Coming of Age in the Milky Way (28 page)

At Besso’s urging, Einstein read the works of the Austrian physicist and philosopher Ernst Mach, one of the few leading scientific thinkers to critique the mechanical paradigm on which rested belief in a Newtonian space pervaded by an aether.
“The simplest mechanical principles are of a very complicated character”
Mach wrote (his italics). “…
They can by no means be regarded as mathematically established truths but only as principles that not only admit of constant control by experience but actually require it.”
²⁸
A scalding critic of Newtonian space in general and of the aether hypothesis in particular, Mach sought to replace such “metaphysical obscurities,” as
he called them, with more economical precepts anchored firmly in the sense data of observation. Space, Mach argued, is not a thing, but an expression of interrelationships among events
.
“All
masses and
all
velocities, and consequently
all
forces, are relative,” he wrote.
²⁹
Einstein agreed, and was encouraged to attempt to write a theory that built space and time out of events alone, as Mach prescribed. He never entirely succeeded in satisfying Mach’s criteria—it may be that no workable theory can—but the effort helped impel him toward relativity.

The emergence of the special theory of relativity was as unconventional as its author. The 1905 paper that first enunciated the theory resembles the work of a crank; it contains no citations whatever from the scientific literature, and mentions the aid of but one individual, Besso, who was not a scientist. (At the time, Einstein knew no scientists.) Einstein’s first lecture in Zurich explaining the theory was delivered not in a university but in the Carpenters’ Union hall; he went on for over an hour, then suddenly interrupted himself to ask the time, explaining that he did not own a watch. Yet here began the reformation of the concepts of space and time.

With the special theory of relativity, Einstein had at last resolved the paradox that had occurred to him at age sixteen, that Maxwell’s equations failed if one could chase a beam of light at the velocity of light. His did so by concluding that one
cannot
accelerate to the velocity of light—that, indeed, the velocity of light is
the same
for all observers, regardless of their relative motion. If, for instance, a physicist were to board a spaceship and fly off toward the star Vega at 50 percent the velocity of light, and while on board measure the velocity of the light coming from Vega, he would find that velocity to be exactly the same as would his colleagues back on Earth.

To quantify this strange state of affairs, Einstein was obliged to employ the Lorentz contractions. (At the time he knew little of Lorentz, whom he was later to esteem as “the greatest and noblest man of our times … a living work of art.”)
³⁰
In Einstein’s hands, the Lorentz equations specify that as an observer increases in velocity, his dimensions, as well as those of his spaceship and any measuring devices aboard, will shrink along the direction of their motion by just the amount required to make the measurement of light’s velocity always come out the same. This, then, was why
Michelson and Morley had found no trace of an “aether drift.” In fact the aether is superfluous, as is Newton’s absolute space and time, for there is no need for any unmoving frame of reference: “To the concept of absolute rest there correspond no properties of the phenomena, neither in mechanics, nor in electrodynamics.”
³¹
What matters are observable events, and no event can be observed until the light (or radio waves, or other form of electromagnetic radiation) that brings news of it reaches the observer. Einstein had replaced Newton’s space with a network of light beams;
theirs
was the absolute grid, within which space itself became supple.

Observers in motion experience a slowing in the passage of time, as well: An astronaut traveling at 90 percent of the velocity of light would age only half as fast as her colleagues back home, so that at, say, a twentieth class reunion of interstellar astronauts, those who had served the most aboard relativistic spacecraft would be the youngest. Mass, too, is rendered plastic within the framework of the light beams; objects approaching the speed of light increase in mass. The effects of relativistic time dilation, mass increase, and change in dimension are minute at ordinary velocities like that of the earth in its orbit or the sun through space (which is why it had not been noticed sooner) but become pronounced as speeds increase, and go to infinity at the speed of light. If the earth could be accelerated to the velocity of light (a feat that would require infinite energy to achieve) it would contract into a two-dimensional wafer of infinite mass, on which time would come to a stop—which is one way of saying that acceleration to light speed is impossible.

Nor are these effects illusory, or merely psychological: They are as real as the stone that Dr. Johnson kicked in his famous refutation of Bishop Berkeley, and have been confirmed in scores of experiments. The relativistic increase in the mass of particles moving at nearly the velocity of light is not only observed in particle accelerators, but is what gives the speeding particles most of their punch. Relativistic time dilation has been tested by flying atomic clocks around the world in commercial aircraft; the clocks were found to run slow by just the tiny amount the theory specifies. A NASA ground controller once threatened to dock astronauts in space a fraction of a penny of their flight pay, to compensate for the decrease in the passage of time they experienced as a result of their velocity in orbit.

These and other implications of special relativity initially struck the lay public, and many scientists as well, as uncommonly strange.
^*
But if Einstein’s approach was radical, his intention was essentially conservative. As is implied by the title of his original relativity paper, “On the Electrodynamics of Moving Bodies,” his aim was to redeem the laws of electrodynamics so that they could be shown to work in every imaginable situation, not just in a quiet laboratory in Zurich but in whirling dynamos and on moving worlds hurtling past one another at staggering speeds. The term
relativity
, coined not by Einstein but by Poincaré and applied to the theory by the physicist Max Planck, is somewhat misleading in this sense; Einstein, stressing, its conservative function, had preferred to call it
Invariantentheorie
—“invariance theory.”

