vagaries of the world. Imagine yourself on the Infinite Featureless Plane of Death.

So what's it like here? Adam's mythbusting aside, it's infinite, and it's featureless. The sky is uniform white, and illuminates everything with a soft, even glow.

Which is actually pretty boring, so the Head Death has ordered the plane decorated. The decorations are shiny red balls, hanging in mid-air, distributed randomly, but more or less evenly. They go on in all directions forever, both near the ground and up into the sky. So if you look up, what do you see?

Obviously a whole lot of shiny red balls. The further away they are, the smaller they look. But no matter what direction you look in, there's eventually a red ball in the way. It's like trying to look through a forest. You can't look very deep into the forest because eventually, no matter where you look, your line of sight hits a tree. And forests end eventually. With the red balls, there's always more of them further out.

But, you think, "What if the balls in some direction are lined up neatly behind one another, so my line of sight misses them all?"

Well firstly: the balls are distributed randomly, so having them line up this precisely is incredibly unlikely. Secondly: even if it does happen, all you have to do is take a tiny fraction of a step to one side, and all of those balls that were lined up won't be any more. So your line of sight will hit one of them now.

So you can't see any of the glowing white sky itself. Everywhere you look, there's a red ball in the way. The sky is just a continuous mass of red.

Now the Head Death wants something a bit more spectacular. He makes all the red balls glow, like light bulbs. So now, everywhere you look, there's a glowing red light bulb in the way.

How bright is the overall light?

When light travels away from a bulb, it spreads out in all directions. At any given distance, the light has to spread out to reach all the points that are the same distance from the bulb. If you increase that distance, the light has to spread out more, because there's more area to spread out into, so the brightness goes down. The further away you are from a light bulb, the less light you get from it. And the amount by which the light looks fainter is the same as the amount by which the surface area of the sphere centred on the light grows. This is because the same total amount of light is being spread out over a bigger area.

But we have lights that are more or less evenly spaced. At a certain distance from your eyes, considering all possible directions, there is a given number of light bulbs. If you look further away, the number of bulbs at that distance must increase as well, because the surface area of the sphere centred on your eyes becomes bigger. Notice we're talking about the surface area of a sphere again.

At a given distance from your eyes, there is some number of light bulbs, and they all look the same brightness. At a larger distance, the lights look dimmer by a factor equal to how much bigger that sphere is, but there are more bulbs, by a factor also equal to how much bigger that sphere is.

So if you add up all the light you can see from the bulbs at some distance, it's the same as the total light from the bulbs at any other distance; they're dimmer but there are exactly enough more of them to compensate. Each spherical shell of bulbs around you provides the same amount of light to your eyes.

Add all of that together and you are getting an infinite amount of light hitting your eyes.

Actually it's not quite that bad. Some of those lights at great distances will be hidden behind closer lights, so their light doesn't contribute to what you can see. This reduces the total light intensity seen by your eyes down to a finite amount. But that finite amount is equal to the brightness of a bulb right up against your eyes. No matter where you look, it's like having a lightbulb in your face.

So you tell the Head Death that he'd better change his decorations, because these glowing balls scattered randomly through space to infinity are simply way too bright to look at.

Your work done, you relax again. You find yourself drifting back to reality. You wake up and open your eyes. You've been dreaming!

You sit up and look out the window into the darkness of the night. You can see the stars. Stars in the inky blackness of the night sky. Enormous glowing balls, like lightbulbs, scattered randomly through space to infinity...

Johannes Kepler was a German astronomer in the early 17th century. He is best known for his work on calculating planetary orbits and formulating his three famous laws of orbital motion. In 1610, he realised that if the universe is infinite and relatively unchanging, then the sky should be ablaze in all directions with a brightness equal to looking directly at the sun. The fact that it is not, he argued, shows that the universe must be finite in extent. In other words, Kepler believed that if you travel far enough, eventually you run out of stars.

Another German astronomer, Heinrich Wilhelm Matthäus Olbers, discussed the same observation in 1823. Rather than concluding that the universe was finite, he supposed that there must be some dark fog in between the stars, that blocks the light from ones further away. Unfortunately, this doesn't work, because anything that blocks the light will heat up to the same temperature as the stars and glow with the same brightness.

For many years, the fact that the night sky is dark was never satisfactorily explained, and this puzzling observation became known as Olbers' paradox.

So why is the sky dark?

Firstly, recall that the speed of light is not infinitely fast. Light travels at 300,000 kilometres (or 186,000 miles) per second. So when you look at something, you are not seeing it as it is right now, but as it was a short while ago when the light left it. Over the large distances between the stars, this time lag is years, sometimes thousands or millions of years.

Secondly, stars are in fact not distributed randomly - they are grouped together into galaxies. This doesn't change the infinite lightbulbs problem. The galaxies are our lightbulbs, not individual stars. The result is the same. The sky should be ablaze at all points with the light of a galaxy in your face, which is basically the same as having a star in your face, only Messier.

Galaxies are a long way away. The nearest large galaxy is Andromeda, some 2.5 million light years away. The light from it takes two and a half million years to reach us. As we look further away, there are more and more galaxies.

But then a curious thing happens. When you get to about 14 billion light years away, we don't see any more galaxies. The sky in between the ones we do see is just empty and black. This is why the night sky is dark.

Have we proved that Kepler was right all along, and the universe is finite in size? What would that mean? We see galaxies evenly spread in all directions, with no side of the sky having more than any other. We don't see any more galaxies beyond a certain distance, the same distance in all directions. If we've reached the edge of the universe, this means that we are at the centre of the universe.

This conclusion should make you a bit suspicious. Is there an explanation that doesn't rely on human beings being the centre of all creation?

Well, remember that the speed of light is finite. When you look at a galaxy 14 billion light years away, you see it as it was 14 billion years ago. When you look at a galaxy 15 billion light years away, you see it as it was 15 billion years ago. But we don't see any galaxies 15 billion light years away... which means that there were no galaxies 15 billion years ago.

If galaxies have only existed for the past 14 billion years, this explains why we don't see any beyond 14 billion light years. It explains why that distance is the same in all directions, without making us the centre of the universe. There almost certainly are galaxies further away, but because of the speed of light, we simply can't see them yet.

Why wouldn't there be any galaxies older than 14 billion years? Simply, because the universe itself is only around 14 billion years old. The universe had a beginning. It hasn't always been here.

This is one of the most fundamental discoveries of modern astrophysics, and it fits in well with multiple other more intricate observations, calculations, and theories.

The universe began a finite, measurable time ago. And you can prove it yourself. Go outside on a clear night, and look up. (closing jingle)

Irregular Podcast!


Narrator - David MM.
Jingle singers - David MM, Loki P, David Mc, Jason R, Andrew S, David K, Zuzanna J.

Programme Notes

It's amazing what we take for granted. And amazing what we can learn by asking apparently stupid questions. If a child were to ask why is the sky dark at night, most adults would dismiss the child as asking a silly question. As you can see, it's actually a very complex question, and the answer has very deep and profound implications.

Next time a child asks in that young wonderment they possess what seems like a trivial or even silly question, think about what the full answer might actually mean.

My comics: Irregular Webcomic! | Darths & Droids | Eavesdropper | Planet of Hats | The Dinosaur Whiteboard | mezzacotta
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