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.

In the previous lectures of this course, we considered the conditions that led to the scientific movement. We also traced the progress of thought from the seventeenth to the nineteenth century. In the nineteenth century, the history of thought can be divided into three parts when viewed in relation to science. These are the contact between the romantic movement and science, the development of technology and physics in the early nineteenth century, and finally the theory of evolution together 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 dominant idea throughout those three centuries was that materialism provided an adequate basis for scientific concepts. This belief was practically unquestioned. When scientists needed waves, they supplied an ether to serve as a material that could carry them. To show the full extent of this assumption, I have outlined an alternative organic theory of nature. In the last lecture, I pointed out that developments in biology, the theory of evolution, the theory of energy, and molecular theories were rapidly undermining the adequacy of orthodox materialism. But no one drew that conclusion until the end of the century. 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 defining feature of our age is the growing complexity of our ideas about matter, space, time, and energy. The reassuring simplicity of the old accepted assumptions has vanished. Clearly, those assumptions will no longer do as Newton left them, or even as Clerk Maxwell left them. They must be reorganized. The new situation in today’s thought arises because scientific theory is moving ahead of common sense. The body of thought inherited by the eighteenth century was a triumph of organized common sense. It had gotten rid of medieval fantasies and Cartesian vortices. As a result, it gave full rein to its distrust of reason, inherited from the revolt of the Reformation period. It based itself on what any ordinary person could see with their own eyes or with a moderately powerful microscope. It measured the obvious things that could be measured and made generalizations about the obvious things that could be generalized. For example, it generalized from ordinary ideas of weight and mass. The eighteenth century began with the quiet confidence that nonsense had finally been put aside. Today, our thinking is at the opposite extreme. Heaven knows what apparent nonsense may be proved true tomorrow. We have recaptured something of the spirit of the early nineteenth century, but at a higher level of imagination.

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.

We are on a higher imaginative level not because we have better imaginations, but because we have better instruments. In science, the most important development of the last forty years has been the improvement of instrument design. This improvement is partly due to a few men of genius, such as Michelson and the German opticians. It is also due to advances in manufacturing technology, particularly in metallurgy. Designers now have materials with a variety of physical properties at their disposal. They can therefore count on getting the materials they want. They can also have those materials ground into the shapes they want, with very little variation from the desired shape. These instruments have raised thought to a new level. A new instrument serves the same purpose as travel abroad: it shows things in unusual combinations. The gain is more than a simple addition. It is a transformation. Progress in experimental ingenuity may also be due to the larger share of national talent now entering science. Whatever the cause, subtle and ingenious experiments have been abundant over the last generation. As a result, a great deal of information has been gathered about parts of nature far removed from ordinary human experience.

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.

Two famous experiments illustrate the claims I have made. Galileo devised one at the beginning of the scientific movement. Michelson carried out the other with his famous interferometer, first in 1881 and again in 1887 and 1905. Galileo dropped heavy objects from the top of the leaning tower of Pisa. He demonstrated that objects of different weights, if released at the same time, would reach the ground together. The experiment could have been performed at any time in the previous five thousand years. It required no more experimental skill or precision equipment than people had during that time. The ideas involved were simply weight and speed of travel, both familiar in everyday life. The family of King Minos of Crete might have been familiar with all these ideas. They might have dropped pebbles into the sea from high battlements rising above the shore. We cannot be too careful to recognize that science began by organizing ordinary experiences. This is why science fit so readily with the anti-rationalistic bias of the historical revolt. Science did not ask about ultimate meanings. It confined itself to investigating the connections that govern the sequence of obvious events.

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.

Michelson’s experiment could not have been conducted earlier than it was. It required both a general advance in technology and Michelson’s experimental genius. The experiment concerns the measurement of the earth’s motion through the ether. It assumes that light consists of waves of vibration that travel through the ether at a fixed speed in any direction. Of course, the earth is also moving through the ether, and Michelson’s apparatus is moving with the earth. At the center of the apparatus, a ray of light is split in two. One half-ray travels a set distance along the apparatus and is reflected back to the center by a mirror. The other half-ray travels the same distance across the apparatus, at right angles to the first ray. It too is reflected back to the center. The reunited rays are then reflected onto a screen in the apparatus. If precautions are taken, you will see interference bands. These are dark bands where the crests of one ray’s waves have filled the troughs of the other ray’s waves. This happens because the paths taken by the two half-rays to certain parts of the screen differ slightly in length. The earth’s motion will affect these differences, because what matters is the length of the paths through the ether. The apparatus moves with the earth, so this motion will affect the path of each half-ray differently. Imagine yourself moving in a railway carriage, first along the train and then across it. Mark out your paths on the railway track, which in this analogy corresponds to the ether. The earth moves very slowly compared with light. So, in the analogy, imagine the train almost at a standstill and yourself 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.

