The Mystery of Time
 

Every schoolchild knows what time is. But, for every schoolchild, there is a moment when they first encounter the paradoxes that lie just behind our everyday understanding of time. I recall when I was a child being struck all of a sudden by the question of whether time could end or whether it must go on forever. It must end, for how can we conceive of the infinity of existence stretching out before us if time is limitless? But if it ends, what happens afterward?

I have been studying the question of what time is for much of my adult life. But I must admit at the beginning that I am no closer to an answer now than I was then. Indeed, even after all this study, I do not think we can answer even the simple question: "What sort of thing is time?" Perhaps the best thing I can say about time is to explain how the mystery has deepened for me as I have tried to confront it. Here is another paradox about time which I began to worry about only after growing up. We all know that clocks measure time. But clocks are complex physical systems and hence are subject to imperfection, breakage, and disruptions of electrical power. If I take any two real clocks, synchronise them, and let them run, after some time, they will always disagree about what time it is.

So which of them measures the real time? Indeed, is there a single, absolute time which, although measured imperfectly by any actual clock, is the true time of the world? It seems there must be, otherwise, what do we mean when we say that some particular clock runs slow or fast? On the other hand, what could it mean to say that something like an absolute time exists if it can never be precisely measured?

A belief in an absolute time raises other paradoxes. Would time flow if there were nothing in the universe? If everything stopped, if nothing happened, would time continue?
On the other hand, perhaps there is no single absolute time. In that case, time is only what clocks measure and, as there are many clocks and they all, in the end, disagree, there are many times. Without an absolute time, we can only say that time is defined relative to whichever clock we choose to use.

This seems to be an attractive point of view, because it does not lead us to believe in some absolute flow of time we can't observe. But it leads to a problem, as soon as we know a little science.
One of the things physics describes is motion, and we cannot conceive of motion without time. Thus, the notion of time is basic for physics. Let me take the simplest law of motion, which was invented by Galileo and Descartes, and formalised by Isaac Newton: A body with no forces acting on it moves in a straight line at a constant speed. Let's not worry here about what a straight line is (this is the problem of space, which is perfectly analogous to the problem of time, but which I won't discuss here). To understand what this law is asserting, we need to know what it means to move at a constant speed. This concept involves a notion of time, as one moves at a constant speed when equal distances are covered in equal times.

We may then ask: With respect to which time is the motion to be constant? Is it the time of some particular clock? If so, how do we know which clock? We must certainly choose because, as we observed a moment ago, all real clocks will eventually go out of synchronisation with one another. Or is it rather that the law refers to an ideal, absolute time?
Suppose we take the point of view that the law refers to a single, absolute time. This solves the problem of choosing which clock to use, but it raises another problem, for no real, physical clock perfectly measures this imagined, ideal time. How could we truly be sure whether the statement of the law is true, if we have no access to this absolute, ideal time? How do we tell whether some apparent speeding up or slowing down of some body in a particular experiment is due to the failure of the law, or only to the imperfection of the clock we are using?

Newton, when he formulated his laws of motion, chose to solve the problem of which clock by positing the existence of an absolute time. Doing this, he went against the judgements of his contemporaries, such as Descartes and Gottfried Leibniz, who held that time must be only an aspect of the relationships among real things and real processes in the world. Perhaps theirs is the better philosophy, but as Newton knew better than anyone at the time, it was only if one believed in an absolute time that his laws of motion, including the one we have been discussing, make sense. Indeed, Albert Einstein, who overthrew Newton's theory of time, praised Newton's "courage and judgement" to go against what is clearly the better philosophical argument, and make whatever assumptions he had to make to invent a physics that made sense.

This debate, between time as absolute and preexisting and time as an aspect of the relations of things, can be illustrated in the following way. Imagine that the universe is a stage on which a string quartet or a jazz group is about to perform. The stage and the hall are now empty, but we hear a ticking, as someone has forgotten, after the last rehearsal, to turn off a metronome sitting in a corner of the orchestra pit. The metronome ticking in the empty hall is Newton's imagined absolute time, which proceeds eternally at a fixed rate, prior to and independently of anything actually existing or happening in the universe. The musicians enter, the universe all of a sudden is not empty but is in motion, and they begin to weave their rhythmic art. Now, the time that emerges in their music is not the absolute preexisting time of the metronome; it is a relational time based on the developing real relationships among the musical thoughts and phrases. We know this is so, for the musicians do not listen to the metronome, they listen to one another, and through their musical interchange, they make a time that is unique to their place and moment in the universe.

