The Philosophy of the Act
Essay 30 Fragments on Relativity
A. CLASSICAL AND RELATIVE MEASUREMENT
All scientific objects are assumed to be in motion. This implies that if we isolate any one object in its relations to those about it at an assumed instant, it would be impossible to find at the next instant any group of objects which have maintained the same relations to this object which they occupied at the preceding instant.
However, motion with which experimental science deals must be regarded as taking place in a field of objects which do maintain the same relations to one another, i.e., motion with which science deals implies rest; otherwise stated, motion cannot be measured except with reference to points which, so far as this motion is concerned, are fixed. For experimental science points can be fixed only with reference to objects occupying points, and motion is measured with reference to objects continuing to occupy the same points while the motion is going on.
The actual field of objects within which motion takes place for experimental science is that of the distance perception of vision. While actual or implied contact experiences provide the reality which distance experience implies, distances that can be measured are always in the form of visually determined space.
The measurement of motion, therefore, involves a field of objects whose motions with reference to one another can be ignored. Such a field is found in vision, within which no changes of position appear within the minimum visible, and whose period falls within that of visual discrimination, something like an eighth of a second.
Within this field a distance measured between points determined by objects at rest may be subdivided by indirect proc-
(550) -esses beyond the limits of vision, but the whole measurable distance lies between points which must be minima visibilia.
Any measurement of velocity involves time as well as space, that is, we must know the relative dates at which the body leaves a point and at which it arrives at another point. If this measurement is to be accurate, the dates in perception of the objects that determine these points must be identical with those of the time of departure and the time of arrival. As long as the size of the objects measured and the rate of motion lie within the range of vision, this is the case. Where this is not the case, e.g., when we are measuring the velocity of light and are dealing with the bodies and the changes which are the conditions of vision, these dates are not identical.
The date of all visual objects in a field of vision is that of the incidence of the wave on the retina of the eye, or on the photographic plate of a camera. We may correct this date if we know the position of the object and that of the velocity of light, as we do in the case of the vision of stars; but, if we have to determine experimentally an unknown velocity of such an order, the determination must be undertaken with reference to objects occupying points in a visual space, and the points of departure and arrival will have the dates of the incidence of the wave of light upon the retina or the photographic plate, while the occupation of these points by the moving object will depend upon its velocity; and, if the size and velocity of the object excludes it from the field of vision, there will be no means of dating it as it leaves or as it arrives.
There would seem, therefore, to be an experimental error that attaches to all experimental determination of velocities of a high order. This error is, however, a function of the velocity of light, for the difference between the dates of the terminal objects and of the moving object depends upon the time that it takes light to reach the retina or the photographic plate. Could, then, the velocity of the object be affected by a coefficient containing some expression of this velocity of light which would correct this error?
(551) In the measurement of the velocity of light, experimentally, the procedure is of the following general type. The light to and from a measured distant object passes through the aperture in a revolving wheel. By increasing the velocity of the wheel it is possible to shut out the light wave. The explanation of this is found in the length of time consumed in the passage of the wave, and a calculation of the velocity of the revolution of the wheel enables us to determine the time which the wave takes in reaching the wheel. The waves that leave the distant source are a composite of the action of many vibrations of particles at different positions and are moving with reference to one another, but all lying within what we call a point of visual space, i.e., within a minimum visible, from which the distance is measured to the wheel. Thus by making the distance between the source of light and the wheel great enough and the velocity of the wheel great enough, it is possible to obtain visual effects which reveal the velocity of light, although this velocity itself falls far beyond the field of visual discrimination. The interferometer enables us to enter the minimum visible of the source light and, through the interference of waves of light, to recognize the difference of distances of the sources of light which lie beyond the range of visual discrimination. In these cases we are determining by indirect methods distances which lie beyond the range of visual discrimination but between objects that are assumed to be at rest at points in a visual space. We are still assuming that these objects are or can be at these points, indirectly determined, at the same moment, that is, simultaneously with the other objects at rest in this space, and all the visual effects that can take place in this space must conform to this assumption, otherwise points would become lines and lines surfaces.
The determining factor in the situation is the succession of events. If a body is at rest in a certain spatial situation, the event which succeeds is one in which the body is in the same situation with reference to all other bodies that are at rest in that situation. If it is in motion, the succeeding event is one in
(552) which these relations have shifted. If one were outside the earth watching the Michelson-Morley experiment, the points determined by objects resting on the earth would be succeeded by those objects in different relative positions to the other planetary bodies, and the points would become lines. The question as to what events will succeed is answered by the position of the retina or the photographic plate with reference to the situation. And what holds for objects at rest will also hold pari passu for objects in motion, i.e., the positions that succeed will vary according to the position in which lies the object of reference, whether it is the retina or the photographic plate. In the visual space of the surface of the earth, which includes the object of reference, the relative positions of the vibrating electrons which determine the light wave will be such as will allow points to remain points and lines lines, that is, they will be such that the light wave from each mirror will have the same distance to travel.
Against this position stands the classical doctrine which assumes that the process of the transmission of light, which is itself the condition of visual spaces, is one in which the succession of events is fixed independently of any object of reference. This comes back largely to the conception which we entertain of the space of the stagnant ether, which is supposed to have this character. It is easy to see that there are two implications here. One is that the space determined by the stellar co-ordinates is that into which ultimately the findings in all other spaces should be translated. Here are found the ultimate Points determined by their occupation by bodies at rest, the ultimate lines actually or conceivably traversed by bodies between these or other points determined with reference to these points. The points, lines, surfaces, and volumes of other spaces are only apparently such. It is confessedly or by implication assumed that such points can be derived from the reference of all points of observation. But, while for the observation of the astronomical observatory such co-ordinates can be fixed with sufficient definiteness to secure uniformity of results, there is no stellar body
(553) that is at rest at any point, and there is, therefore, no structure of points with reference to which such a space can be presented, even by the supposition of a body at rest, alpha, which could be made the organizing center, for there is no way of locating alpha. For the purposes of visual observation the fixed star does not move relatively to other fixed stars, but refinement of reference to the observations of long periods of time has elicited their actual movements, and the spectroscope reveals them indirectly as in present movement-and our astrophysics demands that we take account of this movement. What we actually have, therefore, is a space of astronomical observation, fixed by the co-ordinates of stars which for that observation do not move with reference to one another, with the recognition that for the purposes of the study of the movement of these stars we are in the same position as that in which we find ourselves in translating our daily Ptolemaic perception into the recognized space of the Copernican hypothesis. There is no absolute space, only an indefinite number of spaces of different co-ordinates, the structure of which can be translated into one another, and the question is shifted to the constants which make such translation possible.
The other implication of the classical doctrine is that of the stagnant ether. Here we have a body at rest, and its different parts seem to serve the purpose of determining an absolute space, or at least the conception of one, even if we find ourselves before the hopeless task of distinguishing different parts of this ether so as to determine the different points for the construction of the absolute space it occupies. However, just as the earth reveals itself as occupying the stellar space in the Foucault experiment, so the passage of a wave of light ought to reveal its occupation of the space of the stagnant ether in the Michelson-Morley experiment-and the experiment has failed to exhibit this evidence of the space of stagnant ether.
We still assume that a train traveling along the line of the earth's orbit covers a greater distance in a given time in stellar space than a train traveling at right angles to this train and
(554) with equal tellurian velocity; and, if we had apparatus which could detect differences in the velocities of these trains as parts of the earth, it would exhibit the one train as traveling faster than the other. Such an experiment would be of the same order as that of Foucault. That is, the reality of the different succession of events in another space, which is determined by this particular succession of events, would reveal itself in the earth space by an addition of velocities through an appropriate apparatus. If we state this in terms of the different succession of events, it implies that there is a space-time within which the train is moving such that the position of the train at any one moment will be succeeded by a position of the train which will be different from that which succeeds the first position of the train in the space-time of the earth. The failure of the Michelson-Morley experiment to exhibit evidence of the movement of light in a space-time independent of the bodies that move through it seems to indicate that, if we were able so to place ourselves in the process of the transmission of light that we could be at rest there while objects moved by us with the velocity of light, there would be no one succession of events which would be the same in every space, but that there would be in each space-time a succession which answers to the structure of that space-time, i.e., the space-time of the earth, in which the distance traveled between the two sets of mirrors of the Michelson-Morley experiment would be the same, and the space-time outside the earth, in which the distance traveled between the two sets would be different, owing to the earth moving with the one wave. Another way of expressing this would be the recognition of a uniform velocity of light in every space-time.
If we assume that the velocity of light remains the same in all space-times while the events that succeed one another in two space-times differ, it would follow that this difference between the events must exhibit itself in different spatial and temporal values when we undertake to transform that which is taking place from one space-time to another. If the velocity of light remains the same on the earth and in stellar space, and yet the
(555) distance traveled on the earth between the sets of mirrors remains the same, while in stellar space the distance traveled is different, then from the standpoint of the earth the corresponding distance must be shorter and the time longer if we would transform them from one system to the other.
The determining factor in this difference in the succession of events is the velocity with which one system moves with reference to the other. This velocity is not one that is determined by an outside observer who regards both, but one which is conceived of as recognized by each. If we assume an outside observer, he would be in another system which must be assumed to be in motion with reference to the other two, and the same problem would arise with reference to the comparative velocities of all three systems. To say that one system is moving with reference to another is to say that an event-every event by implication lying in all systems-is succeeded in one system by a different event from that by which it is succeeded in the other. When the objects within the systems lie within the range of vision, the velocities can be calculated, and with opposite directions the velocity is the same in both systems, e.g. , in the case of the landscape moving by the passenger in the train while the train moves by the observer at a station. To determine velocities, it is necessary to determine simultaneities between the moving objects at points which are occupied by objects at rest. This takes place in vision, in which, as we have seen, all objects at the points seen have the identical date of the incidence of the light wave at the retina or the photographic plate. Those objects which retain the same relative positions are at rest, while other objects are in motion. We can correct these dates by the velocity of light, but it is important to recognize that the corrected positions at which the objects are placed by calculation are determined with reference to positions visually given, that is, they belong to the space-time of the object of reference.
