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## Space and Time

All events we witness are labeled by a series of numbers, three to tell us where it happened, and one to determine when it happened. All in all four numbers are needed. These numbers are determined by some measuring devices such as measuring rods and clocks.

According to Newton (see Sect. 4.3.1) the properties of measuring rods and clocks can be made completely independent of the system which they measure (if it does not look like that, you can buy a higher quality device which will satisfy this criterion). But Einstein showed this is not the case: even Cartier watches slow down when compared to Seiko watches when they move with respect to each other. Even high density steel beams will be measured to be shorter than wimpy papers when their relative velocity is non-zero.

The measurements obtained by two observers in motion relative to each other are not identical, but they are related. For example, the times measured by two clocks are related by the time-dilation formula given earlier. Suppose observer A measures the location and time at which an event occurs: spider-man ran the 100 yard dash in 3 seconds flat. Now observer B, moving with respect to A, wants a description of this feat in his own coordinates. In order to find how many yards spider man ran as measured by B this observer needs to know his velocity with respect to A, the distance spidy ran as measured by A (100 yds) and how long did he take as measured by A's clock (3 sec); it is not enough to know the distance and relative velocity, the time it took is also needed.

The fact that in order to compare results from different observers both position and time are required is completely foreign to Newtonian mechanics. Yet this is the way the universe is organized. Far from being independent, space (that is, position) and time are interlinked. In fact, the mathematical description of the Special Theory of Relativity is most naturally expressed by combining space and time into one object: space-time. A point in space-time determines the position and time of occurrence of an event.

Within Special Relativity space-time is unaltered by whatever is in it. There are rules that state how the measurements of two observers are related, but these rules are unaltered by the objects (and beings) that populate space-time, they are the same whether we look at a pea, an elephant or a star millions of times more massive than the Sun. Space and time are still the arena where Nature unfolds.

We will see when we describe the General Theory of Relativity (Chap. 7) that space-time is far from being this imperturbable object where things just happen, it is in fact a dynamical system which affects and is affected by the matter in it. The development of our ideas of space and time from being independent of each other and imperturbable, to being meshed into space-time system, to being a dynamical object is one of the most profound developments derived from the general and special theories of relativity.

Next: The top speed. Up: Enter Einstein Previous: Paradoxes.
Jose Wudka
9/24/1998