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In a distant galaxy, a star unexplodes. Just moments ago a shell of tortured matter was flying together at 30 000 kilometres a second. Now it has become a star, and the last shreds of glowing debris are being sucked in. With the explosion undone, the star begins the long journey back to the time when it will be unborn into the gas and dust of an interstellar cloud.

Is someone running the film backwards for comic effect? Not necessarily. In a paper published in the last week of 1999, Lawrence Schulman of Clarkson University in Potsdam, New York dropped a bombshell. He showed that regions where time flows in the normal direction can coexist with regions where it flows backwards. There could be places, perhaps even within our Galaxy, where stars unexplode, eggs unbreak and living things grow younger with every second.

To understand how time could run backwards, you need to understand why it has a preferred direction at all. The equations of physics say that particles of matter don’t care what direction time runs in: any interaction between two particles could happen just as easily in reverse. (Some nuclear interactions do show a small bias, but no one has found a way to turn this into an arrow of time.)

But when you have a lot of particles instead of just two, things change. Messy, disordered states tend to develop from tidier ones. This tendency is called the thermodynamic arrow of time. Physicists say that entropy-a measure of disorder-always increases. “It’s easy to break an egg, difficult or impossible to put the pieces back together,” says Schulman.

Say the air in a large room is confined in a 1-metre cube in one corner, then released. It is perfectly possible that, after five minutes, the air molecules will all be back in the same 1-metre cube. Perfectly possible but hugely improbable, because there are far more ways to arrange the individual molecules when they are spread out than when they are confined. In fact, the most disordered state-in which the air molecules are spread more or less evenly throughout the room-can be achieved in far more ways than any other state. “This is the second law of thermodynamics,” says Schulman, “which seals the fate of Humpty Dumpty.”

However, argues Schulman, a reverse arrow is perfectly possible: “It’s all down to the ‘boundary conditions’-the external constraints imposed on the system.” In the room, the air has to be in the 1-metre cube only at the start of the five-minute period. There is no constraint on it at the end of the five minutes-the system can find its own final state.

But say a final condition is imposed. After five minutes, the air molecules have to be back in the 1-metre cube. On Earth, this is clearly an artificial situation. But for Schulman, it is perfectly legitimate to consider such a state of affairs. “There is no reason in principle why the Universe might not have a future boundary condition imposed on it,” he says.

The future condition would constrain the molecules to follow only a tiny subset of trajectories, ending up in the 1-metre cube. From our point of view, time would be running backwards.

But there’s an objection to having forward and backward time regions in the same universe. Surely the arrow of a reverse-time region would be wiped out by the slightest interaction with a normal-time region, leaving a completely disordered system with no arrow at all?

Imagine a game of snooker in which the triangle of red balls is struck by the cue ball and scattered around the table. Now imagine the reverse-time scenario. For the balls to follow the precise trajectories necessary to finish in a triangle will take a monumental amount of coordination. The slightest disturbance will spoil it. Any interaction with a region with normal time-for instance, the smallest cry of amazement from someone watching-could vibrate the air, nudge the balls and wreck everything. So the backward arrow of a reverse-time region would be instantly destroyed by any interaction with a normal-time region.

Schulman sees a flaw in this idea. The two systems are on an equal footing, so the reverse-time region is as likely to destroy the arrow of the normal-time region as vice versa. “All we can say is that if the two regions interact their arrows will either both be destroyed or both survive.”

Most physicists would have put good money on the former possibility. But Schulman’s startling conclusion is that as long as the interaction between the two regions is weak, both arrows will survive. He bases this claim on a simple computer model that allows him to set up weakly interacting systems with opposite arrows of time and see what happens.

Here’s how it works. Take a square 1 unit on each side, and add a particle with coordinates x and y. Move the particle by repeatedly replacing x with x + y and y with x + 2y, and discarding any integer parts of the results (so x and y stay in the range from 0 to 1). The particle will flit about the square chaotically. “This mimics the essential behaviour of a gas particle, while being a lot simpler than reality,” according to Schulman.