It is, perhaps, not amiss to call attention to the obvious fact that the reference is not solely to the retina or photographic plate but to these and their fields as mutually determining each
(556) other. It is true that the passenger in the moving train may now see the landscape rushing by him, and again at rest while his train rushes through it. In the latter case the organized structure of the landscape, especially at considerable distances, enables him to place himself with reference to this and to correct the repugnant impressions in terms of the moving train. It is also not amiss to refer again to the fact that our visual objects always exist in terms of the contact values which they would have if we carried out the reactions which as distant objects they suggest. This inevitable correction of vision by contact finds its recognition in theories of relativity in the reference to the rigid measuring rod, but one must not overlook the fact that the dimensions even of a rigid measuring rod belong to a visual, or more generally to a distance, system. The rigidity of the rod insures its retaining its dimensions within this system; it does not offer dimensions independent of this distance system, out of which such a system might be constructed. To any group of objects that retain the same positions with reference to one another an observer can actually or in imagination place himself in the relation of simultaneity. This is attained, as we have seen, in the attitude of vision, in which all objects have the identical date of the incidence of the light wave upon the retina. If this is accomplished, as in the case of the passenger in the moving train, the events that succeed are different from what they would have been if he had not taken this attitude. As the order of succession of events is different, the time systems of the two situations may be said to be different. Difference of time systems here does not signify different rates of passage of events but the succession of different events. This simultaneity is an expression of the fact of distance experience. It is visual in human experience because of the actual, or, if one prefers, accidental, development in the human animal of a highly refined and accurate apparatus of visual distance experience. The congenitally blind individual does not lack the experience of simultaneity. Objects exist for him as simultaneous with himself, but none of the experiences of sound, temperature, or contact of
(557) waves of air offers the definiteness and refinement of dimensions of simultaneous objects which belong to the world of normal vision.
If we undertake to determine velocities in another system from within a given system, this can only be done by obtaining simultaneities of events in the other system with these in the given system. For the purposes of this determination the events of the other system must become members of this system, unless one can, as in the moving train, actually shift from the system of the moving landscape to that of the moving train. In that case one is not determining the velocity of one system by means of simultaneities of objects in the other system with those in one's own system. One has passed from one system to the other. Assume, however, that within the train the passenger is undertaking to estimate the velocity of the train moving through the landscape by means of a calculation of the distances measured within the train that are coincident with stretches of the landscape. He identifies an object without that is coincident with the edge of a window and an object that is coincident with the edge of another window. He has measured the distance between these two edges and assumes that the outer distance is identical with the inner distance. If now he notes the time at which the first object has been coincident with the farther window edge, and the time that the second object becomes coincident with the same edge, he has while remaining within his own system measured the time it has taken the train to cover that distance in the other system, if the further assumption that the time systems are the same be allowed. If we accept the fact of vision that all seen objects are at the moment of vision simultaneous, his calculation within this visual world will be correct. The moment, however, that we take into account the time that elapses in the passage of light, a minute error is introduced. His identification of the outer distance as coincident with the distance between the two window edges has been made while the train is in motion. He moves to meet the light wave that comes from one window and away from that which comes
(558) from the other. If the velocity of the train is uniform, the advance in the advent of one wave will be equal to the lag in the advent of the other, if he was situated midway between the two window edges. He estimates the velocity of the train, however, by the time that elapses between the advent of waves both of which come from outer objects that are coincident with the same window edge, toward which the landscape is advancing. The advent of the light wave at his eye will in each case be shorter than that which would have been the case if he had established himself in the other system, midway between the two outer objects. If, to avoid a further complication, we assume that coincidence is registered by an electrical contact that lights electric bulbs within and without, the man within the train will calculate a greater velocity of the train in the other system than he would have calculated if he had been actually located in that other system outside the train. In making his transformation, he will have to assume that times are longer without, i.e., in the system that seems to him to be moving, than within. Also if he notes the point in the landscape at which he is when the light reaches him from the first coincidence, when he is midway between the two measured points, it will be closer to that point than the corresponding point at the center of the two measured positions outside the train which agreed with the measured positions within the train, for he has been moving toward this position of coincidence while the light wave has been coming to him. If he had been outside the train, this would not have been the case. For him within the train, then, the distance outside the train will be shorter than the corresponding distance within the train, by the distance he will have traveled while the light wave was reaching him. This shortening of distance and lengthening of time will depend upon the velocity of the train.
There is no way of determining a space of bodies which are at rest, except by the relative position of these bodies and other positions calculated from these and regarded as the positions of possible bodies. This involves distance perception, and the im-
(559) -plication of distance perception is that the bodies perceived exist where they are at the moment of perception. The immediate perception places them where they are perceived. This is subject to correction, as in the case of an object seen in a mirror, but this correction does not displace the bodies in perception. It is a further judgment that corrects the perception. The space of this consentient set (to use the language of the relativists) of bodies which are at rest is the space of experimental science, and all of the points so determined and objects occupying them have the same date-the date of the perception. All measurements of experimental science however refined must be made in this space. For this science the date of perception is replaced by the moment of incidence of light waves upon the retina or the photographic plate. All objects at rest in that space have this date, that is, are simultaneous.
If we retain this simultaneity of perception, and do not go behind it to take account of the velocity of light, none of the paradoxes of relativity arise. The estimates of distances and times remain the same in determining the velocity either of the train or of the landscape, as long as we abide by the simultaneity of perception.
When we take account of the velocity of light, the dates of all objects about us depend upon their distances from us, though we may have sufficient reason for assuming that they have remained where they were perceived. This dislocation we have just noticed in the case of the object outside the car in determining its distance from the observer within the car. The spatial structure determined by the relative position of objects at rest, however, remains that of the perceptual field. However refined the measurements are by which the position.- of objects are determined, they still lie inside this space of experimental science, and its units are but subdivisions of this space. So long as we remain inside this space, no complications are introduced; but, when we take into account the space of another consentient set that is moving (i.e., a group of objects that retain the same relative position to one another, and would therefore be
(560) at rest for a retina or a photographic plate, but do not retain the same positions with reference to this first consentient set), their motions with reference to the first consentient set at once affect their assumed positions with reference to the first consentient set, if we take into account the velocity of light. Within the first consentient set this is not the case, for we assume that, though some time has passed in the passage of light, the body at rest in that system is still at the point at which it was when the light wave left it, and the moving body, as long as it is regarded as within that system, can be accurately located by our knowledge of the velocity of light, provided we may accept its velocity in that system as determined experimentally, though we have seen this determination is subject to an error if we are considering an object whose dimensions and velocity lie beyond the discrimination of vision, for, the velocity being unknown and the body being indiscernible, we cannot tell when it is at any point in the space of this consentient set. The same error appears in determining the positions and velocities of bodies in another consentient set that is moving with reference to the first consentient set. For instance, what are the motions and positions of planetary bodies in the solar system, as determined by their positions and motions as given to the observer on the earth? If we take into account the velocity of light, the planetary body was not at the position it occupied when the light wave left it; and, as we do not know its velocity but are attempting to determine it, the accepted velocity of light does not enable us to place it. The error will vary with the velocity of the whole consentient set with reference to the earth. There are, however, certain conclusions which we may draw from the situation. Assume that A and B arc two objects in the second system, or consentient set, which is being observed from the first, and that the line connecting them is in the direction of the motion of the second system away from the first. B is farther from the observer than is A. In the vision of the observer they are simultaneous. B has the same date as A. At the date of A, however, the light wave from B that arrives simultaneously
(561) with that from A actually had left B earlier; or, otherwise stated, the wave that leaves B simultaneously with the wave from A will arrive at the retina of the observer later than that from A, as B is farther from the observer than is A. As the wave that reaches the eye of the observer from B simultaneously with the wave from A has always left B earlier than the corresponding wave from A, and as they are both with their system moving away from the observer's system, the position represented by the light wave from B will be closer to A than it would have been if simultaneous waves from A and B had reached the retina of the observer. That is, distances in the second system in the direction of the motion of the second system away from the first will register themselves either on the retina or on a photographic plate in the first system as shorter than they would be measured in the second system. Furthermore, the interval between A and B, as they move by a point in the first system, is the same interval as that of the passage of the point in the first system by A and B in the second system viewed or photographed from the second system, but the time of passage measured on the time co-ordinate of the first system represents the passage over a shorter distance, while the same passage measured on the time co-ordinate on the second system is a passage over a longer distance. If the identity of the passage of these two systems by each other implies that the velocity of the passage is the same whether one system is regarded as passing by the other, or vice versa, then the time interval in the first system must be longer than the corresponding time interval in the second. That is, while corresponding spaces will be shorter, times will be longer in the system which is regarded as in motion by the other system and these differences will increase with the velocity of the system.
The crux of the difficulty, as the relativists assert, lies in the difference in simultaneities that are involved in the relation of
(562) the simultaneous objects to different systems. Simultaneity refers to the maintenance of the same relative position of objects to one another during any duration however short. For a retina or a photographic plate within that group of objects, these objects will be at rest, or, in the language of Whitehead, they will be cogredient, if the duration is not shorter than that implied in visual discrimination. In the perceptual world, and that is the world of experimental science, simultaneity and rest are synonymous. If the velocity of light were not finite, we could also speak of objects in motion as being simultaneous with other objects at rest at the moment at which the moving object passes through a certain point. Objects at rest remain simultaneous even under the condition of the finite velocity of light, for, upon the supposition of rest, they have not moved during the passage of the light wave. Taking into account the time period of the light wave, a moving object is not where it is seen at the moment at which it is seen, nor, assuming that we do not know its velocity, can we calculate its position. If there are other objects that maintain the same relative position to it and one another, it will be simultaneous with them for a retina or photographic plate in that system, but simultaneity there will evidently have a different significance in that system from that which it will have in the other, and the consequences of different spatial and temporal measurements of the same interval in the two systems, which have already been noted, will result.
