Is Time An Illusion?

IT IS the invisible presence that governs your world. Trailing you like an unshakeable shadow, it ticks and tocks incessantly - you can sense it in your heartbeat, in the rising and setting of the sun, and in your daily rush to make meetings, trains and deadlines. It brings order to our lives through the categories of past, present and future.

Time. There is nothing with which we are so familiar, and yet when you try to pin it down you find only a relentless torrent of questions. Why does time appear to flow? What makes it different from space? What exactly is it? It's enough to make your neurons misfire, then sizzle and smoke.

You are not alone. Physicists have long struggled to understand what time really is. In fact, they are not even sure it exists at all. In their quest for deeper theories of the universe, some researchers increasingly suspect that time is not a fundamental feature of nature, but rather an artefact of our perception. One group has recently found a way to do quantum physics without invoking time, which could help pave a path to a time-free "theory of everything". If correct, the approach suggests that time really is an illusion, and that we may need to rethink how the universe at large works.

For decades, physicists have been searching for a quantum theory of gravity to reconcile Einstein's general relativity, which describes gravity at the largest scales, with quantum mechanics, which describes the behaviour of particles at the tiniest scales. One reason it has been so difficult to merge the two is that they are built on incompatible views of time. "I am more and more convinced that the problem of time is key both to quantum gravity and to issues in cosmology," says Lee Smolin of the Perimeter Institute for Theoretical Physics in Waterloo, Ontario, Canada.

According to general relativity, time is stitched together with space to form four-dimensional space-time. The passage of time is not absolute - no cosmic clock ticks away the hours of the universe. Instead, time differs from one frame of reference to the next, and what one observer experiences as time, another might experience as a mixture of time and space. For Einstein, time is a useful measure of things, but nothing special.

Not so in quantum mechanics. Here time plays a key role, keeping track of the ever-changing probabilities that define the microworld, which are encoded in the "wave function" of a quantum system. The clock by which the wave function evolves records not just the time in one particular frame of reference, but the absolute time that Einstein worked so hard to topple. So while relativity treats space and time as a whole, quantum mechanics splits the universe into two parts: the quantum system being observed and the classical world outside. In this fractured universe, a clock always remains outside the quantum system (see Diagram).

Something has to give. The fact that the universe has no outside, by definition, suggests that quantum mechanics will be the one to surrender - and to many, this suggests that time is not fundamental. In the 1990s, for instance, physicist Julian Barbour proposed that time must not exist in a quantum theory of the universe. All the same, physicists are loath to throw out quantum theory, as it has proven capable of extraordinarily accurate predictions. What they need is a way to do quantum mechanics in the absence of time.

Carlo Rovelli, a physicist at the University of Marseille in France, has found just that. In the past year, he and his colleagues have worked out a method to compress multiple quantum events in time into a single event that can be described without reference to time [gr-qc/0610140] Multiple-event probability in general-relativistic quantum mechanics

It is an intriguing achievement. While Rovelli's approach to dealing with time is one of many, and researchers working on other models of quantum gravity may have different opinions on the matter, nearly every physicist agrees that time is a key obstacle to finding an ultimate theory. Rovelli's approach seems tantalisingly close to surmounting that obstacle. His model builds upon research into generalising quantum mechanics by physicist James Hartle at the University of California, Santa Barbara, as well as Rovelli's earlier work on quantum systems.

The idea is this: suppose we have an electron characterised by its spin, a quantum property that is either "up" or "down" along whatever direction you measure it. Say we want to make two consecutive measurements of its spin, one in the x direction and one in the y direction. The probabilities of the possible outcomes will depend on the order in which we perform the measurements. That's because a measurement "collapses" the indeterminate state of the wave function, forcing it to commit to a given state; the first measurement will change the particle's state, which affects the second measurement.

Say we already know the electron's spin is up in the x direction. If we now measure the spin in the x direction followed by the y direction, we will find the x spin up - no change there - and then there is a 50:50 chance of finding the y spin up or down. But if we begin by measuring the y spin, that disturbs the spin in the x direction, creating a 50-50 probability for both measurements.

If reordering the measurements in time changes the probabilities, how can we calculate the probabilities of sequences of events without reference to time? The trick, says Rovelli, is to adjust the boundary between the quantum system under observation and the classical outside world where measuring devices are considered to reside. By shifting the boundary, we can include the measuring device as part of the quantum system.

In that case we no longer ask, "What is the probability of the electron having spin up and then spin down?" Instead we ask, "What is the probability of finding the measuring devices in a particular state?" The measuring device no longer collapses the wave function; rather, the electron and the measuring device together are described by a single wave function, and a single measurement of the entire set-up causes the collapse.

Where has time gone? Evolution in time is transformed into correlations between things that can be observed in space. "To give an analogy," Rovelli says, "I can tell you that I drove from Boston to Los Angeles but I passed first through Chicago and later through Denver. Here I am specifying things in time. But I could also tell you that I drove from Boston to LA along the road marked in this map. So I can replace the information about which measurement happens first in time with the detailed information about how the observables are correlated."

