In a similar vein, nearly all physicists presume that cosmic singularities actually have a finite, if high, density. Relativity theory errs because it fails to capture some important aspect of gravity or matter that comes into play near singularities and keeps the density under control. "Most people would say that they signal that the theory is breaking down there," says physicist James B. Hartle of the University of California, Santa Barbara.
To figure out what goes on will take a more encompassing theory, a quantum theory of gravity. Physicists are still working on such a theory, but they figure that it will incorporate the central insight of quantum mechanics: that matter, like light, has wavelike properties. These properties should smear the putative singularity into a small wad, rather than a point, and thereby banish the divide-by-zero error. If so, time may not, in fact, end.
Physicists argue it both ways. Some think time does end. The trouble with this option is that the known laws of physics operate within time and describe how things move and evolve. Time's end points are off the reservation; they would have to be governed not just by a new law of physics but by a new type of law of physics, one that eschews temporal concepts such as motion and change in favor of timeless ones such as geometric elegance. In one proposal in 2007, Brett McInnes of the National University of Singapore drew on ideas from the leading candidate for a quantum theory of gravity—string theory. He suggested that the primordial wad of a universe had the shape of a torus; because of mathematical theorems concerning tori, it had to be perfectly uniform and smooth. At the big crunch or a black-hole singularity, however, the universe could have any shape whatsoever, and the same mathematical reasoning need not apply; the universe would in general be extremely raggedy. Such a geometric law of physics differs from the usual dynamical laws in a crucial sense: it is not symmetrical in time. The end wouldn't just be the beginning played backward.
Other quantum gravity researchers think that time stretches on forever, with neither beginning nor end. In their view the big bang was simply a dramatic transition in the eternal life of the universe. Perhaps the prebangian universe started to undergo a big crunch and turned around when the density got too high—a big bounce. Artifacts of this prehistory may even have made it through to the present day. By similar reasoning, the singular wad at the heart of a black hole would boil and burble like a miniaturized star. If you fell into a black hole, you would die a painful death, but at least your timeline would not end. Your particles would plop into the wad and leave a distinct imprint on it, one that future generations might see in the feeble glow of light the hole gives off.
By supposing that time marches on, proponents of this approach avoid the need to speculate about a new type of law of physics. Yet they, too, run into trouble. For instance, the universe gets steadily more disordered with time; if it has been around forever, why is it not in total disarray by now? As for a black hole, how would the light bearing your imprint possibly manage to escape the hole's gravitational clutches?
The bottom line is that physicists struggle with antinomy no less than philosophers have. The late John Archibald Wheeler, a pioneer of quantum gravity, wrote, "Einstein's equation says 'this is the end' and physics says 'there is no end.'" Faced with this dilemma, some people throw up their hands and conclude that science can never resolve whether time ends. For them the boundaries of time are also the boundaries of reason and empirical observation. But others think the puzzle just requires some fresh thinking. "It is not outside the scope of physics," says physicist Gary Horowitz of the University of California, Santa Barbara. "Quantum gravity should be able to provide a definite answer."
How Time Slips Away
The HAL 9000 may have been a computer, but he was probably the most human character in 2001: A Space Odyssey—expressive, resourceful, a bundle not just of wires but also of contradictions. Even his death was evocative of human death. It was not an event but a process. As Dave slowly pulled out his circuit boards, HAL lost his mental faculties one by one and described how it felt. He articulated the experience of regression in a way that people who die are often unable to. Human life is a complex feat of organization, the most complex known to science, and its emergence or submergence passes through the twilight between life and not life. Modern medicine shines a lantern into that twilight, as doctors save premature babies who once would have been lost and bring back people who have passed what was once a point of no return.
As physicists and philosophers struggle to grasp the end of time, many see parallels with the end of life. Just as life emerges out of lifeless molecules that organize themselves, time might emerge from some timeless stuff that brings itself to order. A temporal world is a highly structured one. Time tells us when events occur, for how long and in what order. Perhaps this structure was not imposed from the outside but arose from within. What can be made can be unmade. When the structure crumbles, time ends.
By this thinking, time's demise is no more paradoxical than the disintegration of any other complex system. One by one, time loses its features and passes through the twilight from existence to nonexistence.
The first to go might be its unidirectionality—its "arrow" pointing from past to future. Physicists have recognized since the mid-nineteenth century that the arrow is a property not of time per se but of matter. Time is inherently bidirectional; the arrow we perceive is simply the natural degeneration of matter from order to chaos, a syndrome that anyone who lives with pets or young children will recognize. (The original orderliness might owe itself to the geometric principles that McInnes conjectured.) If this trend keeps up, the universe will approach a state of equilibrium, or "heat death," in which it cannot possibly get any messier. Individual particles will continue to reshuffle themselves, but the universe as a whole will cease to change, any surviving clocks will jiggle in both directions, and the future will become indistinguishable from the past. A few physicists have speculated that the arrow might reverse, so that the universe sets about tidying itself up, but for mortal creatures whose very existence depends on a forward arrow of time, such a reversal would mark an end to time as surely as heat death would.