In the experiment, the earth’s motion would affect the positions of the interference bands on the screen. Also, if you turn the apparatus through a right angle, the effects on the two half-rays will be reversed. The positions of the interference bands would then shift. We can calculate the small shift that should result from the earth’s motion around the sun. We also have to add the effect of the sun’s motion through the ether. The instrument’s sensitivity can be tested. It can be proved that these shifts are large enough for the instrument to detect. But the point is that nothing was observed. The bands did not shift as the instrument was turned.

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 conclusion is either that the earth is always stationary in the ether, or that something is wrong with the basic principles used to interpret the experiment. Clearly, this experiment takes us far from the thoughts and games of the children of King Minos. Its ideas are remote from ordinary experience: the ether, waves in it, interference, the earth’s motion through the ether, and Michelson’s interferometer. But remote as these ideas are, they are simple and obvious compared with the accepted explanation for the experiment’s null result.

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 explanation is that the scientific ideas of space and time are too simple and must be revised. This conclusion directly challenges common sense. Earlier science had merely refined the ideas of ordinary people. Such a radical change in ideas would not have been adopted without support from many other observations. We need not discuss those observations here. Some form of relativity theory seems the simplest way to explain many facts. Otherwise, each fact would require an ad hoc explanation. The theory therefore does not depend only on the experiments that led to its development.

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.

The central point of the explanation is that every instrument necessarily records the same definite speed of light relative to itself. This includes Michelson’s apparatus as used in the experiment. I mean that an interferometer in a comet and one on Earth would necessarily measure the same speed of light relative to themselves. This is an obvious paradox, since light moves at a definite speed through the ether. Earth and the comet move through the ether at different speeds. So we might expect them to have different speeds relative to rays of light. For example, consider two cars on a road, traveling at ten and twenty miles an hour, respectively. Another car passes them at fifty miles an hour. The faster car will pass one car at a relative speed of forty miles an hour. It will pass the other at a relative speed of thirty miles an hour. Now suppose we replaced the faster car with a ray of light. The claim is that the light’s speed along the road would be exactly the same as its speed relative to either car it overtakes. The speed of light is immensely high, about three hundred thousand kilometers per second. Our ideas of space and time must allow for this particular speed to have this peculiar character. It follows that all our ideas about relative speed must be revised. But those ideas follow directly from our usual ideas of space and time. So we return to the conclusion that something has been overlooked in the usual explanations of what we mean by space and 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.

We usually assume that space has one definite meaning and time has one definite meaning. So, whatever meaning we give spatial relations for an instrument on Earth, we must give them the same meaning for an instrument on the comet. We must also give them the same meaning for an instrument at rest in the ether. The theory of relativity denies this assumption. As far as space is concerned, the obvious facts of relative motion make this easy to accept. But even here, the change in meaning must go further than common sense would allow. Relativity makes the same demand for time. So the relative dates of events and the time between them must be calculated differently for each instrument. The results will differ for the instrument on Earth, the instrument on the comet, and the instrument at rest in the ether. This is harder to believe. We need not examine the question beyond one conclusion. Space and time each have different meanings under different conditions, such as those on Earth and on the comet. Accordingly, velocity has different meanings for the two bodies. Thus the modern scientific assumption is this: if anything has the speed of light according to any one meaning of space and time, 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.

This is a serious blow to classical scientific materialism. That view assumes one definite present instant when all matter is real at the same time. In modern theory, there is no such single present instant. You can give meaning to the idea of an instant that is simultaneous throughout all nature. But its meaning will differ depending on how you understand time.

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.