But, all the while, in its corner the metronome ticks on, unheard by the music makers. For Newton, the time of the musicians, the relational time, is a shadow of the true, absolute time of the metronome. Any heard rhythm, as well as the ticking of any real physical clock, only traces imperfectly the true absolute time. On the other hand, for Leibniz and other philosophers, the metronome is a fantasy that blinds us to what is really happening; the only time is the rhythm the musicians weave together.
The debate between absolute and relational time echoes down the history of physics and philosophy, and confronts us now, at the end of the twentieth century, as we try to understand what notion of space and time is to replace Newton's. If there is no absolute time, then Newton's laws of motion don't make sense. What must replace them has to be a different kind of law that can make sense if one measures time by any clock. That is, what is required is a democratic rather than an autocratic law, in which any clock's time, imperfect as it may be, is as good as any other's. Now, Leibniz was never able to invent such a law. But Einstein did, and it is indeed one of the great achievements of his theory of general relativity that a way was found to express the laws of motion so that they make sense whichever clock one uses to embody them with meaning. Paradoxically, this is done by eliminating any reference to time from the basic equations of the theory. The result is that time cannot be spoken about generally or abstractly; we can only describe how the universe changes in time if we first tell the theory exactly which real physical processes are to be used as clocks to measure the passage of time.

So, this much being clear, why then do I say that I do not know what time is? The problem is that general relativity is only half of the revolution of twentieth-century physics, for there is also the quantum theory. And quantum theory, which was originally developed to explain the properties of atoms and molecules, took over completely Newton's notion of an absolute ideal time.
So, in theoretical physics, we have at present not one theory of nature but two theories: relativity and quantum mechanics, and they are based on two different notions of time.

The key problem of theoretical physics at the present moment is to combine general relativity and quantum mechanics into one single theory of nature that can finally replace the Newtonian theory overthrown at the beginning of this century. And, indeed, the key obstacle to doing this is that the two theories describe the world in terms of different notions of time. Unless one wants to go backward and base this unification on the old, Newtonian notion of time, it is clear that the problem is to bring the Leibnizian, relational notion of time into the quantum theory. This is, unfortunately, not so easy. The problem is that quantum mechanics allows many different, and apparently contradictory, situations to exist simultaneously, as long as they exist in a kind of shadow or potential reality. (To explain this, I would have to write another essay at least as long as this one about the quantum theory.) This applies to clocks as well, in the same way that a cat in quantum theory can exist in a state that is at the same time potentially living and potentially dead, a clock can exist in a state in which it is simultaneously running the usual way and running backward. So, if there were a quantum theory of time, it would have to deal not only with freedom to choose different physical clocks to measure time, but with the simultaneous existence, at least potentially, of many different clocks. The first, we have learned from Einstein how to do; the second has, so far, been too much for our imaginations.

So the problem of what time is remains unsolved. But it is worse than this, because relativity theory seems to require other changes in the notion of time. One of them concerns my opening question, whether time can begin or end, or whether it flows eternally. For relativity is a theory in which time can truly start and stop.
One circumstance in which this happens is inside of a black hole. A black hole is the result of the collapse of a massive star, when it has burned all its nuclear fuel and thus ceased to burn as a star. Once it is no longer generating heat, nothing can halt the collapse of a sufficiently massive star under the force of its own gravity. This process feeds on itself, because the smaller the star becomes, the stronger the force by which its parts are mutually attracted to one another. One consequence of this is that a point is reached at which something would have to go faster than light to escape from the surface of the star. Since nothing can travel faster than light, nothing can leave. This is why we call it a black hole, for not even light can escape from it.

However, let us think not of this, but of what happens to the star itself. Once it becomes invisible to us, it takes only a short time for the whole star to be compressed to the point at which it has an infinite density of matter and an infinite gravitational field. The problem is, what happens then? The problem, indeed, is what, in such a circumstance, "then" might mean. If time is only given meaning by the motion of physical clocks, then we must say that time stops inside of each black hole. Because once the star reaches the state of infinite density and infinite gravitational field, no further change can take place, and no physical process can go on that would give meaning to time. Thus, the theory simply asserts that time stops.

The problem is in fact even worst than this, because general relativity allows for the whole universe to collapse like a black hole, in which case, time stops everywhere. It can also allow for time to begin. This is the way we understand the big bang, the most popular theory, currently, of the origin of the universe.
Perhaps the central problem that those of us who are trying to combine relativity and quantum mechanics think about is what is really happening inside a black hole. If time really stops there, then we must contemplate that all time, everywhere, comes to a stop in the collapse of the universe. On the other hand, if it does not stop, then we must contemplate a whole, limitless world inside each black hole, forever beyond our vision. Moreover, this is not just a theoretical problem, because a black hole is formed each time a massive enough star comes to the end of its life and collapses, and this mystery is occurring, somewhere in the vast universe we can see, perhaps one hundred times a second.

So, what is time? Is it the greatest mystery? No, the greatest mystery must be that each of us is here, for some brief time, and that part of the participation that the universe allows us in its larger existence is to ask such questions. And to pass on, from schoolchild to schoolchild, the joy of wondering, of asking, and of telling each other what we know and what we don't know. By Prof.Lee Smolin Pennsylvania State university.