Space And Time And Special Relativity
Since light brings us the information about the universe and it travels at a finite rate (albeit a very large one), we are looking back in time when we look into our night sky. The nearer the object, the shorter the look back in time; but the objects we see farthest away are the objects we are seeing as they were longest ago. Thus the night sky alone shows us the coupling of space and time.
To make this point somewhat more precise, let us consider we have suppressed two spatial dimensions and show only one spatial dimension and the time dimension. If the origin represents where we are located, "Here and now," then two, "There and then" are accessible to us by trips that are within our realm of experience. But to go to point C requires that we travel faster than the speed of light, which is contrary to Einstein's second postulate. Thus the first consequence of Einstein's two postulates is that there are realms of the space-time continuum from which we could not have come in our past and realms in the future to which we cannot go. Or in other words not all realms of space and time are readily accessible to us either in the past or in the future. Let us examine some other consequences of these two postulates, having to do with the measurement of space, mass, and time.
Suppose we have two observers in different frames of reference that are at rest relative to each other. If both
make measurements of lengths in space and intervals of time, they would agree on the measurements; so they must occupy the same realm of space-time. Now suppose the frame of reference containing observer B moves at a large fraction of the speed of light relative to the frame containing observer A. Do the two observers still occupy the same realm space-time as before?
On the basis of his two postulates Einstein derived three important formulas for length, mass, and time in which the factor root of 1 - (V2/C2), called the Lorentz contraction factor, plays a crucial role. The length, mass, and time interval for an object, say, a clock, in 8's reference frame are measured by observer A, who sees the object in motion. If A has an identical clock with him, then his measurements of 8's clock are related by the Lorentz contraction factor to his identical clock's length, mass, and time interval. The effect of the Lorentz factor on length, mass, and time is shown graphically. These formulas are unimportant for all ordinary speeds (v/c = 0) so thatA and B still occupy approximately the same realm of space-time. But this is not the case for speeds comparable to the velocity of light.
What do the formulas tell us? The observer A, who sees the object moving with B's reference frame, will measure a shorter length for the object in the direction in which it is moving than will observer B, to whom the object is stationary. For example observer A would notice that B's rocket ship is also contracted in length compared with his own rocket ship, which is, of course, his frame of reference. Thus there is a contraction of space in the direction of motion for the moving frame of reference. Observer A will also measure a greater mass for the object in B's moving rocket ship than observer B will; and observer A will also measure a longer time between two events, such as the tick of the clock taking place on B's rocket ship, than observer B will for the same two events. The latter effect is called time dilation, or spreading out of time. The faster observer B travels relative to observer A, the slower his clock appears to run as observer A sees it (observer A's own clock is seen by observer B also to be running slow). Neither observer sees any effect on his own clock. Thus measurements of length, mass, and time vary with the frame of reference. Clearly, observer A and observer B occupy different realms of space-time.
From the discussion above what can we infer about space and time for the universe as a whole? Newton's concept of an absolute space and time envisions a material universe inserted into a realm of space and time. But in the Einsteinian concept space and time are in the universe; that is, the universe defines space and time. There is no space beyond the universe, and there is neither time before nor after the universe. Space and time and their local features are properties of the universe.
So confrary to ordinary experience are the concepts of relativity theory that they seem to violate common sense and to be too abstract to be of any consequence. This is far from the c~se; for relativity theory has amalgamated old ideas of space and time into a unified arrangement leading to new and unsuspected revelations that make it possible to test the consequences of the theory. At the appropriate points in the remaining chapters we have inserted these tests of relativity theory as supplemental reading.