There has been a tendency to interpret this new doctrine in an extremely subjectivist way. By this I mean that people have understood the relativity of space and time as depending on the observer’s choice. It is perfectly legitimate to bring in the observer if that helps explain things. But it is the observer’s body we need, not his mind. Even his body is useful only as an example of a very familiar kind of apparatus. On the whole, it is better to focus on Michelson’s interferometer and leave Michelson’s body and mind out of the picture. The question is why the interferometer had black bands on its screen. And why did these bands not shift slightly as the instrument turned? The new relativity connects space and time more closely than anyone had previously imagined. It also assumes that space and time can be separated in concrete reality by different methods of abstraction. These methods yield different meanings. But each method of abstraction draws attention to something in nature and isolates it for consideration. What matters for the experiment is the interferometer’s relation to just one of the many alternative systems of spatio-temporal relations 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.

We must now ask philosophy to explain the place of space and time in nature, while preserving the possibility of alternative meanings. These lectures are not suited to working out the details. But it is not difficult to point out where to look for the origin of the distinction between space and time. I am assuming 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.

An event brings a pattern of aspects together into a unity. An event affects what lies beyond it through those of its aspects that help form the prehended unities of other events. If the mirrored pattern belongs only to the event as a whole, this effect is trivial. The exception is the systematic aspects of geometrical shape. But suppose the pattern endures throughout the event’s successive parts and also appears in the whole. The event is then the life history of the pattern. Because the pattern endures, the event has a greater effect beyond itself. The event’s own effect is reinforced by the corresponding aspects of all its successive parts. The event forms a patterned value that persists throughout its own parts. Because this pattern endures, the event plays an important part in changing 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.

Time differs from space in the way a pattern endures. The pattern exists in space now, and this position in time defines its relation to each partial event. For the pattern is reproduced as these spatial parts of its own life succeed one another in time. I mean that this particular rule of temporal order allows the pattern to be reproduced in each moment of its history. In a sense, each enduring object finds in nature, and requires from nature, a principle that distinguishes space from time. Without an enduring pattern, this principle might still be there, but it would be latent and trivial. Thus, space and time have become important in contrast to each other as enduring organisms have developed. Enduring objects signify a distinction between space and time in the patterns that form part of events. Conversely, this distinction in those patterns expresses the capacity of the community of events to sustain enduring objects. The community might exist without objects. But enduring objects could not exist without the community and its special capacity to sustain 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.

It is very important not to misunderstand this point. Endurance means that a pattern appears in the prehension of an event. The same pattern also appears in the prehension of those parts of the event selected by a certain rule. Not every part of the whole event will yield the same pattern as the whole. For example, consider the overall bodily pattern shown in the life of a human body during one minute. One of the thumbs during that same minute is part of the whole bodily event. But the pattern of this part is the pattern of the thumb, not of the whole body. So endurance requires a definite rule for choosing the parts. In this example, we know the rule at once: Take the life of the whole body during any portion of that same minute. You might take it during a second or a tenth of a second, for example. In other words, the meaning of endurance presupposes a meaning for the passage 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.

The question now arises whether all enduring objects distinguish space from time according to the same principle. Could one object even distinguish space and time differently at different stages of its own history? Until a few years ago, everyone assumed without hesitation that there was only one such principle. Time would therefore have exactly the same meaning for the endurance of one object as for another. It would also follow that spatial relations had one unique meaning. But now it seems that the observed effects of objects can only be explained by another assumption. Objects moving relative to each other use different meanings of space and time for their endurance. Each enduring object should be understood as at rest in its own space. It is in motion through any space defined differently from the space inherent in its particular way of enduring. If two objects are at rest relative to each other, they use the same meanings of space and time to express their endurance. If they are in relative motion, their spaces and times differ. Suppose, then, that we can conceive of a body at one stage of its history as moving relative to itself at another stage. It follows that the body at these two stages uses different meanings of space and, correspondingly, different 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

In an organic philosophy of nature, nothing favors the old hypothesis of a single way to distinguish time over the new hypothesis of multiple ways. The choice depends entirely on evidence from observation.⁵

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.

In an earlier lecture, I said that an event had contemporaries. Under the new hypothesis, can we say this without specifying a particular space-time system? That is an interesting question. We can say it in the sense that the two events are simultaneous in some time-system or other. In other time-systems, the two contemporary events will not be simultaneous, though they may overlap. Similarly, one event precedes another without qualification if it precedes the other in every time-system. Starting from a given event A, we can generally divide other events into two sets. One set contains events that are contemporaneous with A without qualification. The other contains events that either precede or follow A. But a set of events remains. These events form the boundary between the two sets. Here we have a critical case. You will remember that we have a critical velocity to explain, namely the theoretical velocity of light in a vacuum.⁶ You will also remember that using different space-time systems involves the relative motion of objects. When we analyze the critical relation between this special set of events and any given event A, we find the explanation we need for the critical velocity. I am leaving out all the details. Clearly, we must introduce points, lines, and instants to make the statement exact. We must also discuss the origin of geometry. This includes, for example, the measurement of lengths, the straightness of lines, the flatness of planes, and perpendicularity. I have tried to carry out these investigations in earlier books, under the heading of the theory of extensive abstraction. But they are too technical for the present occasion.

