From Eternity to Here (13 page)

The real Einstein is more interesting than the icon. For one thing, the rumpled look with the Don King hair attained in his later years bore little resemblance to the sharply dressed, well-groomed young man with the penetrating stare who was responsible for overturning physics more than once in the early decades of the twentieth century.
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For another, the origins of the theory of relativity go beyond armchair speculations about the nature of space and time; they can be traced to resolutely practical concerns of getting persons and cargo to the right place at the right time.

Figure 10:
Albert Einstein in 1912. His “miraculous year” was 1905, while his work on general relativity came to fruition in 1915.

Special relativity, which explains how the speed of light can have the same value for all observers, was put together by a number of researchers over the early years of the twentieth century. (Its successor, general relativity, which interpreted gravity as an effect of the curvature of spacetime, was due almost exclusively to Einstein.) One of the major contributors to special relativity was the French mathematician and physicist Henri Poincaré. While Einstein was the one who took the final bold leap into asserting that the “time” as measured by any moving observer was as good as the “time” measured by any other, both he and Poincaré developed very similar formalisms in their research on relativity.
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Historian Peter Galison, in his book
Einstein’s Clocks, Poincaré’s Maps: Empires of Time
, makes the case that Einstein and Poincaré were as influenced by their earthbound day jobs as they were by esoteric considerations of the architecture of physics.
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Einstein was working at the time as a patent clerk in Bern, Switzer land, where a major concern was the construction of accurate clocks. Railroads had begun to connect cities across Europe, and the problem of synchronizing time across great distances was of pressing commercial interest. The more senior Poincaré, meanwhile, was serving as president of France’s Bureau of Longitude. The growth of sea traffic and trade led to a demand for more accurate methods of determining longitude while at sea, both for the navigation of individual ships and for the construction of more accurate maps.

And there you have it: maps and clocks. Space and time. In particular, an appreciation that what matters is not questions of the form “Where are you really?” or “What time is it actually?” but “Where are you with respect to other things?” and “What time does your clock measure?” The rigid, absolute space and time of Newtonian mechanics accords pretty well with our intuitive understanding of the world; relativity, in contrast, requires a certain leap into abstraction. Physicists at the turn of the century were able to replace the former with the latter only by understanding that we should not impose structures on the world because they suit our intuition, but that we should take seriously what can be measured by real devices.

Special relativity and general relativity form the basic framework for our modern understanding of space and time, and in this part of the book we’re going to see what the implications of “spacetime” are for the concept of “time.”
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We’ll be putting aside, to a large extent, worries about entropy and the Second Law and the arrow of time, and taking refuge in the clean, precise world of fundamentally reversible laws of physics. But the ramifications of relativity and spacetime will turn out to be crucial to our program of providing an explanation for the arrow of time.

LOST IN SPACE

Zen Buddhism teaches the concept of “beginner’s mind”: a state in which one is free of all preconceptions, ready to apprehend the world on its own terms. One could debate how realistic the ambition of attaining such a state might be, but the concept is certainly appropriate when it comes to thinking about relativity. So let’s put aside what we think we know about how time works in the universe, and turn to some thought experiments (for which we know the answers from real experiments) to figure out what relativity has to say about time.

To that end, imagine we are isolated in a sealed spaceship, floating freely in space, far away from the influence of any stars or planets. We have all of the food and air and basic necessities we might wish, and some high school-level science equipment in the form of pulleys and scales and so forth. What we’re not able to do is to look outside at things far away. As we go, we’ll consider what we can learn from various sensors aboard or outside the ship.

But first, let’s see what we can learn just inside the spaceship. We have access to the ship’s controls; we can rotate the vessel around any axis we choose, and we can fire our engines to move in whatever direction we like. So we idle away the hours by alternating between moving the ship around in various ways, not really knowing or caring where we are going, and playing a bit with our experiments.

Figure 11:
An isolated spaceship. From left to right: freely falling, accelerating, and spinning.

What do we learn? Most obviously, we can tell when we’re accelerating the ship. When we’re not accelerating, a fork from our dinner table would float freely in front of us, weightless; when we fire the rockets, it falls down, where “down” is defined as “away from the direction in which the ship is accelerating.”
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If we play a bit more, we might figure out that we can also tell when the ship is spinning around some axis. In that case, a piece of cutlery perfectly positioned on the rotational axis could remain there, freely floating; but anything at the periphery would be “pulled” to the hull of the ship and stay there.

So there are some things about the state of our ship we can determine observa tionally, just by doing simple experiments inside. But there are also things that we
can’t
determine. For example, we don’t know where we are. Say we do a bunch of experiments at one location in our unaccelerated, non-spinning ship. Then we fire the rockets for a bit, zip off somewhere else, kill the rockets so that we are once again unaccelerated and non-spinning, and do the same experiments again. If we have any skill at all as experimental physicists, we’re going to get the same results. Had we been very good record keepers about the amount and duration of our acceleration, we could possibly calculate the distance we had traveled; but just by doing local experiments, there doesn’t seem to be any way to distinguish one location from another.

