Introduction: need for modification of Special Theory of Relativity
Formulation of Special Theory of Relativity solved a major philosophical and practical dilemma; namely that laws of physics must have the same mathematical form for all inertial observers. Those observers that accelerate with respect to each other, according to Newton's law of F = ma, must measure different values for forces because of the difference in their relative accelerations. So, the question remained as to how to solve the same dilemma for non-inertial observers?
It is difficult for us earth bound creatures not to think of our day-to-day frame of reference, namely the seemingly reliable and motionless surface of the earth (!), as absolute. But physicists had already gone though this false path with the earth-centered model of the universe. If there is no absolute frame of reference, then unless we can come up with a similar solution for non-inertial observers, we will be forced to come up with an innumerable number of physical laws, one for each non-inertial observer! This solution, clearly, was not acceptable to Einstein.
Einstein's genius came through again by realizing the special role that gravitational forces play. In fact Special Theory's result of rest mass energy implied that light, electromagnetic waves, with no matter attributes (remember that waves are disturbances) posses rest mass! So, like any form of matter that has inertial mass they must be affected by gravitational forces, even though they are NOT a form of matter! This prediction was verified through measurements that showed that light arriving on earth from distant stars was bent, ever so slightly, by the gravitational attraction of the sun.
The clever way that Einstein incorporated the special role of gravitational force into solving the dilemma for non-inertial frames was by observing that any acceleration can be instead thought of as a "fall" due to a gravitational pull. This is referred to as the Principle of Equivalence. That is to say, forces that are results of accelerations (remember F = ma) are an equivalent forms of gravitational forces. Forces that are results of accelerations are like the force that a passenger experiences as the car makes a sharp turn, a push away from the turn. This force is in contrast, for example, to electromagnetic or nuclear forces, which have no equivalent gravitational presentation.
Simply stated, if an observer is placed in a "windowless laboratory" making it impossible to compare positions of the lab with the rest of the universe, then there are NO POSSIBLE experiments that would allow the observer to distinguish between a gravitational force and an acceleration causing force. For example, a falling rock could be due to a gravitational pull toward the "floor", or equivalently no gravity, but an "upward" acceleration of the laboratory.
If force of gravity is equal to acceleration, then objects are moving because they are "falling". So, the effect of gravitation could be equally represented by stating that instead of a uniform and uneventful space, objects are moving in a warped space. Our sun is much more massive than the earth. Its gravitational force is much stronger than earth's. So, we could instead state that sun warps the space near it much more than does the earth. In this mode of thought, we could totally remove the sun and the earth and replace them by a curved space. The physical effects remain the same. Of course special theory makes a strong connection between time and space by making time a fourth dimension. So, in fact, gravity warps not just space, but space-time.
The light coming to earth from a distant star is curved as it passes near the sun. One way of thinking about this observed fact is that light by the virtue of its non-zero rest mass is pulled by the gravitational attraction of the large mass of the sun. Another, equivalent, representation is to think that space-time is curved near the sun, so light which travels in a straight line is forced to curve its path. Now, what is the mass of the sun were many times more than its current value? Then the light would bend even more.
Black holes are thought to be large masses that warp the space-time into a hole. Even light will get sucked into them, once it passes close enough, and will not get out. Hence, a black hole!
Further Reading: Chapter 3 of "The Elegant Universe," by Professor Brian Greene (I have not read a better description on these stuff!): pdf file
Questions on Einstein's General Theory of Relativity
Last Modified: September 26, 2007 alekis@union.edu
Newton discovered that any two objects of masses m1 and m2 attract each other with a force that its strength depends on the separation distance between the two objects as well as on their values of their masses. So, two very massive objects attract each other more strongly than two less massive ones separated by the sane distance. Also, the further two objects are, the weaker their force of attraction. As with regard to the direction of the force of attraction, it is always along the line connecting the centers of the two objects.
Mathematically, we write:
Fof 1 on 2 = (G*m1*m2)/d2
where G is a measured constant and is called the Universal Gravitational constant, and d is the distant between the two objects.
In words this says that to calculate the strength of the force of attraction of object 1 on object 2 we need to multiply the value of the mass of object 1 with that of object 2 then multiply it by the value of a constant G and then divide the result with the square of the separation distant between the two objects. Please note that this formulation of force of gravity agrees with Newton's 3rd law, which states that force of 2 on 1 has to equal the force of 1 on 2, i.e. the reaction force.