The crucial importance of the velocity of light arises from the fact that in the perceptual field of experimental science the distant object that is at rest, or is simultaneous with other objects and the observer, is a visual object. Other distance perceptions than that of vision carry the same implication but do not allow of the exact determination which vision permits. The space of experimental science implies distant objects that are at rest otherwise that space could not be differentiated for the conduct either of the man of science or of the man in the street, and all that exists or takes place in the space of any one perceptual situation will have the dimensions which belong to that
(563) differentiation. If we take into account high velocities that are comparable with that of light, or minute objects that cannot be located in this visual space, or both of these, dimensions will be subject to the error which has been developed above, and the statement of this error will evidently contain some expression of the velocity of light.
Recurring now to the Michelson-Morley experiment, we can say on the basis of this analysis that, while there is no contradiction in the appearance of optical effects which evidence the velocity of light coming from positions that may be regarded as occupied by an object at rest (since these would not run counter to the assumption of the system of objects that are simultaneous or at rest), optical effects which would reveal the fact that a light wave which left an object at rest and moved toward another object which belongs to the same system (that is, is at rest with reference to it) had reached that object in another position, would imply that spatial positions determined by objects at rest are not so determined, i.e., these optical effects would be in contradiction with the space within which they occur. This is just what would be the case if the interferometer revealed the fact that the path of a light wave from one mirror to the other is longer than the measured distance between these mirrors. This cannot be the case in the space of this system of simultaneous objects.
There is a fundamental difference between the Foucault experiment and the Michelson-Morley experiment. Whatever explanation we may give of the revolution of the axis of the pendulum beat, the perception of it does not necessarily imply an extra-terrestrial standpoint, a stellar landscape. However absurd it may be to assume that the revolution of enormously distant stellar bodies is the cause of centrifugal motion on the earth, the assumption introduces no confusion into our consentient set.
Suppose that the Michelson-Morley experiment had shown
(564) that the light wave that traveled from the central source to the mirror traveling with the earth covered a different distance from that which traveled from the same source to the mirror at right angles with this, but at an equal measured distance. There could have been no Ptolemaic statement of this, that is, there could have been no statement made of it in terms of our terrestrial perception, that within which, however we may interpret it, all the immediate findings of experimental science lie.
In the illustration given above, the revolution of the earth is represented in perception by the revolution of the heavens; and, if we are Einsteinian relativists, what is ascribed to one from one point of view will be ascribed to the other from the other standpoint. If the interferometer had revealed the evidence in ourown space-time of this different distance, there would have been nothing in our space-time which could have answered to it. It would have been a brutal irruption of the space-time of ether into perception. There would have been no one to one correspondence such as subsists in the relative movements of two perceptual consentient sets. It would have been without precedent. For, while we can find a revolution of the sun with the heavens that corresponds to a revolution of the earth in the two consentient sets in the two space-times, it would have been impossible to assume that the ether of the revolving heavens revolved with it, since the ether of physical science is stagnant, and such a movement of the ether in the opposite direction to the movement of the earth would have been necessary to find the correspondent to the sought-for Michelson-Morley effect if it had been found.
The undertaking of physical science to state, within the field of distance perception, the process which makes distance perception possible seems to set up a space-time that is independent of distance perception, while it utilizes the space-time of distance perception for the undertaking. This undertaking encounters no serious difficulties so long as the dimensions of its hypothetical scientific objects and their motions can be stated in terms of the space-time within which the tests of the hy-
(565) -potheses must be made. The distance space-time of experimental science is visual, but we can subdivide this visual continuum not only beyond the minimum visible but beyond the dimensions at which an object could subtend a light wave, i.e., beyond the point at which even in imagination it could be a visual object, because these physical particles can still be presented to the scientific imagination as having the contact value of resistance, i.e., in terms of mass or energy, and we can obtain indirect experimental evidence of these values. By means of the location of these particles we can construct a space which endures a subdivision of visual space even beyond the limits of conceivable vision, and it is only by the relative location of objects at positions that a space can be constructed at all.
When we pass from a geocentric to a heliocentric space, or to a space of stellar co-ordinates, we still assume that experimental results obtained in a geocentric space can be used to test hypotheses built on stellar co-ordinates, although the spatial and, therefore, the temporal elements in the geocentric space-time are not identical with the corresponding elements in the spacetime of stellar co-ordinates, i.e., a point in the one is a line in the other, and the answering temporal unit, by which is measured duration from point to point, will vary. Still, as long as there is a strict one to one correspondence between dimensions in the one space-time and in the other, the experimental results in the one will hold for testing hypotheses built on the other. Now such a one to one correspondence obtains as long as simultaneities in the one are simultaneities in the other, e.g., the conjunction of two stars for the terrestrial observer means the position of the two bodies at the same moment on the same line connecting them with the telescope, in the space of stellar co-ordinates.
As we have already seen, the conception of an indefinitely extended ether that is stagnant, or at least cannot be conceived of as belonging to a system that moves, say, relatively to that of the fixed stars, allows of no such correspondence between its space-time and that of other space-times. And yet, while such a stagnant ether would occupy its own space, it does not deter-
(566) -mine that space as a system of spatial elements, for ether, since the deliquescence of the vortex theory of atoms, cannot be regarded as made up of physical particles, and can therefore determine no positions. It occupies a dog-in-the-manger position. It pre-empts a space but does not permit of its being used as the fixed space which it fills. Any positions determined in this space can only be relative to the system of objects, determining these positions, and any other system of objects moving with reference to this system will determine another space. Of course, such a fixed space of ether is no space at all, for space is a system of distances between objects in some sort of a system. In other words, an absolute space is a contradiction in terms. It is a denial of the fact that is involved in the very nature of space that there is or may be a set of objects so organized with reference to one another that they are simultaneous with one another, that is, are at rest, but which are or may be moving with reference to another system. Admit this, and one admits at once that the spatial relations in one system will be different from what they will be in their relation to the other system. In a terrestrial system a clock tower remains where it is from one hour to the next. In the solar system it is 70,000 miles away from where it was when the clock struck an hour ago. An absolute space is a denial of temporal perspective, and by the same mark there is no such thing as space; there are space-times.
If the looked-for effect had appeared in the Michelson-Morley experiment, it would have appeared in terrestrial space-time, i.e., the actual interference or reinforcement of light waves in certain definitions of spatiotemporal extension would have been an integral part of the terrestrial space-time and, as such, could have been translated into the space-time of the stellar coordinates, and in this translation their spatial and temporal dimensions would have been different. Such an assumption runs counter to the presuppositions of ether and its space. The looked-for Michelson-Morley effect would be one that appears with the fixed spatiotemporal dimensions which belong to the absolute space-time of ether and would be the same in every
(567) space-time. This may be expressed in two ways. Either we may say that the theory of ether implies that in every space-time it is stagnant, while what is at rest in one space-time must be moving in another space-time, in our actual experience; or we may say that as it is in a visual space that we determine the simultaneities of objects in other space-times with those in our own, and that in the other space-times simultaneities with our own are determined also in a visual space, and since we are able to translate successfully from one to the other notwithstanding the different spatial and temporal configurations in different space-times, the velocity of light which is essential to determining the positions of objects must remain the same, though the relative dimension of the spatial and temporal units for measuring this will vary from one space-time to another. That is, the space covered and the time elapsed in the passage of a light wave from an object in another system from ours to our retinas will have a uniform ratio to each other, though the spatial units of measurement in the other system will be shorter than they would have been if that system were at rest, i.e., were a part of our own system, and the temporal units will be longer.
As has been already stated, if we could maintain the attitude of visual perception of the simultaneity of all objects of vision, all having the date of the incidence of the light waves upon the eye or the photographic plate, there would be no difference in the spatial and temporal units in different systems in the case of any perceptual velocities.
B. MEASUREMENT AND ACTION
Measurement of duration takes place through motion. It is of either the spatial or the temporal aspects of the duration. The fundamental character of measurement is the repetition of an act which is functionally equal in its durational content in the different repetitions. The most elemental illustration of this functional equality is found in the rhythmical motions owing to our bilateral symmetry. We get ahead by moving first one side of the body and then the other. To reach a distant goal, the
(568) motion of one side must equal the other. The equal pulls on each side of our organism, owing to the equal stimuli which the two sides of the environment exercise upon us through vision, is another instance. It is the equality of these pulls which assists us in preserving our balance in an erect position. But beside such rythmical(sic) functionally equal steps there is implied in measurement a durational extension toward the goal that extends over all the steps and to which the steps as such are functionally equal, i.e., they run through in the rhythmic process (in which each step is functionally equal to the one before it and the one succeeding it-and thus all steps are individually equal to every one) the extension which appears in experience through the location of the persistent object with its content of an inside. The fundamental relation of betweenness exists in experience through the establishment of this distant location and the consequent organization of the environment with reference to this goal. There is, then, a functional equality of the steps that reach the goal and the pre-existent distance given in the distance experience. While the steps ultimately exhaust the distance experience, the number of steps required is not given, nor is there in this relation any functional limit set, i.e., there is in the situation what answers to indefinite divisibility. Assuming a number series established through the relation of betweenness, and different series of steps functionally equal to the same distance experience of a given goal, there is no limiting number involved in the distance extension, or consequently any ultimate step. Whatever limit is set up must be found in the other characters of the steps besides those of so-called extension, i.e., the point is not inherent in the extensional relations. Such a step is the unit of measure of the distance extension, and the functional equality of different series of steps is given with the possibility of an indefinite number of units of measure.
The collapsing of the act through the identity of content in the interior of the distant object and in that of the physical organism abstracts the spatial content of extension and sets up a space of the moment, to which are referred the steps which
(569) measure it. This leaves the temporal phase of extension as a content which is not involved immediately in this measurement of the spatial extension. While the temporal phase is abstracted from in this process of spatial measurement, it is always present in the process, and, when recognized, the relation between the two becomes that of velocity when it can be stated in units. And this involves a temporal extension which can be correspondingly measured.
