The Quantum Theory

The theory of relativity has justly excited a great amount of public attention. But, for all its importance, it has not been the topic which has chiefly absorbed the recent interest of physicists. Without question that position is held by the quantum theory. The point of interest in this theory is that, according to it, some effects which appear essentially capable of gradual increase or gradual diminution are in reality to be increased or decreased only by certain definite jumps. It is as though you could walk at three miles per hour or at four miles per hour, but not at three and a half miles per hour.

The theory of relativity has rightly attracted a great deal of public attention. But despite its importance, it has not been the main focus of physicists’ recent interest. Without question, quantum theory holds that position. The interesting point about quantum theory is that some effects seem capable of increasing or decreasing gradually. According to the theory, however, these effects can actually increase or decrease only in definite jumps. It is as though you could walk at three miles per hour or four miles per hour, but not three and a half miles per hour.

The effects in question are concerned with the radiation of light from a molecule which has been excited by some collision. Light consists of waves of vibration in the electromagnetic field. After a complete wave has passed a given point everything at that point is restored to its original state and is ready for the next wave which follows on. Picture to yourselves the waves on the ocean, and reckon from crest to crest of successive waves. The number of waves which pass a given point in one second is called the frequency of that system of waves. A system of light-waves of definite frequency corresponds to a definite colour in the spectrum. Now a molecule, when excited, vibrates with a certain number of definite frequencies. In other words, there are a definite set of modes of vibration of the molecule, and each mode of vibration has one definite frequency. Each mode of vibration can stir up in the electromagnetic field waves of its own frequency. These waves carry away the energy of the vibration; so that finally (when such waves are in being) the molecule loses the energy of its excitement and the waves cease. Thus a molecule can radiate light of certain definite colours, that is to say, of certain definite frequencies.

The effects in question involve light radiated by a molecule that has been excited by a collision. Light consists of waves of vibration in the electromagnetic field. After a complete wave passes a given point, everything at that point returns to its original state. It is then ready for the next wave. Picture waves on the ocean, and measure from the crest of one wave to the crest of the next. The number of waves that pass a given point in one second is called the frequency of that wave system. A system of light waves with a definite frequency corresponds to a definite color in the spectrum. When a molecule is excited, it vibrates at a certain number of definite frequencies. In other words, the molecule has a definite set of ways in which it can vibrate. Each way of vibrating has one definite frequency. Each can produce waves of its own frequency in the electromagnetic field. These waves carry away the energy of the vibration. So, when such waves are present, the molecule eventually loses the energy of its excitement and the waves stop. Thus a molecule can radiate light of certain definite colors, or, in other words, of certain definite frequencies.

You would think that each mode of vibration could be excited to any intensity, so that the energy carried away by light of that frequency could be of any amount. But this is not the case. There appear to be certain minimum amounts of energy which cannot be subdivided. The case is analogous to that of a citizen of the United States who, in paying his debts in the currency of his country, cannot subdivide a cent so as to correspond to some minute subdivision of the goods obtained. The cent corresponds to the minimum quantity of the light energy, and the goods obtained correspond to the energy of the exciting cause. This exciting cause is either strong enough to procure the emission of one cent of energy, or fails to procure the emission of any energy whatsoever. In any case the molecule will only emit an integral number of cents of energy. There is a further peculiarity which we can illustrate by bringing an Englishman onto the scene. He pays his debts in English currency, and his smallest unit is a farthing which differs in value from the cent. The farthing is in fact about half a cent, to a very rough approximation. In the molecule, different modes of vibration have different frequencies. Compare each mode to a nation. One mode corresponds to the United States, and another mode corresponds to England. One mode can only radiate its energy in an integral number of cents, so that a cent of energy is the least it can pay out; whereas the other mode can only radiate its energy in an integral number of farthings, so that a farthing of energy is the least that it can pay out. Also a rule can be found to tell us the relative value of the cent of energy of one mode to the farthing of energy of another mode. The rule is childishly simple: Each smallest coin of energy has a value in strict proportion to the frequency belonging to that mode. By this rule, and comparing farthings with cents, the frequency of an American would be about twice that of an Englishman. In other words, the American would do about twice as many things in a second as an Englishman. I must leave you to judge whether this corresponds to the reputed characters of the two nations. Also I suggest that there are merits attaching to both ends of the solar spectrum. Sometimes you want red light and sometimes violet light.

