Albert Einstein

Einstein was 26 in 1905 when he published his paper “Zur Elektrodynamik bewegter Körper” (“On the Electrodynamics of Moving Bodies”).

In it, he made the simple assumption that the laws of physics and in particular the speed of light should appear to be the same to all uniformly moving observers.

This idea demands a revolution in our concept of space and time. Imagine 2 events that happen at the same spot but at different times, in a jet aircraft.

To an observer on the jet, there will be zero distance between those two events. But to a second observer on the ground the events will be separated by the distance the jet has traveled in the time between the events.

This shows that two observers who are moving relative to each other will not agree on the distance between two events.

Suppose the two observers observe a pulse of light traveling from the tail of the aircraft to its nose. Just as in the above example, they will not agree on the distance the light has traveled from its emission at the plane’s tail to its reception at the nose.

Since speed is distance traveled divided by the time taken, this means that if they agree on the speed at which the pulse travels—the speed of light—they will not agree on the time interval between the emission and the reception.

What makes this strange is that, though the two observers measure different times, they are watching the same physical process.

Einstein did not attempt to construct an artificial explanation for this.

He drew the logical, if startling, conclusion that the measurement of the time taken, like the measurement of the distance covered, depends on the observer doing the measuring. That effect is one of the keys to the theory in Einstein’s 1905 paper, which has come to be called special relativity.

We can see how this analysis could apply to timekeeping devices if we consider two observers looking at a clock.

Special relativity holds that the clock runs faster according to an observer who is at rest with respect to the clock. To observers who are not at rest with respect to the clock, the clock runs slower.

If we liken a light pulse traveling from the tail to the nose of the plane to the tick of a clock, we see that to an observer on the ground the clock runs slower because the light beam has to travel a greater distance in that frame of reference.

But the effect does not depend on the mechanism of the clock. It holds for all clocks, even our own biological ones.

Einstein showed that, like the concept of rest, time cannot be absolute, as Newton thought.

In other words, it is not possible to assign to every event a time with which every observer will agree.

Instead, all observers have their own measures of time, and the times measured by two observers who are moving relative to each other will not agree.

Einstein’s ideas go counter to our intuition because their implications aren’t noticeable at the speeds we normally encounter in everyday life.

But they have been repeatedly confirmed by experiment.

For example, imagine a reference clock at rest at the center of the earth, another clock on the earth’s surface, and a third clock aboard a plane, flying either with or against the direction of the earth’s rotation. With reference to the clock at the earth’s center, the clock aboard the plane moving eastward—in the direction of the earth’s rotation—is moving faster than the clock on the earth’s surface, and so it should run slower.

Similarly, with reference to the clock at the earth’s center, the clock aboard the plane flying westward—against the earth’s rotation—is moving slower than the surface clock, which means that clock should run faster than the clock on the surface.

That is exactly what was observed when, in an experiment performed in October 1971, a very accurate atomic clock was flown around the world. So you could extend your life by constantly flying eastward around the world, though you might get tired of watching all those airline movies.

However, the effect is very small, about 180 billionths of a second per circuit (and it is also somewhat lessened by the effects of the difference in gravity, but we need not get into that here).

Due to the work of Einstein, physicists realized that by demanding that the speed of light be the same in all frames of reference, Maxwell’s theory of electricity and magnetism dictates that time cannot be treated as separate from the three dimensions of space.

Instead, time and space are intertwined. It is something like adding a fourth direction of future/past to the usual left/right, forward/backward, and up/down. Physicists call this marriage of space and time “space-time,” and because space-time includes a fourth direction, they call it the fourth dimension.

In space-time, time is no longer separate from the three dimensions of space, and, loosely speaking, just as the definition of left/right, forward/backward, or up/down depends on the orientation of the observer, so too does the direction of time vary depending on the speed of the observer.

Observers moving at different speeds would choose different directions for time in space-time. Einstein’s theory of special relativity was therefore a new model, which got rid of the concepts of absolute time and absolute rest (i.e., rest with respect to the fixed ether).

Einstein soon realized that to make gravity compatible with relativity another change was necessary.

According to Newton’s theory of gravity, at any given time objects are attracted to each other by a force that depends on the distance between them at that time. But the theory of relativity had abolished the concept of absolute time, so there was no way to define when the distance between the masses should be measured.

Thus Newton’s theory of gravity was not consistent with special relativity and had to be modified.

The conflict might sound like a mere technical difficulty, perhaps even a detail that could somehow be worked around without much change in the theory.

As it turned out, nothing could have been further from the truth.

Over the next eleven years Einstein developed a new theory of gravity, which he called general relativity. The concept of gravity in general relativity is nothing like Newton’s. Instead, it is based on the revolutionary proposal that space-time is not flat, as had been assumed previously, but is curved and distorted by the mass and energy in it.

A good way to picture curvature is to think of the surface of the earth. Although the earth’s surface is only two-dimensional (because there are only two directions along it, say north/south and east/west), we’re going to use it as our example because a curved two-dimensional space is easier to picture than a curved four-dimensional space.

The geometry of curved spaces such as the earth’s surface is not the Euclidean geometry we are familiar with. For example, on the earth’s surface, the shortest distance between two points—which we know as a line in Euclidean geometry—is the path connecting the two points along what is called a great circle.

(A great circle is a circle along the earth’s surface whose center coincides with the center of the earth. The equator is an example of a great circle, and so is any circle obtained by rotating the equator along different diameters.)

Imagine, say, that you wanted to travel from New York to Madrid, two cities that are at almost the same latitude.

If the earth were flat, the shortest route would be to head straight east. If you did that, you would arrive in Madrid after traveling 3,707 miles. But due to the earth’s curvature, there is a path that on a flat map looks curved and hence longer, but which is actually shorter.

You can get there in 3,605 miles if you follow the great-circle route, which is to first head northeast, then gradually turn east, and then southeast. The difference in distance between the two routes is due to the earth’s curvature, and a sign of its non-Euclidean geometry. Airlines know this, and arrange for their pilots to follow great-circle routes whenever practical.

According to Newton’s laws of motion, objects such as cannonballs, croissants, and planets move in straight lines unless acted upon by a force, such as gravity.

But gravity, in Einstein’s theory, is not a force like other forces; rather, it is a consequence of the fact that mass distorts space-time, creating curvature. In Einstein’s theory, objects move on geodesics, which are the nearest things to straight lines in a curved space. Lines are geodesics on the flat plane, and great circles are geodesics on the surface of the earth.

In the absence of matter, the geodesics in 4D space-time correspond to lines in three-dimensional space. But when matter is present, distorting space-time, the paths of bodies in the corresponding three-dimensional space curve in a manner that in Newtonian theory was explained by the attraction of gravity.

When space-time is not flat, objects’ paths appear to be bent, giving the impression that a force is acting on them.