Sunday, August 24, 2008

Causal Dynamical Triangulations

What? You ask. Say what? And well you might. But this is the working description of the most exciting cosmological theory I've read about in probably twenty years. It was written up in the July 2008 Scientific American and you can find the article here, entitled The Self-Organizing Quantum Universe.

I began to try to summarize it; and realized that I don't know enough about it to do it justice. Read the article yourself - it's surprisingly accessible - but here's what excites me about it:

I read cosmology and quantum physics articles as a challenge. I don't understand the math; I want to see if I can read the words and get a feel for what they're talking about. I have a general feel for quantum theory - the broad concept that any entity from an atom to the universe exists in what they call "superposition", which means that it "exists" in all possible states simultaneously, and only "collapses" into a single state when you measure it. (I told you this wasn't my world.) But quantum theories don't explain gravity and never really have.

Increasingly expansive attempts to develop a "theory of everything" (including gravity) have postulated ever-increasing crowds of elementary particles (quarks, gluons, etc.) and even minuscule vibrating "strings" - and the theories based on these predict universes that exist in dozens of dimensions, all so small they can't be detected. Nothing they predict resembles anything you can see when you look around, or point a telescope at the universe. And their theories are so complicated they require massive supercomputers to work out the mathematics of the simulations. Frankly, they've never made any sense to me; and they've always made me think of the epicycles that medieval philosophers developed, to explain why their increasingly precise measurements of planetary motion didn't match what the Ptolemaic theory predicted.

It's probably too much to suggest that this team of
scientists - a Dane, a Pole, and a German - is the equivalent of Copernicus and his heliocentrism. For one thing, I doubt anyone will actually burn at the stake for advocating their theory. But the theory, which they call causal dynamical triangulations, has a number of points in common with Copernicus':
  • It's based on a few simple assumptions, using only very basic quantum principles.
  • The calculations are simple enough that they can do their simulations on a laptop. (Keep in mind that today's laptops have a lot of computing horsepower!)
  • What it predicts looks remarkably like what we see.
  • When they change details in their simulations, the results barely change at all.
What made me sit up and shout, "Yes!" when I read it was the basis of their theory: causality. They assume that "events occur in a specific temporal sequence of cause and effect, rather than as a haphazard jumble." Also, "the distinction between cause and effect is fundamental to nature, rather than a derived property."

All cosmological theories assume basic building blocks, which have certain properties. In the authors' theory, each triangular building block is assigned an arrow of time, pointing from past to future; and the rules governing gluing building blocks together require that their arrows of time point in the same direction. The spacetime this predicts looks like the four-dimensional spacetime we live in, and conforms to the predictions of Einstein's theory of general relativity (which has never been disproved). I was actually reminded of the computer game "Life", where you define a starting state and a fairly simple set of rules, and let the program run to produce a world.

Additionally, as far as the authors can tell to date, the universe predicted by this theory is fractal - that is, it looks the same at any scale, as far down as one can measure. I don't know why this appeals to me, except that as far as I can tell, the living universe tends to be fractal.

I don't know if this will appeal to anyone else the way it did to me, but it fascinated me and I had to share it.


  1. Theoretical physicists speak in the language of higher mathematics. Few of us can follow them to that rarefied level of discourse, and so must take what they imply in their condescending descriptions on faith (I don't mean condescension in the negative sense here.) My wife and I have tried reading Feynman's lectures, just to get a sense of the insights, but it's nearly impossible, since the payoff usually is a formula, whose beauty and simplicity are lost on us. String theory, for instance, sounds intriguing, but the mathematical reasons for its theoretical basis are far beyond my comprehension.

    What I find fascinating is that our perception of what the universe is "about" is limited to the dimensionality of our nervous system(s): Empirical measure, as you point out, works very well within the closed system of our earth-based experience; but it's perfectly possible to be completely taken in by data, as for instance when the desert horizon appears like a body of water on a hot day. In what sense, along these lines, do many of the astronomical phenomena present similarly deceptive views? What is "sound" for instance, where there is no "atmosphere" to transmit it? Exploding suns make no noise? If the universe is limitless, then we are literally no-where. The human mind boggles at these notions. One thing's sure: If we can't put our own house in order, it's unlikely we're going to have access to a replacement.

  2. Actually, I think you could argue that exploding suns do make noise: they create an outbound pressure wave in the surrounding medium - you can hardly say, "atmosphere", but there is stuff out there, and it can be compressed in the aftermath of an explosion.

    There just isn't any entity available with sensory organs that can interpret those pressure waves and turn them into sound, the way our ears do.

    At least, no entity that we know about.

  3. Yeah, there's speculation now that there is some kind of "stuff" where we once thought there was an absence of matter--anti-matter, whatever. "Black stuff." Too small to be measured, but there. Like the "aether." Doesn't give off light, but it's there. Very weird.

    If there is no one to hear a sound, can there "be" sound? Maybe in the Wittgensteinian sense, it doesn't exist without a perceiver. And then, we can't "talk" about it without distancing ourselves from the reality, or by assigning surrogates (symbols or definitions). Only in the theoretical sense, I think. In the abstract.

    I think that a lot of what astronomers are postulating about the heavens will turn out to be a misinterpretation of the data they use. If time is indeed fluid, then large extents of it might be subject to exaggeration or distortion. We are clearly a part of something happening that happened so long ago that what is happening to us at this moment is part of an aftermath that has occurred eons in the future ("after" the events we can see): The future (us) looking so far into the past, while the future (that which we can't see, because the light takes so long to reach us) will have happened so long after that. A human life seems such a minute blip (or sputter) in the void.

    We are light. Everything we can see and touch is light. It seems to be the measure of everything. In a religious sense, it is so powerful a concept--so far reaching in its complexity--that it really does achieve the status of miracles. Or, at least that's the word we can use to describe something so baffling and impressive, but which we can't easily get our minds around.

    Sputter, sputter.