You might think that each mode of vibration could be excited to any intensity. If so, the energy carried away by light of that frequency could be any amount. But that is not the case. There seem to be certain minimum amounts of energy that cannot be divided. Consider a citizen of the United States paying debts in the currency of his country. He cannot divide a cent to match some tiny fraction of the goods he receives. The cent corresponds to the smallest amount of light energy. The goods received correspond to the energy of the exciting cause. The exciting cause is either strong enough to produce an emission of one cent of energy, or it produces no emission of energy at all. In any case, the molecule will emit only a whole number of cents of energy. There is another peculiarity, which we can illustrate by bringing an Englishman into the picture. He pays his debts in English currency, and his smallest unit is a farthing. A farthing has a different value from a cent. In fact, a farthing is roughly half a cent. In a molecule, different modes of vibration have different frequencies. Compare each mode to a nation. One mode corresponds to the United States, and another to England. One mode can radiate energy only in a whole number of cents. A cent of energy is therefore the least it can pay out. The other mode can radiate energy only in a whole number of farthings. A farthing of energy is therefore the least it can pay out. There is also a rule for comparing the value of one mode's cent of energy with another mode's farthing of energy. The rule is childishly simple: The value of each smallest coin of energy is strictly proportional to the frequency of its mode. By this rule, and comparing farthings with cents, an American's frequency would be about twice an Englishman's. In other words, an American would do about twice as many things in a second as an Englishman. I must leave you to judge whether this matches the reputed characters of the two nations. I also suggest that there are merits to both ends of the solar spectrum. Sometimes you want red light and sometimes violet light.

There has been, I hope, no great difficulty in comprehending what the quantum theory asserts about molecules. The perplexity arises from the effort to fit the theory into the current scientific picture of what is going on in the molecule or atom.

I hope there has been no great difficulty in understanding what quantum theory says about molecules. The difficulty arises when we try to fit the theory into the current scientific picture of what happens inside a molecule or atom.

It has been the basis of the materialistic theory, that the happenings of nature are to be explained in terms of the locomotion of material. In accordance with this principle, the waves of light were explained in terms of the locomotion of a material ether, and the internal happenings of a molecule are now explained in terms of the locomotion of separate material parts. In respect to waves of light, the material ether has retreated to an indeterminate position in the background, and is rarely talked about. But the principle is unquestioned as regards its application to the atom. For example a neutral hydrogen atom is assumed to consist of at least two lumps of material; one lump is the nucleus consisting of a material called positive electricity, and the other is a single electron which is negative electricity. The nucleus shows signs of being complex, and of being subdivisible into smaller lumps, some of positive electricity and others electronic. The assumption is, that whatever vibration takes place in the atom is to be attributed to the vibratory locomotion of some bit of material, detachable from the remainder. The difficulty with the quantum theory is that, on this hypothesis, we have to picture the atom as providing a limited number of definite grooves, which are the sole tracks along which vibration can take place, whereas the classical scientific picture provides none of these grooves. The quantum theory wants trolley-cars with a limited number of routes, and the scientific picture provides horses galloping over prairies. The result is that the physical doctrine of the atom has got into a state which is strongly suggestive of the epicycles of astronomy before Copernicus.

Materialistic theory has been based on the idea that events in nature can be explained by the movement of matter. Following this principle, scientists explained light waves as the movement of a material ether. They now explain events inside a molecule as the movement of separate material parts. In the case of light waves, the material ether has receded into an uncertain place in the background. It is rarely discussed. But the principle remains unquestioned when applied to the atom. For example, a neutral hydrogen atom is assumed to contain at least two lumps of matter. One is the nucleus, made of a material called positive electricity. The other is a single electron, which is negative electricity. The nucleus shows signs of being complex and divisible into smaller lumps. Some are made of positive electricity, and others are electronic. The assumption is that any vibration in the atom comes from the movement of a piece of matter. That piece can be detached from the rest of the atom. The difficulty with quantum theory is that, on this assumption, we must picture the atom as having a limited number of fixed grooves. These grooves are the only tracks along which vibration can occur. Yet the classical scientific picture provides none of these grooves. Quantum theory calls for trolley-cars with a limited number of routes, but the scientific picture offers horses galloping over prairies. As a result, the physical theory of the atom is in a state strongly reminiscent of astronomy's epicycles before Copernicus.

On the organic theory of nature there are two sorts of vibrations which radically differ from each other. There is vibratory locomotion, and there is vibratory organic deformation; and the conditions for the two types of change are of a different character. In other words, there is vibratory locomotion of a given pattern as one whole, and there is vibratory change of pattern.