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.

If the geometrical relations of distance have no single definite meaning, the law of gravitation clearly needs to be restated. The law says that two particles attract each other in proportion to the product of their masses. Their attraction is also inversely proportional to the square of the distance between them. This statement quietly assumes that the instant at which the attraction is considered has one definite meaning. It also assumes that distance has one definite meaning. But distance is a purely spatial idea. So, under the new theory, distance has an unlimited number of meanings, depending on the space-time system you adopt. If the two particles are at rest relative to each other, we might accept the space-time systems both particles use. Unfortunately, this suggestion gives no hint about what to do when the particles are not at rest relative to each other. The law must therefore be restated without assuming any particular space-time system. Einstein has done this. Naturally, the result is more complicated. He introduced methods from pure mathematics into mathematical physics. These methods make the formulas independent of the particular systems of measurement adopted. The new formula introduces various small effects that are absent from Newton’s law. But Newton’s law and Einstein’s law agree on the major effects. The extra effects in Einstein’s law explain irregularities in the planet Mercury’s orbit that Newton’s law could not explain. This strongly confirms the new theory. Curiously, more than one alternative formula is based on the new theory of multiple space-time systems. Each of these formulas includes Newton’s law and also explains the peculiarities of Mercury’s motion. The only way to choose between the formulas is to wait for experimental evidence about the effects on which they 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.

I need only add that Einstein would probably reject the theory of multiple space-time systems I have been explaining. He would interpret his formula in terms of distortions in space-time that alter the invariance theory for measurement properties. He would also interpret it in terms of the proper times of each historical route. His way of stating the theory is mathematically simpler. It also allows only one law of gravitation, ruling out the alternatives. But I cannot reconcile his theory with what our experience tells us about simultaneity and spatial arrangement. There are also other, more abstract difficulties.

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.

The theory of the relationship between events that we have now reached begins with a doctrine about their relations. All the relations of an event are internal to that event, though not necessarily to the other things related to it. For example, the eternal objects involved in these relations are externally related to events. Because of this internal relatedness, an event can be found only exactly where and as it is. In other words, it can be found in only one definite set of relationships. Each relationship forms part of the event’s essence, so that without it, the event would not be itself. This is what the very idea of internal relations means. It has been usual, indeed universal, to hold that relationships in space and time are external. This is the doctrine denied here.

The conception of internal relatedness involves the analysis of the event into two factors, one the underlying substantial activity of individualisation, and the other the complex of aspects—that is to say, the complex of relatednesses as entering into the essence of the given event—which are unified by this individualised activity. In other words, the concept of internal relations requires the concept of substance as the activity synthesising the relationships into its emergent character. The event is what it is, by reason of the unification in itself of a multiplicity of relationships. The general scheme of these mutual relationships is an abstraction which presupposes each event as an independent entity, which it is not, and asks what remnant of these formative relationships is then left in the guise of external relationships. The scheme of relationships as thus impartially expressed becomes the scheme of a complex of events variously related as wholes to parts and as joint parts within some one whole. Even here, the internal relationship forces itself on our attention; for the part evidently is constitutive of the whole. Also an isolated event which has lost its status in any complex of events is equally excluded by the very nature of an event. So the whole is evidently constitutive of the part. Thus the internal character of the relationship really shows through this impartial scheme of abstract external relations.

The idea of internal relatedness involves analyzing an event into two factors. One is the underlying substantial activity that makes the event an individual. The other is the complex of aspects unified by this activity. These aspects are the relationships that enter into the essence of the event. In other words, the concept of internal relations requires the concept of substance. Substance is the activity that combines relationships into the character that emerges. An event is what it is because it unifies many relationships within itself. The general scheme of these mutual relationships is an abstraction. It assumes that each event is an independent entity, though no event is independent. It then asks what remains of these formative relationships in the form of external relationships. When the scheme is expressed impartially in this way, it becomes a scheme of a complex of events. These events are related in various ways, as wholes to parts and as parts together within one whole. Even here, internal relationships force themselves on our attention. The part is clearly part of what makes the whole what it is. Also, an isolated event that has lost its place in any complex of events is impossible by its very nature. So the whole is clearly part of what makes the part what it is. Thus the internal character of the relationship shows through this impartial scheme of abstract external relations.

