No going back

Why is time the only dimension to flow in one direction?

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I had my licence for exactly three days before I wrote off my first car. Had I paid more attention in physics class, I would have known that the fiasco of velocity, trajectory and probable outcomes I had construed had no chance of going well. All the theory Mr Newall had tried to explain in class played out—in that slow-motion way that accidents do—in practice as the Hillman Minx rolled twice, then came to rest upside down on the side of Rosedale Road on Auckland’s North Shore.

Physics—and ineptitude—had got me here, but as I squirmed through the shattered driver’s window, I became preoccupied with the nature of time. First, of course, I considered the future: the moment when I had to explain to my dad what had just happened. That got me thinking—irrationally, now that shock was kicking in—about the recent past: about how, in a perfect world, I could just go back in time and take that corner again.

As far as Isaac Newton was concerned, there was nothing to stop me. He said that any event could happen in reverse, at any time. His laws of physics work just as well running forwards or backwards. So why couldn’t I un-crash the Minx? Why did my future look worryingly different from the past?

The second law of thermodynamics ensures we’ll always need panelbeaters: it says the entropy within a system can never decrease over time. Entropy either increases, or remains constant, if the system is in equilibrium. In other words, things only ever get more messed up, not less.

Einstein gave us the term “spacetime”, a conjunction that paints a picture of a fused, four-dimensional space. But space and time are fundamentally different. In space, you can move about however you wish—forwards, backwards—but you can’t go back to yesterday. Your life trajectory follows a single direction—the trajectory of what British astronomer Arthur Eddington called “the arrow of time”.

Why? We’re still not sure, but the answer almost certainly lies somewhere in the second law of thermodynamics. It was an Austrian physicist, Ludwig Boltzmann, who first wondered whether time and matter might be in some kind of lockstep. Over the late 1800s, he changed the way we think about entropy—the degree of disorder in the universe. Boltzmann deduced that entropy was really just about atoms, the energy they hold, and, crucially, the way they’re arranged. The formula that bears his name today connects entropy with probability.

Objects, systems, he figured, will always move from a state of low entropy to high. What does that mean? Merely that the atoms are getting more jumbled up, and the messiness of them is on the increase. Why? Think of an ice cube: molecular physics gives it so many ways to disassemble—to melt—and so few options for remaining intact. Just like the physical forces I had inflicted on the Minx gave it no chance of making that corner.

On the straight, the car was an intact, low-entropy system. Lying mangled on the verge, it displayed a dismaying degree of disorder. Atoms all over the place.

Everywhere, every day, stuff is getting more muddled, across a whole universe of physical systems. By now, you may begin to appreciate why entropy may be frogmarching time in a single direction. You can’t put that ice cube back together how it was, any more than I could reassemble the Minx. What’s done cannot be undone. Ergo: time.

Wait, what? Didn’t Newton insist the direction of time’s arrow doesn’t matter to matter? If entropy increases as time goes, wouldn’t it increase as you go back into the past, as well? Boltzmann, who spent much of his career dealing with critics, went back to the blackboard, and eventually published his “past hypothesis”. It was simple: if time is going only forwards, it must mean that the early universe was neatly organised—in a state of low entropy.

Well, okay. But didn’t we just decide that low entropy is a rare and unlikely state, given that matter tends towards clutter? This time, Boltzmann had no answer, and the incessant repudiation was taking a toll. Drowning in depression, doubt and rejection, he hanged himself during a family holiday near Trieste in 1906. Time went on without him. Ironically, it was only a decade before Boltzmann’s theories about atoms were accepted as correct.

What’s more, by the 1920s, cosmologists had noticed that galaxies were moving apart from one another. That meant the universe must have had a beginning—one in which everything was jammed up together. Until, suddenly, it wasn’t.

What’s the difference between the past and the future? “Let us draw an arrow,” wrote Arthur Eddington. If, following the arrow, you find the world is increasingly chaotic, the arrow is pointing towards the future. If randomness decreases, the arrow is pointing towards the past. Eddington called this the assymetry of time: the fact that atoms, molecules, and bodies are not equally well-organised in both the past and in the future.

If anything sounds like a high-entropy situation, it’s a Big Bang. A car crash to the power of a gazillion zeroes. But we now suspect that entropy behaves very oddly when there’s so much matter close to hand, because that matter holds an equally unthinkable amount of gravity.

We don’t know why, but inside uber-massive objects—like the entire universe crammed into a dot—higher entropy means that atoms get clumpy, rather than scattered, thanks to gravity. Boltzmann was right. He didn’t know why he was right, and neither do we, but the infant universe was almost certainly a place of low entropy.

You know the rest. Since then, the universe has splayed itself beyond the gaze of our most powerful telescopes, across near-limitless space and time. Bits of it are still clumped together, but the whole thing is expanding in an apparently chaotic way, always towards higher entropy. Boltzmann’s atoms are doing exactly what he predicted, and they’re taking time with them. Eventually, the universe will attain some atomic nirvana, the ultimate entropic state. Nothingness.

In the Zentralfriedhof in Vienna, Boltzmann’s tombstone stands above the family plot. Engraved upon it is his formula that tells us so: S = k. log W.

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