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The Theory of Relativity
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We can determine the position of any point in space. Suppose that we have lo­cated two points, P1 and P2. We want to trace the movement of a particle from P1 to P2, Ordinarily, we would take a time read­ing when the particle is at P1 and another when it is at P2-or rather when we would see the particle arrive at P1, and P2. Time readings of this sort would not be abso­lutely accurate, because it would take time for light to travel from a light source to the particle and to be reflected from the particle to our eyes.

The discrepancy between the apparent and actual times of arrival of a particle at a given point would not be significant ordi­narily because of the great velocity of light. Even if the particle's speed were one-tenth the speed of light, the discrepancy would be so small that it could be detected only with the most refined measurements. But at a speed of one-half that of light-150,000 kilometers per second-the discrepancy would begin to be apparent. It would be great at nine-tenths of the speed of light, and enormous at ninety-nine-hundredths of that speed.

If we were to chart accurately the progress of a particle at such great speeds, we would have to apply the special theory of relativity, which takes into account the time needed by light to traverse space. We could make the necessary calculations with accuracy. For the speed of light always re­mains the same, regardless or the particular position in which the observer may happen to be located.

FOUR-DIMENSIONAL UNIVERSE?

According to classical physics, there are two separate factors we must consider in charting the progress of a particle in space. These factors are space (the three dimensions of length, breadth, and height) and time. According to the relativity the­ory, we cannot consider time as something apart. It represents a fourth dimension, which must be added to length, breadth, and height. We should refer not to space and time, but to space-time. As a famous German physicist, Hermann Minkowski, put it: "From now on, space by itself and time by itself are mere shadows and only a blend of the two exists in its own right."

We can represent four dimensions mathematically, but we cannot draw more than three dimensions in a diagram. Fur­ther, the fourth dimension - time - should not be thought of as a spatial dimension. In mathematics, a dimension is simply a quantity that must he specified in order to define a situation.

Most people find it hard to grasp even the idea of a fourth dimension. It would be just as hard for a dot-like man living in a world made up or two dimensions - length and breadth - to conceive of a third one.

If our dot-man traveled from point A (see diagram) in his two-dimensional world, he would go ahead for an infinite period of time in a straight line. Suppose he were transported to a three-dimensional world­ - a sphere of enormous size. The dot-man would not be aware of any change in the surface, since the curvature, from his point of view, would be slight. But if he started from point A on the sphere and advanced in what for him would be a straight line, he would be mystified to find he returned to point A. Our dot-man could not visualize a sphere, since he would be familiar only with a two-dimensional world. However, a dot-man mathematician could explain the structure of the sphere in terms of mathematics. He could show by means of mathematical symbols and equations just what had happened to the dot-man who had returned to the place from which he had started out. But unless the dot-man traveler, were familiar with the language and methods of mathematics, the explanation would not clear up his doubts. Many humans would find it as hard to follow an explanation of the fourth dimension.

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