Progress, disorder and Einstein’s elastic clocks
Deep in your brain there lies a lump of tissue called the striatum. This assortment of neurons is, to the best of our knowledge, the only dwelling place of time. It accumulates the first record of the moments of your life, and provokes your sense that your childhood was a tumbling assortment of significant and fascinating moments, while adult life hurtles by too fast to be properly appreciated.
You shouldn’t set too much store by these sentiments, though. The striatum’s gift is actually to create an impression—perhaps even an illusion—of time passing. The problem is, its measure of time depends on what is going on in your conscious mind. Every time you perform a conscious task such as putting the kettle on, the various electrical circuits in your brain spike in unison. The striatum records this simultaneous signaling and starts to note the subsequent patterns of electrical signaling from areas such as the frontal cortex. Your notion of how much time has passed before the kettle boils is nothing more than a measure of the accumulated electrical signals.
That’s not so bad at home, where you can calibrate it with a glance at the kitchen clock. But as soon as you are denied access to clocks, things go awry. When, in the early 1960s, the French geologist Michel Siffre took off his watch and lowered himself into a dark cave for 60 days, his perception of passing time unraveled. By the end of the experiment, what Siffre thought was an hour was often four or five. Drugs such as valium, caffeine or LSD will send your sense of time similarly awry. As will your memory.
We often think busy times make life flash by, but experiments show that’s only true while you’re busy. Afterward, when you reflect on your existence, your busy periods will seem much longer. That’s why your childhood now seems to have been a series of long, golden summers—life was exciting when you still had so much to experience, and your brain thinks that those heightened signaling levels must correspond to huge stretches of time. Your grip on the passage of time, then, is as precarious as you may always have suspected. But it turns out that our problems with the perception of time are as nothing compared with our problems with the notion of time itself.
You might think we ought to have a handle on time by now. After all, time is a universally understood concept—every human culture knows about it, talks about it, feels it. And we have been thinking about what it means for millennia. In 350 BC, Aristotle, for instance, wrote a work called Physics, which included one of the first attempts to grapple with the notion of time.
“First, does it belong to the class of things that exist or to that of things that do not exist?”
ARISTOTLE
Aristotle’s work on time begins with a question. “First,” it says, “does it belong to the class of things that exist or to that of things that do not exist?” Here in the second millennium AD, that is still an open question. If our minds are fooled by the passage of time, that may be because time itself is an illusion. From the Greeks to modern-day physics, the main conclusion about time has remained constant: it is, at the very least, about change. Through time, one thing changes into another.
But while Aristotle’s Greek peers were obsessed with the circle as the most fundamental concept in the universe, meaning that time must flow in cycles, modern physics is focused on linear processes: beginning to end, Big Bang to cosmic shutdown. With time, that translates into an overwhelming sense of time’s arrow: in our modern view of the universe, time moves irreversibly forward. Eggs break, and cannot be unbroken. Clocks wind down, and do not spontaneously wind up.
This process of change, in which systems move irreversibly into disorder, is known as the thermodynamic arrow of time. It arises from one of the most fundamental laws of physics: the second law of thermodynamics. This states that, as a whole, the universe is caught in a process of unraveling order. Entropy, a measure of the disorder in a system, is always increasing.
The arrow of time might arise from a variety of sources. The “cosmological arrow of time,” for example, cites the creation of the universe as a move away from a special, low entropy state where everything was neatly ordered. It is rather like handing a fully solved Rubik’s Cube to a curious child; as time progresses, the universe moves to an ever-more disordered state, just as the neat order on the faces of the Rubik’s Cube will give way to a messy jumble of colors. While some things, such as galaxies, appear ordered, with structures that are often intricately beautiful, the order of the universe as a whole is decreasing. The end will come when there is no more disorder to be created; or, as Lord Kelvin put it, when the universe has reached “a state of universal rest and death.”
Our familiar arrow of time could equally result from quantum theory. In one (probably the most popular) school of thought, quantum systems undergo an irreversible “collapse” when they are measured. This originates from the remarkable ability of a quantum object such as an atom to exist in two entirely different states at once. It might, for example, be spinning clockwise and anticlockwise at the same time. When the measurement is made, however, that double state is forced to become one or the other: the measured atom will be found to be spinning clockwise or anticlockwise, and will not spontaneously revert to the state of doing both.
There is a problem with these descriptions of time’s arrow, however. They get us nowhere because they require the concept of change. And change, as Aristotle noted, is a marker of time passing. Through considerations of the arrow of time we are really no further forward in defining time. All we have is a putative explanation for the direction it appears to take. And even that has been undermined. Time’s arrow might be part of our individual experience, but we have no reason to believe that makes it real. Worse still, we have good reason to believe it isn’t.
We have Albert Einstein to thank for this alarming insight: it lies at the heart of his special theory of relativity. Einstein was relatively unknown when he published his ideas in 1905. Special relativity was a revolutionary work, dismissing in a single stroke the popular and long-lived concept of the ether, a kind of ghostly fluid that fills all of space and provides a background through which electromagnetic fields such as light could move.