Likewise, we can’t seem to distinguish one velocity from another. Once we turn off the rockets, we are once again freely floating, no matter what velocity we have attained; there is no need to decelerate in the opposite direction. Nor can we distinguish any particular orientation of the ship from any other orientation, here in the lonely reaches of interstellar space. We can tell whether we are spinning or not spinning; but if we fire the appropriate guidance rockets (or manipulate some onboard gyroscopes) to stop whatever spin we gave the ship, there is no local experiment we can do that would reveal the angle by which the ship had rotated.

These simple conclusions reflect deep features of how reality works. Whenever we can do something to our apparatus without changing any experimental outcomes—shift its position, rotate it, set it moving at a constant velocity—this reflects a
symmetry
of the laws of nature. Principles of symmetry are extraordinarily powerful in physics, as they place stringent restrictions on what form the laws of nature can take, and what kind of experimental results can be obtained.

Naturally, there are names for the symmetries we have uncovered. Changing one’s location in space is known as a “translation”; changing one’s orientation in space is known as a “rotation”; and changing one’s velocity through space is known as a “boost.” In the context of special relativity, the collection of rotations and boosts are known as “Lorentz transformations,” while the entire set including translations are known as “Poincaré transformations.”

The basic idea behind these symmetries far predates special relativity. Galileo himself was the first to argue that the laws of nature should be invariant under what we now call translations, rotations, and boosts. Even without relativity, if Galileo and Newton had turned out to be right about mechanics, we would not be able to determine our position, orientation, or velocity if we were floating freely in an isolated spaceship. The difference between relativity and the Galilean perspective resides in what actually happens when we switch to the reference frame of a moving observer. The miracle of relativity, in fact, is that changes in velocity are seen to be close relatives of changes in spatial orientation; a boost is simply the spacetime version of a rotation.

Before getting there, let’s pause to ask whether things could have been different. For example, we claimed that one’s absolute position is unobservable, and one’s absolute velocity is unobservable, but one’s absolute acceleration can be measured.
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Can we imagine a world, a set of laws of physics, in which absolute position is unobservable, but absolute velocity can be objectively measured?
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Sure we can. Just imagine moving through a stationary medium, such as air or water. If we lived in an infinitely big pool of water, our position would be irrelevant, but it would be straightforward to measure our velocity with respect to the water. And it wouldn’t be crazy to think that there is such a medium pervading space.
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After all, ever since the work of Maxwell on electromagnetism we have known that light is just a kind of wave. And if you have a wave, it’s natural to think that there must be something doing the waving. For example, sound needs air to propagate; in space, no one can hear you scream. But light can travel through empty space, so (according to this logic, which will turn out not to be right) there must be some medium through which it is traveling.

So physicists in the late nineteenth century postulated that electromagnetic waves propagated through an invisible but all-important medium, which they called the “aether.” And experimentalists set out to actually detect the stuff. But they didn’t succeed—and that failure set the stage for special relativity.

THE KEY TO RELATIVITY

Imagine we’re back out in space, but this time we’ve brought along some more sophisticated experimental apparatus. In particular, we have an impressive-looking contraption, complete with state-of-the-art laser technology, that measures the speed of light. While we are freely falling (no acceleration), to calibrate the thing we check that we get the same answer for the speed of light no matter how we orient our experiment. And indeed we do. Rotational invariance is a property of the propagation of light, just as we suspected.

But now we try to measure the speed of light while moving at different velocities. That is, first we do the experiment, and then we fire our rockets a bit and turn them off so that we’ve established some constant velocity with respect to our initial motion, and then we do the experiment again. Interestingly, no matter how much velocity we picked up, the speed of light that we measure is always the same. If there really were an aether medium through which light traveled just as sound travels through air, we should get different answers depending on our speed relative to the aether. But we don’t. You might guess that the light had been given some sort of push by dint of the fact that it was created within your moving ship. To check that, we’ll allow you to remove the curtains from the windows and let some light come in from the outside world. When you measure the velocity of the light that was emitted by some outside source, once again you find that it doesn’t depend on the velocity of your own spaceship.

A real-world version of this experiment was performed in 1887 by Albert Michelson and Edward Morley. They didn’t have a spaceship with a powerful rocket, so they used the next best thing: the motion of the Earth around the Sun. The Earth’s orbital velocity is about 30 kilometers per second, so in the winter it has a net velocity of about 60 kilometers per second different from its velocity in the summer, when it’s moving in the other direction. That’s not much compared to the speed of light, which is about 300,000 kilometers per second, but Michelson designed an ingenious device known as an “interferometer” that was extremely sensitive to small changes in velocities along different directions. And the answer was: The speed of light seems to be the same, no matter how fast we are moving.