Walter Isaacson - Einstein - His Life and Universe

Another way to picture this is to use Galileo’s ship. Imagine a light beam being shot down from the top of the mast to the deck. To an observer on the ship, the light beam will travel the exact length of the mast. To an observer on land, however, the light beam will travel a diagonal formed by the length of the mast plus the distance (it’s a fast ship) that the ship has traveled forward during the time it took the light to get from the top to the bottom of the mast. To both observers, the speed of light is the same. To the observer on land, it traveled farther before it reached the deck. In other words, the exact same event (a light beam sent from the top of the mast hitting the deck) took longer when viewed by a person on land than by a person on the ship. 59

This phenomenon, called time dilation, leads to what is known as the twin paradox. If a man stays on the platform while his twin sister takes off in a spaceship that travels long distances at nearly the speed of light, when she returns she would be younger than he is. But because motion is relative, this seems to present a paradox. The sister on the spaceship might think it’s her brother on earth who is doing the fast traveling, and when they are rejoined she would expect to observe that it was he who did not age much.

Could they each come back younger than the other one? Of course not. The phenomenon does not work in both directions. Because the spaceship does not travel at a constant velocity, but instead must turn around, it’s the twin on the spaceship, not the one on earth, who would age more slowly.

The phenomenon of time dilation has been experimentally confirmed, even by using test clocks on commercial planes. But in our normal life, it has no real impact, because our motion relative to any other observer is never anything near the speed of light. In fact, if you spent almost your entire life on an airplane, you would have aged merely 0.00005 seconds or so less than your twin on earth when you returned, an effect that would likely be counteracted by a lifetime spent eating airline food. 60

Special relativity has many other curious manifestations. Think again about that light clock on the train. What happens as the train approaches the speed of light relative to an observer on the platform? It would take almost forever for a light beam in the train to bounce from the floor to the moving ceiling and back to the moving floor. Thus time on the train would almost stand still from the perspective of an observer on the platform.

As an object approaches the speed of light, its apparent mass also increases. Newton’s law that force equals mass times acceleration still holds, but as the apparent mass increases, more and more force will produce less and less acceleration. There is no way to apply enough force to push even a pebble faster than the speed of light. That’s the ultimate speed limit of the universe, and no particle or piece of information can go faster than that, according to Einstein’s theory.

With all this talk of distance and duration being relative depending on the observer’s motion, some may be tempted to ask: So which observer is “right”? Whose watch shows the “actual” time elapsed? Which length of the rod is “real”? Whose notion of simultaneity is “correct”?

According to the special theory of relativity, all inertial reference frames are equally valid. It is not a question of whether rods actually shrink or time really slows down; all we know is that observers in different states of motion will measure things differently. And now that we have dispensed with the ether as “superfluous,” there is no designated “rest” frame of reference that has preference over any other.

One of Einstein’s clearest explanations of what he had wrought was in a letter to his Olympia Academy colleague Solovine:

The theory of relativity can be outlined in a few words. In contrast to the fact, known since ancient times, that movement is perceivable only as

relative

movement, physics was based on the notion of

absolute

movement. The study of light waves had assumed that one state of movement, that of the light-carrying ether, is distinct from all others. All movements of bodies were supposed to be relative to the light-carrying ether, which was the incarnation of absolute rest. But after efforts to discover the privileged state of movement of this hypothetical ether through experiments had failed, it seemed that the problem should be restated. That is what the theory of relativity did. It assumed that there are no privileged physical states of movement and asked what consequences could be drawn from this.

Einstein’s insight, as he explained it to Solovine, was that we must discard concepts that “have no link with experience,” such as “absolute simultaneity” and “absolute speed.” 61

It is very important to note, however, that the theory of relativity does not mean that “everything is relative.” It does not mean that everything is subjective.

Instead, it means that measurements of time, including duration and simultaneity, can be relative, depending on the motion of the observer. So can the measurements of space, such as distance and length. But there is a union of the two, which we call spacetime, and that remains invariant in all inertial frames. Likewise, there are things such as the speed of light that remain invariant.

In fact, Einstein briefly considered calling his creation Invariance Theory, but the name never took hold. Max Planck used the term Relativtheorie in 1906, and by 1907 Einstein, in an exchange with his friend Paul Ehrenfest, was calling it Relativitätstheorie.

One way to understand that Einstein was talking about invariance, rather than declaring everything to be relative, is to think about how far a light beam would travel in a given period of time. That distance would be the speed of light multiplied by the amount of time it traveled. If we were on a platform observing this happening on a train speeding by, the elapsed time would appear shorter (time seems to move more slowly on the moving train), and the distance would appear shorter (rulers seem to be contracted on the moving train). But there is a relationship between the two quantities—a relationship between the measurements of space and of time—that remains invariant, whatever your frame of reference. 62

A more complex way to understand this is the method used by Hermann Minkowski, Einstein’s former math teacher at the Zurich Polytechnic. Reflecting on Einstein’s work, Minkowski uttered the expression of amazement that every beleaguered student wants to elicit someday from condescending professors. “It came as a tremendous surprise, for in his student days Einstein had been a lazy dog,” Minkowski told physicist Max Born. “He never bothered about mathematics at all.” 63

Minkowski decided to give a formal mathematical structure to the theory. His approach was the same one suggested by the time traveler on the first page of H. G. Wells’s great novel The Time Machine, published in 1895: “There are really four dimensions, three which we call the three planes of Space, and a fourth, Time.” Minkowski turned all events into mathematical coordinates in four dimensions, with time as the fourth dimension. This permitted transformations to occur, but the mathematical relationships between the events remained invariant.

Minkowski dramatically announced his new mathematical approach in a lecture in 1908. “The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength,” he said. “They are radical. Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.” 64