This temporal content cannot be collapsed as can the spatial content. It arises in experience out of change over against the object which persists. The functional equality of the steps does not carry with it a functional equality in the same sense as it does in the case of space. As the preservation of the physical organism moving in a straight path toward a goal calls for uniform velocity in the taking of the opposite steps, there is a functional equality in the times of these steps, but the continuum of duration which is broken up into equal units by the process and the units themselves are not there for comparison as are the spatial steps and the spatial whole. There is the nicest sort of adjustments to the different temporal intervals involved in meeting and avoiding objects. But as durations pass in their very nature it is impossible to hold on to them for comparison and determination. What takes place is that we come back to the experience of uniform velocity that we maintain in bilateral movement made up of functionally equal steps and break up the distance covered under assumed unaccelerated velocity into equal parts to which we assign equal temporal elements, while our instruments of precision in time measurement are fashioned to produce functionally equal steps, such as the swing of the pendulum or the vibration of an electron; but we can never recapture the duration passed to compare its extent with the steps taken, or the steps to compare their extents with one another. Time measurements depend upon an assumption of uniform velocities that can never be made to be actually congruent with one another. However, this seeming advantage of the spatial content over that of time loses its foundation with
(570) the abandonment of an absolute space and with the recognition that what has appeared as an absolute space is only that of the collapsed act belonging only to the space of the duration in question. The act does not take place within a given space, but the space of measurement is an abstraction from the act in so far as in perception it is collapsible. Distance experience, notably that of vision, extends this space of the momentary act indefinitely, until we assume it to take in the whole of the universe at the moment. As this space is relative to the organism and its act, spatial elements, points, lines, surfaces, and volumes preserve their character only for this space. The same elements from the standpoint of another organism, or the same organism at a later moment, may be fundamentally different. These spaces thus pass with durational experience, and the same problem of obtaining congruence between the elements of the space of one duration with those of another arises which appeared in the case of time.
The possibility of reaching a congruence of the space of one duration with that of another appears in the tendencies to different acts with reference to the same distant object, e.g., reaching and manipulating in different fashions the same object. These acts would involve different durations and different velocities. As we approach a distant object, the object of one moment has passed away before we find ourselves over against the object of the next moment, and a congruence of these objects is impossible. The identity of the object as a collapsed act in the whole process does not in itself give congruence because the inner content of effort or resistance may be variously defined spatially; but, if the action, such as dividing the object, either takes place under our hands while we are regarding the object or takes place imaginatively, the two processes of locating the thing before us and of dividing it intersect each other. This amounts to the familiar experience of operating either actually or imaginatively upon something which persists, while the operations stretch into the future and imply different moments which still are presented in their results as existing in the nature
(571) of that which belongs to the now. The now is that of the present duration passing on in a period of the so-called specious present at a certain rate. There arises in particular a certain terrain of objects, which Whitehead calls cogredient with the percipient event, and which have the same date with the organism as a physical object. If we undertake to state this rate, it would be stated in terms of the so-called passage of time and in terms of our watches or the movement of the sun. Within this field other things are happening at different rates. Within the limits of two events, such as the position of the watch hands at nine or the position of the sun at a certain point in the heavens, and the later position of the watch hands at twelve or the corresponding position of the sun, from the point of view of a so-called fixed environment nothing happens. This would represent the immediate nature within which the individual is placed at rest so far as the location of his body is concerned. The events in this system (we will call it a time system) would be the mere tickings; of the watch, or the passage of the sun. Within this static environment let us suppose that another individual paces off or marks off with a yardstick a portion of the environment; then there will be with reference to the individual at rest this portion simply elapsing at a slow rate of the ticks of the watch, or the motion of the sun. There will be from the standpoint of the other individual a series of relatively rapid motions or events affecting this portion but lying within the same limits of the original and final positions of the hands on the watch or of the sun at nine and at twelve. If the individual at rest watches and follows, with his vision and tendencies to move, the action of an engineer, there will be within his spatial environment divisions introduced by the engineer's pegs. This individual at rest will then have two distinct attitudes, one that of 'inert passage of nature from minute to minute, in which the nature of one minute will have passed on and will not be there to be congruent with any discerned elements of the next minute. That is, if we assume the almost impossible individual entirely at rest in his relation to the passing of nature and of himself, no order could
(573) be introduced into space which could have a persistent character. To attain order in space, or an ordered space, there must be coincidence between the event of a mere passing nature at rest and a series of more numerous events lying within the same limits. That is, we must have a coincidence of a stretch which is a single event passing on and a series of events which is a 1, 2, 3, . . . . within the same extension. Within a single duration, say, a specious present, there is an unbroken event at rest but elapsing, and a rapid series of events that coincide with it. If two time systems represent two different series of events, different in number, filling out the same extension, then order in space is dependent upon the intersection of two time systems in the same extension.
There are, then, two ways of conceiving of timeless space. In the one case, one assumes the state of rest which represents the space of the spread that is cogredient with the percipient event or organism, and in this case the moments intersecting the event-particle will fall into three classes, standing for the three dimensions of empirical space. There being no fourth class, the event-particle is uniquely determined. The other case is that in which no state of rest is assumed, and, in consequence, no direction of motion can be determined, no order can be introduced into the space, and no determined simultaneities exist anywhere. As the spatial character of extension, which is spatiotemporal, answers to simultaneity as distinguished from the passage of duration, the absence of any determined simultaneity would answer to a negative account of a curved space or an n-dimensional space or both. This would answer to nothing in nature, but seems to be the implication of a space in which more than one line can he drawn through a point parallel to a line, or one in which the angles of a triangle are not equal to two right angles, as in the geometries of Lobatschevsky, Bolyai, and Gauss, and the bizarre geometries of more recent speculations. It seems to be also the background of the doctrine of Einstein, who assumes a situation in which an individual introduces his own co-ordinates of space-time into such an indetermined exten
(574) sion. It seems also to be the implication of Einstein's use of the tensor in his mathematical treatment of the problems of physics. So far as my feeble understanding of the tensor goes, it seems to indicate certain physical characters or factors of motion which may belong to a point irrespective of any determined relation to any spatial order. The linear elements of motions answering to these characters are calculated on the basis of a Euclidean geometry, with infinitesimal distances, and can then be related to any spatiotemporal order consequent upon any frame of reference .....
C. VISUAL SPACE AND SIMULTANEITY
In case objects are all where they are at the moment of the incidence of the light wave at the retina, all objects and the spatial locations of these are simultaneous. This amounts to making the velocity of light for the immediate perceptual world infinite; and, if it is infinite, the ground for the difference in spatial and temporal units in a system which is moving with reference to another system disappears. There could be translation from one system to the other without error.
Classical mechanics presents a world analyzed in terms of visual space. The content of the body, which represents the contact experience which visual experience promises, is stated as mass, and mass is defined as the quantity of matter. Quantity of matter is determined by its volume, a function of visual space. However, another element enters, that of density, and densities vary in the same volume; but, by taking a standard density, such as that of water, it is possible to present physical changes in distance experience in terms which are all geometrical units, including, of course, the vector elements of dynamics. The simultaneities are those of visual experience, it being assumed that bodies that maintain the same positions with reference to one another continue to occupy the same positions in space though the velocity of light is a finite quantity. The simultaneity of the elements of a seemingly permanent visual space is given in advance of the changes that are plotted and
(574) calculated in it, and also in advance of the experiences of push and pull, of stress and strain, which as contact experience constitute the fulfilment of the promise of the distance experience which is organized in visual space. What is taking place within a distant volume is assumed to have the same temporal dimensions as the volume which is simultaneous with all the other volumes, light waves from which reach the retina or photographic plate at the same moment. This assumption breaks down with the discovery of the finite velocity of light. The corpuscular theory of the transmission of light promised a refinement of visual space which would still have maintained the simultaneities of the gross and fine structure of things. With the defeat of this hypothesis came ether as another physical object filling all space but incapable of analysis into geometrical parts. Our experimental science operates in a space of simultaneous objects and is organized only through these objects. The expression in physical science of this simultaneity is that of the incidence of the light waves upon the retina or photographic plate. If this simultaneity were pushed back from the retina to the objects themselves, it would imply the infinite velocity of light. The space, then, of experimental science is built upon the assumption of the infinite velocity of light.
If the object is at rest, if it continues to maintain the same spatiotemporal relations with other objects in the consentient set or system, the difference in date between the departure and arrival of the light wave does not affect its spatiotemporal determination. For all intents and purposes we can say that all objects at rest have the date of the arrival of the wave at the retina or the photographic plate. When the object is in motion, we can no longer give it the date that belong., to it in the visual space, all of whose positions have the date of the arrival of the waves of light at the retina.
In order to determine its velocity, we take a reading of it at one visual position and then a second later at a second position and measure the distance. But where it will actually be at the moment when the light wave from it reaches the retina
(576) simultaneously with the light waves from all objects at rest in the system depends upon its velocity. If its velocity has been very considerable, it may be measurably beyond that point. We could locate its position only in case we knew the velocity, which we, in fact, are trying to discover. The problem takes on the form of securing some formula such as the Larmor-Lorentz transformation, which will correct the errors in the determination of such velocities. These transformations were obtained from the Maxwell equations in the field of electrodynamics, which had generalized the Faraday conception of tubes of force into that of fields of force. It does not seem to have been recognized that this conception, which is implicitly present in the assumption of instantaneous action at a distance of mass attraction or the infinite velocity of the action of this force at a distance, undertakes to establish simultaneity in space at a distance in terms of mass or electrical energy, i.e., in terms of contact as distinguished from visual experience. The easiest imaginative presentation of this is in the form of stresses and strains, and Maxwell did work out the mathematical doctrine of such stresses and strains in an ether, which was adequate to the expression of fields of force in electromagnetism. As, however, no other characters of a physical substance, such as are implied in stress and strain, could be identified, the account of what takes place in the ether reduces to mathematical expressions for an energy situation in one object, and the corresponding energy situation in another object, with the assumption that at any point betwixt and between the two objects an answering energy situation could be identified if any object were there. These objects or systems of objects are simultaneous; but, if we attempt to state this simultaneity in terms, of the minute subdivisions of visual space, we find ourselves in the position of locating an object at a point which it was not occupying at the date of that spatial position. The simultaneities of a visual space cannot be assumed to be those of the physical system that is assumed to be the condition for the appearance of the visual space. The field of force, on the other hand, is the expression of
(576) a simultaneity between objects surrounded by such fields, that is, not dependent upon any such phenomenon as the identical date of the incidence of light waves.
