Stars Fill the Sky

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January 2nd: Stars Fill the Sky

Quote of the Day

"if stars are uniformly distributed through the sky, their number should counterbalance their faintness and the night sky should be as bright as the day;" - H.W.M. Olbers, 1826

"Dark energy is crazy, right?" - Dr. Anthony Tyson

"Philosophically, I liked the steady-state cosmology. So I thought that we should report our results as a simple measurement; the measurement might be true after the cosmology was no longer true!" — Robert Woodrow Wilson

Thoughts for the Day

Sometimes you may read that the observable universe is roughly 13.8 billion light years across and also that the universe is roughly 13.8 billion years old. This may seem like a coincidence but it isn't.

The light that has reached us from the furthest parts of the observable universe has travelled 13.8 billion light years because a light year is how far light travels in a year and no light has had longer than that to travel.

Of course, we don't know that number of years with perfect precision. The best measurement of that time made to date has been to the closest 40 million years or so. For the first 380 000 years after the Big Bang, the universe was so densely filled with matter that it was opaque to light. But 380 000 years is much smaller than 40 million years so this initial opaque period doesn't change the time that light had to travel since the beginning of the universe to any appreciable amount.

The first light that was emitted in the universe that wasn't absorbed long ago was emitted by the hot gasses as they thinned due to the expansion of the universe. This light was emitted from every point in the universe at more or less the same time and in every direction. Of course, any light that was emitted nearby our current location was either received here long ago or headed off to far off places long ago. Only light, that was emitted toward us at a distance such that, accounting for the expansion of the universe in between, it could travel 13.8 billion light years in a more-or-less straight line to arrive here now, is being received now. The region from which such light could be emitted now forms a spherical shell around us at an apparent distance of 13.8 billion light years. This light is called the Cosmic Background Radiation. The Cosmic Background appears to be that distance away because the light that travel here from there travelled 13.8 billion light years and that light is the only means by which we can gain any information about the Cosmic Background.

But, as you know, the universe is and has always been expanding. So when the Cosmic Background set out, the distance between its point of origin and the gases from which we formed was considerably less than 14 billion light years; the universe hadn't expanded much yet. And, now that the Cosmic Background has arrived here, the distance to its point of origin is much more than 13.8 billion light years; the space behind the light has been expanded as the light travelled. In fact, cosmologists estimate that the distance to the point of origin of the Cosmic Background is now about 44 billion light years, roughly three times the distance that the light travelled. This means that the galaxies that by now must have formed in the region that we see as the Cosmic Background are travelling away from us at more than twice the speed of light. But nothing can travel faster than the speed of light so how is this possible?

The key there is the word nothing. No thing with a mass or made of energy can travel faster than the speed of light. But space itself has no limit on the speed it can travel. The galaxies themselves aren't moving with any appreciable speed with respect to the space that they are embedded in. But the space itself is moving away from us at twice the speed of light. This means that without being able to bend space ourselves, we will never catch them up. We will never be able to visit those galaxies. Also, the light emitted by those galaxies today will never reach us. Those galaxies are forever beyond the event horizon of the Big Rip. What is the Big Rip?

The Big Rip is a phenomenon that could determine the fate of the universe. The Big Rip is this effect that parts of the universe move away from each other superluminally or faster than the speed of light. The universe is pretty uniform so the space in different parts of the universe is all expanding at pretty much the same rate. In fact, it is each bit of space that is expanding. Each tiny bit of space is expanding by a small factor every second. But if every bit of space between two distant objects expands by a factor of 1 billionth each second then the distance between the two objects also expands by a factor of 1 billionth each second. If the two objects are a meter apart the rate of expansion is a nanometer per second and no one really notices. But if the objects are a billion light seconds apart then the objects would be moving apart at a light second per second which is the speed of light. Any objects further apart than that will be moving apart superluminally.

During the early universe there was a rapid inflation so that space was expanding very quickly and, in fact, accelerated its rate of expansion. The factor by which space expanded each second increased with each passing second. Objects closer and closer together went superluminal with respect to each other. But the acceleration passed and the universe settled down to a reasonable rate of expansion. Just recently, within the last few billion years, inflation has returned. We are once again accelerating. This is believed to be related to the growth of dark energy in the universe. If dark energy continues to grow, acceleration will continue and if acceleration continues at a high enough rate then eventually the distance between superluminal objects will begin to shrink rapidly. All other galaxies may disappear from the night sky as the light from them is cut off. Then the most distant stars of our own galaxy will disappear and ever nearer and nearer stars until the outer reaches of the solar system slip over the Big Rip event horizon. The event horizon will then rapidly constrict around us, eventually cutting us off from the Sun. Luckily by this point, the acceleration will be so rapid that we won't have time to freeze. The Moon will disappear and then the far sides of the Earth will cross the event horizon with respect to each other. At that point, Earth will no longer be gravitationally bound to itself and it will tear apart. If we survive that it will be only a fraction of second before the opposite sides of our bodies are over the event horizon from each other and we ourselves are torn apart and before nerve signals can reach your brain so that you could feel pain, the event horizon will cut off every atom in your body from every other atom and you will cease to exist as a being at all.

When will this happen? We don't know. Cosmologists are trying to measure the effect of dark energy on the universe and their measurements must increase in precision before they know whether this will happen let alone when. However, it is unlikely to be less than 10s of billions of years from now and could easily be quadrillions of years from now, if ever. Yet the horizon already exists, left over from the first inflationary period. How can we relate to that horizon? Should our attitude be one simply of awe that such a horizon exists? Should we hate it for the limit it places on our opportunities for exploration? Or should we be grateful for it?


Consider one of the nightmare scenarios envisioned for the static equilibrium universe that Einstein proposed in 1917 before Edwin Hubble discovered red shifted galaxies beyond our own. It is known as Olbers' paradox. If the universe had begun at its current size 14 billion years ago and been held in a more or less static equilibrium between the attraction of gravity and the Einstein's cosmological constant. As time went on we would be able to observe ever more distant populations of galaxies as the light from those galaxies reached us from further and further away. But there are only so many square degrees of sky. As more and more galaxies appeared the sky would get brighter and brighter. At first this might be quite convenient for finding your way around on nights with a new Moon but as time went on the heat of this brighter and brighter sky would become intolerable until the surface of the Earth reached thermal equilibrium with the surfaces of all those distant stars and the surface of the Earth (or what would be left of the Earth by that point) was also the temperature of the surface of a star.

If the universe had expanded slowly enough then that would indeed be the fate of the Earth. But by expanding quickly enough to create the Big Rip horizon, the universe ensured that this would never be our fate. The Cosmic Background will get cooler, not hotter over time. We have enough stars in our universe in order to provide tremendous opportunities for Life and intelligence, but we don't have so many as to cook us with their light.

Contemplation for the Day

Let us imagine

Watch this animation of Olbers' paradox in action and consider your reasons for gratitude for the Big Rip horizon.

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