Once Before Time - Martin Bojowald [122]
THE ARROW OF TIME:
A WORLD IN SHAMBLES
Every moment just comes to imply those that follow.
—JEAN-PAUL SARTRE, Nausea
The existence of an arrow of time is often seen as one of the great mysteries in physics, especially cosmology. Sometimes entropy is identified as the reason for the directedness of time, as it would cause the total disorder in the universe to increase and thus distinguish the past from the future. But when one considers the partially microscopic character of our observations in the universe, entropy ceases to be a candidate for explaining time’s arrow. Entropy always depends on the degree of precision used for observations and then allowed for a theoretical description. This cannot possibly explain the everyday phenomenon that we are continuously being pushed ahead in time without ever being able to step back or just have a little rest. Otherwise, atomic precision of observations combined with a photographic memory, making accessible time-reversible microscopic physics, would allow us to go back in time—which is hardly imaginable.
Before going into more details we should, to avoid misunderstandings, first clarify what the arrow of time is supposed to mean and, perhaps more important, what it is not. In particular, the question of why one cannot single-handedly reverse the arrow of time is independent of the enticing fantasy of time travel. During time travel in the usual sense, whose (im)possibility shall not concern us here, time does not run backward; it merely proceeds differently for some people. A person or a group of people is enclosed in a bounded region that, after a process rarely specified further, arrives in the past of its neighborhood. Neither for external bystanders nor for the time travelers does a step back in time occur; rather one region of space is merely separated from the outer world and subject to a modified process of time. While time travelers do venture into their neighborhood’s past, their own time keeps running forward. After all, they retain their memories of all their past, a part of which is now in the future of their neighborhood, and they do not grow younger, or even die when a time before their birth date is reached. The question of why time, in contrast to space, is a strict one-way street is independent of the question of whether time travel is possible.
Why is there no going back in time? When all is said and done, this question is based solely on a misunderstanding. The primary experience is motion, and we move neither in space nor in time, but in space-time. It makes no sense to speak of motion in space independently of time, or of motion in time independently of space. What constitutes motion is only a change of position in space during a given interval of time. Even before we grapple with relativity, we can say that space and time are unbreakably linked with each other. Motion itself would be impossible if we had to decide the direction in time as well as in space. Elementary time abstracted from the fact of motion—independently of whether life invents such clever things as memory—is not a rigid parameter but merely a way of specifying change and motion.
As described at the beginning of this chapter, in physics one often uses the picture of a process happening in mathematical time; in fact, this is how calculations of theoretical physics are most often organized. But what one really measures are relationships of some observables with respect to others. Time itself is measured by an apparatus such as a clock; a measurement process thus provides the relation of, for instance, the position of an object to the hand of a clock. Introducing time is an additional step, defined by convention. Nor in cosmology does one measure the expansion of the universe as a function of time, even though this is the form that solutions to general relativity initially take. One measures the escape velocity of a star by the redshift in its emission spectrum as well as its distance from us by comparison with standard candles. Using general relativity,