But this exhibition of the actual universe as extensive and divisible has left out the distinction between space and time. It has in fact left out the process of realisation, which is the adjustment of the synthetic activities by virtue of which the various events become their realised selves. This adjustment is thus the adjustment of the underlying active substances whereby these substances exhibit themselves as the individualisations or modes of Spinoza’s one substance. This adjustment is what introduces temporal process.

But this account of the actual universe as extended and divisible leaves out the distinction between space and time. In fact, it leaves out the process of realisation. This process is the adjustment of the synthetic activities through which events become their realised selves. This adjustment is therefore an adjustment of the underlying active substances. Through it, these substances show themselves as individualisations or modes of Spinoza’s one substance. This adjustment introduces temporal process.

Thus, in some sense, time, in its character of the adjustment of the process of synthetic realisation, extends beyond the spatio-temporal continuum of nature.⁷ There is no necessity that temporal process, in this sense, should be constituted by one single series of linear succession. Accordingly, in order to satisfy the present demands of scientific hypothesis, we introduce the metaphysical hypothesis that this is not the case. We do assume (basing ourselves upon direct observation), however, that temporal process of realisation can be analysed into a group of linear serial processes. Each of these linear series is a space-time system. In support of this assumption of definite serial processes, we appeal: (1) to the immediate presentation through the senses of an extended universe beyond ourselves and simultaneous with ourselves, (2) to the intellectual apprehension of a meaning to the question which asks what is now immediately happening in regions beyond the cognisance of our senses, (3) to the analysis of what is involved in the endurance of emergent objects. This endurance of objects involves the display of a pattern as now realised. This display is the display of a pattern as inherent in an event, but also as exhibiting a temporal slice of nature as lending aspects to eternal objects (or, equally, of eternal objects as lending aspects to events). The pattern is spatialised in a whole duration for the benefit of the event into whose essence the pattern enters. The event is part of the duration, i.e., is part of what is exhibited in the aspects inherent in itself; and conversely the duration is the whole of nature simultaneous with the event, in that sense of simultaneity. Thus an event in realising itself displays a pattern, and this pattern requires a definite duration determined by a definite meaning of simultaneity. Each such meaning of simultaneity relates the pattern as thus displayed to one definite space-time system. The actuality of the space-time systems is constituted by the realisation of pattern; but it is inherent in the general scheme of events as constituting its patience for the temporal process of realisation.

Thus, in some sense, time extends beyond the space-time continuum of nature. It does so as the adjustment of the process of synthetic realisation.⁷ Temporal process, in this sense, need not consist of a single series of events in linear succession. Accordingly, to meet the present demands of scientific hypothesis, we introduce the metaphysical hypothesis that it does not. We do assume, however, based on direct observation, that the temporal process of realisation can be analysed into a group of linear serial processes. Each of these linear series is a space-time system. We support this assumption of definite serial processes by appealing to three things: (1) our senses immediately present an extended universe beyond ourselves and simultaneous with ourselves, (2) we can intellectually grasp the meaning of the question of what is now immediately happening in regions beyond the reach of our senses, and (3) an analysis of what is involved in the endurance of emergent objects. This endurance of objects involves the display of a pattern as now realised. The pattern is displayed as inherent in an event. But it also shows a temporal slice of nature as lending aspects to eternal objects. Equally, it shows eternal objects as lending aspects to events. The pattern is spatialised throughout a whole duration for the benefit of the event whose essence includes it. The event is part of the duration, i.e., it is part of what is shown in the aspects inherent in itself. Conversely, the duration is the whole of nature simultaneous with the event, in that sense of simultaneity. Thus, an event displays a pattern as it realises itself. This pattern requires a definite duration, determined by a definite meaning of simultaneity. Each such meaning of simultaneity relates the pattern as displayed to one definite space-time system. The actuality of space-time systems is constituted by the realisation of pattern. But this actuality is inherent in the general scheme of events as constituting its patience for the temporal process of realisation.

