Reference: The Nature of the Physical World
This paper presents Chapter III (section 2) from the book THE NATURE OF THE PHYSICAL WORLD by A. S. EDDINGTON. The contents of this book are based on the lectures that Eddington delivered at the University of Edinburgh in January to March 1927.
The paragraphs of original material are accompanied by brief comments in color, based on the present understanding. Feedback on these comments is appreciated.
The heading below links to the original materials.
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Location of Events
In Fig. 1 you see a collection of events, indicated by circles. They are not at present in their right places; that is the job before me–to put them into proper locations in my frame of space and time. Among them I can immediately recognize and label the event Here-Now, viz. that which is happening in this room at the moment. The other events are at varying degrees of remoteness from Her-Now, and it is obvious to me that the remoteness is not only of different degrees but of different kinds. Some events spread away towards what in a general way I call the Past; I can contemplate others which are distant in the Future; others are remote in another kind of way towards China or Peru, or in general terms Elsewhere. In this picture I have only room for one dimension of Elsewhere; another dimension sticks out at right angles to the paper; and you must imagine the third dimension as best you can.
Fig. 1 represents a local frame of space. All these locations are mapped from a local viewpoint.
Now we must pass from this vague scheme of location to a precise scheme. The first and most important thing is to put Myself into the picture. It sounds egotistical; but, you see, it is my frame of space that will be used, so it all hangs round me. Here I am—a kind of four-dimensional worm (Fig. 2). It is a correct portrait; I have considerable extension towards the Past and presumably towards the Future, and only a moderate extension towards Elsewhere. The “instantaneous me”, i.e. myself at this instant, coincides with the event Here- Now. Surveying the world from Here-Now, I can see many other events happening now. That puts it into my head that the instant of which I am conscious here must be extended to include them; and I jump to the conclusion that Now is not confined to Here-Now. I therefore draw the instant Now, running as a clean section across the world of events, in order to accommodate all the distant events which are happening now. I select the events which I see happening now and place them on this section, which I call a moment of time or an “instantaneous state of the world”. I locate them on Now because they seem to be Now.
This method of location lasted until the year 1667, when it was found impossible to make it work consistently. It was then discovered by the astronomer Roemer that what is seen now cannot be placed on the instant Now. (In ordinary parlance—light takes time to travel.) That was really a blow to the whole system of worldwide instants, which were specially invented to accommodate these events. We had been mixing up two distinct events; there was the original event somewhere out in the external world and there was a second event, viz. the seeing by us of the first event. The second event was in our bodies Here-Now; the first event was neither Here nor Now. The experience accordingly gives no indication of a Now which is not Here; and we might well have abandoned the idea that we have intuitive recognition of a Now other than Here-Now, which was the original reason for postulating world-wide instants Now.
Fig. 2 makes the map even more local by referencing it from the body of an observer. It makes a distinction between the moment an event takes place, and the moment when the observer becomes aware of it. Here the awareness is located in the body of the observer, and the information from the event travels at the speed of light to reach observer’s awareness. Thus, an event seen at a distance actually happened sometime in the past.
However, having become accustomed to world-wide instants, physicists were not ready to abandon them. And, indeed, they have considerable usefulness provided that we do not take them too seriously. They were left in as a feature of the picture, and two Seen-Now lines were drawn, sloping backwards from the Now line, on which events seen now could be consistently placed. The cotangent of the angle between the Seen-Now lines and the Now line was interpreted as the velocity of light.
Accordingly when I see an event in a distant part of the universe, e.g. the outbreak of a new star, I locate it (quite properly) on the Seen-Now line. Then I make a certain calculation from the measured parallax of the star and draw my Now line to pass, say, 300 years in front of the event, and my Now line of 300 years ago to pass through the event. By this method I trace the course of my Now lines or world-wide instants among the events, and obtain a frame of time-location for external events. The auxiliary Seen-Now lines, having served their purpose, are rubbed out of the picture.