Relativity nonetheless cast its net wide, embracing the study not only of light and space and time, but of matter as well. The theory derives its catholic impact from the fact that electromagnetism is implicated not only in the propagation of light but also in the architecture of matter: Electromagnetism is the force that holds electrons in their orbits around nuclear particles to make atoms, binds atoms together to form molecules, and ties molecules together to form objects. Every tangible thing, from stars and planets to this page and the eye that reads it, carries electromagnetism in the fiber of its being. To alter one’s conception of electromagnetism is, therefore, to reconsider the very nature of matter. Einstein caught sight of this connection only three months after the first account of special relativity had appeared, and published a paper titled, “Does the Inertia Content of a Body Depend Upon Its Energy Content?” The answer was yes, and ours has been a sadder and wiser world ever since.

In the first paper, as we have seen, Einstein demonstrated that the inertial mass of an object increases when it absorbs energy. It follows that its mass
decreases
when it
radiates
energy. This holds true, not only for a spaceship gliding toward the stars, but for an object at rest as well: A camera loses a (very) little mass when the flash goes off, and the people whose picture is being taken become a little more massive in the exchange. Mass and energy are interchangeable, with electromagnetic energy doing the bartering between them.

Einstein, contemplating this fact, concluded that energy and inertial mass are the same, and he expressed their identity in the equation

in which
m
is the mass of an object,
E
is its energy content, and
c
is the velocity of light. In composing this singularly economical little equation, which unifies the concepts of energy and matter and relates both to the velocity of light, Einstein initially was concerned with mass. If instead we solve for energy, it takes on a more familiar and more ominous form, as

E = mc
²

Viewed from this perspective, the theory says that matter is frozen energy. This of course is the key to nuclear power and nuclear weapons, though Einstein did not consider these applications at the time and rejected them as impractical once they were proposed by others. In the hands of the astrophysicists, the equation would be used to discern the thermonuclear processes that power the sun and stars.

But for all its protean achievements, special relativity was silent with regard to gravitation, the other known large-scale force in the universe. The special theory has to do with
inertial
mass, the resistance objects offer to change in their state of motion—their “clout,” or “heft,” so to speak. Gravitation acts upon objects according to their
gravitational
mass—i.e., their “weight.” Inertial mass is what you feel when you slide a suitcase along a polished floor; gravitational mass is what you feel when you lift the suitcase. There would appear to be distinct differences between the two: Gravitational mass manifests itself only in the presence of gravitational force, while inertial mass is a permanent property of matter. Take the suitcase on a spaceship and, once in orbit, it will weigh nothing (i.e., its gravitational mass will measure zero), but its inertial mass
will remain the same: You’ll have to work just as hard to wrest it around the cabin, and once in motion it will have the same momentum as if it were sliding across a floor on Earth.
^*

Yet for some reason, the inertial and gravitational mass of any given object are equivalent. Put the suitcase on the airport scale and find that it weighs thirty pounds: That is a result of its gravitational mass. Now set it on a sheet of smooth, glazed ice or another relatively friction-free surface, attach a spring scale to the handle, and pull it until you get it accelerating at the same rate at which it would fall (i.e., 16 feet per second, on Earth), and the scale will register, again, thirty pounds: That is a result of its
inertial
mass. Experiments have been performed to a high degree of precision on all sorts of materials, in many different weights, and the gravitational mass of each object repeatedly turns out to be exactly equal to its inertial mass.
^†

The equality of inertial and gravitational mass had been an integral if inconspicuous part of classical physics for centuries. It can be seen, for instance, to explain Galileo’s discovery that cannonballs and boccie balls fall at the same velocity despite their differing weight: They do so because the cannonball, though it has greater gravitational mass and ought (naively) to fall faster, also has a greater inertial mass, which makes it accelerate more slowly; since these two quantities are equivalent they cancel out, and the cannonball consequently falls no faster than the boccie ball. But in Newtonian mechanics the equivalence principle was treated as a
mere coincidence. Einstein was intrigued. Here, he thought, “must lie the key to a deeper understanding of inertia and gravitation.”
³²
His inquiry set him on his way up the craggy road toward the general theory of relativity.

Einstein’s first insight into the question came one day in 1907, in what he later called “the happiest thought of my life.” The memory of the moment remained vivid decades later:

To appreciate why this seemingly straightforward picture should have so excited Einstein, imagine that you awaken to find yourself floating, weightless, in a sealed, windowless elevator car. A diabolical set of instructions, printed on the wall, informs you that there are two identical such elevator cars—one adrift in deep space, where it is subject to no significant gravitational influence, and the other trapped in the sun’s gravitational field, plunging rapidly toward its doom. You will be rescued only if you can
prove
(not guess) in which car you are riding—the one floating in zero gravity, or the one falling in a strong gravitational field. What Einstein realized that day in the patent office was that you
cannot
tell the difference, neither through your senses nor by conducting experiments. The fact that you are weightless does not mean that you are free from gravitation; you might be in free fall. (The “weightlessness” experienced by astronauts in orbit is precisely of this sort: Though trapped by the earth’s gravitational field they feel no weight—i.e., no effect of gravitation—because they and their spaceship are constantly falling.) The gravitational field, therefore, has only a
relative
existence. One is reminded of the joke about the man who falls from the roof of a tall building and, seeing a friend looking aghast out a window on the way down, calls out encouragingly, “I’m okay so far!” His point was Einstein’s—that the gravitational field does not exist for him, so long as he remains in his inertial framework. (The sidewalk, alas, is in an inertial framework of its own.)