≡ Menu

The Theory Of Relativity


In the early decades of the 20th century, a young Swiss patent clerk named Albert Einstein published the theory of relativity and changed the face of physics and astronomy forever.

The theory of relativity is perhaps the most successful development in the history of science in terms of its agreement with experimental results and its ability to predict new phenomena – only quantum mechanics can claim to compete with its success. Einstein’s theory immediately explained some of the major problems in the physics and astronomy of his day, and it has continued to explain new developments that were not even hinted at 90 years ago, including the existence of black holes and recent observations in cosmology.

Yet, accepting the theory of relativity requires us to throw out almost all of our previous notions about the universe, as well as most of what we would call “common sense.” Space and time, which to humans locked on planet Earth appear to be a fixed, unchanging background upon which the events of the cosmos play out, are in fact anything but. Empty space can contract, expand, or curve depending on how close you are to a massive object, and the rate at which time passes can change as well. Space and time can even change depending on who is measuring them; the hands on a clock will look smaller and tick slower the faster the clock is moving with respect to you.

Applications of Relativity

The theory of relativity is required whenever we study objects that are either (a) moving in a strong gravitational field, or (b) moving near the speed of light. If (b) is true but not (a), we can get away with using a simpler version of the theory called special relativity; historically, this is what Einstein developed first, while the more encompassing theory of general relativity came later.

In everyday life on Earth, neither (a) nor (b) is true, so we usually don’t have to worry about relativity at all. Nonetheless, its effects can still be important when extremely high precision is needed; for example, one of the most crucial applications of relativity involves the Global Positioning System (GPS), which wouldn’t work at all if we didn’t take relativistic effects into account. If you’ve ever used a GPS receiver, you’ve benefited directly from Einstein’s theory of relativity!

Moving in a Strong Gravitational Field

One of the most amazing aspects of the theory of relativity is that it completely changes the way we understand gravity.

Scientists have known for a long time that gravity is unusual. Take a bunch of wooden blocks, some big and some small, and sweep them off a table; they will all fall at the same speed and hit the ground at the same time. Glue a piece of metal to each and attract them with a magnet, though, and they will move at different rates; try to pull them with a rope, and you’ll have to pull harder to get the bigger objects up to speed. Why is it that gravity, and gravity alone, is able to adjust itself to pull everything towards the Earth at the same rate?

Einstein answered this question in a revolutionary way. According to Einstein, gravity is not a force which pulls on things; rather, it is a curvature of space and time caused by the presence of a nearby massive object (like the Earth). When something comes along and moves past the massive object, it will appear to be pulled towards it, but in reality, it isn’t being pulled at all. It is actually moving along the same straight line that it was moving along in empty space, but this straight line will now look like it is curved, due to gravity’s warping of the underlying “space-time” continuum.

Curved space: a simple analogy

If the above paragraph doesn’t make sense (and it is unlikely to!), consider the following analogy having to do with a “curved space” you are more used to: the surface of the Earth. Suppose you are in Ithaca, New York (home of Cornell University) and want to travel to Rome, Italy, which is approximately due east of Ithaca and a quarter of the way around the globe. You might think the best way to get there is to start off heading east and keep going straight until you reach Rome, as shown in the red path on this map:

Map of the Earth, with an east-west path between Ithaca and Rome marked in red, and a
Original map credit: WorldAtlas.com

In fact, though, if you start off heading east and continue to go straight, carefully putting one foot in front of the other, you will wind up taking the blue path; by the time you’re as far east as Rome, you’ll be somewhere in western Africa, near the equator! (If you don’t believe this statement, try it out with a globe and a piece of string. Stretch the string tight so that it is forced to be straight, then place it east-west across New York. The rest of the string will pass through Africa and cross the equator, just like the blue path in the above map.)

What’s going on here? Nothing too complicated, really. As we all know, the surface of the Earth is round, but when we try to represent it on a two-dimensional map we have to “flatten” it out. In the process of this flattening, it turns out, things get screwed up, and some lines which are actually straight (like the blue path) look curved, while some lines which are actually curved (like the red path) look straight.

According to Einstein, the same thing happens near a massive object, only the curvature happens to something that has four dimensions (the space we live in plus one dimension of time) rather than two dimensions (the surface of the Earth). Space and time near a massive object are “curved,” but we are unable to perceive this directly since we are limited to seeing things in three dimensions. Our brains therefore assume that space is flat, and in the process of making this assumption, things get screwed up. Objects which are actually moving along straight lines appear, in the “map” we construct inside our heads, to be traveling along curves and to be pulled by the massive object nearby.

Once you get used to it, this new way of looking at gravity is actually very natural! Have you ever seen astronauts in orbit around the Earth? Do they look like they’re being pulled by anything? No, they don’t; they experience weightlessness, and if they didn’t look out the window to see the Earth below, they could reasonably conclude that their ship was floating through empty space, far away from the Earth’s gravity. According to Einstein, this is a perfectly reasonable conclusion because the two situations are equivalent! Whether floating through space or orbiting the Earth, the astronauts are moving along the same, straight line path. In fact, we could experience weightlessness too, if it weren’t for the surface of the Earth which keeps us from falling on our straight line path to the Earth’s center. It is not gravity we feel, Einstein says, but simply the ground pushing up on our feet.