It is worth mentioning at this point that while, as the late Carl Sagan once said, extraordinary theories require extraordinary evidence, special relativity is one of the few such theories where extraordinary evidence has been found to back it up. What you are about to read may seem absurd, but there is every reason to take it seriously.
The central point of special relativity is that the laws of physics work the same for everyone, regardless of how they are moving through the universe. The most important consequence of this is that the speed of light is a constant, universally known as c. If you were to measure the speed of the light emitted from the headlights of a vehicle traveling toward you at 100 kilometers per hour, the speed of the light would be c, not c plus 100 kilometers per hour (62 mph). The speed of light does not change depending on the relative motion of the emitter and observer. The extraordinary upshot of the constancy of c is that, when conditions require it, everything else does change—and that includes time. The passage of time is as flexible an affair in the real, physical world as it is inside your mind.
Let’s imagine a scene where you are standing 100 meters from an intersection controlled by traffic lights. You are equipped with a stunningly accurate stopwatch, a meter rule and lightning reflexes. The light changes to red, and you are able to measure the time it takes for the first pulse of red light to travel the length of your meter rule. At that moment, a car passes you, traveling toward the intersection at 100 kilometers per hour. The passenger in the front seat has the same skills and equipment as you, and makes the same measurement: the time taken for the light to travel the length of the ruler.
You have both measured the speed of light, and Einstein insists that you must both get the same result. But as the car moved past you toward the traffic light, the meter rule within it also moved past you. By the time the light reached the end of the ruler in the car, the far end of the ruler was closer to the traffic lights, and so the light had to travel less distance compared with yours. The passenger in the car should measure light as faster, completing a meter in less time. How then, can you both get the same result? The answer has to do with the passage of time in different situations. Compared with your clock, the clock in the moving car runs slow. So, although the light apparently had less distance to travel, the time measurement was larger than yours, canceling out the effect.
This is not a sleight of hand where a combination of illusions leads to you getting the right result. The effect, known as time dilation, only becomes markedly noticeable when the clock moves at speeds close to the speed of light, but it remains true that a clock that is moving relative to you really will run slower than a clock held in your hand. And the word “clock” refers to anything that can mark the passage of time. Dissect that statement, and you’ll find that all kinds of disturbing implications emerge.
Let’s start with something that is just about conceivable. Take a lump of polonium, a radioactive material discovered by Pierre and Marie Curie around 100 years ago. One form of polonium, polonium-209, has a half-life of about 100 years; that is, after a century, half of its atoms will have emitted a burst of radiation and transmuted into more stable atoms.
If the Curies had taken two identical lumps of this material when they discovered it, and left one in their Paris laboratory while shooting the other one on a round trip into space at 0.99 of the speed of light, returning to Earth today, we would notice something remarkable about the amount of radiation they were giving off. The lump that stayed in Paris would lose half of its radioactive polonium atoms during that century. The thing is, its twin, the lump that had rocketed into space and back while 100 years passed on Earth, would only have lost 10 percent of its radioactive polonium atoms.
That is because the motion relative to Earth at 0.99 the speed of light (setting aside practical issues such as acceleration, deceleration and turning round) slows time for this lump. Its “clock,” as measured by the rate at which its atoms experience radioactive decay, is running at only 14 percent of the speed of its twin that never left the planet. That is why so many of its radioactive atoms remain intact. This, perhaps, is hard enough to swallow. But now for something truly inconceivable.
Let’s allow Pierre and Marie Curie to guard the two lumps of polonium. Pierre will accompany one lump on that same return trip into space, while Marie remains in Paris with her lump. The scientists’ bodies have internal clocks, too: as with the polonium, their atoms change with the passage of time, creating a heartbeat, for instance, and cells that shut down after performing a certain number of divisions—a phenomenon that biologists believe to be the root of aging and death.
Turning a blind eye to the likely catastrophic effects of the radiation, the atoms—and thus the cells and the heartbeat—in Pierre’s body will run slow compared to Marie’s, just as the polonium’s radioactive decay runs slower than on Earth. When Pierre returns, 100 Earth years later, Marie is long dead, but Pierre’s body has aged only 14 years. One immediately obvious conclusion from this is that, given the right resources, time travel into the future is entirely possible. But it is a short step from this point to the astonishing revelation that Einstein’s special theory of relativity does away with the notion of some common future anyway. And neither is there a common present or past.
You might claim, as you stand looking at the traffic lights, that you saw two events happen simultaneously. But as we have seen, the passenger in the car has a clock that runs at a different speed. The information they gain about the timing of those two events could well be different. Worse, you might see two events, A and B, happening at distinct times, with B following A. Depending on how your relative friend is moving, however, they could see A follow B. That is potentially catastrophic: if you think A caused B, how is that explicable to someone who saw B happen first?
Past, present, future, simultaneity, cause and effect—nothing is universal. When it comes to time and the processes it governs, you and your striatum really are on your own. There is a simple answer to all this confusion, however, and it is an answer that is appealing to many physicists and philosophers. We could do away with the very notion that time exists.
