Science and the modern world · Alfred North Whitehead
RELATIVITY
In the previous lectures of this course we have considered the antecedent conditions which led up to the scientific movement, and have traced the progress of thought from the seventeenth to the nineteenth century. In the nineteenth century this history falls into three parts, so far as it is to be grouped around science. These divisions are, the contact between the romantic movement and science, the development of technology and physics in the earlier part of the century, and lastly the theory of evolution combined with the general advance of the biological sciences. The dominating note of the whole period of three centuries is that the doctrine of materialism afforded an adequate basis for the concepts of science. It was practically unquestioned. When undulations were wanted, an ether was supplied, in order to perform the duties of an undulatory material. To show the full assumption thus involved, I have sketched in outline an alternative doctrine of an organic theory of nature. In the last lecture it was pointed out that the biological developments, the doctrine of evolution, the doctrine of energy, and the molecular theories were rapidly undermining the adequacy of the orthodox materialism. But until the close of the century no one drew that conclusion. Materialism reigned supreme.
The note of the present epoch is that so many complexities have developed regarding material, space, time, and energy, that the simple security of the old orthodox assumptions has vanished. It is obvious that they will not do as Newton left them, or even as Clerk Maxwell left them. There must be a reorganization. The new situation in the thought of to-day arises from the fact that scientific theory is outrunning common sense. The settlement as inherited by the eighteenth century was a triumph of organised common sense. It had got rid of medieval phantasies, and of Cartesian vortices. As a result it gave full reign to its anti-rationalistic tendencies derived from the historical revolt of the Reformation period. It grounded itself upon what every plain man could see with his own eyes, or with a microscope of moderate power. It measured the obvious things to be measured, and it generalised the obvious things to be generalised. For example, it generalised the ordinary notions of weight and massiveness. The eighteenth century opened with the quiet confidence that at last nonsense had been got rid of. To-day we are at the opposite pole of thought. Heaven knows what seeming nonsense may not to-morrow be demonstrated truth. We have recaptured some of the tone of the early nineteenth century, only on a higher imaginative level.
The reason why we are on a higher imaginative level is not because we have finer imagination, but because we have better instruments. In science, the most important thing that has happened during the last forty years is the advance in instrumental design. This advance is partly due to a few men of genius such as Michelson and the German opticians. It is also due to the progress of technological processes of manufacture, particularly in the region of metallurgy. The designer has now at his disposal a variety of material of differing physical properties. He can thus depend upon obtaining the material he desires; and it can be ground to the shapes he desires, within very narrow limits of tolerance. These instruments have put thought onto a new level. A fresh instrument serves the same purpose as foreign travel; it shows things in unusual combinations. The gain is more than a mere addition; it is a transformation. The advance in experimental ingenuity is, perhaps, also due to the larger proportion of national ability which now flows into scientific pursuits. Anyhow, whatever be the cause, subtle and ingenious experiments have abounded within the last generation. The result is, that a great deal of information has been accumulated in regions of nature very far removed from the ordinary experience of mankind.
Two famous experiments, one devised by Galileo at the outset of the scientific movement, and the other by Michelson with the aid of his famous interferometer, first carried out in 1881, and repeated in 1887 and 1905, illustrate the assertions I have made. Galileo dropped heavy bodies from the top of the leaning tower of Pisa, and demonstrated that bodies of different weights, if released simultaneously, would reach the earth together. So far as experimental skill, and delicacy of apparatus were concerned, this experiment could have been made at any time within the preceding five thousand years. The ideas involved merely concerned weight and speed of travel, ideas which are familiar in ordinary life. The whole set of ideas might have been familiar to the family of King Minos of Crete, as they dropped pebbles into the sea from high battlements rising from the shore. We cannot too carefully realise that science started with the organisation of ordinary experiences. It was in this way that it coalesced so readily with the anti-rationalistic bias of the historical revolt. It was not asking for ultimate meanings. It confined itself to investigating the connections regulating the succession of obvious occurrences.
