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 was 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.

• An observer on the jet will see zero distance between those two events
• An observer on the ground will see those events 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. They will likewise not agree on the distance the light has traveled from its emission at the plane’s tail to its reception at the nose.

Speed is distance traveled divided by the time taken. The pulse travels at the speed of light. And so they will not agree on the time interval between the emission and the reception.

The 2 observers measure different times for the same physical process.

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

He drew the logical 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 to an observer who is at rest relative to the clock
• runs slower to an observer who is moving relative to the clock

We can liken a light pulse traveling from the tail to the nose of the plane to the tick of a clock.

• To an observer on the ground, the clock runs slower because the light beam has to travel farther 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. 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.

Imagine 2 clocks:

1. A reference Clock 1 at rest at the earth’s center
2. Clock 2 on the earth’s surface
3. Clock 3 aboard a plane

Relative to Clock 1, Clock 3 moving eastward with the earth’s rotation is moving faster than Clock 2.

• So it should run slower.

Relative to Clock 1, Clock 3 moving westward against the earth’s rotation is moving slower than Clock 2.

• So it should run faster.

In an October 1971 experiment, a very accurate atomic clock was flown around the world.

You could extend your life by constantly flying eastward around the world.

• However, the effect is very small, about 180 billionths of a second per circuit. It is also lessened by the effects of the difference in gravity.

Due to Einstein’s work, physicists demanded that the speed of light be the same in all frames of reference.

This made Maxwell’s theory of electricity and magnetism treated time as part of the 3 dimensions of space, as the fourth dimension of space-time.

In space-time, time is no longer separate from the 3 dimensions of space.

• Left/right, forward/backward, or up/down depends on the orientation of the observer
• Likewise, the direction of time also varies depending on the observer’s speed

Observers moving at different speeds would choose different directions for time in space-time.

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

Newton’s theory of gravity says that objects are attracted to each other by a force that depends on the distance between them at that time.

But 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.

Over the next 11 years, Einstein developed a new theory of gravity called General Relativity.

Gravity in general relativity is different from Newton’s.

Instead, it is based on space-time being:

• curved, not flat
• distorted by the mass and energy in it.

A good way to picture curvature is to think of the earth’s surface.

The earth’s surface is only two-dimensional because there are only north/south and east/west.

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 in Einstein’s theory, gravity is not a force. 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.