The simultaneity of vision is that of a coincidence of effects, found in the incidence of various light waves upon a retina or photographic plate. The visual objects as causes of these effects have different dates, when we accept the finite velocity of light, and the problem is to locate them according to these dates in a space which is visual in the sense that all its determinations of position imply the presence of a visual object at the position in question. If we place a star or an electron in a position from which it was the causal antecedent of the visual effect, it is still a star or an electron at that position. If we state it in terms of energy, we are assuming a system of things which are there irrespective of any process of relating these things at a distance to organisms, though no such system can be presented except with reference to some perspective, to some perceptive event or organism. It is only in contact experience that we have perception of objects without an outer medium and without some process connecting the object with the organism. Force is the physical expression of what in experience we refer to as push and pull, or stress and strain. It is the feel of a connection with something that is not given in tactual experience. There is no direct perception of that which is, so to speak, at the other end of the pull or strain, or of the system of things which are responsible for the stress. What is present is effort which looks toward a future, while light involves a past, an elapsed period of its transmission. We have, in other words, that which is causal, as distinguished from the effect, so far as this is given in immediate experience. This system, however, cannot be given except in terms of things which are already related to the organism, because the feeling of effort does not give the object or system but merely the action which the system interprets. Force does not and cannot locate and define objects at a distance. For this we are thrown back upon visual space and its objects. The simul-
(577) -taneity, then, of an energy system is a statement of action going on in a system that must be visually defined.
In visual space the minimum visible is a point, i.e., it is without extension and has position. When we magnify this minimum visible, we are substituting another space for the minimum visible in another visual space. The substitution is by means of inference. We cannot actually make the magnified image fit into the whole space of unarmed vision, nor can we extend the magnified image to take in the whole of space. We come back to other points which are minima visibilia, and which answer to possible contact objects whose location, in case they are moving, cannot be identified with their visual location. Even if we carry this process on indefinitely in imagination, we are in visual spaces and therefore always temporally behind the contact objects which we regard as the causes of the visual experience. Otherwise stated, we are always presupposing bodies which have earlier dates than the visual objects and objects which cannot be placed in this visual space, for the visual point will answer to some line which will correspond to the distance which the body will have traveled while the light wave is reaching the retina. If we pursue this process of magnifying down to the electron, reaching the galaxies which physical theory presents in its hypothesis of the electromagnetic doctrine of matter, we reach a situation in which the bodies could not subtend a wave of light, that is, could not even for an indefinitely magnifying eye be a minimum visible, or visible at all. The question arises: Is the space of the electronic atom a visual space? So far as the imagination is concerned, it evidently is. We present models and subdivide the distances of visual space, but in the same fashion as that in which we make use of the microscope. We see before the mind's eye a galaxy of electrical particles, whose distances from one another are not visible, but which stand for minute fractions of the minimum visible. We conceptualize this space and seem to escape from the bondage of the eye. The visual model of the scientist's imagination answers
(578) to the somethings which are the conditions of the visual experience. But even the conceptualization of this space must take its structure with it into its minutest details, for a conceptual space is nothing but the statement of the spatial relations obtaining between things. It does not relieve the spatial elements of their temporal coefficients, their dates. The space occupied by a glowing minimum visible may be reduced down to vibrating or streaming electrons. It continues to have the date of the glowing particle. We cannot catch the electron in its net, for the electron's movement has carried it out of this space, and the points of this space represent lines in the space of the electron. If we are to reach -the space of the electron, we must get at it in terms of its elements which have dates, and hence spatial positions, which are independent of the dates of the visual consequences of what goes on in the electronic space.
Such a space has no perceptual points. There is no limit to the subdivision that may go on within it. This subdivision is unlimited, and it approaches no limit. We introduce limits only by taking some physical constant which obtains through any series of a continually subdivided object or system of objects and asserting that this must obtain, therefore, at the limit of the series. The series does approach a limit, though it never reaches it. The space ideally occupied by this limit would then be the point of this space. If we abandon the simultaneities of visual experience, we come back simply to a happening or an event which appears in experience as a feel. It has spatial and temporal characters, it extends in both senses, and it extends over happenings or events which are thus parts of it, and there is no theoretical limit to the partial events which it covers or to the more extensive events which cover it. Thus the feel of twenty seconds covers the feel of all the seconds, and, if we had a feel of a whole minute, would in turn be covered by this latter. The feel that is the content of the event is that sense of pressure, of pushiness, which is the imaginative content in the physical conception of energy.
This method takes a constant out of a series affected with
(579) quantitive characters which approaches a limit and locates that limit ideally in a series that is constantly descending but which approaches no limit, for a point as a spatial limit belongs to visual space. Its character as a limit of a quantitative series answers to the Euclidean predicate of "without parts." The other element in the definition of the point "without magnitude" refers to its occupation of space in a given system. Such a given system exists for perception only in distance perception, in the normal human experience in visual perception. There is, however, another method of determining position besides that of determining the relations of an object to other objects in a given simultaneous system of visual space. A man in a railroad train is in one space in which the succeeding objects in the landscape are the events that pass by. In so far as he keeps his eye on the more distant landscape, he is part of the space through which the train is moving. His immediate pressure experience belongs to both. It is a fact of contact which has its place in either space. It is an event which could be ideally reduced from the surface of his feet to any required minuteness of spatial and temporal extension. If we conceive of the extension of this fact as occupied by such an intrinsic element as was described above, we would reach not only this element but the whole series of simultaneous elements which would be in each system, in other words, a plane. If now, placing a ruler across this plane, we take into account another space represented by this motion, in the events which would be found in all these spaces we would have a line of simultaneous events. A fourth motion of a pencil would represent still another space, and a single element of a point, which could not be further subdivided in our three-dimensional spatial experience. In all the spaces there is an identical event of which there is in each a different succeeding event. That is, these different spaces answer to different time systems. In the train the flying objects of the landscape succeed one another. Identified with the landscape itself the succeeding parts of the speeding train succeed one another while in the different motions of the hands we have either the
(580) passage of the hand over the paper or the passage of the paper under the hand. In all these different space-times there is the identical event represented by the contact of the point of the pencil on the paper.
This event which exists in actual or possible contact is for experience the reality of the perception. The distant objects are promises of this experience. The identification of such an event as belonging to different space-times of distance experience enables us to give to it position. Position, however, always implies relationship to other locations. There is no such thing as absolute position, and in a space-time these will be simultaneous, i.e., they will lie in an instantaneous space. The resting of the hand upon a table, or of the foot upon the ground, does give an approach to an instantaneous space within which different locations are there in their relationship to some central point or points with reference to which they are oriented. Certain locations are realized as more distant than others. The actual organization of such a space, however, involves an act which culminates in measurement. We cannot use the simultaneity of the contact experience for the structure of the space of conduct. This always arises in the relation of distance experience to the point of reference of contact experience, and as the determination of a location in distance experience implies the possible presence of a physical particle at the position, and since this physical particle must be related to the point of reference and to other positions by physical processes which involve time, the structure of a space can never be instantaneous. For the physical processes which locate the distant particles at a distance at least occupy a measurable time period. The distant portions always have different dates from that of the point of reference. Supposing that we have located a number of points by the intersection of four different time systems, these could be organized into an instantaneous space only by the location of physical particles at these points, and this involves, as we have seen, different dates of the particle which is that for reference and other points. If the physical process which connected these
(581) points, in this case that of light, were infinite, we would have simultaneity; or, if we could date back the position of the particle by the time elapsed in the passage of the light wave, we could construct a simultaneous space. The velocity of light is not infinite, and the process of dating-back the position of the distant particle is subject to the error of its proper motion, while the light wave is reaching the point of reference, when we do not know its proper motion and have no way of determining it except by visual positions.
The fundamental fact in the spatially and temporally extended world is that what event succeeds another event is not determined by the nature of spatiotemporal extension. In other words, we have to look for the laws of change outside the geometry of a spatiotemporal world. These laws are empirically deduced from the behavior of the material objects that occupy the events. Furthermore, the order of the succession is not absolutely determined. It depends upon a point of reference. That is, the world that is there is subject to temporal perspective as it is to spatial perspective. What object will lie between the individual and the object of his distant perception depends upon his location. Location is determined within a field of simultaneous objects, objects that are simultaneous with the percipient object. These are objects all of whose spatial coordinates remain unchanged, while their temporal co-ordinate varies.
D. RELATIVE SIMULTANEITY
Assume that an individual stands beside a moving railroad train. The problem is to determine what events will fall within the field of simultaneity of the man on the platform as the train passes and of the traveler sitting within the train.
The statement is to be made in terms of events, without prejudging the question whether objects are themselves as, objects timeless and only occupy events, or whether objects also pass and are therefore to be considered as events.
Simultaneity is the temporal property of nature that is there
(582) over against a living form. It may be called the environment of the individual from the standpoint of the passage of nature. This property is dependent on that relation of the individual to his environment which is expressed in the so-called specious present, that pulse of existence in which passage is going on, in which therefore both some past and some future is there in that relation which is denominated the present. The extent of this specious present is not immediately determined either by the field or by the individual. Its edges are uncertain, and the temporal extent expands and shrinks. One's temporal grasp varies, and the changes that are taking place in the field and in the individual affect the spread of this specious present. Within certain gross limits that could be stated in terms of the outside limits of the apperceptive grasp, the shifts of attention determined by the changes in the field and in shifts in the act would presumably determine the spread of this specious present. The changes in the field that would affect this spread would depend partly upon the relation of the objects in the field to the act and partly upon the necessity of readjustment of the organism in maintaining its spatiotemporal balance in its own conduct. In both considerations we are referring to the securing and holding of the posture called for by the carrying out of the act. In running, for example, movement does not necessarily involve more rapid succession of specious presents. If dodging becomes necessary, such rapid succession would probably become necessary; or rapid change of the objects, especially if unanticipated, would involve this. Where mutual change of the field and the organism-or change of either-involves change in posture, a new specious present would probably appear.