That Rovelli's approach yields the correct probabilities in quantum mechanics seems to justify his intuition that the dynamics of the universe can be described as a network of correlations, rather than as an evolution in time. "Rovelli's work makes the timeless view more believable and more in line with standard physics," says Dean Rickles, a philosopher of physics at the University of Sydney in Australia.

With quantum mechanics rewritten in time-free form, combining it with general relativity seems less daunting, and a universe in which time is fundamental seems less likely. But if time doesn't exist, why do we experience it so relentlessly? Is it all an illusion?

Yes, says Rovelli, but there is a physical explanation for it. For more than a decade, he has been working with mathematician Alain Connes at the College de France in Paris to understand how a time-free reality could give rise to the appearance of time. Their idea, called the thermal time hypothesis, suggests that time emerges as a statistical effect, in the same way that temperature emerges from averaging the behaviour of large groups of molecules [gr-qc/9406019] Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in General Covariant Quantum Theories.

Imagine gas in a box. In principle we could keep track of the position and momentum of each molecule at every instant and have total knowledge of the microscopic state of our surroundings. In this scenario, no such thing as temperature exists; instead we have an ever-changing arrangement of molecules. Keeping track of all that information is not feasible in practice, but we can average the microscopic behaviour to derive a macroscopic description. We condense all the information about the momenta of the molecules into a single measure, an average that we call temperature.

According to Connes and Rovelli, the same applies to the universe at large. There are many more constituents to keep track of: not only do we have particles of matter to deal with, we also have space itself and therefore gravity. When we average over this vast microscopic arrangement, the macroscopic feature that emerges is not temperature, but time. "It is not reality that has a time flow, it is our very approximate knowledge of reality that has a time flow," says Rovelli. "Time is the effect of our ignorance."

**Cosmic Time**

It all sounds good on paper, but is there any evidence that the idea might be correct? Rovelli and Connes have tested their hypothesis with simple models. They started by looking at the cosmic microwave background (CMB) radiation that pervades the sky - relic heat from the big bang. The CMB is an example of a statistical state: averaging over the finer details, we can say that the radiation is practically uniform and has a temperature of just under 3 kelvin. Rovelli and Connes used this as a model for the statistical state of the universe, tossing in other information such as the radius of the observable universe, and looked to see what apparent time flow that would generate.

What they got was a sequence of states describing a small universe expanding in exactly the manner described by standard cosmological equations - matching what physicists refer to as cosmic time. "I was amazed," says Rovelli. "Connes was as well. He had independently thought about the same idea, and was very surprised to see it worked in a simple calculation."

To truly apply the thermal time hypothesis to the universe, however, physicists need a theory of quantum gravity. All the same, the fact that a simple model like that of the CMB produced realistic results is promising. "One of the traditional difficulties of quantum gravity was how to make sense of a theory in which the time variable had disappeared," Rovelli says. "Here we begin to see that a theory without a time variable can not only still make sense, but can in fact describe a world like the one we see around us."

What's more, the thermal time hypothesis gives another interesting result. If time is an artefact of our statistical description of the world, then a different description should lead to a different flow of time. There is a clear case in which this happens: in the presence of an event horizon.

When an observer accelerates, he creates an event horizon, a boundary that partitions off a region of the universe from which light can never reach him so long as he continues to accelerate. This observer will describe a different statistical state of the universe from an observer who doesn't have a horizon, since he is missing information that lies beyond his event horizon. The flow of time he perceives should therefore be different.

Using general relativity, however, there is another way to describe his experience of time. The geometry of the space-time he inhabits, as defined by his horizon, determines a so-called proper time - the time flow he would register if he were carrying a clock. The thermal time hypothesis predicts that the ratio of the observer's proper time to his statistical time - the time flow that emerges from Connes and Rovelli's ideas - is the temperature he measures around him.

It so happens that every event horizon has an associated temperature. The best known case is that of a black hole event horizon, whose temperature is that of the "Hawking radiation" it emits. Likewise, an accelerating observer measures a temperature associated with something known as Unruh radiation. The temperature Rovelli and Connes derived matches the Unruh temperature and the Hawking temperature for a black hole, further boosting their hypothesis.

"The thermal time hypothesis is a very beautiful idea," says Pierre Martinetti, a physicist at the University of Rome in Italy. "But I believe its implementation is still limited. For the moment one has just checked that this hypothesis was not contradictory when a notion of time was already available. But it has not been used in quantum gravity."

Others also urge caution in interpreting what it all means for the nature of time. "It is wrong to say that time is an illusion," says Rickles. "It is just reducible or non-fundamental, in the same way that consciousness emerges from brain activity but is not illusory."

So if time really does prove to be non-fundamental, what are we to make of it? "For us, time exists and flows," says Rovelli. "The point is that this nice flow becomes something much more complicated at the small scale."

At reality's deepest level, then, it remains unknown whether time will hold strong or melt away like a Salvador Dali clock. Perhaps, as Rovelli and others suggest, time is all a matter of perspective - not a feature of reality but a result of your missing information about reality. So if your brain hurts when you try to understand time, relax. If you really knew, time might simply disappear.