After completing the special theory of relativity, Einstein was compelled to build on what we had already stated and expand into additional dimensions. Therefore, in 1915, he developed his general theory of relativity, a theory which was even more revolutional than the special theory. While the special theory of relativity stated that any object could consider itself to be at rest relative to other objects, the general theory considered objects to be accelerated with respect to each other. Einstein developed this theory to explain obvious conflicts between the laws of relativity and the law of gravity. To resolve these conflicts he developed an entirely new approach to the concept of gravity, based on the principle of equivalence.

So, what is the principle of equivalence? Here is a simple definition:

Here is an example to explain what this means. Remember our good friends Bob and Tom back at the train station? Well, let's say that both of them are now sitting in a completely enclosed boxcar with no way to tell what is going on outside the car. Let us also say that they are rolling along the "railroad track of the future" (one that is absolutely smooth) in a perfectly straight line, and they are moving at a speed which is perfectly constant. Now, according to the special theory of relativity, neither Bob nor Tom (no matter how intelligent they are) could determine by any conceivable experiment whether the boxcar was at rest or in uniform motion. Let us now say that the car is no longer moving at a constant speed or in a straight line. The boxcar could increase or decrease in speed or be driven around a curve, and Bob and Tom would definitely feel the resulting forces. However, according to the general theory of relativity, neither one of them could tell whether those forces were caused by gravitation or whether they were acceleration forces brought about by applying pressure on the accelerator or brake, or by turning the car sharply to the left or right.

Acceleration is defined as the rate of change of velocity. Consider the following situation. Bob and Tom are now astronauts standing in a rocket on Earth which is preparing for liftoff. Because of gravity, Bob and Tom's feet are pressed against the floor of the rocket with a force equal to their weight, w. If the same rocket is in outer space, far from any other object and not influenced by gravity, Bob and Tom will once again be pressed against the floor by the acceleration of the rocket. Also, if the acceleration is 9.8 m/sec2 (the acceleration of gravity at the surface of the earth), Bob and Tom will be pressed against the floor with a force which is again equal to w (the weight of Bob and Tom back on Earth). Without looking out the window, Bob and Tom would find it impossible to tell whether the rocket was at rest on Earth or accelerating in outer space. The force due to acceleration is in no way discernible from the force due to gravity. According to Einstein's theory, Newton's law of gravitation is unnecessary (by the way, in case you want to know, Isaac Newton's law states that every object attracts every other object in direct proportion to its mass).

Einstein's general theory of relativity attributes all forces to the effects of acceleration. This means that when the rocket is standing still on the surface of the earth, it is attracted toward the center of the earth. Einstein states that this impression of attraction is caused by an acceleration of the rocket. "Now, wait just one minute" you are probably saying. "How can the rocket be accelerating if it is standing still?" Well, in three-dimensional space, the rocket is indeed standing still and is therefore not accelerating at all. However, in four-dimensional space-time, the rocket is moving along its world line. According to Einstein, the world line is curved, because of the curvature of the space-time continuum in the proximity of the earth. Yes, that's right. Massive objects actually curve the space-time continuum. Einstein's law of gravity states that the world line of every object is a geodesic in the continuum. A geodesic is the shortest distance between two points, but in curved space it is not usually a straight line. Now, by this time you may be thinking that Einstein spent too much time alone and was in need of some psychological therapy. Nonetheless, as amazing as it may seem, Einstein was able to prove with several different experiments that this theory was correct.

• The general theory of relativity predicts that the world line of a ray of light will be curved in the immediate vicinity of a massive object such as the sun. To verify this prediction, scientists first chose to examine a star appearing very close to the edge of the sun. These observations cannot normally be made, because the brightness of the sun conceals a nearby star. During a total eclipse, however, stars can be observed and their positions can be accurately measured even when they appear to be quite close to the edge of the sun. Expeditions were sent out to observe the eclipses of 1919 and 1922 and both expeditions made similar observations. The apparent positions of the stars were then compared with their apparent positions a few months later, when they appeared at night far from the sun. Einstein predicted an apparent shift in position of 1.745 seconds of an arc for a star at the very edge of the sun, with progressively smaller shifts for more distant stars. The expeditions that were sent to study the eclipses verified these predictions. In recent years, similar tests were made using radio-wave deflections from distant quasars. The results of these tests agreed with the values predicted by general relativity, with only about a one percent error.
• Another confirmation of general relativity involves the perihelion of the planet Mercury. For many years it had been known that the perihelion (the point at which Mercury passes closest to the sun) revolves about the sun at the rate of once in 3 million years, and that part of this perihelion motion is completely unexplainable by classical theories. The theory of relativity, however, does predict this part of the motion, and recent radar measurements of Mercury's orbit have confirmed this agreement to within about 0.5 percent.
• Another phenomenon predicted by general relativity is the time-delay effect. Signals sent past the sun to a planet or spacecraft on the far side of the sun experience a small delay, when relayed back, compared to the time of return as suggested by classical theory. Although the time intervals involved are very small, various tests made through planetary probes have provided values very close to those predicted by general relativity.
• The time-delay effect was also confirmed with the use of two perfectly synchronized atomic clocks. Both clocks were placed on planes. Ones of these planes flew around the earth heading east and the other flew around heading west. When both planes arrived back at their starting point, the atomic clocks onboard were found to be displaying slightly different times.

As you can see, Einstein's theory of relativity is more than just a theory. It has been proven well enough to be taken seriously by the scientific world. However, other theories have been developed since then. Some of them build on the basic concepts of relativity, while others completely contradict relativity altogether.

• Other Theories

• Back to Main Page