The action of the organism with reference to the field calls for an attitude of rest, however short. Activity of the organism is always from the environment, where the organism for the moment holds itself at rest. The structure of the world in the specious present is, then, one that will hold the organism in balance while the next reaction is undertaken. The here-now will be that structure, the there-then an earlier or a later one
(583) which lies outside the immediate specious present. The definition of a critical change of posture would presumably depend upon the degree to which habitual adjustment enabled the individual to respond to changes in the field or in himself or in both without shift of attention from a spatiotemporally distant stimulus. Where the action of the organism is maintenance of a posture in a field which is not changing, one specious present may pass into another with no sense of succession.
A consentient set is such a structure of the field that enables the organism to carry out its next reaction, and whatever (changing or not) lies in that field will be regarded as simultaneous with the individual. Such a consentient set may, in imagination, be extended indefinitely. In existence it extends only through specious presents, as they pass imperceptibly into one another or as they perceptibly succeed one another.
Let the man on the platform and the man in the train each regard a distant telegraph pole. The event in the telegraph pole, or that occupied by the telegraph pole, which lay in the level which enabled the man on the platform to maintain his balanced position would be simultaneous with him. Would the level which enabled the traveler within the train to maintain his balanced attitude include the same event? We will overlook the fact that any possible difference would be so slight that it could be only stated in decimals far removed from the decimal point. The question is whether the consentient set of the traveler as he rapidly approaches the telegraph pole will include the same event in that pole as that which lies in the consentient set of the man on the platform.
The difference lies in the fact that the traveler is orienting himself with reference to a moving landscape. The difference may be expressed by the fact that, if the traveler held his pencil upon a point before him, eventually a point which would be in the same level with the telegraph pole would occupy that point for the traveler; that is, the point-track at the end of the traveler's pencil would spread itself into a rect for the man on the platform. Does the traveler, in orienting himself with reference
(584) to a landscape in which distant points are going to occupy points which are at rest with reference to himself, place himself in a level of events which antedate or postdate those of a man at rest in the landscape?
He is moving toward the waves of light that come to him from the telegraph pole; that is, the wave of light will reach him earlier than it would if he were at rest with the man on the platform. The effect then is as if the wave of light had started earlier than that which would have reached him if he had been at rest. In other words, it would be from an earlier event than that which is responsible for the vision of the man on the platform. If his orientation with reference to the surrounding landscape is through processes that take time, his levels of orientation will all of them be dated as if the stimuli came from events that were earlier or later than the events responsible for the experience of the man at rest.
This statement is from the standpoint of the man at rest, setting up the object in his experience as the actual object, and assuming that the same path is followed by the light wave which reaches both eyes, those of the man at rest and those of the traveler. It only seems to the traveler to come from an earlier event. The statement implies that it comes from the same event, its erroneous dating being due to the hurrying forward of the traveler toward the oncoming wave.
Against this assumption we can place the relativity of motion. So far as the relative change in position is concerned, there is no criterion by which to determine which is moving, the train or the landscape. If the landscape is moving, the light wave that comes from the part of the train that is opposite to the telegraph pole will seem to the man on the platform to be as much postdated as, the light wave from the telegraph pole was antedated for the traveler. If we abandon an absolute space and an absolute time, i.e., if we assume that the fundamental fact is passage which affects spatial relations as well as events, that spatial relations must be reckoned between events rather than between timeless objects, that time is the relation of succession
(585) of events, and that there may be different systems of time within which events succeeded one another in different orders, then the situations which have been stated as different private or psychical interpretations of absolute spatial and temporal situations may be conceived as existing in nature. In the case before us the different specious presents of the man on the platform and of the traveler are, then, real phases of nature, although the same events appear in each. In fact, of course, the traveler identifies himself with the man on the platform and experiences himself as moving, and he is able to do this because with any velocities which he is capable of perceiving the differences in the order of the temporal passage of events are imperceptible. If the traveler never descended from the train, and if its accelerations and decelerations were never immediately experienced, in his specious present the landscape would be flying by him and not he through the landscape, though he might have other evidence that the other succession of events was the accepted order and be able in imagination to place himself outside the train and see it fly through the landscape. In other words, he would be in our position as respects the relative movements of the earth and the sun and the other heavenly bodies. We cannot perceive the motion of the earth with the consequent staying of these bodies in the heaven, though we can imagine it. We can imagine this as readily as we can place ourselves on the ground and see the train pass, because it involves no paradox, i . e., there is nothing in the reversed order of events which involves a different order in our present experience. Such a paradox does appear in the Michelson-Morley experiment. Here the light should reach a mirror moving with the earth and return at a later interval than that in which it goes to and returns from a mirror placed at the same distance from the observer but at right angles to the axis connecting the first mirror with the observer. All the paradoxes of relativity come back to this-that, if under its assumptions we placed ourselves in the situation in which we assume the other system is moving, the relative order and position of events would not be the same as they are on the
(586) assumption that the first system is moving. The relative position and order of the heavenly bodies are the same whether we assume a Copernican or a Ptolemaic order. The relative position and order of objects and the train are the same whether we assume the train is moving or assume that the landscape is moving. This is not the case under the assumptions of relativity. From the standpoint of relativity an event which lies in the time system of the man on the platform and in that of the traveler, the common event, say, when the traveler flashes by the man on the platform, is not simultaneous with the same events in the systems of the two men, though the difference is too minute to be recognizable. Because it is not recognizable, there appears to be no paradox when we place ourselves either in the train or on the platform. Consider the Michelson-Morley experiment. The space of the earth is determined by the consentient set of its observers, i.e., the co-ordinates of the earth are at rest, so that the distances between objects at rest remain unchanged from minute to minute. Stated in terms of events, so-called objects at rest occupy point-tracks and not rects. As the distances between the mirrors of the apparatus remain at the same distances from each other, and as the distances which light travels in this consentient set are the intervals between these objects or the parallel point-tracks which they occupy, there is no possibility of a longer period in the passage of the light between the mirrors set on one axis and those set on the other. From the standpoint of an individual outside the earth the light that traveled toward a mirror that was moving with the earth would have a longer distance to cover than that which traveled to the mirror at right angles to the axis of the mirror that was traveling with the earth. If these event-, had been regarded from the standpoint of his consentient set, in which the earth is in motion, the discrepancy which Professor Michelson sought would have appeared.
One determines simultaneity by reference to the co-ordinates of objects at rest in relation to the percipient individual. In terms of events the determination is with reference to the point
(587) tracks which the objects occupy, if the objects are not conceived of as passing. The point-tracks which extend through a specious present, or the points that are there, are simultaneous; also the lines in a permanent space which occupy point-tracks, or surfaces and volumes, would then be simultaneous. If a system, such as a railway train, is moving with reference to this system, the question propounded above is with what event-particles in this system does an individual in the train find himself simultaneous, if he does feel himself to be cogredient with the system of the landscape through which the train is moving.
Simultaneity is a relation primarily between a point-track and the moments of a time system, within which that pointtrack is a point. That a point-track should be a point within any time system implies that it has the relation of cogredience with the durations of that system, i.e., has a definite relation of "here" in these durations.
Assume now two time systems that intersect in a level, e.g., the time systems of the traveler and of the man on the platform. As the train passes the station, there will be a level of events which are in the time systems of each. Assume a single event-particle in this level, say, that under the pencil point of the traveler as he sits in the train with a piece of paper before him. In the successive durations of the traveler this lies in a point-track, i.e., constitutes a point in his timeless space. It also is an event-particle in the time system of the man on the platform, and there occupies a point-track which constitutes a point in his timeless space.
Being in different time systems this event-particle will be succeeded by different event-particles in each. These pointtracks will not coincide. The event-particle which succeeds that under the point of the pencil of the timeless space of the traveler will occupy another point in the timeless space of the man on the platform. As these points retain the same character of "here" in the timeless space of the man on the platform, the pointtracks will be parallel. The succeeding event-particles which occupy the point under the traveler's pencil will occupy points,
(588) i.e., point-tracks in the time system of the man on the platform which will be parallel to one another. If we take into account simply these two time systems, the event-particles in question will occupy two different routes. In the time system of the passenger they will occupy the historical route of a point-track, while in the time system of the man on the platform they will lie in point-tracks whose points would constitute a "spatial" route.