Notice that the pattern requires a duration involving a definite lapse of time, and not merely an instantaneous moment. Such a moment is more abstract, in that it merely denotes a certain relation of contiguity between the concrete events. Thus a duration is spatialised; and by ‘spatialised’ is meant that the duration is the field for the realised pattern constituting the character of the event. A duration, as the field of the pattern realised in the actualisation of one of its contained events, is an epoch, i.e., an arrest. Endurance is the repetition of the pattern in successive events. Thus endurance requires a succession of durations, each exhibiting the pattern. In this account ‘time’ has been separated from ‘extension’ and from the ‘divisibility’ which arises from the character of spatio-temporal extension’. Accordingly we must not proceed to conceive time as another form of extensiveness. Time is sheer succession of epochal durations. But the entities which succeed each other in this account are durations. The duration is that which is required for the realisation of a pattern in the given event. Thus the divisibility and extensiveness is within the given duration. The epochal duration is not realised via its successive divisible parts, but is given with its parts. In this way, the objection which Zeno might make to the joint validity of two passages from Kant’s Critique of Pure Reason is met by abandoning the earlier of the two passages. I refer to passages from the section ‘Of the Axioms of Intuition’; the earlier from the subsection on Extensive Quantity, and the latter from the subsection on Intensive Quantity where considerations respecting quantity in general, extensive and intensive, are summed up. The earlier passage runs thus:⁸

Notice that the pattern requires a duration involving a definite passage of time, not merely an instant. An instant is more abstract because it only denotes a certain relation of contact between concrete events. A duration is therefore spatialised. By ‘spatialised’, I mean that the duration is the field in which the realised pattern forms the character of the event. A duration is an epoch, i.e., an arrest, when it is the field of the pattern realised in the actualisation of an event it contains. Endurance is the repetition of the pattern in successive events. Thus endurance requires a succession of durations, each exhibiting the pattern. In this account, ‘time’ has been separated from ‘extension’ and from the ‘divisibility’ arising from the character of spatio-temporal extension’. We must therefore not go on to think of time as another form of extensiveness. Time is simply the succession of epochal durations. But the entities that succeed one another in this account are durations. A duration is what is required for the realisation of a pattern in the given event. Thus the divisibility and extensiveness are within the given duration. The epochal duration is not realised via its successive divisible parts, but is given with its parts. In this way, we meet an objection that Zeno might make to the joint validity of two passages from Kant’s Critique of Pure Reason. We do so by abandoning the earlier passage. I refer to passages from the section ‘Of the Axioms of Intuition’. The earlier passage is from the subsection on Extensive Quantity. The later one is from the subsection on Intensive Quantity. There, considerations about quantity in general, both extensive and intensive, are summed up. The earlier passage reads as follows:⁸

“I call an extensive quantity that in which the representation of the whole is rendered possible by the representation of its parts, and therefore necessarily preceded by it.⁹ I cannot represent to myself any line, however small it may be, without drawing it in thought, that is, without producing all its parts one after the other, starting from a given point, and thus, first of all, drawing its intuition. The same applies to every, even the smallest portion of time. I can only think in it the successive progress from one moment to another, thus producing in the end, by all the portions of time, and their addition, a definite quantity of time.”

“I call a quantity extensive when representing the whole is possible through representing its parts, and must therefore be preceded by it.⁹ I cannot imagine a line, however small, without drawing it in my mind. That means producing all its parts one after another, starting from a given point. In this way, I first form an intuition of the line. The same applies to every portion of time, even the smallest. I can think of a portion of time only as a progression from one moment to the next. By adding all these portions together, I arrive at a definite quantity of time.”

The second passage runs thus:

The second passage reads as follows:

“This peculiar property of quantities that no part of them is the smallest possible part (no part indivisible) is called continuity. Time and space are quanta continua, because there is no part of them that is not enclosed between limits (points and moments), no part that is not itself again a space or a time. Space consists of spaces only, time of times. Points and moments are only limits, mere places of limitation, and as places presupposing always those intuitions which they are meant to limit or to determine. Mere places or parts that might be given before space or time, could never be compounded into space or time.”

“This distinctive property of quantities is called continuity. It means that no part is the smallest possible part (no part is indivisible). Time and space are continuous quantities, because every part of them lies between limits (points and moments). Every part is itself a space or a time. Space consists only of spaces, and time only of times. Points and moments are only limits, mere places that mark limits. As places, they always presuppose the intuitions they are meant to limit or define. Mere places or parts that could be given before space or time could never be combined to form space or time.”

