# Tom Siegfried, Randomness

## Time’s arrow and reality’s randomness succumb to quantum thermodynamics

**SN Prime March 26, 2012 | Vol. 2, No. 12**

Randomness and reality go together like pizza and beer. March and madness. Ice and cream.

It didn’t used to be that way. Isaac Newton supposedly established that reality wasn’t random at all. It was “deterministic” — as regular as clockwork. Tock always followed tick. If you knew where everything was and how it was moving, you could figure out what everything would be doing at any time in the future.

But in the 19th century,
determinism’s grip on the scientific view of reality began to slip.

Maxwell, Boltzmann and other physicists pointed out that you couldn’t really
know every molecule’s location and speed. You had to assume that the molecules
bumped into each other at random, then calculate the likely outcome of all
their collisions. Enshrined as the second law of thermodynamics, that approach
allowed precise predictions of the behavior of gases and other physical systems. And it
explained why time flowed in only one direction. Entropy, the measure of how
messed up a system is, always increases until equilibrium is reached — thanks
to the way randomness produces highly probable arrangements of things. (Messy, of course, is always much more probable than
neat.)

In the 20th century, quantum mechanics seemed to cement randomness’s rule over reality. Woven into the fabric of the cosmos was an indeterminism in the outcomes of observations. Physics can offer only the odds of finding a particle in any given location, not where a particle will be found for sure. Quantum versions of statistical physics made it clear that randomness reigned at a fundamental level, not just in the realm of human ignorance.

But some scientists yearn to look deeper. For one thing, the second law has always been a bit troubling. If it depends on particles bouncing around at random, after a long enough time they’d eventually bounce back into their original positions — which is to say, time could flow backward. And quantum randomness has long annoyed many people because of that pesky observation part. In the quantum story, particles are actually deterministic waves until an observer spots one, causing the wave to “collapse” into a particle.

Curiously, both these conundrums might go away if the second law is actually a consequence of quantum theory. You can keep determinism, explain the direction of time and resolve paradoxes of an infinite universe all at once, a new paper proposes.

“We get an irreversible, deterministic approach to equilibrium,” physicists David Snoke and Gangqiang Liu of the University of Pittsburgh and Steven Girvin of Yale write in a paper to appear in Annals of Physics. “We never invoked collapse, measurement, observation, or randomness.”

Instead, the physicists used quantum field theory to demonstrate that the second law follows naturally from the way quantum physics works. In quantum field theory, “particles,” like electrons or photons, are merely knots in a pervasive underlying field. Vibrations in the photon’s field are electromagnetic waves; for electrons, the field carries electron probability waves. Your odds of finding an electron in a particular place depend on the strength (or amplitude) of the wave in the field at that point.

Besides amplitude, waves also have phases — positionings of amplitudes that determine whether the waves add or cancel (as when water waves meet). In a quantum system, Snoke and colleagues calculate, the path to equilibrium can be described deterministically if information about phases is thrown out of the math. And systems described by quantum field theory do naturally discard such information, the physicists show — it gets spread out in the universe, forever eluding any possible measurement.

That means that you can quit worrying about some weird things that might happen if the second law was merely highly probable. In an infinite universe, for instance, somewhere stars would suck in energy rather than emit it. But not if the second law is deterministic. “The quantum mechanical formulation presented here says that if stars are coupled to an infinite universe, then the second law is absolute, not just a likelihood,” the physicists write.

Their analysis also implies that the wave equation describing quantum states is itself real in a meaningful way, while denying that observers are needed to generate reality.

“ ‘Collapse’ of the wave function ... comes entirely from the mathematics of quantum field theory without need for invoking external observers,” the physicists write, supporting “the philosophical view that the field of quantum field theory is ‘real.’ ”

Don’t expect that everybody will now stop writing papers about these quantum controversies. Links between quantum theory and the second law are certainly intriguing, and the prospect of clarifying the nature of reality, the direction of time and randomness’s role in physics with one fell swoop has its appeal. But such sticky issues are not swept away so swiftly. In the quantum world, even profound new insights often lead to deeper confusions.