Michelson’s experiment could not have been made earlier than it was. It required the general advance in technology, and Michelson’s experimental genius. It concerns the determination of the earth’s motion through the ether, and it assumes that light consists of waves of vibration advancing at a fixed rate through the ether in any direction. Also, of course, the earth is moving through the ether, and Michelson’s apparatus is moving with the earth. In the centre of the apparatus a ray of light is divided so that one half-ray goes in one direction _along_ the apparatus through a given distance, and is reflected back to the centre by a mirror in the apparatus. The other half-ray goes the same distance _across_ the apparatus in a direction at right angles to the former ray, and it also is reflected back to the centre. These reunited rays are then reflected onto a screen in the apparatus. If precautions are taken, you will see interference bands; namely bands of blackness where the crests of the waves of one ray have filled up the troughs of the other rays, owing to a minute difference in the lengths of paths of the two half-rays, up to certain parts of the screens. These differences in length will be affected by the motion of the earth. For it is the lengths of the paths in the ether which count. Thus, since the apparatus is moving with the earth, the path of one half-ray will be disturbed by the motion in a different manner from the path of the other half-ray. Think of yourself as moving in a railway carriage, first along the train and then across the train; and mark out your paths on the railway track which in this analogy corresponds to the ether. Now the motion of the earth is very slow compared to that of light. Thus in the analogy you must think of the train almost at a standstill, and of yourself as moving very quickly.
In the experiment this effect of the earth’s motion would affect the positions on the screen of the interference bands. Also if you turn the apparatus round, through a right-angle, the effect of the earth’s motion on the two half-rays will be interchanged, and the positions of the interference bands would be shifted. We can calculate the small shift which should result owing to the earth’s motion round the sun. Also to this effect, we have to add that due to the sun’s motion through the ether. The delicacy of the instrument can be tested, and it can be proved that these effects of shifting are large enough to be observed by it. Now the point is, that nothing was observed. There was no shifting as you turned the instrument round. The conclusion is either that the earth is always stationary in the ether, or that there is something wrong with the fundamental principles on which the interpretation of the experiment relies. It is obvious that, in this experiment, we are very far away from the thoughts and the games of the children of King Minos. The ideas of an ether, of waves in it, of interference, of the motion of the earth through the ether, and of Michelson’s interferometer, are remote from ordinary experience. But remote as they are, they are simple and obvious compared to the accepted explanation of the nugatory result of the experiment.
The ground of the explanation is that the ideas of space and of time employed in science are too simple-minded, and must be modified. This conclusion is a direct challenge to common sense, because the earlier science had only refined upon the ordinary notions of ordinary people. Such a radical reorganization of ideas would not have been adopted, unless it had also been supported by many other observations which we need not enter upon. Some form of the relativity theory seems to be the simplest way of explaining a large number of facts which otherwise would each require some _ad hoc_ explanation. The theory, therefore, does not merely depend upon the experiments which led to its origination. The central point of the explanation is that every instrument, such as Michelson’s apparatus as used in the experiment, necessarily records the velocity of light as having one and the same definite speed relatively to it. I mean that an interferometer in a comet and an interferometer on the earth would necessarily bring out the velocity of light, relatively to themselves, as at the same value. This is an obvious paradox, since the light moves with a definite velocity through the ether. Accordingly two bodies, the earth and the comet, moving with unequal velocities through the ether, might be expected to have different velocities relatively to rays of light. For example, consider two cars on a road, moving at ten and twenty miles an hour respectively, and being passed by another car at fifty miles an hour. The rapid car will pass one of the two cars at the relative velocity of forty miles per hour, and the other at the rate of thirty miles per hour. The allegation as to light is that, if we substituted a ray of light for the rapid car, the velocity of the light along the roadway would be exactly the same as its velocity relatively to either of the two cars which it overtakes. The velocity of light is immensely large, being about three hundred thousand kilometres per second. We must have notions as to space and time such that just this velocity has this peculiar character. It follows that all our notions of relative velocity must be recast. But these notions are the immediate outcome of our habitual notions as to space and time. So we come back to the position, that there has been something overlooked in the current expositions of what we mean by space and of what we mean by time.
Now our habitual fundamental assumption is that there is a unique meaning to be given to space and a unique meaning to be given to time, so that whatever meaning is given to spatial relations in respect to the instrument on the earth, the same meaning must be given to them in respect to the instrument on the comet, and the same meaning for an instrument at rest in the ether. In the theory of relativity, this is denied. As far as concerns space, there is no difficulty in agreeing, if you think of the obvious facts of relative motion. But even here the change in meaning has to go further than would be sanctioned by common sense. Also the same demand is made for time; so that the relative dating of events and the lapses of time between them are to be reckoned as different for the instrument on the earth, for the instrument in the comet, and for the instrument at rest in the ether. This is a greater strain on our credulity. We need not probe the question further than the conclusion that for the earth and for the comet spatiality and temporality are each to have different meanings amid different conditions, such as those presented by the earth and the comet. Accordingly velocity has different meanings for the two bodies. Thus the modern scientific assumption is that if anything has the speed of light by reference to any one meaning of space and time, then it has the same speed according to any other meaning of space and time.
