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# General Relativity: A Simple Discussion

Updated: Oct 8, 2023

Author: Arpan Dey

Albert Einstein developed his special theory of relativity, which predicted modifications on the structure of space and time to account for the fact that the speed of light is always constant in vacuum, to any observer regardless of the frame of reference they are in. However, Einstein was not the type to be satisfied by the special theory of relativity. He sought a deeper theory, that would apply to all sorts of reference bodies (accelerating or non-accelerating). After over ten years of struggle through the thickets of spacetime and matter-energy, Einstein wrote down the field equations for gravity. This is perhaps the best example of a theory comparable to quantum mechanics that has been developed almost single-handedly. General relativity, like quantum mechanics, remains one of the greatest theories in physics, and has been repeatedly verified experimentally as well. It has predicted the existence of black holes, dark energy, gravitational waves etc..

## Einstein's New Theory Of Gravitation

General relativity has successfully superseded Newton’s classical theory of gravitation. General relativity forms the basis of modern astrophysics and has provided a new interpretation of spacetime. General relativity treats gravity not as a force, but as the consequence of movement of bodies in curved spacetime. For instance, the Sun ‘sinks’ the spacetime continuum, due to which planets like Earth follow a circular path. The Sun is not exactly pulling the Earth.

Have you noticed how water spirals inward toward the center, in a basin? The basin is curved inward. It appears as if a huge, invisible body had been placed on a flat surface, which, due to the body’s weight, has sunk. The same is the case with the Sun and Earth. Imagine spacetime to be a big, flat sheet which stretches away infinitely in all direction. If you put a heavy object (the Sun) at a point on this sheet, it will sink. The sheet will be curved downward at that point. Now drag in another, smaller body (the Earth) into the picture. Give it a minimum velocity, and it will continue to move around this big body in circles. (The water comes closer and closer to the center since it lacks the velocity required to orbit continuously. This is why the Earth doesn’t move closer and closer to the Sun, but moves in almost a fixed orbit.) Now, is the bigger body exerting a force on the smaller one to keep the latter in orbit? No! It seems true. But it’s just a consequence of the curvature of spacetime.

Another interesting prediction of general relativity is that the stars you see in the night sky are not where they seem to be. Why? We saw that gravity can bend the path of a body, like the Earth. Can gravity bend light as well? Yes! The apparent positions of stars are not their actual positions because light bends a little if it comes near a massive body (or a deep curvature in spacetime). The apparent position is given by the tangent to the curve nearest to the observer. Refer to the figure below. Light from the star bends around the gravitational field of another body (the Sun, in this case) and reaches the observer on Earth, to whom it appears, on tracing the light backward in a straight line, that the star is at a different position. Einstein’s predictions regarding this were experimentally verified during a solar eclipse.

So how exactly did Einstein figure out that gravity bends light? Imagine the following situation. A body is accelerating upward with a person in it. If a light is switched on outside it, and the light beam propagates in a straight line, from the accelerating body, the light would seem to be following a bent path (a parabolic curve, to be more precise). As the body accelerates upward, with time, the light that was near the top of the body seems to have reached the bottom of the body. Light seems to be following a curved path. And gravity also causes acceleration. Thus, light must also follow a curved path under the influence of gravity (i.e., in a gravitational field). Einstein reasoned that light is actually following the shortest path, which isn’t always the straight line path. (The shortest path from country A to country B is a curved one, for instance.)

## What's So Special About Gravity?

In his book “Relativity,” Einstein writes:

This is the equivalence principle. An observer in a closed body can’t distinguish between the effects produced by a gravitational field and those produced by an actual acceleration of the body. So, there are no gravitational fields. You are accelerating upward now. In curved spacetime, you must accelerate just to remain stationary. Of course you can’t feel it, since everything around you is accelerating upward at the same rate as well. A man who is falling downward can see this acceleration. Suppose you fall from the roof of a very high building. When you are falling through the air, you don’t feel your weight. If you drop something, it falls with you at the same rate. And you are not accelerating. You are not in any gravitational field. There is no such thing as a gravitational field. This was Einstein’s ‘happiest thought.’ Now consider a man in a spaceship in deep space, away from large masses. This man feels no acceleration. The spaceship is at rest or moving at a constant velocity. This situation is equivalent to the situation of the falling man. The general principle of relativity states that all reference bodies are equivalent for the description of natural phenomena, irrespective of their state of motion. This, in some sense, restores the symmetry among all reference bodies.

## Toward The North Pole

Suppose the spaceship we discussed above comes close to a planet. It will gradually stop moving in a straight line and start to move toward the planet. However, the man inside will not be able to feel anything. (Maybe he can see what’s happening if the planet is visible through a window in the spaceship, but for the sake of argument assume that the spaceship has no window.) To the man, he and the spaceship are moving in a straight line. So why does the path of the spaceship curve? The answer is simple. The spacetime around the planet is curved. You are moving in a straight line in curved spacetime. So ultimately, to an external observer, it seems that you are following a curved path.

Suppose you and your friend start moving toward the North Pole, some distance apart from the equator. If you both keep on walking in a straight line toward the North, you will come closer and closer to each other till you bump into each other at the North Pole. It appears as if some force is pushing you closer. Both of you followed a straight path, so what caused you to come closer? Of course, the curvature of the Earth.

## The Legacy Of General Relativity

General relativity is a generalization of the special theory. General relativity has passed many experimental tests. General relativity also successfully explained a phenomenon which Newton’s theory couldn’t. As Weinberg says in “Dreams Of A Final Theory”: "The shifting of the perihelion (or the point on the orbit closest to the Sun) of Mercury. The presence of other planets and stars in the universe slightly perturb the Sun’s gravitational field. This causes the elliptical orbits of the planet to precess or swing around slowly in space."

Newton’s prediction of Mercury’s precession doesn’t match with observations, while the predictions of general relativity does match. General relativity has passed a lot of experimental tests. But at the same time, some of the predictions of general relativity are paradoxical (like black holes), while some are yet to be tested rigorously (like gravitational waves). While it has been a great problem in physics to unify general relativity with quantum mechanics, general relativity remains the only theory which satisfactorily explains the gravitational interaction and it will undoubtedly be remembered as one of the greatest revolutions in physics, and science.