Losing Track of Time
More recent research suggests that the arrow is not the only feature that time might lose as it suffers death by attrition. Another could be the concept of duration. Time as we know it comes in amounts: seconds, days, years. If it didn't, we could tell that events occurred in chronological order but couldn't tell how long they lasted. That scenario is what the University of Oxford physicist Roger Penrose presents in a book published in 2010, Cycles of Time: An Extraordinary New View of the Universe.
Throughout his career, Penrose really seems to have had it in for time. He and the University of Cambridge physicist Stephen Hawking showed in the 1960s that singularities do not arise only in special settings but should be everywhere. He has also argued that matter falling into a black hole has no afterlife and that time has no place in a truly fundamental theory of physics.
In his latest assault, Penrose begins with a basic observation about the very early universe. It was like a box of Legos that had just been dumped out on the floor and not yet assembled—a mishmash of quarks, electrons, and other elementary particles. From them, structures such as atoms, molecules, stars, and galaxies had to piece themselves together step by step. The first step was the creation of protons and neutrons, which consist of three quarks apiece and are about a femtometer (10-15 meter) across. They came together about 10 microseconds after the big bang (or big bounce, or whatever it was).
Before then, there were no structures at all—nothing was made up of pieces that were bound together. So there was nothing that could act as a clock. The oscillations of a clock rely on a well-defined reference such as the length of a pendulum, the distance between two mirrors, or the size of atomic orbitals. No such reference yet existed. Clumps of particles might have come together temporarily, but they could not tell time, because they had no fixed size. Individual quarks and electrons
could not serve as a reference, because they have no size, either. No matter how closely particle physicists zoom in on one, all they see is a point. The only sizelike attribute these particles have is their so-called Compton wavelength, which sets the scale of quantum effects and is inversely proportional to mass. And they lacked even this rudimentary scale prior to a time of about 10 picoseconds after the big bang, when the process that endowed them with mass had not yet occurred.
"There's no sort of clock," Penrose says. "Things don't know how to keep track of time." Without anything capable of marking out regular time intervals, either an attosecond or a femtosecond could pass, and it made no difference to particles in the primordial soup.
Penrose proposes that this situation describes not only the distant past but also the distant future. Long after all the stars wink out, the universe will be a grim stew of black holes and loose particles; then even the black holes will decay away and leave only the particles. Most of those particles will be massless ones such as photons, and again clocks will become impossible to build. In alternative futures where the universe gets snuffed out by, say, a big crunch, clocks don't fare too well, either.
You might suppose that duration will continue to make sense in the abstract, even if nothing could measure it. But researchers question whether a quantity that cannot be measured even in principle really exists. To them the inability to build a clock is a sign that time itself has been stripped of one of its defining features. "If time is what is measured on a clock and there are no clocks, then there is no time," says the philosopher of physics Henrik Zinkernagel of the University of Granada in Spain, who also has studied the disappearance of time in the early universe.
Despite its elegance, Penrose's scenario does have its weak points. Not all the particles in the far future will be massless; at least some electrons will survive, and you should be able to build a clock out of them. Penrose speculates that the electrons will somehow go on a diet and shed their mass, but he admits he is on shaky ground. "That's one of the more uncomfortable things about this theory," he says. Also, if the early universe had no sense of scale, how was it able to expand, thin out, and cool down?
If Penrose is on to something, however, it has a remarkable implication. Although the densely packed early universe and ever emptying far future seem like polar opposites, they are equally bereft of clocks and other measures of scale. "The big bang is very similar to the remote future," Penrose says. He boldly surmises that they are actually the same stage of a grand cosmic cycle. When time ends, it will loop back around to a new big bang. Penrose, a man who has spent his career arguing that singularities mark the end of time, may have found a way to keep it going. The slayer of time has become its savior.
Time Stands Still
Even if duration becomes meaningless and the femtoseconds and attoseconds blur into one another, time isn't dead quite yet. It still dictates that events unfold in a sequence of cause and effect that is the same for all observers. In this respect, time is different from space. Two events that are adjacent within time—when I type on my keyboard, letters appear on my screen—are inextricably linked. But two objects that are adjacent within space—a keyboard and a Post-it note—might have nothing to do with each other. Spatial relations simply do not have the same inevitability that temporal ones do.
But under certain conditions, time could lose even this basic ordering function and become just another dimension of space. The idea goes back to the 1980s, when Hawking and Hartle sought to explain the big bang as the moment when time and space became differentiated. In 2007 Marc Mars of the University of Salamanca in Spain and José M. M. Senovilla and Raùl Vera of the University of the Basque Country applied a similar idea not to time's beginning but to its end.