This is a heavy blow at the classical scientific materialism, which presupposes a definite present instant at which all matter is simultaneously real. In the modern theory there is no such unique present instant. You can find a meaning for the notion of the simultaneous instant throughout all nature, but it will be a different meaning for different notions of temporality. There has been a tendency to give an extreme subjectivist interpretation to this new doctrine. I mean that the relativity of space and time has been construed as though it were dependent on the choice of the observer. It is perfectly legitimate to bring in the observer, if he facilitates explanations. But it is the observer’s body that we want, and not his mind. Even this body is only useful as an example of a very familiar form of apparatus. On the whole, it is better to concentrate attention on Michelson’s interferometer, and to leave Michelson’s body and Michelson’s mind out of the picture. The question is, why did the interferometer have black bands on its screen, and why did not these bands slightly shift as the instrument turned. The new relativity associates space and time with an intimacy not hitherto contemplated; and presupposes that their separation in concrete fact can be achieved by alternative modes of abstraction, yielding alternative meanings. But each mode of abstraction is directing attention to something which is in nature; and thereby is isolating it for the purpose of contemplation. The fact relevant to experiment, is the relevance of the interferometer to just one among the many alternative systems of these spatio-temporal relations which hold between natural entities.
What we must now ask of philosophy is to give us an interpretation of the status in nature of space and time, so that the possibility of alternative meanings is preserved. These lectures are not suited for the elaboration of details; but there is no difficulty in pointing out where to look for the origin of the discrimination between space and time. I am presupposing the organic theory of nature, which I have outlined as a basis for a thoroughgoing objectivism. An event is the grasping into unity of a pattern of aspects. The effectiveness of an event beyond itself arises from the aspects of itself which go to form the prehended unities of other events. Except for the systematic aspects of geometrical shape, this effectiveness is trivial, if the mirrored pattern attaches merely to the event as one whole. If the pattern endures throughout the successive parts of the event, and also exhibits itself in the whole, so that the event is the life history of the pattern, then in virtue of that enduring pattern the event gains in external effectiveness. For its own effectiveness is reënforced by the analogous aspects of all its successive parts. The event constitutes a patterned value with a permanence inherent throughout its own parts; and by reason of this inherent endurance the event is important for the modification of its environment.
It is in this endurance of pattern that time differentiates itself from space. The pattern is spatially _now_; and this temporal determination constitutes its relation to each partial event. For it is reproduced in this temporal succession of these spatial parts of its own life. I mean that this particular rule of temporal order allows the pattern to be reproduced in each temporal slice of its history. So to speak, each enduring object discovers in nature and requires from nature a principle discriminating space from time. Apart from the fact of an enduring pattern this principle might be there, but it would be latent and trivial. Thus the importance of space as against time, and of time as against space, has developed with the development of enduring organisms. Enduring objects are significant of a differentiation of space from time in respect to the patterns ingredient within events; and conversely the differentiation of space from time in the patterns ingredient within events expresses the patience of the community of events for enduring objects. There might be the community without objects, but there could not be the enduring objects without the community with its peculiar patience for them.
It is very necessary that this point should not be misunderstood. Endurance means that a pattern which is exhibited in the prehension of one event is also exhibited in the prehension of those of its parts which are discriminated by a certain rule. It is not true that any part of the whole event will yield the same pattern as does the whole. For example, consider the total bodily pattern exhibited in the life of a human body during one minute. One of the thumbs during the same minute is part of the whole bodily event. But the pattern of this part is the pattern of the thumb, and is not the pattern of the whole body. Thus endurance requires a definite rule for obtaining the parts. In the above example, we know at once what the rule is: You must take the life of the whole body during any portion of that same minute; for example, during a second or a tenth of a second. In other words, the meaning of endurance presupposes a meaning for the lapse of time within the spatio-temporal continuum.
The question now arises whether all enduring objects discover the same principle of differentiation of space from time; or even whether at different stages of its own life-history one object may not vary in its spatio-temporal discrimination. Up till a few years ago, everyone unhesitatingly assumed that there was only one such principle to be discovered. Accordingly, in dealing with one object, time would have exactly the same meaning in reference to endurance as in dealing with the endurance of another object. It would also follow then that spatial relations would have one unique meaning. But now it seems that the observed effectiveness of objects can only be explained by assuming that objects in a state of motion relatively to each other are utilising, for their endurance, meanings of space and of time which are not identical from one object to another. Every enduring object is to be conceived as at rest in its own proper space, and in motion throughout any space defined in a way which is not that inherent in its peculiar endurance. If two objects are mutually at rest, they are utilising the same meanings of space and of time for the purposes of expressing their endurance; if in relative motion, the spaces and times differ. It follows that, if we can conceive a body at one stage of its life history as in motion relatively to itself at another stage, then the body at these two stages is utilising diverse meanings of space, and correlatively diverse meanings of time.
