Existential Physics (eBook)

Chapter 1

DOES THE PAST
STILL EXIST?

Now and Never

Time is money. It’s also running out. Unless, possibly, it’s on your side. Time flies. Time is up. We talk about time . . . all the time. And yet time has remained one of the most difficult-to-grasp properties of nature.

It didn’t help that Albert Einstein made it personal. Before Einstein, everybody’s time passed at the same rate. Post-Einstein, we know that the passage of time depends on how much we move around. And while the numerical value we assign to each moment—say 2:14 p.m.—is a matter of convention and measurement accuracy, in pre-Einstein days, we believed that your now was the same as my now; it was a universal now, a cosmic ticking of an invisible clock that marked the present moment as special. Since Einstein, now is merely a convenient word that we use to describe our experience. The present moment is no longer of fundamental significance because, according to Einstein, the past and the future are as real as the present.

This doesn’t match with my experience and probably doesn’t match with yours either. But human experience is not a good guide to the fundamental laws of nature. Our perception of time is shaped by circadian rhythms and our brain’s ability to store and access memories. This ability is arguably good for many things, but to disentangle the physics of time from our perception of it, it is better to look at simple systems, like swinging pendulums, orbiting planets, or light that reaches us from distant stars. It is from observations on such simple systems that we can reliably infer the physical nature of time without getting bogged down by the often inaccurate interpretation that our senses add to the physics.

A hundred years’ worth of observation have confirmed that time has the properties Einstein conjectured at the beginning of the twentieth century. According to Einstein, time is a dimension, and it joins with the three dimensions of space to one common entity: a four-dimensional space-time. The idea of combining space and time to space-time goes back to the mathematician Hermann Minkowski, but Einstein was the one to fully grasp the physical consequences, which he summarized in his theory of special relativity.

The word relativity in special relativity means there is no absolute rest; you can merely be at rest relative to something. For example, you are now probably at rest relative to this book; it’s moving neither away from nor toward you. But if you throw it into a corner, there are two ways of describing the situation: the book moves at some velocity relative to you and the rest of planet Earth, or you and the rest of the planet move relative to the book. According to Einstein, both are equivalent ways to describe the physics and should give the same prediction—that’s what the word relativity stands for. The special just says that this theory doesn’t include gravity. Gravity was included only later, in Einstein’s theory of general relativity.

The idea that we should be able to describe physical phenomena the same way regardless of how we move in Einstein’s four-dimensional space-time sounds rather innocuous, but it has a host of counterintuitive consequences that have entirely changed our conception of time.

° ° °

In our usual three-dimensional space, we can assign coordinates to any location using three numbers. We could, for example, use the distance to your front door in the directions east-west, north-south, and up-down. If time is a dimension, we just add a fourth coordinate, let’s say the time that has passed at your front door since 7:00 a.m. We then call the complete coordinates an event. For example, the space-time event at 3 meters east, 12 meters north, 3 meters up, and 10 hours might be your balcony at 5:00 p.m.

This choice of coordinates is arbitrary. There are many different ways to put coordinate labels on space-time, and Einstein said these labels shouldn’t matter. The time that actually passes for an object can’t depend on what coordinates we chose. And he showed that this invariant, internal time—proper time, as physicists call it—is the length of a curve in space-time.

Suppose you go on a road trip from Los Angeles to Toronto. What matters to you is not the straight-line coordinate distance between these points, about 2,200 miles, but the distance on highways and streets, which is more like 2,500 miles. It’s similar in space-time. What matters is the length of the trip, not the coordinate distance. But there’s an important difference: in space-time, the longer the curve between two events, the less time passes on it.

How do you make a curve between two space-time events longer? By changing your velocity. The more you accelerate, the slower your proper time will pass. This effect is called time dilation. And, yes, in principle, this means if you run in a circle, you’ll age more slowly. But it’s a tiny effect, and I can’t recommend it as an antiaging strategy. By the way, this is also why time passes more slowly near a black hole than far away from one. That’s because, according to Einstein’s principle of equivalence, a strong gravitational field has the same effect as a fast acceleration.

What does this mean? Imagine I have two identical clocks; I hand you one, and then you go your way and I go mine. In pre-Einstein days, we’d have thought that whenever we met again, these clocks would show exactly the same time—this is what it means for time to be a universal parameter. But post-Einstein, we know this isn’t right. How much time passes on your clock depends on how much and how fast you move.

How do we know this is correct? Well, we can measure it. It would lead us too far off topic to go into detail about which observations have confirmed Einstein’s theories, but I will leave you recommendations for further reading in the endnotes. To move on, let me just sum it up by saying that the hypothesis that the passage of time depends on how you move is supported by a large and solid body of evidence.

I have been speaking of clocks for illustration, but the fact that acceleration slows time down has nothing in particular to do with the devices we call clocks; it happens for any object. Whether it’s combustion cycles, nuclear decay, sand running through an hourglass, or heartbeats, each process has its own individual passage of time. But the differences between individual times are normally minuscule, which is why we don’t notice them in everyday life. They become noticeable, however, when we keep track of time very precisely, which we do, for example, in satellites that are part of the global positioning system (GPS).

The GPS, which your phone’s navigation system most likely uses, allows a receiver—like your phone—to calculate its position from signals of several satellites that orbit Earth. Because time is not universal, time on these satellites passes subtly differently compared with how it passes on Earth, both because of the satellites’ motion relative to the surface of Earth and because of the weaker gravitational field that the satellites experience in their orbits. The software on your phone needs to take this into account to correctly infer its location, because the different passage of time on the satellites oh-so-slightly distorts the signals. It’s a small effect, all right, but it’s not philosophy; it’s physically real.

° ° °

The fact that the passage of time isn’t universal is pretty mind-bending already, but there’s more. Because the speed of light is very fast but finite, it takes time for light to reach us, so, strictly speaking, we always see things as they looked a little bit earlier. Again, though, we don’t normally notice this in everyday life. Light travels so fast that it doesn’t matter on the short distances we see on Earth. For example, if you look up and watch the clouds, you actually see the clouds the way they looked a millionth of a second ago. That doesn’t really make a big difference, does it? We see the Sun as it looked eight minutes ago, but because the Sun doesn’t normally change all that much in a few minutes, light’s travel time doesn’t make a big difference. If you look at the North Star, you see it as it looked 434 years ago. But, yeah, you may say, so what?

It is tempting to attribute this time lag between the moment something happens and our observation of it as a limitation of perception, but it has far-reaching consequences. Once again, the issue is that the passage of time is not universal. If you ask what happened “at the same time” elsewhere—for example, just exactly what you were doing when the Sun emitted the light you see now—there is no meaningful answer to the question.

This problem is known as the relativity of simultaneity, and it was well illustrated by Einstein himself. To see how this comes about, it helps to make a few drawings of space-time. It’s hard to draw four dimensions, so I hope you will excuse me if I use only one dimension of space and one dimension of time. An object that doesn’t move relative to the chosen coordinate system is described by a vertical straight line in this diagram (figure 1). These coordinates are also referred to as the rest frame of the object. An object moving at constant velocity makes a straight line tilted at an angle. By...