The General Theory of Relativity a.k.a Einstein's Theory of Gravitation

A BRIEF HISTORY

After Einstein's Special Theory was published in 1905, Einstein turned his attention to a phenomena that occurred when observers were not restricted to movement with constant relative velocities but with varying velocities. The results of his reasoning embody the General Theory of relativity, which was presented in 1916.

INTRODUCTION

Well, basically the General Theory revolves around Principle of Equivalence which states that the effects of gravitation and accelerated are equivalent. There are three basic important conclusions from the Principle of Equivalence. Three experiments were to conducted to arrive at these results.

Newton's Law of Universal Gravitation and Einstein's Theory

Effect of a Gravitational Mass on a Light Beam

Effect of a Gravitational Mass on Time

NEWTON'S LAW OF UNIVERSAL GRAVITATION AND EINSTEIN'S THEORY

It was quite interesting to people in the past how gravitation worked. A free falling object always fell towards earth but the question was how is it possible for the earth to pull the object toward it without literally reaching up and grabbing object? Another thing that intrigued them was what force the sun had on the other planets to keep them continually revolving about the sun. In 1687 his law of gravitational of universal gravitation answered these questions. Newton's law of univesal gravitation states every object in the universe attracts every other object with a gravitational force. Newton's equation for this law is:

F = Gmm1 / d^2
m = mass of one object
m1 = mass of another
d = distance between them
G = G gravitational constant

However, Newton's law was entirely the result of observation. He observed falling objects and the movements of the planets about the sun and evolved his formula as the one which best fitter the facts. Einstein also determined the equations of the paths the planets make in their journey about the sun. The result was about the same as Newton's but there was a slight difference. Although Einstein also found that the planet's orbits were ellipsesm he found that these ellipses were not stationary but were slowly rotating in space. Figure A shows a planet's orbit according to Newton. Figure B according to Einstein.

 Figure A Figure B

So what was so important about this? A proof of the General Theory of relativity consisted in looking for a planet whose orbit rotated the most over a given period of time. The theory showed that the amount of rotation would be greatest for the planet with the highest orbital velocity. It was also necessary to use a planet whose orbit was as elliptical as possible. Mercury turned out to have one of the flattest orbits and the greates orbital velocty. There as a puzzling behavior that Mercury exerted: it had a rotation of about forty-three seconds of arc per century which could not be accounted for. The cause of the rotation of Mercury's orbit remained a mystery untiol the introduction of the General Theory of Relativity. When the General Theory was used to compute the amount of rotation, the result was forty-three seconds of arc.

EFFECT OF A GRAVITATIONAL MASS ON A LIGHT BEAM

Einstein also investigated the behavior of a beam of light under the influence of the gravitational field due to a large mass. The General Theory states that the gravitational field due to the planet's mass will attract the light beam toward it in the same way that the earth will pull a flying bullet or arrow toward it. To test this prediction, it would be necessary to "weigh a beam of light". Since it is impossible to catch a lot of photons and weigh them, the photons must be weighed while in flight. To do this we require the sun as a "scale" to use for "weighing". First, a beam of light must come from a star. The inital postion of the star A is shown in Figure C. There are no intervening gravitational masses, so the star's light travels in a straight line from the star to the observer on earth. In Figure D, the Earth has traveled in its orbit so that the sun comes between the earth and the star so that the light beam from the star just grazes the sun's surface on its way to the observer on the earth.

Figure C   Figure D

EFFECT OF A GRAVITATIONAL MASS ON TIME

The prediction of the General Theory is that the all time processes will be slower on a large mass than on a small mass, or that time will move more slowly on a relatively larger planet such as Jupiter than on earth. Einstein found that a second of time on the sun should correspond to 1.000002 earth seconds. If we were to measures light difference, literally, one would have to put a clock on the sun and synchronize it with one on the earth. Then one would periodically compare the two. Unfortunately, there would be no way to put a clock on the sun. However, there are many atomic clocks. Since the light from the sun is caused by many different types of vibrating atoms,the frequencies of these vibrations can be determined experimentally, from which the times per vibration can be computed. The frequencies and corresponding times pre vibration also can be measured for the same atoms vibrating on earth. If the frequencies of vibration of the atoms in the sun are less than those for the same atoms on earth, it means that the times per vibration have increased, or that time itself is slowed down on the sun.