The Concept of Nature — the Tarner Lectures, 1920

If iPi> p2y p3' Pi) be a set of measurements of this system, then the event-particle which is thus determined will be said to have pi, p2y Psy Pi ^s its co-ordinates in this system of measurement. Suppose that we name it the/)-system of measurement. Then in the same />-system by properly varying (/>!, p2y pz, Pi) every event-particle that has been, or will be, or instantaneously is now, can be indicated. Furthermore, according to any system of measurement that is natural to us,p. 176 three of the co-ordinates will be measurements of space and one will be a measurement of time. Let us always take the last co-ordinate to represent the time-measurement. Then we should naturally say that (pi, p^, p^) determined a point in space and that the event-particle happened at that point at the time ^4. But we must not make the mistake of thinking that there is a space in addition to the space-time manifold. That manifold is all that there is for the determination of the meaning of space and time. We have got to determine the meaning of a space-point in terms of the event-particles of the four-dimensional manifold. There is only one way to do this. Note that if we vary the time and take times with the same three space co-ordinates, then the eventparticles, thus indicated, are all at the same point. But seeing that there is nothing else except the eventparticles, this can only mean that the point (pi, p^, p^) of the space in the ^-system is merely the collection of event-particles {pi, p^, pz^ [pj)? where ^4 is varied and (Pi, p2, ps) is kept fixed. It is rather disconcerting to find that a point in space is not a simple entity; but it is a conclusion which follows immediately from the relative theory of space.

Furthermore the inhabitant of Mars determines event-particles by another system of measurements. Call his system the ^-system. According to him i9i> ?2> 93) 9i) determines an event-particle, and (?!> ?2J ^3) determines a point and q^ a time. But the collection of event-particles which he thinks of as a point is entirely different from any such collection which the man on earth thinks of as a point. Thus the ^-space for the man on Mars is quite different from the p-space for the land-surveyor on earth.

vni] SUMMARY

p. 177

So far in speaking of space we liave been talking of the timeless space of physical science, namely, of our concept of eternal space in which the world adventures. But the space which we see as we look about is instantaneous space. Thus if our natural perceptions are adjustable to the /)-system of measurements we see instantaneously all the event-particles at some definite time p^, and observe a succession of such spaces as time moves on. The timeless space is achieved by stringing together all these instantaneous spaces. The points of an instantaneous space are event-particles, and the points of an eternal space are strings of event-particles occurring in succession. But the man on Mars will never perceive the same instantaneous spaces as the man on the earth. This system of instantaneous spaces will cut across the earth-man's system. For the earthman there is one instantaneous space which is the instantaneous present, there are the past spaces and the future spaces. But the present space of the man on Mars cuts across the present space of the man on the earth. So that of the event-particles which the earthman thinks of as happening now in the present, the man on Mars thinks that some are already past and are ancient history, that others are in the future, and others are in the immediate present. This break-down in the neat conception of a past, a present, and a future is a serious paradox. I call two event-particles which on some or other system of measurement are in the same instantaneous space 'co-present' event-particles. Then it is possible that A and B may be co-present, and that A and C may be co-present, but that B and C may not be co-present. For example, at some inconceivable distance from us there are events co-present with us

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p. 178

now and also co-present with the birth of Queen Victoria. If A and B are co-present there will be some systems in which A precedes B and some in which B precedes A. Also there can be no velocity quick enough to carry a material particle from A to B or from B to A. These different measure-systems with their divergences of time-reckoning are puzzling, and to some extent affront our common sense. It is not the usual way in which we think of the Universe. We think of one necessary time-system and one necessary space. According to the new theory, there are an indefinite number of discordant time-series and an indefinite number of distinct spaces. Any correlated pair, a time-system and a space-system, will do in which to fit our description of the Universe. We find that under given conditions our measurements are necessarily made in some one pair which together form our natural measure-system. The difficulty as to discordant timesystems is partly solved by distinguishing between what I call the creative advance of nature, which is not properly serial at all, and any one time series. We habitually muddle together this creative advance, which we experience and know as the perpetual transition of nature into novelty, with the single-time series which we naturally employ for measurement. The various time-series each measure some aspect of the creative advance, and the whole bundle of them express all the properties of this advance which are measurable. The reason why we have not previously noted this difference of time-series is the very small difference of properties between any two such series. Any observable phenomena due to this cause depend on the square of the ratio of any velocity entering into the observation to vin] SUMMARY

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