I am in complete agreement with the second extract if ‘time and space’ is the extensive continuum; but it is inconsistent with its predecessor. For Zeno would object that a vicious infinite regress is involved. Every part of time involves some smaller part of itself, and so on. Also this series regresses backwards ultimately to nothing; since the initial moment is without duration and merely marks the relation of contiguity to an earlier time. Thus time is impossible, if the two extracts are both adhered to. I accept the later, and reject the earlier, passage. Realisation is the becoming of time in the field of extension. Extension is the complex of events, quâ their potentialities. In realisation the potentiality becomes actuality. But the potential pattern requires a duration; and the duration must be exhibited as an epochal whole, by the realisation of the pattern. Thus time is the succession of elements in themselves divisible and contiguous. A duration, in becoming temporal, thereby incurs realisation in respect to some enduring object. Temporalisation is realisation. Temporalisation is not another continuous process. It is an atomic succession. Thus time is atomic (i.e., epochal), though what is temporalised is divisible. This doctrine follows from the doctrine of events, and of the nature of enduring objects. In the next chapter we must consider its relevance to the quantum theory of recent science.

I completely agree with the second extract if ‘time and space’ means the extensive continuum. But the second extract is inconsistent with the first. Zeno would object that the two extracts involve a vicious infinite regress. Every part of time contains a smaller part of itself, and so on. This series ultimately goes backward to nothing. The initial moment has no duration and merely marks the relation of contiguity to an earlier time. So time is impossible if we accept both extracts. I accept the later passage and reject the earlier one. Realisation is the becoming of time in the field of extension. Extension is the complex of events, quâ their potentialities. In realisation, potentiality becomes actuality. But the potential pattern requires a duration. The realisation of the pattern must also present the duration as an epochal whole. Thus time is the succession of elements that are themselves divisible and contiguous. As a duration becomes temporal, it is thereby realised in relation to some enduring object. Temporalisation is realisation. Temporalisation is not another continuous process. It is an atomic succession. Thus time is atomic (i.e., epochal), though what is temporalised is divisible. This doctrine follows from the doctrine of events and the nature of enduring objects. In the next chapter we must consider its relevance to the quantum theory of recent science.

It is to be noted that this doctrine of the epochal character of time does not depend on the modern doctrine of relativity, and holds equally—and indeed, more simply—if this doctrine be abandoned. It does depend on the analysis of the intrinsic character of an event, considered as the most concrete finite entity.

The doctrine that time has an epochal character does not depend on the modern doctrine of relativity. It holds equally well, and indeed more simply, if relativity is abandoned. The doctrine of time’s epochal character does depend on an analysis of the intrinsic character of an event, considered as the most concrete finite entity.

In reviewing this argument, note first that the second quotation from Kant, on which it is based, does not depend on any peculiar Kantian doctrine. The latter of the two is in agreement with Plato as against Aristotle.¹⁰ In the second place, the argument assumes that Zeno understated his argument. He should have urged it against the current notion of time in itself, and not against motion, which involves relations between time and space. For, what becomes has duration. But no duration can become until a smaller duration (part of the former) has antecedently come into being [Kant’s earlier statement]. The same argument applies to this smaller duration, and so on. Also the infinite regress of these durations converges to nothing—and even on the Aristotelian view there is no first moment. Accordingly time would be an irrational notion. Thirdly, in the epochal theory Zeno’s difficulty is met by conceiving temporalisation as the realisation of a complete organism. This organism is an event holding in its essence its spatio-temporal relationships (both within itself, and beyond itself) throughout the spatio-temporal continuum.

In reviewing this argument, note first that it rests on the second quotation from Kant. That quotation does not depend on any distinctive Kantian doctrine. The second quotation agrees with Plato rather than Aristotle.¹⁰ Second, the argument assumes that Zeno did not make the full case he could have made. He should have argued against the current notion of time itself, not against motion. Motion involves relations between time and space. For whatever comes into being has duration. But no duration can come into being until a smaller duration, part of the first, has already come into being [Kant’s earlier statement]. The same argument applies to this smaller duration, and so on. This infinite regress of durations converges to nothing. Even on the Aristotelian view, there is no first moment. Time would therefore be an irrational notion. Third, the epochal theory meets Zeno’s difficulty by conceiving temporalisation as the realisation of a complete organism. This organism is an event. Its essence includes its spatio-temporal relationships, both within itself and beyond itself, throughout the spatio-temporal continuum.