They were inspired by string theory and its conjecture that our four-dimensional universe—three dimensions of space, one of time—might be a membrane, or simply a "brane," floating in a higher-dimensional space like a leaf in the wind. We are trapped on the brane like a caterpillar clinging to the leaf. Ordinarily, we are free to roam around our 4-D prison. But if the brane is blown around fiercely enough, all we can do is hold on for dear life; we can no longer move. Specifically, we would have to go faster than the speed of light to make any headway moving along the brane, and we cannot do that. All processes involve some type of movement, so they all grind to a halt.
Seen from the outside, the timelines formed by successive moments in our lives do not end but merely get bent so that they are lines through space instead. The brane would still be 4-D, but all four dimensions would be space. Mars says that objects "are forced by the brane to move at speeds closer and closer to the speed of light, until eventually the trajectories tilt so much that they are in fact superluminal and there is no time. The key point is that they may be perfectly unaware that this is happening to them."
Because all our clocks would slow down and stop, too, we would have no way to tell that time was morphing into space. All we would see is that objects such as galaxies seemed to be speeding up. Eerily, that is exactly what astronomers really do see and usually attribute to some unknown kind of "dark energy." Could the acceleration instead be the swan song of time?
Your Time Is Up
By this late stage, it might appear that time has faded to nothingness. But a shadow of time still lingers. Even if you cannot define duration or causal relations, you can still label events by the time they occurred and lay them out on a timeline. Several groups of string theorists have recently made progress on how time might be stripped of this last remaining feature. Emil J. Martinec and Savdeep S. Sethi of the University of Chicago and Daniel Robbins of Texas A&M University, as well as Horowitz, Eva Silverstein of Stanford University, and Albion Lawrence of Brandeis University, among others, have studied what happens to time at black-hole singularities using one of the most powerful ideas of string theory, known as the holographic principle.
A hologram is a special type of image that evokes a sense of depth. Though flat, the hologram is patterned to make it look as though a solid object is floating in front of you in 3-D space. The holographic principle holds that our entire universe is like a holographic projection. A complex system of interacting quantum particles can evoke a sense of depth—that is to say, a spatial dimension that does not exist in the original system.
But the converse is not true. Not every image is a hologram; it must be patterned in just the right way. If you scratch a hologram, you spoil the illusion. Likewise, not every particle system gives rise to a universe like ours; the system must be patterned just so. If the system initially lacks the necessary regularities and then develops them, the spatial dimension pops into existence. If the system reverts to disorder, the dimension disappears whence it came.
Imagine, then, the collapse of a star to a black hole. The star looks 3-D to us but corresponds to a pattern in some 2-D particle system. As its gravity intensifies, the corresponding planar system jiggles with increasing fervor. When a singularity forms, order breaks down completely. The process is analogous to the melting of an ice cube: the water molecules go from a regular crystalline arrangement to the disordered jumble of a liquid. So the third dimension literally melts away.
As it goes, so does time. If you fall into a black hole, the time on your watch depends on your distance from the center of the hole, which is defined within the melting spatial dimension. As that dimension disintegrates, your watch starts to spin uncontrollably, and it becomes impossible to say that events occur at specific times or objects reside in specific places. "The conventional geometric notion of space-time has ended," Martinec says.
What that means in practice is that space and time no longer give structure to the world. If you try to measure objects' positions, you find that they appear to reside in more than one place. Spatial separation means nothing to them; they jump from one place to another without crossing the intervening distance. In fact, that is how the imprint of a hapless astronaut who passes the black hole's point
of no return, its event horizon, can get back out. "If space and time do not exist near a singularity, the event horizon is no longer well defined," Horowitz says.
In other words, string theory does not just smear out the putative singularity, replacing the errant point with something more palatable while leaving the rest of the universe much the same. Instead it reveals a broader breakdown of the concepts of space and time, the effects of which persist far from the singularity itself. To be sure, the theory still requires a primal notion of time in the particle system. Scientists are still trying to develop a notion of dynamics that does not presuppose time at all. Until then, time clings stubbornly to life. It is so deeply ingrained in physics that scientists have yet to imagine its final and total disappearance.
Science comprehends the incomprehensible by breaking it down, by showing that a daunting journey is nothing more than a succession of small steps. So it is with the end of time. And in thinking about time, we come to a better appreciation of our own place in the universe as mortal creatures. The features that time will progressively lose are prerequisites of our existence. We need time to be unidirectional for us to develop and evolve; we need a notion of duration and scale to be able to form complex structures; we need causal ordering for processes to be able to unfold; we need spatial separation so that our bodies can create a little pocket of order in the world. As these qualities melt away, so does our ability to survive. The end of time may be something we can imagine, but no one will ever experience it directly, any more than we can be conscious at the moment of our own death.
As our distant descendants approach time's end, they will need to struggle for survival in an increasingly hostile universe, and their exertions will only hasten the inevitable. After all, we are not passive victims of time's demise; we are perpetrators. As we live, we convert energy to waste heat and contribute to the degeneration of the universe. Time must die that we may live.