In tonight's post I intend to tackle a minor, trivial issue – the universe as a whole. I am going to discuss the question of whether the universe is finite or infinite. This will not be a long post, not because the topic isn't complicated and deserves voluminous discussion, but because the points I wish to make are simple.
To begin with, when we discuss the universe, we need first to make an important distinction. We need to distinguish between the observable universe and the universe as a whole. The observable universe is simply that part of the universe that we can see. The edge of the observable universe is about 46 billion lightyears away. When we look at a galaxy at the edge of the observable universe, we are also looking back in time close to 13.8 billion years because that is the length of time it has taken for light from that galaxy to reach us (13.8 billion years being the age of the universe.) The reason the size of the universe is so much greater in lightyears than its age in years is, I think, because the furthest galaxy has continued to recede away from us after emitting the photons that have reached us, and because space itself has expanded. The figures I have cited come from Wikipedia but, in fact, the size and age of the universe are continually being recalculated and revised and next week the Wikipedia entry may have completely altered its estimates.
In this post, I don't want to discuss the observable universe but rather the universe as a whole. By using this term, the universe as a whole, I am including the many stars and galaxies that exist in regions so remote from us that we can't see them and never will. It seems to me that there are three possible hypotheses we can entertain about the universe as a whole.
1. The universe is finite and the mass-energy it contains is also finite.
2. The universe is infinite but the mass-energy it contains is finite.
3. The universe is infinite and the mass-energy it contains is also infinite.
Now, you'd think the physicists would know which of these three options is correct but in fact they don't. When I was younger, I used to read lots of books about physics intended for popular consumption and believed that the issue was settled –the first option was correct, the universe is finite. Let us consider this option for a moment as though the question indeed had been settled. Readers may wonder how the universe could be finite: wouldn't that imply that it has boundaries? However, the universe can be finite but unbounded in the same way that the surface area of a sphere can be finite but unbounded. Space-time curves in such a way that it joins up with itself, circles back on itself. If we could send a space-craft much, much faster than the speed of light directly up in a straight line it would eventually return to us from the opposite direction in the same way that if we travelled due west from Auckland we would circle the globe and arrive back at Auckland from the east. I also used to think that we could only make sense of the claim that the universe is expanding by assuming that the universe is finite. How else could we say that the universe is getting bigger?
I simply assumed, based on what I read, that the universe is finite. I think my first inkling that in fact my belief that there was a consensus about this issue was wrong occurred in 2012. There is a scene in the film A Beautiful Mind in which Nash's love interest Alecia, in an attempt to prove to Nash that he takes some things he believes on faith, asks him if he thinks the universe to be finite or infinite. He replies, "Infinite". She says, "How do you know?" He says, "I just know." (This may not be a totally accurate recapitulation of this scene because I am working from memory.) In a film already stuffed to the gunnels with factual errors, I thought this another howler. How could a genius like Nash believe the universe to be infinite? I know now that there is no consensus about whether the universe is finite or infinite. The second or third option could be the right one.
Consider the second hypothesis. In this hypothesis space is infinite and the material universe is finite. The universe as a whole is an archipelago in an endless ocean that contains no other land. The universe is expanding into empty space. This option may be the correct one but is not one I wish to dwell on here. Consider now the third hypothesis. The universe is infinite and the mass-energy is contains is also infinite. This statement is equivalent to saying that the universe as a whole contains infinitely many stars. This proposal has some odd consequences which I do wish to dwell on. (In the following discussion, I am indebted to Sam Harris for a throwaway comment he made when debating the issue of free will with Bret Weinstein, a throwaway comment that inspired this post).
Suppose we say that the probability of a star having a planet or planets capable of supporting life is one in a billion. If the universe as a whole contains an infinite number of stars, it must therefore contain an infinite number of planets capable of supporting life – infinity divided by a billion is still infinity. Suppose we go on to say that the probability of such a planet bearing intelligent life is also one in a billion. Infinity divided by a billion again is still infinity. Therefore there must be an infinite number of star systems in the universe as a whole inhabited by intelligent life. If the universe is indeed truly infinite, the question "Are we alone in the universe?" has a trivial answer. Of course, we aren't alone! There are an infinite number of other intelligent species out there in space – even though we may never be able to contact them.
We can take this logic still further. If there are an infinite number of stars in the greater universe, every possibility, no matter how minuscule, is instantiated somewhere, in fact instantiated an infinite number of times. There are planets where time runs backwards, where entropy decreases. There are planets that are exact doppelgängers for our own – in fact, there must be an infinite number of planets exactly identical to Earth. An infinite number of planets exist that are exactly the same as this one except that you stopped reading this post after the first paragraph. An infinite number of Earths exist in which Hilary Clinton is President rather than Donald Trump. In saying that every possibility is instantiated, I am not necessarily talking about quantum indeterminacy – the differences between different planets could result from such quantum effects but could also arise from very slight differences in initial conditions exaggerated by recursion. Everything that is possible is actual an infinite number of times, out planet is possible, so an infinite number of other Earths exist.
This argument is like a reductio ad absurdum. If you believe that the picture I have limned in the last two paragraphs is ridiculous, you will be forced to conclude either that there is some problem in our notion of probability, or that the third hypothesis must be false, that the material universe is finite. Alternatively, you might embrace this picture, particularly if you enjoy science fiction.
Cosmology is currently faced by profound and presently unanswerable questions. Where is the missing mass in the universe? Why is the universe's rate of expansion increasing? In previous posts I have argued that quantum physics places limits on what we can know about the microscopic world. Perhaps the same thing is true on the greatest possible scale. Perhaps there are questions about the universe as a whole that we will never know the answers to. Or perhaps the power of human intelligence will take steps towards solving them. Here's to hoping.