The localized awareness makes “Now” subjective to the observer. If the observer knew the necessary universal laws to be able to visualize the events universally as they were happening, then his viewpoint would be universal and objective.
That is how I locate events; how about you? We must first put You into the picture (Fig. 3). We shall suppose that you are on another star moving with different velocity but passing close to the earth at the present moment. You and I were far apart in the past and will be again in the future, but we are both Here- Now. That is duly shown in the picture. We survey the world from Here-Now, and of course we both see the same events simultaneously. We may receive rather different impressions of them; our different motions will cause different Doppler effects, FitzGerald contractions, etc. There may be slight misunderstandings until we realise that what you describe as a red square is what I would describe as a green oblong, and so on. But, allowing for this kind of difference of description, it will soon become clear that we are looking at the same events, and we shall agree entirely as to how the Seen- Now lines lie with respect to the events. Starting from our common Seen-Now lines, you have next to make the calculations for drawing your Now line among the events, and you trace it as shown in Fig. 3.
How is it that, starting from the same Seen-Now lines, you do not reproduce my Now line? It is because a certain measured quantity, viz. the velocity of light, has to be employed in the calculations; and naturally you trust to your measures of it as I trust to mine. Since our instruments are affected by different Fitz- Gerald contractions, etc., there is plenty of room for divergence. Most surprisingly we both find the same velocity of light, 299,796 kilometres per second. But this apparent agreement is really a disagreement; because you take this to be the velocity relative to your planet and I take it to be the velocity relative to mine. (The measured velocity of light is the average to-and-fro velocity. The velocity in one direction singly cannot be measured until after the Now lines have been laid down and therefore cannot be used in laying down the Now lines. Thus there is a deadlock in drawing the Now lines which can only be removed by an arbitrary assumption or convention. The convention actually adopted is that (relative to the observer) the velocities of light in the two opposite directions are equal. The resulting Now lines must therefore be regarded as equally conventional.) Therefore our calculations are not in accord, and your Now line differs from mine.
Fig. 3 adds another observer at a different location and maps the Now-lines for both observers based on their relative motion. We now have two localized and subjective maps of Now-lines. The relationship provided between these two subjective viewpoints can never be accurate and scientific. The only scientific viewpoint shall be an objective viewpoint based on universal laws. This objective viewpoint shall be the same for both observers.
If we believe our world-wide instants or Now lines to be something inherent in the world outside us, we shall quarrel frightfully. To my mind it is ridiculous that you should take events on the right of the picture which have not -happened yet and events on the left which are already past and call the combination an instantaneous condition of the universe. You are equally scornful of my grouping. We can never agree. Certainly it looks from the picture as though my instants were more natural than yours; but that is because I drew the picture. You, of course, would redraw it with your Now lines at right angles to yourself.
But we need not quarrel if the Now lines are merely reference lines drawn across the world for convenience in locating events—like the lines of latitude and longitude on the earth. There is then no question of a right way and a wrong way of drawing the lines; we draw them as best suits our convenience. World-wide instants are not natural cleavage planes of time; there is nothing equivalent to them in the absolute structure of the world; they are imaginary partitions which we find it convenient to adopt.
We have been accustomed to regard the world—the enduring world—as stratified into a succession of instantaneous states. But an observer on another star would make the strata run in a different direction from ours. We shall see more clearly the real mechanism of the physical world if we can rid our minds of this illusion of stratification. The world that then stands revealed, though strangely unfamiliar, is actually much simpler. There is a difference between simplicity and familiarity. A pig may be most familiar to us in the form of rashers, but the unstratified pig is a simpler object to the biologist who wishes to understand how the animal functions.
Eddington is going through contortions of logic here to develop some kind of standard relationship between two highly relative and subjective viewpoints. The truth is that in the range of inertia for material substance the relativity of time is negligible and can be ignored. Such changes in the constitution of time become significant only for the field-substance.
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