Randomness

By Tom Siegfried

Web edition: January 11, 2013

In olden days, before the Star Trek holodeck and movies like TRON and The Matrix, philosophers used to wonder whether life was but a dream. Nowadays they’re more concerned that reality could be just a computer simulation.

Sure, that’s not very likely. But you can’t rule out the possibility. Computers simulate all sorts of things, and some scientists have seriously suggested that nature’s supposedly rock-solid reality is really just some smart alien teenager’s science fair project.

Most people respond to that suggestion with a shrug. What does it matter? You have to row, row, row your boat anyway. As Gottfried Leibniz pointed out over three centuries ago, all that matters is that the world behaves real enough so that sound reasoning won’t deceive you. In other words, there’s no way to distinguish a real world from a simulation that convinces everybody they’re real.

Oh, that’s such limited thinking. If you contemplate how superior programmers would go about simulating a universe like the one humans inhabit, perhaps it wouldn’t be impossibly difficult to tell rock-hard reality from software simulation.

In fact, physicists are already simulating universes with their computers. It’s just that the simulated universes are pretty darn small, as Silas Beane and colleagues write in a recent paper online at arXiv.org. Using the equations for quantum chromodynamics — the math governing the strong force that holds atomic nuclei together — physicists routinely simulate how subatomic particles called quarks interact in order to see how nuclear matter should behave. 

Simulations are easier than solving the equations exactly — that would require infinite precision. Instead, a computer simulation performs calculations on a “lattice” — a set of points, all very close together, to approximate laws that actually operate at infinitesimally short distances. In these lattice simulations, points are fractions of femtometers apart (one femtometer being a quadrillionth of a meter, aka very tiny). The “universe” explored in such simulations is typically several femtometers across.

A universe so small is not likely to be of much interest to anybody who cares about anything bigger than a quark. But that size is limited merely by present-day computing power. 

“It stands to reason,” write Beane and colleagues, “that future simulation efforts will continue to extend to ever-smaller pixelations and ever-larger volumes of space-time.”

Using assumptions about the growth of computing capability, the researchers forecast that a simulation the size of a human body might be within reach in 130 years or so. Since such a simulation would describe the activity of a body’s worth of atoms (it’s no big deal to add electrons to the math describing nuclei), human thought and behavior could appear. In a few more centuries, or millennia, computing power could simulate a universe of any size you want, as long as you aren’t constrained by shortsighted budget cutters.

“If there are sufficient high-performance computing resources available, then future scientists will likely make the effort to perform complete simulations of molecules, cells, humans and even beyond,” write Beane, of the Institute for Nuclear Theory in Seattle, and University of Washington collaborators Zohreh Davoudi and Martin Savage.

Still, you could be just a simulated automaton, but nobody would ever know. Except now, Beane and colleagues have gone a step further and figured out that such a simulation might very well leave signs that human scientists could detect, even if they are merely simulated scientists.

One promising possibility involves details about the distribution of high-energy cosmic rays in the cosmos. In a universe governed by the full-scale equations (no lattice-simulation approximation), you’d expect to see a symmetric range of directions of such cosmic rays traveling through space. But if a lattice simulation is generating reality, the distribution of directions would be skewed. If future observations measure enough high-energy rays to determine whether such a discrepancy exists, “reality” could be exposed as a cruel hoax.

Some perplexing physics problems might be explained by the simulation hypothesis. For years physicists have pondered the mysterious acceleration of the universe’s expansion, apparently caused by a small amount of “dark energy” residing in the vacuum of space. Experts used to think the vacuum should have precisely zero energy. But if the universe is a computer simulation, Beane and coauthors point out, a slight non-zero amount of vacuum energy might occur as a result of rounding errors in the computations.

For even more fun, consider the possibility that patterns in the glow of cosmic microwave radiation left over from the Big Bang contain messages from the simulation’s programmers. OK, maybe it’s a stretch. But if such messages exist, the prospect might exist that humans could send messages back to the programmers.

And maybe a simulation would offer an additional benefit: In a universe governed by infinitely precise laws, human freedom would be an illusion. In a lattice simulation, laws would be less rigid, perhaps providing the simulated inhabitants with free will. Or so you could dream.