According to the organic theory of nature, there are two fundamentally different kinds of vibration. One is vibratory movement, and the other is vibratory organic deformation. The conditions for these two types of change are different. In other words, a given pattern can vibrate as it moves as a whole, or the pattern itself can change through vibration.

A complete organism in the organic theory is what corresponds to a bit of material on the materialistic theory. There will be a primary genus, comprising a number of species of organisms, such that each primary organism, belonging to a species of the primary genus, is not decomposable into subordinate organisms. I will call any organism of the primary genus a primate. There may be different species of primates.

In organic theory, a complete organism corresponds to a piece of material in materialistic theory. There will be a primary genus containing several species of organisms. Each organism in a species of the primary genus cannot be divided into smaller organisms. I will call any organism of the primary genus a primate. There may be different species of primates.

It must be kept in mind that we are dealing with the abstractions of physics. Accordingly, we are not thinking of what a primate is in itself, as a pattern arising from the prehension of the concrete aspects; nor are we thinking of what a primate is for its environment, in respect to its concrete aspects prehended therein. We are thinking of these various aspects merely in so far as their effects on patterns and on locomotion are expressible in spatio-temporal terms. Accordingly, in the language of physics, the aspects of a primate are merely its contributions to the electromagnetic field. This is in fact exactly what we know of electrons and protons. An electron for us is merely the pattern of its aspects in its environment, so far as those aspects are relevant to the electromagnetic field.

We must remember that we are dealing with the abstractions of physics. So we are not considering what a primate is in itself, as a pattern arising from its prehension of concrete aspects. Nor are we considering what a primate is for its environment, in terms of its concrete aspects as prehended by that environment. We are considering these various aspects only insofar as their effects on patterns and movement can be expressed in terms of space and time. So, in the language of physics, the aspects of a primate are simply its contributions to the electromagnetic field. This is exactly what we know of electrons and protons. For us, an electron is simply the pattern of its aspects in its environment, insofar as those aspects are relevant to the electromagnetic field.

Now in discussing the theory of relativity, we saw that the relative motion of two primates means simply that their organic patterns are utilising diverse space-time systems. If two primates do not continue either mutually at rest, or mutually in uniform relative motion, at least one of them is changing its intrinsic space-time system. The laws of motion express the conditions under which these changes of space-time systems are effected. The conditions for vibratory locomotion are founded upon these general laws of motion.

In discussing the theory of relativity, we saw what the relative motion of two primates means. It simply means that their organic patterns use different space-time systems. Two primates may not remain at rest relative to each other or continue moving at a constant speed relative to each other. If so, at least one of them is changing its own space-time system. The laws of motion describe the conditions under which these changes in space-time systems occur. The conditions for vibratory locomotion are based on these general laws of motion.

But it is possible that certain species of primates are apt to go to pieces under conditions which lead them to effect changes of space-time systems. Such species would only experience a long range of endurance, if they had succeeded in forming a favourable association among primates of different species, such that in this association the tendency to collapse is neutralised by the environment of the association. We can imagine the atomic nucleus as composed of a large number of primates of differing species, and perhaps with many primates of the same species, the whole association being such as to favour stability. An example of such an association is afforded by the association of a positive nucleus with negative electrons to obtain a neutral atom. The neutral atom is thereby shielded from any electric field which would otherwise produce changes in the space-time system of the atom.

But certain species of primates may tend to break apart under conditions that cause them to change space-time systems. Such species could endure for a long time only if they formed a favorable association with primates of different species. In such an association, the surrounding primates would neutralize the tendency to break apart. We can imagine the atomic nucleus as composed of many primates of different species, perhaps including many of the same species. The association as a whole would favor stability. One example of such an association is a positive nucleus combined with negative electrons to form a neutral atom. The neutral atom is thereby shielded from any electric field that would otherwise change its space-time system.