To set up two gases with opposite arrows of time, Schulman imposes appropriate boundary conditions. In one model gas, the particles start in one corner of the square and spread out until they are completely disordered. They have a “normal” arrow of time (that is, the same arrow as us). In the other, Schulman imposes the final condition that after, say 20 moves, corresponding to 20 time steps, the particles are all in the corner of the square. This system has a backward arrow of time. Call the normal-time region Alice and the reverse-time region Bob.

The next step is to let Alice and Bob interact. Schulman tweaks the coordinates of each normal-time particle according to the coordinates of the reverse-time test particle, and vice versa.

When Schulman lets both systems run, he finds that neither arrow of time is destroyed by the other. “All that happens is that Bob adds a bit of noise to Alice and Alice adds a bit of noise to Bob,” says Schulman. The two arrows of time are remarkably robust.

“I had no idea when I started my work that this would be the outcome,” he says. “The result surprised me as much anyone else.” But this surprise, he adds, comes from a prejudice against future boundary conditions. Once you are used to the idea of matter having some memory of what we call its future, it ceases to surprise. From our point of view, the memory of future organisation drags any reverse time region in the direction of increasing order, despite any small disturbances from our own “normal” region.

The paper has created quite a stir. “This is very cool stuff indeed,” says Max Tegmark of the University of Pennsylvania. At the Technion-Israel Institute of Technology, where Sculman began this work, Amos Ori agrees. “Schulman has shown that the consistency of a model with two simultaneous time arrows can be explored by relatively simple means. This is a very important observation.”

And he has some equivocal support from David Pegg of Griffith University in Brisbane. “I see no obvious flaw in the calculations Schulman has done. He makes his case quite well and I am willing to accept it, at least until convinced otherwise.”

Other physicists don’t believe that Schulman’s computer model is relevant to the real world. According to Paul Davies of the University of Adelaide, a real physical system with a backward arrow would be so fantastically sensitive to an outside influence that it would be easily destroyed. “Imagine a box of gas with molecular velocities reversed to bring about an ordered state,” he says. “The gravity of a single electron at the edge of the observable Universe is enough to throw out the motion of a given molecule by 90 degrees after only 20 or so intermolecular collisions. That’s pretty sensitive.”

Crossing the divide

Surprisingly, Schulman does not dispute Davies’ point. “He’s absolutely right. But the very set-up of his thought experiment, with initial conditions only, precludes an opposite-directed arrow,” he says. “My result applies when boundary conditions are imposed at two separate times.”

Some might attack the realism of Schulman’s interaction, which he admits is an abstract mathematical one and not related to a real physical force such as gravity. “Nevertheless, I maintain that the interaction is adequate for treating the conceptual issue of the effects of future-conditioning,” he says.

So could we actually see reverse-time beings if they exist, and maybe even wave to them? Remarkably, Schulman says yes. Using a theory originally developed by Richard Feynman and John Wheeler, which treats light waves travelling in both time directions on an equal footing, he shows that forward and reverse regions could communicate by light signals.

But communicating with the other side has its dangers. If normal-time Alice were to see rain pouring out through reverse-time Bob’s window, she could wait until before the rain started and shout to Bob to close his window. “So did Bob’s floor get wet or not?” says Schulman.

Perhaps something intermediate happens which smears out the paradox. “Alice sees the window open, shouts to Bob but the message gets blurred and Bob doesn’t close the window,” says Schulman.

And there’s another, more disturbing possibility. “If you impose initial and final boundary conditions, it may turn out that the events described simply can’t happen,” he says. “In mathematical terms, they are simply not a solution.” In other words, we might just be fated not to cause any paradoxes.

