No matter what direction you look in the night sky, it looks basically the same. In astronomy terms we say the Universe is homogeneous and isotropic. Sure there are areas where galaxies cluster together, and other areas where galaxies are rare, but on average the distribution of stars is pretty even. Because of this, an early idea for the cosmos is that it is the same everywhere forever. It seems both ageless and infinite in expanse. But if that’s the case it raises a few troubling paradoxes.
The first paradox is perhaps the most famous. Known as Olber’s paradox, it questions how an infinite ageless universe could be mostly dark. At first glance it might seem obvious. The more distant a star, the dimmer it appears, so stars very far away are simply too dim to be seen. But the apparent brightness of a star follows a specific relationship known as the inverse square law. A single star some distance away is as bright as four similar stars twice as distant, or nine three times farther away. But if stars are distributed fairly evenly, then there are four times the number of stars twice as far away, and nine times more that are three times away. So while stars appear dimmer with distance, there are more stars at greater distances. So an infinite ageless universe should have a sky as bright as the Sun.
On the other hand, Clausius’ paradox argues that the sky should be completely dark, with no stars in the sky at all. First postulated by Rudolf Clausius, the paradox is based upon thermodynamics. One of the basic laws of thermodynamics is that heat flows from hotter regions to colder regions until they equalize in temperature. In other words, your morning coffee will always cool down until it reaches room temperature. It will never spontaneously heat up by cooling the surrounding room slightly. According to thermodynamics, even the stars will eventually cool. In an ageless universe the stars should have faded long ago, and the vast cosmos should be a sea of completely uniform temperature. So why is the universe not cold and dark?
Of course you might argue that stars still shine because gravity causes clouds of gas and dust to collapse in on themselves. New stars are being formed all the time, so naturally the Universe won’t be completely dark. But this raises another paradox: why does gravity work at all? As with light, gravity obeys the inverse square law. An object some distance away pulls upon you gravitationally with a force four times larger than an object of the same mass twice as far away. With distance a gravitational force gets ever weaker, but it never completely goes away. In an infinite universe the amount of mass at a particular distance also follows the square law. For every gravitational pull in one direction, there will always be enough mass in the other direction to balance it out. This is known as Seeliger’s paradox, and it means that gravity shouldn’t be able to act on anything. Gravitational forces should always balance out, so stars shouldn’t form and planets shouldn’t orbit stars. And yet they do.
The solution to these paradoxes is pretty clear. The Universe is not ageless, nor is it stationary. We now know it is only about 13.8 billion years old, and ever expanding. Because of expansion and a finite age, the observable universe doesn’t extend to infinity, so Olber’s and Seeliger’s arguments don’t apply. Since the Universe is finite in age, Clausius’ argument is also invalid. It seems an obvious solution to us, but it’s an excellent example of how incorrect assumptions are difficult to overcome. Before Hubble’s observation of cosmic expansion, it seemed obvious that the Universe must be ageless and stationary. The idea that it might begin with a primordial fireball seems downright creationist in comparison. But in the end, evidence for the big bang became overwhelming, and the paradoxes of an infinite cosmos were finally solved.
Next time: Nothing can be colder than absolute zero, or can it? Consider an ancient cold white dwarf. It’s temperature is near absolute zero, but it’s matter is tightly squeezed by gravity. If you took a chuck of the white dwarf away, would that chunk expand and cool even further? Arthur Eddington wrestles with stellar thermodynamics in tomorrow’s post.