The requirements of physics now suggest an idea which is very consonant with the organic philosophical theory. I put it in the form of a question: Has our organic theory of endurance been tainted by the materialistic theory in so far as it assumes without question that endurance must mean undifferentiated sameness throughout the life-history concerned? Perhaps you noticed that (in a previous chapter) I used the word ‘reiteration’ as a synonym of ‘endurance.’ It obviously is not quite synonymous in its meaning; and now I want to suggest that reiteration where it differs from endurance is more nearly what the organic theory requires. The difference is very analogous to that between the Galileans and the Aristotelians: Aristotle said ‘rest’ where Galileo added ‘or uniform motion in a straight line.’ Thus in the organic theory, a pattern need not endure in undifferentiated sameness through time. The pattern may be essentially one of aesthetic contrasts requiring a lapse of time for its unfolding. A tune is an example of such a pattern. Thus the endurance of the pattern now means the reiteration of its succession of contrasts. This is obviously the most general notion of endurance on the organic theory, and ‘reiteration’ is perhaps the word which expresses it with most directness. But when we translate this notion into the abstractions of physics, it at once becomes the technical notion of ‘vibration.’ This vibration is not the vibratory locomotion: it is the vibration of organic deformation. There are certain indications in modern physics that for the rôle of corpuscular organisms at the base of the physical field, we require vibratory entities. Such corpuscles would be the corpuscles detected as expelled from the nuclei of atoms, which then dissolve into waves of light. We may conjecture that such a corpuscular body has no great stability of endurance, when in isolation. Accordingly, an unfavourable environment leading to rapid changes in its proper space-time system, that is to say, an environment jolting it into violent accelerations, causes the corpuscles to go to pieces and dissolve into light-waves of the same period of vibration.

Physics now suggests an idea that fits well with the organic philosophical theory. I will put it as a question: Has the materialistic theory influenced our organic theory of endurance? Has it led us to assume unquestioningly that endurance means remaining unchanged throughout the life-history in question? You may have noticed that (in a previous chapter) I used ‘reiteration’ as a synonym for ‘endurance.’ The two words obviously do not mean quite the same thing. I now want to suggest that the difference makes reiteration closer to what the organic theory requires. The difference is much like the one between the Galileans and the Aristotelians. Where Aristotle said ‘rest,’ Galileo added ‘or uniform motion in a straight line.’ Thus, in the organic theory, a pattern need not remain unchanged through time. The pattern may depend on aesthetic contrasts that take time to unfold. A tune is an example of such a pattern. The endurance of the pattern now means the repetition of its sequence of contrasts. This is obviously the most general idea of endurance in the organic theory. Perhaps ‘reiteration’ expresses it most directly. But when we translate this idea into the abstractions of physics, it immediately becomes the technical idea of ‘vibration.’ This vibration is not vibration as movement from place to place. It is the vibration of organic deformation. Certain indications in modern physics suggest that we need vibrating entities to serve as corpuscular organisms at the base of the physical field. These corpuscles would be those detected when expelled from atomic nuclei, which then dissolve into waves of light. We may conjecture that such a corpuscular body does not endure very stably in isolation. Accordingly, an unfavorable environment may cause rapid changes in its proper space-time system. Such an environment jolts the corpuscles into violent accelerations. As a result, the corpuscles break apart and dissolve into light waves with the same period of vibration.

A proton, and perhaps an electron, would be an association of such primates, superposed on each other, with their frequencies and spatial dimensions so arranged as to promote the stability of the complex organism, when jolted into accelerations of locomotion. The conditions for stability would give the associations of periods possible for protons. The expulsion of a primate would come from a jolt which leads the proton either to settle down into an alternative association, or to generate a new primate by the aid of the energy received.

A proton, and perhaps an electron, would be a combination of such primates layered on top of one another. Their frequencies and spatial dimensions would be arranged to keep the complex organism stable when jolts cause it to accelerate. The conditions for stability would determine which combinations of periods are possible for protons. A jolt would expel a primate, causing the proton either to settle into a different combination or to use the energy received to generate a new primate.

A primate must be associated with a definite frequency of vibratory organic deformation so that when it goes to pieces it dissolves into light waves of the same frequency, which then carry off all its average energy. It is quite easy (as a particular hypothesis) to imagine stationary vibrations of the electromagnetic field of definite frequency, and directed radially to and from a centre, which, in accordance with the accepted electromagnetic laws, would consist of a vibratory spherical nucleus satisfying one set of conditions and a vibratory external field satisfying another set of conditions. This is an example of vibratory organic deformation. Further [on this particular hypothesis], there are two ways of determining the subsidiary conditions so as to satisfy the ordinary requirements of mathematical physics. The total energy, according to one of these ways, would satisfy the quantum condition; so that it consists of an integral number of units or cents, which are such that the cent of energy of any primate is proportional to its frequency. I have not worked out the conditions for stability or for a stable association. I have mentioned the particular hypothesis by way of showing by example that the organic theory of nature affords possibilities for the reconsideration of ultimate physical laws, which are not open to the opposed materialistic theory.