Effects of curved space and time

The curved space and time predicted by Einstein have some astounding consequences, many of which have been confirmed by experimental tests. Perhaps the most famous of these involves gravity’s ability to bend light as it passes through the warped space near a massive object; this effect was first observed by Arthur Eddington in 1919, an event which rocketed Einstein to international fame. Eddington’s original results are now considered controversial, but improved technology has spectacularly demonstrated that Einstein’s prediction was correct. In recent years, astronomers have not only confirmed gravity’s ability to bend light but also found very strong circumstantial evidence for the existence of black holes, objects which bend light so much that it cannot even escape.

Another major success of Einstein’s theory was that it fixed some serious problems that astronomers of his day had in understanding the orbit of Mercury, the closest planet to the Sun. Some people thought that there must have been another, unseen planet (which they called Vulcan) whose gravitational pull was affecting Mercury’s orbit, but Einstein showed that all the problems went away once the theory of relativity was taken into account.

There are also interesting effects having to do with the “curved time” predicted by the theory of relativity. This effect manifests itself by causing time to go slower near a massive object, so much so that if you watched someone fall into a black hole you would see their time stop completely, and they would appear to “freeze” and fade away. Gravity’s slowing down of time also affects the frequency of light waves and therefore their color; light becomes bluer as it approaches a massive object and redder as it moves away. This effect was first observed in 1960 by Robert Pound and Glen Rebka, who shot gamma rays up to the top of a building and measured the change in their color as they got farther away from the Earth.

In recent years, the theory of relativity has gotten a serious workout as astronomers try to understand cosmology, the origin and large scale structure of the universe. Astronomers are also keenly interested in the results of LIGO and other detectors, which are trying to observe the gravitational waves predicted by the theory of relativity that could give us a whole new way of looking at the universe.

Moving Near the Speed of Light

Some of the most interesting aspects of the theory of relativity are discussed above, but the first part of the theory (special relativity) was developed without taking the complicated effects of gravity into account. In fact, Einstein developed special relativity in response to a simple problem faced by physicists of his day. It requires little more than high school mathematics to understand; Einstein’s contribution was not mathematical brilliance, but rather a willingness to consider ideas that most people would have dismissed as ridiculous without even thinking about them.

Constancy of the speed of light

In the 19th century, physicists interpreted the laws of electromagnetism to require a “preferred reference frame” for the universe, one in which light traveled. Just as you feel the wind blow by faster when you’re in a car that is moving with respect to the air, physicists also thought they would see light move slightly faster (or slightly slower) depending on how the Earth’s motion through space coincided with the invisible medium, or ether, in which light traveled.

In the 1880s, however, experiments by Albert Michelson and Edward Morley showed something remarkable – the ether didn’t seem to exist at all! As the Earth moves around the Sun, its direction changes, so its speed with respect to the ether should also change. But when Michelson and Morley made careful measurements of the speed of light in different directions at different times during the year, they found that it was always the same.

These results have truly bizarre implications.

Imagine trying to measure the speed of a truck on a highway while driving in the lane next to it. The truck is driving a little faster than you are, so you see it creeping by – first it catches up with your rear wheel, then with your rear door. Suddenly, you decide to slam on the brakes. Instead of zooming by you, though, the truck continues to creep up – now it’s in line with your front door. You hit the accelerator, and the truck doesn’t fall behind – it continues to creep up past your front tire. Finally, you stop your car entirely and get out – still the truck creeps by.

It looks like the truck has been shadowing your every move, but then you compare notes with a friend who was driving in the third lane, on the other side of the truck. She thinks that the truck has been shadowing her, even though she was driving completely differently than you were – zooming along at the same time you were stopped, slowing down at the same time you were accelerating! Seems impossible? It might, but the Michelson-Morley experiment proved that if trucks behaved like light beams, this is exactly what they would do.

Einstein’s simple solution

Many physicists looked for complicated ways to dismiss the results of Michelson and Morley, but Einstein did something different – he simply accepted them at face value and asked what the consequences would be if light really did behave in such a bizarre way.

Einstein realized that in order for the speed of light to remain constant as seen by all observers, other things which everyone had always assumed to be constant would have to change. The faster that two people move with respect to each other, the more they disagree about the light (or the truck, in the above example), and the more they think that something with the other person must be out of whack. Einstein showed that the things which seemed out of whack would have to be length and time – each person would observe the other to be shrinking along the direction of motion and their clocks to be ticking more slowly.

As bizarre as these results seem, they do not produce any contradictions with other laws of physics, and in fact enhance our understanding of them. If we accept special relativity, it turns out, electromagnetism no longer needs any kind of “preferred reference frame” in which to operate. Rather, it works correctly from any reference frame you choose – none is more preferred than any other, and the speeds at which different reference frames move with respect to each other are truly relative, as opposed to absolute.

From Einstein’s simple observations followed many more powerful insights, among them the equivalence of mass and energy (expressed by the famous formula E=mc2) and the fact that information can never travel faster than the speed of light. These ideas and others are confirmed daily in particle accelerators all around the world, as well as in many other experiments.

Yet perhaps the most important insight that came from special relativity was the idea that space and time are not a sacred, immutable backdrop for the universe, but rather things that can change, from point to point and person to person. It was this insight that paved the way for the theory of general relativity and its radical interpretation of gravity, whose ramifications are still being felt today.

Source: Cornell University

“Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. That’s relativity.” –Albert Einstein

Comments on this entry are closed.