What good are the laws of physics if we can’t solve the equations that describe them?
That was the question that occurred to me on reading an article in The Guardian by Andrew Pontzen, a cosmologist at University College London who spends his days running computer simulations of black holes, stars, galaxies and the birth and growth of the universe. His point was that he and the rest of us are bound to fail.
“Even if we imagine that humanity will ultimately discover a ‘theory of everything’ covering all individual particles and forces, that theory’s explanatory value for the universe as a whole is likely to be marginal,” Dr. Pontzen wrote.
No matter how well we think we know the basic laws of physics and the ever-expanding list of elementary particles, there is not enough computer power in the universe to keep track of them all. And we can never know enough to predict reliably what happens when all these particles collide or otherwise interact. A decimal point added to an estimation of, say, a particle’s location or velocity can reverberate through history and change the outcome billions of years later, by way of the so-called butterfly effect of chaos theory.
Consider something as simple as, say, Earth’s orbit around the sun, Dr. Pontzen says. Left to its own devices, our world, or its crispy fossil, would go on forever in the same orbit. But in the fullness of cosmic time, gravitational nudges from other planets in the solar system can change its course. Depending on how precisely we characterize these nudges, and the stuff being nudged, gravitational calculations can produce wildly divergent predictions of where the Earth and its siblings will be hundreds of millions of years from now.
As a result, in practice, we cannot predict either the future or the past. Cosmologists like Dr. Pontzen can hedge their bets by zooming out and considering the big picture — large agglomerations of material like clouds of gas, or systems whose collective behavior is predictable and not dependent on individual variations. We can boil pasta without keeping track of every molecule in the water.
But there is a risk of presuming too much order. Take an anthill, Dr. Pontzen suggests. The movements of any individual ant seem random. But if you look at the whole, the anthill seems to be buzzing with purpose and organization. It is tempting to see a collective consciousness at work, Dr. Pontzen writes, but “there are just lone ants” following simple rules. “The sophistication emerges from the sheer number of individuals following these rules,” he notes, quoting the Princeton physicist Philip W. Anderson: “More is different.”
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