The type of measuring instruments is thus exactly the same as in classical science; and all that relativity tells us is that if our classical measurements had been pursued with greater precision, we should have realised long ago that the classical anticipations were belied by experiment. There is no use in pursuing the study of the theory any farther unless we succeed in understanding its physical significance. So far as the mathematician is concerned, with the Lorentz-Einstein transformations issuing as they do from ultra-precise experiment, their mathematical consequences must be deemed to correspond to the workings of the real world; and these consequences indicate clearly that length, duration and simultaneity must be relatives in a real physical sense. However, in view of the importance of the new ideas, we may consider the problem in an indirect way and thereby throw additional light on the concrete significance of these transformations.
Accordingly we shall have to discuss what the physicist means by an “event.” An event is exemplified by a something happening in a certain region of space at a certain moment of time. It matters not what actually happens. It may be a thought flashing through our minds, a bird bursting into song, or two billiard balls colliding; what is essential is a specification of position in space and in time.
When we try to think of an event, we are compelled to credit it with more or less extension in space, and more or less duration in time. But in all problems where accuracy of localisation is demanded, we must conceive of an event as ideally restricted to an instantaneous point in space; or, if we prefer, to a mathematical point in space at a mathematical instant in time. We then get what has been called by Minkowski a Point-Event. This procedure of restricting events ideally is of course purely a mathematical abstraction and is in every way similar to the procedure followed by the geometrician when he speaks of points without dimensions, lines without width, or surfaces without thickness.
Even in ordinary life we are obliged to follow this same method of restricting dimensions ideally, in order to render a precise localisation possible. For instance, when we say we are so many miles from New York our assertion is extremely vague. What part of New York are we referring to? Even when we specify a definite building in the city, it could always be asked: “What part of the building?” We see, then, that to obtain any degree of precision we must select a definite point, and our statement that we are fifty miles from New York is equivalent to regarding New York as reduced to a point. Of course we know full well that a city is not reduced to a point; but arguments of this sort are irrelevant to the problem of localisation with which we are faced.
It is the same for time. An event lasts, it manifests duration; but in order to obtain precision we must conceive of it as ideally restricted. We thus obtain an instantaneous event occurring at a definite point of our space.
We may say, then, that a billiard ball, subsisting motionless at a point of the space of our frame, constitutes a continuous succession of point-events all located at the same point of our space (where the point-event itself would be represented by the instantaneous existence of the ball considered as reduced in size to a spatial point). Likewise, a billiard ball moving through the space of our frame would be represented by a succession of points in space at a succession of instants in time; hence by a chain of point-events.
It is not absolutely necessary to conceive of an event as something objective, actually occurring or existing. We may conceive of events and point-events as empty. Thus, a point of our space a million miles away in a definite direction at six o’clock constitutes a point-event. In the same way it is not absolutely necessary to designate a point on our sheet of paper by a pencil mark; for we can define its position by numbers. In physics, however, we are more generally interested in discussing events that are observable; so although in theory a point-event is merely the localisation of an abstract entity at a point of space at an instant of time, in practice the majority of events to which we shall refer will serve to localise observable existents. For similar reasons we usually tint the colourless liquid in the thermometer so as to render it observable; though by so doing, nothing is changed, of course, in the reading of the instrument.
Let us now pass to the problem of determining the simultaneity of events. As a fact of common experience it is possible to localise our various thoughts and sense impressions in the time-stream of our individual consciousness; and the judgment that two sensations are simultaneous or follow in succession is essentially a priori, in that it cannot be analysed further. Science, however, could never have existed had we restricted ourselves to registering sense impressions without attempting to co-ordinate them and account for them. To these attempts of co-ordination we are indebted for the conception of the outside universe of space and time (or space-time according to the modern view)—the common objective world of science in which events occur. It is objective in that we are enabled to conceive of it as presenting the same relationships of structure for all men, hence as pre-existing as a concrete existent to the mind that discovers it and explores it bit by bit. Whether this objective universe represents a reality in the metaphysical sense (a reality which has merely been discovered by us) or whether, as the majority of scientists would assert, it reduces in the last analysis to a mere mental construct, the product of a synthesis of the mind, is a problem that need not detain us in the present chapter. In either case the physicist may speculate on this objective universe as though it were a reality pre-existing to the observer who discovers it.
Commonplace reason, or rudimentary science, was thus led to conceive of a common external objective universe in which external events occurred, occupying definite positions in space and in time. These external events, such as the explosion of a barrel of gunpowder, were assumed to be the causes responsible for our immediate sense perceptions of light and of sound. Until some three hundred years ago it was thought permissible to identify the instant of time at which an external event occurred with the precise psychological instant at which the event impressed itself on our consciousness in the form of a sound or of a visual sensation. But this very crude view led to inconsistencies when it was realised that an explosion which occurred at our sides and which appeared to us as a simultaneous occurrence of light and sound impressions would have appeared as a sequence of two separate events, a luminous one followed by a sonorous one, had we been situated elsewhere.
If we were to retain our belief in the possibility of conceiving of a common objective universe in which a single event remained a single event regardless of the position of the observer, it became imperative to account for these discrepancies by assuming that sound transmission from place to place was not instantaneous. It was still thought, however, that light propagation was instantaneous, so that at least the instants of our visual perception of external events could be identified with the instants of their occurrence in the objective world. For example, it was usual to claim three hundred years ago that when we beheld a sudden red brightness in a star we were witnessing a stellar catastrophe occurring there-now. It appeared, then, as though men were gifted with the same a priori intuitional understanding of the simultaneity or succession of events throughout space which experience had shown to exist in the case of sense impressions located in the individual streams of consciousness. But, as Eddington points out, “This crude belief was disproved in 1675 by Römer’s celebrated discussion of the eclipses of Jupiter’s satellites; and we are no longer permitted to locate external events in the instant of our visual perception of them.” Following Römer’s discovery, scientists were compelled to discriminate between the instant an external event occurred and the instant we became cognisant of its occurrence. This discovery led them to recognise that pure intuition could yield us no reliable information on the order of succession and on the simultaneity of external events throughout space. For instance, when we suddenly perceive some stellar conflagration through the telescope, we have no means of deciding by direct intuition whether the stellar catastrophe was simultaneous with the signing of the Armistice, the battle of Waterloo or the building of the Pyramids. In the same way, were we to perceive two stellar catastrophes, it would be impossible for us to decide a priori which had preceded the other.