E. VISUAL SPACE AND CONTACT SPACE
The selection of the distant object in visual space is a function of perception, which implies in the cogredient set not only the contemporaneity, or simultaneity, of the distant object as seen but also as possibly felt, i.e., measured. It is there where it is and when it is not only for the eye but also for the measuring rod, but its date for the organism or the photographic plate is the advent of the light wave, not its departure from the object. The date of the contact or possibly measured object is, however, that of the departure of the light wave from the object. If now we take into account the movement of the object within the period lying between these two dates, the seen object and the measurable object belong to two different consentient sets, both determined with reference to the same organism or percipient event. The determining date is that of the measurable object, i.e., that which is cogredient with the organism as a material thing. The object as seen at a distance gives us evidence as to this. Being in different cogredient sets implies that what is simultaneous in one set will be successive in the other. Thus, starting from the contemporaneity of Sirius with ourselves (and this is conceived in terms of possible contact, of mensuration), the visual Sirius is pushed into a distant future, i.e., the visual Sirius is contemporaneous with the Sirius which belongs. to the present world at this instant, while the present visual Sirius is contemporaneous with a measurable Sirius of a distant past. Assuming that we know the direction and velocity of Sirius' motion, we can place the measurable Sirius in the space of the visual Sirius, but the same events in the visual Sirius will not
(589) be contemporaneous which would be contemporaneous in the cogredient set which included the measurable Sirius of the percipient event of that instant. Nor is it necessary to seek illustrations in objects at stellar distances. Assuming movement of that which is seen, what we consider the physical object, i.e., that which is measurable in possible contact terms, cannot be contemporaneous with the visual object at the place where the visual object is and when it is, since the passage of the light wave takes time, and yet what we refer to as the reality in perception is the contact values implied in the distance values when and where they are. If space is absolute, it is very simple to work out the measurable values of the visual object in terms of this absolute space and date them back to the period that has elapsed between the light wave's leaving the object and reaching the eye, saying that the object must have had these measurable values at the moment when the wave left the object. If, however, space is nothing but the formulation of the spatial relations of successive events, these spatial relations will be different if the measurable object and the visual object are regarded from one standpoint as simultaneous and from another as successive. We find ourselves, then, with two consentient sets, one of these is in a space which is extended out from ourselves by the measuring rod, and in terms of this we can state the physical object at the date of the departure of the light wave; the other set is in a space of vision, and by the use of the laws of optics we interpret the magnitudes in this space in terms of the physical object from which the waves of light have come. In each of these cases we reduce the temporal extent until we may assume a simultaneity of events. If in the visual space we reduced this temporal extent below that required to allow the waves of light from the visual object to reach the organism, we would- theoretically lose our visual field entirely. The velocity of light represents a lower limit to the reduction of the temporal extent within visual space; actually the limit is set by our ability to respond to visual stimuli. In our imaginative reduction of this extent within the measurable space we can conceivably go below this limit; other
(590) wise we would be unable to state phenomena of light and of radioactivity, i.e., events which would be simultaneous in the visual space would be successive in the space of the measuring rod. But percepts of distant objects inevitably exist in a visual space, even in our imaginative presentations of the movements of electrical particles. All of our apparatus used in measuring the velocity of light itself requires the discrimination of vision. A temporal limit which is lower than that of our power of response to the light stimulus implies spatial magnitudes which would have to be transformed to bring them within the visual field.
In the Michelson-Morley experiment, a light ray is split. One half travels to a distant mirror in the direction of the earth's motion in its orbit, while the other travels at right angles to this motion. The velocity of the earth is then added to that of the light wave on its forward path and is subtracted from it on its return. It should return later from the reflecting mirror than the wave that travels at right angles. The difference in the velocities of the waves should then be evidenced in interferences between the images that return. Why did this not take place? The mirror which is placed in the line of the earth's motion, as part of the measurable system of physical things that make up the apparatus, is regarded as there as of the instant at which the light wave leaves the source; but, when the light wave reaches it, it is regarded as having moved along with the earth which sustains the apparatus. When it returns from this mirror to the central mirror, it is assumed that this with the earth has advanced toward it, i.e., it has a shorter distance to travel. This implies a series of successive instants, such that the light wave, as a set of vibrations, can be located at successive moments as occupying different positions with reference to the apparatus, much as a swimmer may be located at different positions at different moments with reference to the banks of a stream. This would be theoretically determined by a measuring rod. But as a visual fact the light wave which reaches the central mirror on its return from the distant mirror has not only the date of its
(591) arrival but also that of the distant mirror, for this exists as a visual object only in virtue of light waves which reach the investigator simultaneously with the wave whose velocity is being measured. As visual facts, the light at the distant mirror and at the central mirror are simultaneous. As measuring-rod facts, they are successive. Substitute for the eye of the investigator the photographic plate; then the date of all parts of the visual whole which appears there is that of the arrival of the light waves at the plate. Such a plate could not detect different velocities of light waves passing between different parts of the apparatus, since as visual facts they must all have the same date-they are all visually simultaneous.
Assume successive photographic plates or a cinematographic film; then one exposure would present the apparatus as the light wave is emitted, while, under the assumption of the varying velocity of the two split waves, successive exposures could conceivably record the earlier and later advent of the waves with varying velocity. A film lying between these might present the record of the interference of waves whose velocity varied but slightly. The experimental evidence that approaches such a case closely is that of the failure of a light wave to return from a distant mirror in time to pass through the aperture of a rapidly revolving wheel through which the light wave had passed on its way to the mirror. This is direct evidence of a visual sort that the waves that come from the distant mirror and which date its visual existence can antedate the wave that travels to the mirror and returns from it, and therefore that those of these two classes that do coincide or partially coincide must be of different dates, if we date them from their source. This implies, however, the ability to identify and follow in imagination the wave from the source on its journey to the mirror and back to the source again. A light wave cannot be personally conducted in this fashion in visual terms, for light waves are the antecedent conditions of all visual objects. It is only the measurable contact content of the wave that lends itself to such imaginative surveillance with the different datings
(592) implied. It is only by inference involving such a reference to the light wave behind the visual scenes that we can interpret simultaneous visual contents as the result of waves of different dates. The immediate implication of interference is that of spatial differences in contemporaneous occurrences.
F. RELATIVITY AND PERCEPTION
I have already pointed out that one character of the hypothetical or erroneous objects in the experience of the individual which is regarded as specifically mental is the uncertainty which attaches to the result which would follow upon the carrying-out of the inhibited responses which the distance stimuli in these objects arouse. It is impossible to give its proper reference to this mental character without taking into consideration the import of one of the important contributions which the doctrine of relativity has made to the knowledge of nature. This contribution is most definitely indicated in the recognition that there is no such thing as nature at an instant, nor any physical thing in nature at an instant; that an instant, an element of duration without temporal extension, is a fiction whose only legitimate reference is to the ideal of a limit implied in differential equations; that all extension is temporal as well as spatial, and there is therefore no space that does not pass. The order of events cannot, then, be fixed by a set of timeless positions in space, as one orders the movements of the hands of a clock by the positions of the divisions on its unmoving face. Spatiotemporal perspectives or situations are there, as are other situations, vital or perceptual, that determine their objects. The separation between time and space is, however, also there. We naturally appreciate change in its contrast with what does not change in the perceptual situation, by movement in an unmoving field, and time is a derivative of the movement and space of the field that does not move. That the face of the clock passes as well as the slow-moving finger of time cannot be gainsaid,
(593) but we could only be apprised of its passage by its decay in the midst of a space that did not decay. Space offers the channel and banks within which the stream of time doth flow. The separation of time and space belongs to the perceptual situation or perspective. Place ourselves outside it, and the permanent field of the spatial world itself is flowing, and only from another locus standi can its temporal passage be assessed.
An absolute space and an absolute time imply, then, a perceptual situation that is not a situation, a perspective that is not a perspective. Still the familiar experiences within the railroad train make it evident that we do automatically place ourselves in different situations or perspectives and reach a locus standi that is absolute with reference to a number of perspectives. The most general one of these is the axis of reference of the fixed stars from which all the motions within the known universe may be conceivably plotted. The mechanism of this process I have already indicated in the automatic taking of the attitude of the other in becoming an object to one's self.
But, if the perceptual situation does more or less automatically separate space and time, in so far as it implies a passage without change as a spatial field within which and over against which change takes place, it implies also a spatial change which is passing. Whether it is change of position or of quality, without passage it would not be change. Where one is actually moving, spaces pass, or, stated more accurately, the events which include the whole perceptual field are spatiotemporal. In a moving train, if one can avoid taking the attitude of the fixed landscape, one would be referring to the same succession of spatiotemporal events, whether one spoke of them as passing more or less quickly or of more or fewer of them as passing; that is, one would not separate the spatial and temporal aspects of the events. If, preserving the same attitude, one sought to secure a timeless space-I am assuming that one's entire perceptual field is moving-one would regard one's self as instantaneously at rest, and points in one's space would in the passing field be paths of those points or world-lines, lines would be
(594) surfaces, and surfaces solids, while a solid would give rise to nothing further than would one of its surfaces, since our spatial world is only tridimensional. By arresting one's self at successive moments while the spaces hurried by one, one would identify in each the homologous positions with reference to one's self and so build up a space which would be independent of the passage. What is attempted here must be distinguished from what may be called the normal situation, that in which motion takes place within a nonmoving field, that is, a field in which there is passage without change, in this case change of position. In so far as there is passage without change, time is separated from space. I am asking for such an identification of passage and change as we approach in a rapid motion, in which things fly by us without being placed in a nonmoving field. In such an experience rest would be represented only by homologous positions in successive spaces. The organization of these into a whole would result in a space through which all these successive spaces would be passing. Over against the passing spaces this space would not pass and would be in so far timeless, that is, the recovery of an identical set of spatial relationships in each passing set of events would constitute the permanent structure which does not pass, although there is ceaseless change. If, on the other hand, we solidify these into a changeless landscape through which the train is hurrying, we reach the nonmoving field which is the common background for motion in any particular situation or perceptual perspective. In this solidification of the passing scenes, the motion with its temporal character is removed from the scenes, whereas I have suggested the possibility of capturing a timeless space within the moving scenes themselves. If, instead of capturing a timeless space out of homologous spatial elements, we remark the succession of moving events alone, we reach a passage which constitutes a spaceless time. Such a time is also a system, an order of passage. This order of passage comes to us in varying spans, or specious presents, as we have seen, and the succession of different spaces will give us different series, for the reduction of the passage to
(595) a series takes place by the imaginative compression of a specious present into an instant in which the passage is contracted as much as possible. If we contract two presents of varying spanvarying, that is, with regard to events that are there as simultaneous-we will evidently get two different elements in our series and, therefore, two different time systems of the same passing events. We ordinarily state this difference of time systems in the seeming greater length of time when much has been crowded into a short space. The biblical paraphrase of it is, "One day is with the Lord as a thousand years and a thousand years as one day." However we may force them into the same Procrustean bed of a common Gregorian calendar, the temporal series in the life of one man will differ widely from that of another. If over against a set of events represented, say, by the letters of the alphabet, one were to frame a number of temporal series, in which, for example, one moment would have a span that comprised c, d, and e, while another comprised c, d, e, and f, and another c and d only, and so on in like fashion throughout the whole alphabet, it is evident that the temporal series would differ in so far as, for example, in one case e would follow d, while in another it would be. contemporaneous with d and would be followed by g, and pari passu that the relations of these events to other contemporaneous events implied in the series (what one may call the landscape of the alphabet) would be variously distorted in these discordant series. We have been accustomed to recognize the different spatial perspectives of men differently placed, if for no other reason than because we can photograph them, but we have not been accustomed to recognize their varying temporal perspectives except in such general metaphorical phrasings as those adduced above. It has required the cinematograph to give any sort of photographic representations of them, and these fall short of presenting exactly such differing spatial landscapes answering to different time systems as would correspond to the differing optical perspectives which a projective geometry and draughtsman's penell can fashion for each separate locus of the eye. In fact, it is
(596) known that only when velocities approach a respectable fraction of the velocity of light or when the cumulative differences in vast stellar landscapes betray themselves in minute shifting of stars on the photographic plate or of lines in the spectrum do the corresponding distortions of the spatial landscapes become appreciable. It is only in the subatomic world or in the utmost reaches of the heavens that these temporal perspectives throw spatial shadows that affront the eye.
