I’ve been re-reading James Gleick’s 1987 book Chaos. A lot of chaos theory is about mathematical abstractions, but it also has a very practical side. The Great Red Spot on the surface of Jupiter is still a bit of a mystery, but it appears to be a storm system that has somehow remained relatively stable for several hundred years, while the rest of the atmosphere of Jupiter swirls around it in fantastic disarray.
The essential point here is that islands of stability can arise spontaneously even in the midst of instability. We can see the same thing on Earth. A tornado doesn’t last nearly as long as the Great Red Spot has lasted, but one would naturally expect that such a thing as a tornado could never exist. How could a whirlpool of air come into being and then sustain itself for twenty minutes without flying apart?
Chaos defies our expectations. Gleick describes mathematically sensible objects that have a finite size, an infinite surface, and an interior volume of zero.
Since I’m still fuddling about the unlikely idea that the rapid spin of galaxies is caused by a mysterious substance called dark matter (see my earlier blog entries Spin and Hubble Trouble), the similarity between spinning galaxies and the Great Red Spot was hard to miss. Galaxies are islands of order in a universe whose constituents, as far as we currently understand them, would not seem capable of producing such orderly phenomena.
There are deeper problems in cosmology than the spinning of galaxies. Don’t ask me to do the math, but my hazy impression of subatomic physics is that the world we live in can only exist due to the precise values of certain abstract numbers, such as the Fine Structure Constant (it’s about 0.00729735, if wikipedia is to be believed). If that number was slightly larger or slightly smaller, no atoms. No molecules. No you and me.
It seems inherently absurd to suggest that somehow the universe sprang into existence with all of these numbers precisely tuned so as to give rise to galaxies, stars, and you and me. Various proposals have been made to account for this. For instance, the Weak Anthropic Principle begs the question by saying, “Well, if it was any different you wouldn’t be here to ask the question.” Then there’s the multiverse theory, which posits an infinite number of complete universes, each of them perhaps exploding into existence due to the crunching up of a black hole in a parent universe. In each of these baby universes the values of things like the Fine Structure Constant would be random, so most of them would either collapse or dissipate in a vast gray cloud. But a few, like ours, would be suitable for life to come into existence, along with black holes so the universes can continue to propagate.
We will never be able to observe any of those other universes, however. The multiverse theory has the advantage that it can never be tested observationally. It’s a Just So story.
Our best current understanding of our own universe is that it sprang into existence about 13.8 billion years ago, has been expanding ever since, and will eventually (some trillions of years from now) become a cold dead place for all eternity, when all of the stars have burnt out. This is not a very cheerful prospect. There are some good observational reasons for thinking the Big Bang really happened. But why and how it happened, and how it gave rise to the Fine Structure Constant — there are no answers to questions like these.
The fact that there are no answers leaves the door open for me to suggest one.
To begin with, we don’t even know whether the universe is finite or infinite. We know there are distances beyond which our best telescopes cannot see, but that’s not quite the same thing. So let’s suppose for a moment that our universe is in fact infinite in extent and also chaotic. The part of it we can see, while unimaginably vast, is also infinitesimal compared to the whole. There is not, in this conception, any “whole” at all. But because all of the processes are chaotic, areas of stability will occasionally arise. In fact, an infinite number of areas of stability will arise.
The area we can see is an island of stability — the Great Red Spot writ large. Even basic characteristics like the Fine Structure Constant may be different in different parts of the universe. Somewhere beyond the horizon of what we can see with our telescopes, the rules of physics may change — because there’s no reason why they shouldn’t change. Nobody is in charge. No godlike entity has laid down the laws of physics and decreed that they shall always, everywhere, be the same.
It’s even possible that when we look at the most distant galaxies and see quasars, brightly burning objects that are quite unlike anything in nearby galaxies, we’re seeing regions where the laws of physics are a bit different. To be sure, the quasars we see today existed billions of years ago, because that’s how fast light travels (in our region of stability, anyway), but the idea that the laws of physics that allowed quasars to burst into being are exactly the same as what we observe nearby — that idea is purely speculative. We can’t go out there and perform experiments.
The idea that the universe may be both infinite and chaotic removes a lot of the balky problems in physics, starting with dark matter and dark energy. Dark energy is the theory that something (we don’t know what) is pushing galaxies away from one another faster than would be expected, based on our current theories of how things are. But what if distant galaxies are just rolling downhill, as it were, in a universe where not even the number of physical dimensions of space is fixed?
Turn an aluminum mixing bowl upside down and pour a bag of beebees out on it. The beebees will roll down the sides of the bowl. If you were sitting on one of the beebees, you could be forgiven for imagining that some dark force is pushing the beebees away from one another, when in fact something else (gravity plus the curvature of the bowl) is pulling them apart. The gravitational force is outside of the bowl, and the trajectories of the beebees are determined entirely by the shape of the bowl.
To me, that feels like a more sensible way to look at it. And of course those two ways of looking at the expansion of the visible universe are not necessarily different! We just don’t have the terms with which to talk about this stuff. Nor do we have the apparatus with which to test it. Nor is it guaranteed that such apparatus could ever be built.
Modern cosmology and modern subatomic physics arose in the years between 1900 and 1940, give or take a few years. At that time, linear analysis of physical systems (the kind of analysis that Galileo and Newton did) was assumed to be capable of perfectly explaining all physical phenomena. We now understand that that’s not the case. Nonlinear, chaotic, fractal processes are everywhere in our world. Why should we imagine that the wider universe is simple?