Page:Russell - An outline of philosophy.pdf/127

Rh the difficulty comes in connecting A's time with B's. Suppose A sends a flash to B, B's mirror reflects it, and it returns to A after a certain time. If A is on the earth and B on the sun, the time will be about sixteen minutes. We shall naturally say that the time when B received the light-signal is half-way between the times when A sent it out and received it back. But this definition turns out to be not unambiguous; it will depend upon how A and B are moving relatively to each other. The more this difficulty is examined, the more insuperable it is seen to be. Anything that happens to A after he sends out the flash and before he gets it back is neither definitely before nor definitely after nor definitely simultaneous with the arrival of the flash at B. To this extent, there is no unambiguous way of correlating times in different places.

The notion of a "place" is also quite vague. Is London a "place"? But the earth is rotating. Is the earth a "place"? But it is going round the sun. Is the sun a "place"? But it is moving relatively to the stars. At best you could talk of a place at a given time; but then it is ambiguous what is a given time, unless you confine yourself to one place. So the notion of "place" evaporates.

We naturally think of the universe as being in one state at one time and in another at another. This is a mistake. There is no cosmic time, and so we cannot speak of the state of the universe at a given time. And similarly we cannot speak unambiguously of the distance between two bodies at a given time. If we take the time appropriate to one of the two bodies, we shall get one estimate; if the time of the other, another. This makes the Newtonian law of gravitation ambiguous, and shows that it needs restatement, independently of empirical evidence.

Geometry also goes wrong. A straight line, for example, is supposed to be a certain track in space whose parts all exist simultaneously. We shall now find that what is a straight line for one observer is not a straight line for another. Therefore geometry ceases to be separable from physics.

The "observer" need not be a mind, but may be a