In an organic philosophy of nature there is nothing to decide between the old hypothesis of the uniqueness of the time discrimination and the new hypothesis of its multiplicity. It is purely a matter for evidence drawn from observations.[5] Footnote 5: _Cf._ my _Principles of Natural Knowledge_, Sec. 52:3. In an earlier lecture, I said that an event had contemporaries. It is an interesting question whether, on the new hypothesis, such a statement can be made without the qualification of a reference to a definite space-time system. It is possible to do so, in the sense that in _some_ time-system or other the two events are simultaneous. In other time-systems the two contemporary events will not be simultaneous, though they may overlap. Analogously one event will precede another without qualification, if in _every_ time-system this precedence occurs. It is evident that if we start from a given event A, other events in general are divided into two sets, namely, those which without qualification are contemporaneous with A and those which either precede or succeed A. But there will be a set left over, namely, those events which bound the two sets. There we have a critical case. You will remember that we have a critical velocity to account for, namely the theoretical velocity of light _in vacuo_.[6] Also you will remember that the utilisation of different spatio-temporal systems means the relative motion of objects. When we analyse this critical relation of a special set of events to any given event A, we find the explanation of the critical velocity which we require. I am suppressing all details. It is evident that exactness of statement must be introduced by the introduction of points, and lines, and instants. Also that the origin of geometry requires discussion; for example, the measurement of lengths, the straightness of lines, and the flatness of planes, and perpendicularity. I have endeavoured to carry out these investigations in some earlier books, under the heading of the theory of extensive abstraction; but they are too technical for the present occasion.
Footnote 6: This is not the velocity of light in a gravitational field or in a medium of molecules and electrons. If there be no one definite meaning to the geometrical relations of distance, it is evident that the law of gravitation needs restatement. For the formula expressing that law is that two particles attract each other in proportion to the product of their masses and the inverse square of their distances. This enunciation tacitly assumes that there is one definite meaning to be ascribed to the instant at which the attraction is considered, and also one definite meaning to be ascribed to _distance_. But distance is a purely spatial notion, so that in the new doctrine, there are an indefinite number of such meanings according to the space-time system which you adopt. If the two particles are relatively at rest, then we might be content with the space-time systems which they are both utilising. Unfortunately this suggestion gives no hint as to procedure when they are not mutually at rest. It is, therefore, necessary to reformulate the law in a way which does not presuppose any particular space-time system. Einstein has done this. Naturally the result is more complicated. He introduced into mathematical physics certain methods of pure mathematics which render the formulae independent of the particular systems of measurement adopted. The new formula introduces various small effects which are absent in Newton’s law. But for the major effects Newton’s law and Einstein’s law agree. Now these extra effects of Einstein’s law serve to explain irregularities of the planet Mercury’s orbit which by Newton’s law were inexplicable. This is a strong confirmation of the new theory. Curiously enough, there is more than one alternative formula, based on the new theory of multiple space-time systems, having the property of embodying Newton’s law and in addition of explaining the peculiarities of Mercury’s motion. The only method of selection between them is to wait for experimental evidence respecting those effects on which the formulae differ. Nature is probably quite indifferent to the aesthetic preferences of mathematicians.
It only remains to add that Einstein would probably reject the theory of multiple space-time systems which I have been expounding to you. He would interpret his formula in terms of contortions in space-time which alter the invariance theory for measure properties, and of the proper times of each historical route. His mode of statement has the greater mathematical simplicity, and only allows of one law of gravitation, excluding the alternatives. But, for myself, I cannot reconcile it with the given facts of our experience as to simultaneity, and spatial arrangement. There are also other difficulties of a more abstract character. The theory of the relationship between events at which we have now arrived is based first upon the doctrine that the relatednesses of an event are all internal relations, so far as concerns that event, though not necessarily so far as concerns the other relata. For example, the eternal objects, thus involved, are externally related to events. This internal relatedness is the reason why an event can be found only just where it is and how it is,—that is to say, in just one definite set of relationships. For each relationship enters into the essence of the event; so that, apart from that relationship, the event would not be itself. This is what is meant by the very notion of internal relations. It has been usual, indeed universal, to hold that spatio-temporal relationships are external. This doctrine is what is here denied.
Text from Project Gutenberg, public domain in the United States.