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How Gravity Explains Why Time Never Runs Backward


Even though time is such a fundamental part of our experience, the basic laws of physics don’t seem to care in which direction it goes. For example, the rules that govern the orbits of planets work the same whether you go forward or backward in time. You can play the motions of the solar system in reverse and they look completely normal; they don’t violate any laws of physics. So what distinguishes the future from the past?

“The problem of the arrow of time has been boggling minds forever,” said Flavio Mercati of the Perimeter Institute for Theoretical Physics in Waterloo, Canada.

Most people who’ve thought about this arrow of time say it’s determined by entropy, the amount of disorder in a system (like, say, a bowl of cereal, or the universe). According to the second law of thermodynamics, the overall entropy of a closed system must always increase. And time appears to travel in the same direction as rising entropy.


When an ice cube in your glass melts and dilutes your lemonade, for instance, entropy increases. When you scramble an egg, entropy increases. Both of these examples are irreversible: you can’t freeze a water ice cube out from your lemonade or unscramble an egg. The sequence of events—and thus time—goes in only one direction.

If time’s arrow follows the increase of entropy, and if the entropy in the universe is always increasing, then it means that at some point in the past, entropy must have been low. Therein lies the puzzle: why was the universe in such a low entropy state in the first place?

According to Mercati and his colleagues, there was no special, initial state at all. Instead, a state that gets time pointing forward arises naturally from a universe dictated by gravity. The researchers make this argument in a paper recently published in the journal Physical Review Letters.

To test their idea, they simulated the universe as a collection of 1,000 particles that interact with one another only by gravity, representing the galaxies and stars that float around the cosmos.

The researchers found that regardless of starting positions and velocities, at some point the particles inevitably find themselves clustered together in a ball before dispersing again. This moment of clumping is equivalent to the Big Bang, when the whole universe was squeezed into an infinitesimally small point.

Instead of using entropy, the researchers describe their system with a quantity they call complexity, which they define as roughly the ratio of the distance between the two particles farthest from each other to the distance between the two particles closest to each other. When the particles are clumped together, complexity is at its lowest.

The key idea, Mercati explains, is that this moment of lowest complexity arises naturally from the group of gravitationally interacting particles—no special initial conditions are needed. Complexity then increases as the particles disperse, representing the expansion of the universe and the forward progress of time.

A collection of particles interacting via gravity will inevitably bunch together, as seen in the middle panel. This moment of lowest complexity represents the Big Bang, and two arrows of time point forward and backward, to the left and right.   APS/Alan Stonebraker

If that wasn’t mind-bending enough, the events that occur before the particles clump—that is, before the Big Bang—orients a second direction of time. If you play the events backward from this point, the particles will appear to disperse from the clump. Because complexity is increasing in this backward direction, this second arrow of time also points into the past. Which, according to this second time direction, is actually the “future” of another universe that exists on the other side of the Big Bang. (Deep stuff, right?)

The idea is similar to one proposed 10 years ago by physicists Sean Carroll and Jennifer Chen of the California Institute of Technology, who were linking the arrow of time with ideas describing inflation, the abrupt and rapid expansion of the universe that happened soon after the Big Bang.

“What’s great about this is that it’s not hand waving,” Carroll said about the new work, which defines a concrete model and explicitly shows how it gives rise to an arrow of time. “It’s just fascinating for us to think that the reason we remember yesterday and not tomorrow is because of conditions near the Big Bang,” he said.

Showing how temporal direction comes from such a simple system that follows classical physics is new, says physicist Steve Carlip of the University of California, Davis.

Eschewing entropy in favor of complexity is also a distinct idea, Mercati says. The problem with entropy is that it’s defined in terms of energy and temperature, which are measured based on some external reference such as a thermometer. In the case of the universe, there’s nothing outside it, so you need a quantity that doesn’t rely on any units of measurement. Complexity, as the researchers define it, is a dimensionless ratio and fits the bill.

That’s not to say that entropy is irrelevant, Mercati says. Our day-to-day experiences with time—like your iced lemonade—do rely on entropy. But when considering time at cosmic scales, you need to think of the universe in terms of complexity, not entropy.

One major limitation to this model is that it’s based solely on classical physics, ignoring quantum mechanics. Nor does it include Einstein’s theory of general relativity. There’s no dark energy or anything else that’s needed to more accurately model the universe. But the researchers are thinking of how to incorporate more realistic physics into the model, which could then make testable predictions, Mercati says. “Then you really have nature telling you whether you’re right or wrong,” he said.

“For me, the bigger problem is that there are a whole lot of different physical arrows of time,” Carlip said. The forward direction of time manifests itself in many ways that don’t involve gravity. For example, light always radiates away from a lamp—never toward it. A radioactive isotope decays into lighter atoms; you never see the reverse. Why would an arrow of time derived from gravity also push other arrows of time in the same direction?

“It’s a big open question,” Carlip said. “I don’t think anyone has a good answer as to why these arrows of time should agree. This doesn’t answer that either.”


WiReD: How Gravity Explains Why Time Never Runs Backward

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