So, how would a reverse-time region arise? Schulman says such regions may exist for the same inexplicable reason that regions of normal time exist. But there is one more concrete possibility: perhaps we live in a Universe whose expansion from a big bang will one day be reversed into a contraction down to a “big crunch”, a sort of mirror-image of the big bang in which the Universe was born 13 billion years ago. Although the latest cosmological evidence is against this, the question isn’t settled.

In 1958, Thomas Gold of Cornell University argued that the thermodynamic arrow of time would reverse during the contraction phase, creating order out of chaos. Gold’s reasoning turned out to be flawed, but in the 1970s, Schulman used his own model to show that the conclusions were right. As the big bang and big crunch are both highly ordered (all the matter is in a small volume), thermodynamic arrows of time should point away from both ends. The arrow of time depends on the expansion or contraction of the Universe. “Coffee cools because the quasar 3C 273 grows ever more distant,” says Schulman.

Of course, if you were alive during a cosmic contraction phase you would see nothing untoward-you’d have the same arrow as most of the matter in the Universe, and it would look like expansion (see Diagram). Stepping outside the Universe, the situation appears perfectly symmetrical; it makes just as much sense to call either end the big bang or the big crunch.

A bizarre consequence of Schulman’s theory is that some reverse-time regions from a future contracting phase of the Universe could have survived until today-and could be only a few tens of light years away. “Some bits of the Universe might have reverse arrows while other bits with forward arrows might survive well into the contraction phase.”

As the “turnaround” time when the Universe’s expansion turns into contraction could be many hundreds of billions of years away, any stars would have burnt out. Unfortunately, there would be little prospect of seeing stellar unexplosions or backwards people among such cold stuff. “We would still feel their gravity, though,” says Schulman. “Such reverse-time matter would have all the attributes of the invisible, or ‘dark’, matter thought to make up most of the mass of our Universe.”

Colliding arrows

Another possibility is that in the 13 billion years since the big bang most of the Universe’s matter has collided with reverse-time matter from the future. The result of such collisions would be matter in “equilibrium” with no time direction. “Once again, it would appear exactly like dark matter,” says Schulman. Other physicists are sceptical. “I doubt that this has anything to do with the dark matter problem,” says Tegmark.

So what would it be like in a region that is changing its time direction? Would exploding things suddenly start unexploding? And what would happen to the minds of beings around at the time? Sadly, it would be rather undramatic. For a particular area to change its arrow, it would first have to go through a period of maximum disorder where there could be no stars or explosions or structured, working minds. But if you survived for long enough, you might be able to watch the Universe around you starting to contract, and most of its matter going into reverse.

If all this is getting a bit difficult to stomach, there is a way to test it-even if we can’t spy on a nearby backwards planet. “Things happening today could be influenced by boundary conditions at the end of the Universe,” says Schulman. What he has in mind are ultra-slow processes.

In the 1970s, John Wheeler of Princeton University suggested observing the decays of atomic nuclei with ultra-long half-lives, perhaps many tens of billions of years. The suggestion was that the normal exponential decay would be modified by exponential “undecay” and that this might actually be observable in a sample of a few kilograms in the laboratory. Possible candidates are rhenium-187 and samarium-147, which have half-lives of about 100 billion years.

Unfortunately, Wheeler was too optimistic. For an experiment of a sensible duration, a few years, say, you’d need roughly the total supply of these isotopes in the Universe to see deviations from exponential decay.

“A far better bet is galaxy clustering,” says Schulman. He believes that the way galaxies cluster together could be affected by a future contraction phase. Unfortunately, he has not yet worked out what form this effect might take.

But over the past few years, a small group of of physicists have been claiming that the Universe has an inexplicable fractal structure. Most cosmologists disagree, partly because they have no way to explain such a bizarre pattern. But say there is something in it. Could it perhaps be a memory of the future?


Further reading: Time’s Arrows and Quantum Measurement by L. S. Schulman (Cambridge University Press, 1997)

Author: Marcus Chown
New Scientist issue 5th February 2000