After Albert Einstein had realized the truth of his “Principle of Equivlance,” that is, that gravitational mass and inertial mass seem to be the exact same thing, he was well on his way to developing an entirely new theory regarding gravity itself.
Previously, the force of gravity had been codified by the great Isaac Newton, who summed up the effects of gravity's pull in a famous equation in which the force of gravity between two objects is inversely proportional to the square of the distance between them (for this reason it is called an “inverse square” law). For more than two hundred years this principle had stood, with absolutely no reason (so it seemed) to be questioned. Nearly everything that was affected by gravity could be easily defined using this law.
The Geometry of the Universe
Einstein, however, was not entirely convinced that Newton’s theory (while it seemed, indeed, to be mostly accurate) was the end of the story. After all, while it did a decent job in describing this force, it did absolutely nothing to explain what caused it in the first place. Sure objects are drawn toward each other, but why was this?
The equivalence principle was the key for Einstein to begin to understand this.
In the end, Einstein’s conclusion was quite dramatic, and changed the way physicists from then on would view the universe as a whole. Einstein realized that physicists had been wrong about the shape of the Universe’s very dimensions. Prior to this, the dimensions were seen as flat and smooth, easily quantifiable by way of standard, Euclidean geometries.
After realizing in his Special Theory of Relativity that none of the universe’s four dimensions (three of space and one of time) were indeed not quite so simple, Einstein began to assemble the pieces of the puzzle, realizing that gravity might be a direct result of the “flexibility” of the dimensions. In other words, space and time might not be flat and smooth at all, but might be any number of shapes, twisting and curving. If this were so, the universe would have to be described using a form of non-Euclidean geometry. It was this fact which led Einstein to having to go back to the basics and learn an entirely new form of mathematics known as Tensor Calculus in order to understand what this meant.
Gravity and Curved Space
And what did this mean, exactly?
A good way to picture how gravity works within general relativity is to picture a bowling ball on a trampoline. As the ball sits on the flexible surface, it creates an indentation. In general relativity, the same thing happens when a massive object (like the Earth, the moon or the sun) sits in the “fabric” of spacetime. Space and time must both “curve” around it, and it creates an indentation in the very dimensions of the universe. Just as a bowling ball on a trampoline, the more massive the object, the larger the indentation and the more “spread out.”
It may also be helpful to imagine what would happen (using this same analogy) if a golf ball is rolled toward the bowling ball, though not directly at it. This is easy to imagine – the ball would be “caught up” in the indentation created by the larger ball, and depending on its speed and trajectory, it might just be diverted from its course, or it might circle around the heavier ball a couple times before finally crashing into it. This, in essence, is the same principle by which the moon and satellites orbit the Earth.
Now, if only one was able to truly comprehend how this principle works in four dimensions, rather than two (it is especially difficult for the human mind to truly comprehend how the dimension of time behaves in all of this), the analogy would be complete.
Geodesics and Inertia
Within the framework of the theory of curved spacetime, Einstein could finally explain why his Equivalence Principle was so.
An object traveling through space, according to General Relativity, could be traveling in a perfectly straight line, and if it happened to pass by a large object, it would appear to “curve” toward that object. While prior to Einstein it would have been said that the object had been caught up in the larger object's gravitational field, General Relativity boldly states that this is not so. The object itself continues to travel in a perfectly straight line, but it is space itself which curves. The path the object is following – a straight line through curved space – is known in mathematics as a geodesic. Another example of such a path would be over the surface of a globe – where a “straight” line between two points is still forced to curve as it follows the surface.
The moon, to use this example again, is continually orbiting the Earth, and from the perspective of Earth appears to “curve” as it does so. In reality, the moon is moving in a straight line through space which in itself is curved.
Yes, it is a difficult theory to fully comprehend, and truly does change one’s entire perspective of the universe.
Results of the Theory
With Einstein’s theory of curved spacetime, it was finally possible for physicists to not only understand gravity from a mathematical standpoint, but from a tangible, theoretical standpoint as well. Furthermore, with the mathematics that came with Einstein’s theory, Newton’s mathematics had been given a substantial upgrade (for his equation hadn’t been able to deal with the full effects of curved spacetime), and were now able to answer previously impossible questions, such as certain inconsistencies astronomers had found in predicting the orbit of Mercury around the sun.
Though even today it is being questioned and refined by some physicists, general relativity, which states that gravity is caused by the curvature of spacetime around massive objects, has proven to be a great success, and a beneficial theory to science itself.
References:
Einstein, A. (1961). Relativity: The Special and the General Theory - A clear Explanation that Anyone can Understand. New York, NY: Random House.
Gardner, M. (1962). Relativity Simply Explained. Mineola, NY: Dover Publications, Inc.
The New York Public Library. (1995). Science Desk Reference. New York, NY: Macmillan.
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