A primate must be associated with a definite frequency of vibratory organic deformation. When the primate breaks apart, it dissolves into light waves of the same frequency. These waves then carry off all its average energy. As one particular hypothesis, it is quite easy to imagine stationary vibrations of the electromagnetic field. These vibrations have a definite frequency and are directed radially toward and away from a center. According to accepted electromagnetic laws, they would consist of a vibrating spherical nucleus and a vibrating external field. The nucleus and the external field would each satisfy a different set of conditions. This is an example of vibratory organic deformation. Further, under this particular hypothesis, there are two ways to determine the subsidiary conditions. Both would satisfy the ordinary requirements of mathematical physics. Under one of these ways, the total energy would satisfy the quantum condition. The energy would therefore consist of a whole number of units or cents. A cent of energy for any primate would be proportional to its frequency. I have not worked out the conditions for stability or for a stable association. I have mentioned this particular hypothesis as an example. It shows that the organic theory of nature offers possibilities for reconsidering ultimate physical laws. These possibilities are not available under the opposing materialistic theory.

In this particular hypothesis of vibratory primates, the Maxwellian equations are supposed to hold throughout all space, including the interior of a proton. They express the laws governing the vibratory production and absorption of energy. The whole process for each primate issues in a certain average energy characteristic of the primate, and proportional to its mass. In fact the energy is the mass. There are vibratory radial streams of energy, both without and within a primate. Within the primate, there are vibratory distributions of electric density. On the materialistic theory such density marks the presence of material: on the organic theory of vibration, it marks the vibratory production of energy. Such production is restricted to the interior of the primate.

In this particular hypothesis of vibratory primates, Maxwell’s equations are assumed to hold throughout all space, including inside a proton. They express the laws governing the vibratory production and absorption of energy. For each primate, the whole process results in a certain average energy. This energy is characteristic of the primate and proportional to its mass. In fact, the energy is the mass. Vibratory streams of energy radiate both outside and inside a primate. Inside the primate, electric density is distributed in vibratory patterns. In materialistic theory, such density marks the presence of material. In the organic theory of vibration, it marks the vibratory production of energy. This production occurs only inside the primate.

All science must start with some assumptions as to the ultimate analysis of the facts with which it deals. These assumptions are justified partly by their adherence to the types of occurrence of which we are directly conscious, and partly by their success in representing the observed facts with a certain generality, devoid of ad hoc suppositions. The general theory of the vibration of primates, which I have outlined, is merely given as an example of the sort of possibilities which the organic theory leaves open for physical science. The point is that it adds the possibility of organic deformation to that of mere locomotion. Light waves form one great example of organic deformation.

All science must begin with some assumptions about how the facts it deals with can ultimately be analyzed. These assumptions are justified partly by how well they match the kinds of events we are directly aware of. They are also justified partly by how successfully they represent observed facts in general terms, without ad hoc assumptions. The general theory of the vibration of primates that I have outlined is merely an example. It shows the kinds of possibilities the organic theory leaves open for physical science. The point is that the organic theory adds the possibility of organic deformation to that of mere movement. Light waves are one great example of organic deformation.

At any epoch the assumptions of a science are giving way, when they exhibit symptoms of the epicyclic state from which astronomy was rescued in the sixteenth century. Physical science is now exhibiting such symptoms. In order to reconsider its foundations, it must recur to a more concrete view of the character of real things, and must conceive its fundamental notions as abstractions derived from this direct intuition. It is in this way that it surveys the general possibilities of revision which are open to it.

At any time, a science's assumptions are breaking down when they show signs of an epicyclic state. Astronomy was rescued from such a state in the sixteenth century. Physical science is now showing those signs. To reconsider its foundations, physical science must return to a more concrete view of what real things are like. It must see its basic concepts as abstractions drawn from this direct intuition. In this way, physical science can survey the general possibilities for revising its foundations.

The discontinuities introduced by the quantum theory require revision of physical concepts in order to meet them. In particular, it has been pointed out that some theory of discontinuous existence is required. What is asked from such a theory, is that an orbit of an electron can be regarded as a series of detached positions, and not as a continuous line.

The discontinuities introduced by quantum theory require us to revise our physical concepts to account for them. In particular, some have pointed out that a theory of discontinuous existence is needed. Such a theory must allow an electron's orbit to be seen as a series of separate positions, not a continuous line.

