# Explanations for time’s arrow keep marching on

Time after time, physicists have tried to explain time. Many claim to have succeeded. But they haven’t. Otherwise everybody would quit trying to explain it all over again.

One of the most recent such efforts comes from the mathematician/cosmologist George F.R. Ellis. He thinks solving the time mystery involves figuring out the difference between the past and the future.

That’s not as obvious as it sounds. Physical laws governing motion make no distinction between future and past. Equations describing the scattering of billiard balls on a pool table work equally well if all the balls retrace their paths to form a neat triangle. Films of molecules flailing around look the same in forward or reverse.

But in ordinary experience, time always goes forward. Never backward, except artificially with DVRs or movie special effects. In real life, water waves never compress themselves and eject a rock upward from the middle of a pond. No restaurant menu offers descrambled eggs, sunny side up. Somehow a molecular world with no direction of time builds a big world where time marches on.

Scientists commonly explain this mystery by invoking the second law of thermodynamics: Entropy, or disorder, always increases (until it can increase no more), thereby defining time’s arrow as the direction of increasing disorder. Of course, a bright 5-year-old can immediately demonstrate the weakness of this explanation by asking, “Why?”

Most attempts to answer that question have turned out to be flawed.

In the late 19th century, for instance, Ludwig Boltzmann explained it by pointing out that there are many ways for entropy to increase, and very few ways for it to decrease. So it’s basic probability — entropy going up is way more likely than entropy going down, so going up is what happens. This approach fails to explain time’s direction, though, because entropy is likely to rise no matter which way in time you go, forward or backward.

A popular way around that conundrum was to suggest that at some initial point in time (like the birth of the universe), entropy was for some reason very low. Consequently it started rising and kept on rising. But of course, invoking an “initial point” predefined the direction of time by use of the word “initial.”

Nowadays, the more sophisticated explanation is that in the very young universe, the entropy was not especially low, but was much lower than it might possibly have been given the amount of energy available. But that’s really just part of the whole answer, Ellis contends in a comprehensive new paper.

He argues that time’s direction is connected to the expansion of the universe, which began as a point with no size from which spacetime emerged and began to grow. “Cosmic time starts at the creation of the universe,” writes Ellis, of the University of Cape Town in South Africa. “The arrow of time is defined” as “the direction of time in which spacetime is increasing.”

So even though Einstein’s equations for the universe work fine either direction in time, the real universe has a time direction.

“The universe is expanding, not contracting, because it started off from a zero volume state,” writes Ellis. “It had nowhere to grow but larger.”

As the universe grew, Ellis says, time came into existence — the part of time we call the past. But the future remains unreal. This view contradicts the mainstream belief that all of spacetime already exists. Einstein, for instance, believed that time is an illusion. People (and everything else) travel along a “world line” through preexisting spacetime — a huge container of all events, past and future, in what physicists call the “block universe.”

Ellis, though, contends that the correct picture is an “evolving block universe,” in which the present moment defines a boundary between the established past and uncertain future.

“The part of spacetime that exists at any instant is the past part of spacetime, which continually grows,” he writes. “The future is a possibility space, waiting to be realized. It does not yet exist.”

Many aspects of the arrow of time can be explained from this perspective. After its hot Big Bang beginning, the universe cooled as it expanded, defining a direction of time that’s the same for everybody. “Temperature is decreasing as time increases; this is what determines the arrow of time at each local level,” Ellis maintains.

But that’s not enough. In a Newtonian universe, the past determines the future, so all of existence is established for certain at the outset. Past and future are inseparable. But in a quantum universe, multiple futures are possible. As atoms interact and events occur, possibilities become realities. “This is where the essential difference between the future and the past arises,” Ellis argues.

Still, his explanation leaves one gap unfilled. Somehow the local time defined by quantum collapse of past into future must be linked to the global direction of time defined by the expanding universe. “How this happens,” writes Ellis, “needs to be elucidated.”

In other words, time has still not yet been explained.

SN Prime | March 18, 2013 | Vol. 3, No. 11