It is an argument that harks back to the 17th century. Newton, whose Christian faith required that space and time reflect the character of God, considered time to be a real entity, an absolute that moves on independently of everything in the universe. But his great rival Gottfried Leibniz believed time to be a human construct. All we can do, Leibniz said, is describe how the positions of things in space relate to each other, and how that relation evolves. It is useful that a clock’s pendulum swings back and forth and the clock’s hands circulate around the dial in response, for example, but that doesn’t mean the clock is measuring something that actually exists. Time, in this view, comes out of our desire to make sense of the world, but it is no more than a useful means of orientation. It is a shorthand, like the spatial concept of “up.” “Up” means a certain direction when I am stood in London, but the same direction is actually “down” in Sydney.
This link is slightly more than a convenient illustration. When Einstein published his general theory of relativity (the “special” in “special theory” refers to a special, i.e. particular case, not a special significance), he postulated a bond between time and space. Time, he said, is just one of four dimensions to the universe. The other three are the familiar ones in which you move your physical body: up and down, across, forward and backward. The only difference is that, while we conscious creatures can choose how we move through the spatial dimensions, we have no control over our movement through time.
Einstein’s four dimensions of space and time—together known as space–time—can be thought of rather like a piece of fabric that can be distorted, bent, folded, twisted and even torn by anything within them that has mass or energy. From this foundation, general relativity has equipped us with equations that describe the features of the cosmos with unprecedented accuracy, allowing us to find out how the universe works, send spacecraft to distant destinations and create the array of global positioning satellites that tell us where on Earth we are. But perhaps most intriguingly of all, the pliable nature of Einstein’s four-dimensional fabric hints at the origin of time.
Your mass distorts space–time very little. The mass of the sun distorts it much more—according to general relativity, this distortion is the root of the gravitational attraction that keeps our planet in orbit. Even more powerful is the distortion that is brought about by a collapsed giant star: a black hole. And it is here that we glimpse the true power of Einstein’s work.
The enormously strong gravitational field of a black hole means that there is a spherical region close to its center where the velocity required to move away from the black hole is greater than the speed of light—an impossible velocity to achieve. Nothing, including light, can get out of this region, and so we cannot gain any information about anything that goes on beyond its boundary. Hence its name: the event horizon.
At the event horizon, time dilation is infinite. Somebody watching from a safe distance as you fall toward the event horizon would see your movements slow down then freeze as time runs infinitely slowly for you compared to the observer. Only in the observer’s infinite future would you reach the event horizon, so you never actually disappear from view. Your experience, on the other hand, would be hugely dramatic. Your body is extremely unlikely to survive the enormous gravitational forces, but if you did survive you would eventually encounter what, according to relativity, is a breakdown in the very fabric of space–time. This “singularity” at the center of a black hole occurs as the distortion becomes infinite. Here, we reach the limit of the known laws of physics—beyond this point, they no longer apply.
Though it is commonly associated with destruction, the singularity is also thought to be the key to creation. In the early 1970s, Roger Penrose and Stephen Hawking adapted the mathematical notion of the black hole singularity to explain the origin of the universe. In a black hole everything disappears into the singularity. Reverse the mathematics of the process, though, and the singularity could give birth to the very fabric of space–time. For more than three decades this has been seen as our best description of the Big Bang, the origin of time itself.
If general relativity sheds some light on where time comes from, it still does not tell us a great deal about what time is. What’s more, impressive as Einstein’s formulations of the character of space and time are, we know that special and general relativity are not the final answer.
If the singularity shows us anything, it is that, while general relativity works remarkably well in many scenarios, it offers no satisfactory explanation for the most extreme phenomena of our universe. A more complete description of the cosmos and how all its contents (including the centers of black holes) behave—a theory often referred to as “quantum gravity”—still eludes us. And, as it turns out, the nature of time is right at the heart of the problem.
Quantum gravity has to work relativity’s notions of time into quantum theory, our best description of how the microworld of molecules, atoms and subatomic particles behaves. But quantum theory takes little note of time. In the standard formulation of the theory, you can’t ask questions about how long a process takes, for example. Then there’s the problem that quantum theory tells us that most of the subatomic particles exist independently of the direction of time. Just as they can spin clockwise and anticlockwise at the same time, their quantum states can evolve forward and backward in time. Researchers are even learning to do quantum experiments where information seems to come from the particles’ futures. What’s more, special relativity tells us that massless particles, such as photons and the gluons that bind nuclei together, travel at the speed of light and do not even experience the passage of time.
The great physicist John Wheeler once said, “Time is nature’s way to keep everything from happening at once.” He would have said it with a twinkle in his eye, knowing full well that the apparent simplicity of time belies its true nature. Saint Augustine was more honest when he said, “What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know.”
Despite all our scientific achievements since Augustine, time remains an enigma, possibly the biggest question facing physicists today. But if time is an illusion, it is at least a useful one. Our interpretation of its consequences—our memories of the past, our existence in the present and our hopes for the future—lie at the core of the human experience. Or that’s what your striatum wants you to believe.