The theory of a primate or a vibrating pattern, given above, together with the distinction between temporality and extensiveness in the previous chapter, yields exactly this result. It will be remembered that the continuity of the complex of events arises from the relationships of extensiveness; whereas the temporality arises from the realisation in a subject-event of a pattern which requires for its display that the whole of a duration be spatialised (i.e., arrested), as given by its aspects in the event. Thus realization proceeds viâ a succession of epochal durations; and the continuous transition, i.e., the organic deformation, is within the duration which is already given. The vibratory organic deformation is in fact the reiteration of the pattern. One complete period defines the duration required for the complete pattern. Thus the primate is realised atomically in a succession of durations, each duration to be measured from one maximum to another. Accordingly, so far as the primate as one enduring whole entity is to be taken account of, it is to be assigned to these durations successively. If it is considered as one thing, its orbit is to be diagrammatically exhibited by a series of detached dots. Thus the locomotion of the primate is discontinuous in space and time. If we go below the quanta of time which are the successive vibratory periods of the primate, we find a succession of vibratory electromagnetic fields, each stationary in the space-time of its own duration. Each of these fields exhibits a single complete period of the electromagnetic vibration which constitutes the primate. This vibration is not to be thought of as the becoming of reality; it is what the primate is in one of its discontinuous realisations. Also the successive durations in which the primate is realised are contiguous; it follows that the life history of the primate can be exhibited as being the continuous development of occurrences in the electromagnetic field. But these occurrences enter into realisation as whole atomic blocks, occupying definite periods of time.

The theory of a primate, or vibrating pattern, given above produces exactly this result. It does so together with the distinction between temporality and extensiveness made in the previous chapter. As we have seen, the continuity of the complex of events arises from relationships of extensiveness. Temporality, by contrast, arises from the realization of a pattern in a subject-event. To be displayed, the pattern requires the whole of a duration to be spatialized (i.e., held still). The duration is spatialized as it is given by its aspects in the event. Thus realization proceeds through a succession of epochal durations. The continuous transition, i.e., the organic deformation, occurs within the duration that is already given. The vibratory organic deformation is, in fact, the repetition of the pattern. One complete period defines the duration required for the complete pattern. Thus the primate is realized atomically in a succession of durations. Each duration is measured from one maximum to the next. Accordingly, insofar as the primate is treated as one enduring whole entity, it must be assigned successively to these durations. If the primate is considered as one thing, its path must be shown diagrammatically as a series of separate dots. Thus the primate's movement is discontinuous in space and time. The successive vibratory periods of the primate are quanta of time. If we go below these quanta, we find a succession of vibratory electromagnetic fields. Each field is stationary in the space-time of its own duration. Each field displays one complete period of the electromagnetic vibration that constitutes the primate. This vibration should not be thought of as reality coming into being. It is what the primate is in one of its discontinuous realizations. Also, the successive durations in which the primate is realized are contiguous. It follows that the primate's life history can be shown as the continuous development of occurrences in the electromagnetic field. But these occurrences enter into realization as whole atomic blocks, occupying definite periods of time.

There is no need to conceive that time is atomic in the sense that all patterns must be realised in the same successive durations. In the first place, even if the periods were the same in the case of two primates, the durations of realisation may not be the same. In other words, the two primates may be out of phase. Also if the periods are different, the atomism of any one duration of one primate is necessarily subdivided by the boundary moments of durations of the other primate.

We need not think of time as atomic in the sense that all patterns must be realized in the same successive durations. First, even if two primates have the same periods, their durations of realization may not be the same. In other words, the two primates may be out of phase. Also, if their periods differ, the boundary moments of one primate’s durations necessarily subdivide each atomic duration of the other primate.

The laws of the locomotion of primates express under what conditions any primate will change its space-time system.

The laws of primate motion describe the conditions under which any primate will change its space-time system.

It is unnecessary to pursue this conception further. The justification of the concept of vibratory existence must be purely experimental. The point illustrated by this example is that the cosmological outlook, which is here adopted, is perfectly consistent with the demands for discontinuity which have been urged from the side of physics. Also if this concept of temporalisation as a successive realisation of epochal durations be adopted, the difficulty of Zeno is evaded. The particular form, which has been given here to this concept, is purely for that purpose of illustration and must necessarily require recasting before it can be adapted to the results of experimental physics.

There is no need to pursue this idea further. The concept of vibratory existence can be justified only by experiment. This example shows that the cosmological outlook adopted here is fully consistent with the discontinuity that physicists have argued is necessary. Also, if we adopt this concept of temporalisation as the successive realization of epochal durations, we avoid Zeno's difficulty. The particular form given to this concept here serves only as an illustration. It will necessarily need to be revised before it can be adapted to the results of experimental physics.