CHAPTER XII

"And nu bit and for Godes naman halsath ælcne thara the thas boc rædan lyste that he for hine gebidde, and him ne wite gif he hit rihtlicor ongite thonne he mihte. Forthæmthe alc mon sceal be his ondgites mæthe and be his æmettan sprecan that he sprecth and don that that he deth."-KING Alfred, Preface to his Translation of Bothius.

Sensible and Physical Space-Time

We have at length reached a position where it becomes possible to deal with the concept of physical Space-Time, from which, as we shall see, the concepts of physical Space and of physical Time are abstractions of two different kinds. We shall thus finally work back, from a wholly different starting-point, to the position which we reached at the end of Part I.

Let us first take a backward glance over the country that we have crossed, and see how the universe looks from our present standpoint. We shall then be able to see what part of our journey from crude sensation to the refined concepts of mathematical physics remains to be completed; and, having done so, we can try to complete it.

(a) Statement of the Present Position.-The situation, so far as it has now developed, is roughly as follows: There is a world of physical objects, some of which, like my own body, are connected with observing minds which can communicate with each other. Others, so far as we know, are not connected with minds; but in their general character they are very much like those which are. Correlated with each human body there is a general sense-history, which is split up into several special sense-histories, visual, tactual, auditory, somatic,

and so on. We can sense temporal relations between sensa in our different special sense-histories, just as we can sense temporal relations between different sensa in the same special sense-history. But we cannot sense spatial relations between contemporary sensa in our different special sense-histories, though we can sense such relations between contemporary sensa of the same special history. These spatial characteristics are much more marked in the visual sense-history than in any of the others.

My somatic sense-history contains sensa which are appearances of internal states and processes of my own body. In my other special sense-histories are various sense-objects, some uniform for a time, others nonuniform. There are correlations between certain senseobjects in my different special histories which lead me to regard them as different kinds of appearances of the same external physical object. All these remarks about me and my sense-histories apply equally, mutatis mutandis, to other observers and their sense-histories; as I learn by intercommunication.

to us.

Between sensa in the histories of different observers neither spatial nor temporal relations can be sensed by either of the observers or by any third observer known But there are correlations between certain senseobjects of different observers which lead us to say that the same physical object is appearing to all of them. When this is so, there is generally a certain external place which all these sensa may be said to "occupy in some Pickwickian and definable sense, such as optical occupation. Again, there are certain methods, discussed in the last chapter but one, by which some sensa of different histories are grouped together as "neutrally simultaneous," and others are grouped apart as "neutrally successive."

Then there are the very elaborate correlations between the uniformity or non-uniformity of sense-objects in the visual histories of observers, and certain events

in their somatic histories called "kinæsthetic sensations." We have been studying these in the last chapter. We came to the conclusion that the positional uniformity or non-uniformity of the sense-object by which a certain physical object appears to an observer, depends upon certain physical processes in the external object and the observer's body; and that these processes in one's own body appear to oneself as kinæsthetic sensations. A more careful study of these correlations revealed two further closely connected points. One is that the positional uniformity of a sense-object depends on an identity of character between these two physical processes, and that positional non-uniformity is correlated with certain differences between them. The other is that relative rest between two sense-objects in a sense-history depends on a similar kind of identity between two such physical processes in the bodies which appear as these two sense-objects, whilst relative motion between two sense-objects is correlated with similar kinds of difference between two such physical processes in the bodies which appear as these two sense-objects. Sensible motion and rest are absolute, but they seem to depend on relations of identity and difference respectively between physical processes in the body which appears and the body of the observer to whom it appears.

(b) Statement of the Remaining Problem.-These, then, are some of the facts which have so far been elicited, and some of the highly probable inferences which have been made from them. The next thing is to state clearly the problem which still remains. The rest of the problem is to make, if possible, a further synthesis by analogy with what we already know. Can we treat the world of physical objects and events as forming a whole which is analogous to a single sense-history? That is Can we regard scientific objects as analogous to sense-objects; can we suppose that they have spatial relations to each other, such as we can sense only between sensa in a single sense-field; and can we suppose that

they endure, and have temporal relations to each other, such as we can sense only between sensa within a single general sense-history? Lastly, can we suppose that physical objects rest and move in this spatio-temporal physical whole, as sensa do in their fields, and as senseobjects do in our sense-histories? This, I think, is the real problem about physical Space, Time, and Motion. It is the problem of constructing a single, neutral, public Space-Time of physical objects and events, on the analogy of the many personal private space-times of the various observers' sense-histories.

Now it is not, of course, a question of just making such suppositions in the abstract. Our only possible justification for supposing anything of the kind is that it provides a scheme which summarises all the known correlations between sensa, and is, at the same time, familiar to us because of its analogy to our own sensehistories with which we are directly acquainted. It is theoretically possible that no such supposition would do justice to the actual correlations among sensa. It is still more likely that no supposition which made the structure of physical Space-Time exactly analogous to that of an individual sense-history would account for the known facts. Again, if the physical world can be consistently regarded as a spatio-temporal whole with considerable, though not complete, analogy of structure to an individual sense-history, it is probable that this can be done in a number of alternative ways, all of which will synthesise the known facts equally well. Even if up to a certain date human beings had only happened to think of one view of the structure of physical Space-Time, there is no reason to doubt that, if they thought more carefully and paid less attention to certain traditional points of view, they would be able to devise dozens of alternative structures for physical Space-Time equally capable of doing justice to all the known correlations among sensa. No doubt the physical world has a certain absolute intrinsic structure; and this structure

exhibits itself, in part at least, in the correlations between sensa of the same and of different observers. But we have to treat this structure piecemeal in the sciences of geometry, chronometry, kinematics, dynamics, and electro-magnetics, and by making suitably correlated modifications in the axioms of these various partial sciences we can express the same absolute structure in innumerable different and equally satisfactory ways. If, so far, very few alternative schemes have been proposed, this is due to nothing more recondite than lack of scientific imagination and the imperfection of our technical mathematical and logical apparatus.

It is, nevertheless, an interesting and important inquiry to see how far we can do justice to the known facts by supposing that the structure of the physical world is analogous to that of our sense-histories, and to see what is the minimum difference of structure between the two which we must postulate. For, after all, our physical concepts have their roots in our sense-histories.

It is evident that it might be possible to regard the physical world as forming a spatio-temporal whole analogous in general outline to a single sense-history, and yet that we might have to postulate differences of detail. I do not mean by this simply that the contents of the two might be different. It is perfectly certain that they will be. The ultimate contents of a sensehistory are the sensa of the observer whose sense-history it is. The ultimate contents of physical Space-Time are scientific events. Even if it should be possible to regard scientific events as composed of sensa (which is far from certain), each scientific event will be composed of sensa from the histories of many different observers, and also presumably of many more sensa which do not belong to the history of any observer. Thus, even on this hypothesis, the ultimate contents of physical SpaceTime will be groups of correlated sensa. But, beside this difference which there certainly must be between physical Space-Time and any sense-history, there may well be