In the familiar experience which I am recalling of the traveler in the swiftly moving train, surrendering himself to the perceptual situation, both the landscape and the individual are moving, and both movements are there. There ensues a continual recurrence from the flying landscape to the flying train, a continual cutting of the planes of one set of spaces by those of another, and it is these intersections which locate the homologous elements in the moving spaces and out of which is built up the space within which all takes place. The mathematical theory of such a structure in the midst of motions of varying velocities and directions with their own times and spaces Professor Whitehead has worked out in terms of puncts, rects, and levels in his theory of relativity. It is evident that any particular structure of space is not ultimate. It again intersects with spaces of other motions, but these intersections furnish the elements for the determination of the changes in a world of different families of durations. What strikingly characterizes the experience in the moving train is the shock that accompanies the passage from one attitude to another, owing to the different spans of perception. Now the scene spreads out and takes in a wide field of passage that persists without change and now shrinks to a series of objects that chase one another across the eye, following not only the shift from one's own motion to that of the landscape but from a distant focus to one near at hand. As the telegraph pole leaps into motion from a momentarily permanent field the spaces that belong to each come into confused reticulation with each other. The points of these intersections, that
(598) thus belong to both series of rapidly following spaces, are those from which we bring order into confusion.
What the theory of relativity seems to have undertaken is the generalization of this and kindred situations in which not only times but spaces pass, varying as their mutual relationships (i.e., their velocity) changes, and in which identical events with differing spatial and temporal characters can be isolated. Of fundamental importance in the doctrine is the determination of the simultaneity of events. Einstein proves that events which by any conceivable process of signaling are shown to be simultaneous in any one system, in another system which is moving with reference to the first are shown to be nonsimultaneous by the same process of signaling. Whitehead more fundamentally shows that the organization of any system must come back to a here and a now, that is, to a perceptual situation, and that what he terms cogredience depends upon a relation to the individual that is involved in that situation, so that there result different families of durations such as have been indicated above and differing simultaneities dependent upon differing temporal perspectives. Whitehead insists that these different perceptual situations, with their different families of durations, are not subjective apprehensions but exist in nature.
Over against the interpretation of the theory of relativity stands the classical doctrine which may be said to generalize the situation of the individual at rest observing a moving body in an immobile field. Here space and time are separated. Motion is a temporal process that takes place in a spatially frozen universe. Times are determined by changeless distances passed over by the moving body. If two bodies with different velocities pass over the same distance, the passage that is common to both, that is, time as passage, is rendered absolute by the absolute spatial measure. Both situations are there, and the generalization of each is legitimate, but the relativist, apart from theoretical and experimental proof of his position, is justified in considering his generalization as the more fundamental, for the observer and his fixed field are always found to be moving, and it is the bear-
(598) -ing of this more fundamental generalization of the relativist upon the object in the perceptual situation that I wish to consider.
From the standpoint of the classical doctrine the object at a distance is there and, as a spatially determined object, is what it is at the instant that it is there. Spatial identity is independent of any passage that is involved in the perceptual situation.
If we ask what it is that is there, we come back to a body occupying a portion of the timeless space, and a measuring rod carried to the object would disclose the same dimensions whereever the object might be located. The rough extent of these dimensions is revealed by its visual extent at a distance, and contact imagery fills it in. The statement in terms of the measuring rod implies contact experience, that is, a situation in which there is no visual perspective, and in which all the differences that belong to different perspectives disappear in the contact object which we would reach if we carried out the acts which the objects at a distance tend to call out. From the standpoint of the classical doctrine of a timeless space this object of contact experience is there where it is in visual space at the instant at which it exists in the perceptual situation.
However, the perceptual object at a distance is not an object that is there at the temporal level of the distance experience but is the promise of a contact object that will be there at the end of an act. It is a future contact object that we perceive. If the space of the distance experience is the space of the later contact experience, we may affirm that the contact object of the future was identical with a contact object that continued to occupy that timeless space. If spaces pass, we cannot without reservation make that affirmation. If it may be assumed that the distant contact object in the perceptual situation is in the same family of durations as the perceiving individual, then, if the individual went to this object and applied the measuring rod that belonged to that situation, the distant contact object would be identical with the contact object promised in the distant visual object; otherwise not. Being in the same family of
(599) durations in this case implies that the execution of the act which the distant stimulus calls out or tends to call out would lie in spaces which would be parallel to that of the visual experience. This, further, would be the case if one could reach the object as soon as seen, and this is what is implied in the contact imagery that fills out the visual experience. If, however, during the period- of the advent of the visual stimulus the body had moved, then there would be no assurance that the contact object implied in the visual experience would be in the same space with that of the measuring rod. The body which I see at a distance has a definite measurable content, that is, a contact content. The agreement of these, the laws of optics enable us to work out with great accuracy. So far as the identity of the spaces implied is concerned, agreement between extent implied in vision and the measured extent would be reached if we assumed that we get to the object and applied the measuring rod the moment that the light wave left the object. But if while the light has been traveling to us the object to be measured has moved, then it does not lie in the perceptual situation, or is not cogredient with the percipient event, to use Whitehead's phrase, and we cannot assume that they lie in the same space or in parallel spaces. The implication of perception is that objects at a distance have contact charactcrs-that, if we were there where they are when we saw them, they would be resistant to pressure. This may be interpreted as implying that space is passing with the velocity of the distance stimulus, in this case, light. Stated otherwise the homogeneity of space at an instant is expressed in the agreement between what we see to occupy space and what we find to occupy that space when we measure it. If the space of our instant perception is homogeneous, then, if we reached the object seen as soon as we saw it, the two perceptions would agree. But, if spaces are passing continually, this homogeneity could be assumed only if space passed with the same velocity as light, that is, if we could assume ourselves, so far as spatial determinations are concerned, to be at the object as soon as we saw it. In a space that did not pass we could take what time we
(600) pleased to verify our visual extents by our measuring rods, for it would retain unchanged its structure. We are only justified in projecting our immediate contact experience into visual experience in a space that passes if the space passes as rapidly as light. If, now, the body moved, for example, away from us as the light wave left it, the assumption of our perception that the visual object is in the same space as ourselves would not necessarily hold.
The positions presented here are, then, as follows: (1) the implication of perception is the agreement between the spatial dimensions indicated by distance experience and those revealed by contact experience, i.e., the measuring rod; (2) the presupposition of this implication is that the spatial structure is uniform in the field in which lie the object and the individual or percipient event, to use Whitehead's expression; (3) so far as immediate experience (that approaching the instant) is concerned, we are at liberty to assume this to be Euclidean and uniform; (4) but variations in the spread of the specious present would give a different succession of events, and hence different time systems with consequent different spatial orders, though these may all be Euclidean, i.e., the same events would be differently ordered spatially as well as temporally, if in one case they were contemporaneous and in another they were successive; (5) successive spaces are parallel if they answer to the same specious present, otherwise they involve intersection; (6) if space were timeless, the implication of perception would hold uniformly so far as the uniformity of space is concerned, and it would hold as well in parallel spaces; (7) if spaces pass, however, we could have assurance of this parallelism only if the rate of passage were the same as that of the distance stimulus, for only in that case would the spatial structure involved in the seen thing be that of the contact experience of the individual seeing it; (8) the passage of space does not refer to the movement of objects in space but to the passage of a certain order dependent upon the contemporaneity of a certain group of events and the temporal and therefore spatial order which this
(601) involves, i.e., if from the car window I see a telegraph pole suddenly leap away from other objects in the landscape, the pole and that which is immediately adjacent to it represent a certain spatial set which is followed by other objects in the passage of events, and such a field is different from that spread which preceded it in which the telegraph pole moved with the whole landscape; this order would intersect the order that preceded it; such a succession of spaces by the accompanying shock apprises us of the constant succession of parallel spaces that melt into one another, giving rise to the apparent timeless space; (9) if these spaces pass, there must be some sense in the rate of this passage; (10) as the spaces exist only in the relation of distant objects to the individual or percipient event, and all perceptual spaces have a uniform order, it would seem to follow that the rate of passage must be identical with that of the physical process by which the distant objects and the percipient event are related, otherwise the spatial order in the perceptual field would be disturbed, for, if the spaces hurried on more or less than that process, which serves to constitute a field of distant objects, the order would be confused; (11) the passage of spaces in a perceptual world must be that of light, for these spaces are the orders of the relations of spatial extension between the events which are in passage, and this order involves the transmission of light waves, of which each wave is an event following upon another, and the succession of which constitute the temporal passage; the rate of succession of waves must be the same as the rate of light, for it comes to the same thing, the rate at which a wave moves along, and the rate at which a wave at a certain point is succeeded by another wave or, stated in another form, it would be a contradiction in terms that in a visual space the movement of light should itself be visible; or, again, it is only because in passing spaces the motion of light has the same rate as the passage of space that there is a fixed spatial order within which other motions of less velocity can take place; (12) other motions take place in a visual space, but they are motions of visual objects, for which as visual both the pas-
(602) -sage of light and the passage of space at an identical velocity are prerequisites-in fact, the motions of these objects in a visual space is an expression of the difference in the velocities of light and of the object; (13) for the purposes of analyzing the temporal extent of events we reduce our specious presents as close as we can to instants, although they always involve passage, so that it makes a difference what is included within this approach to an instant, as in one case an event will succeed another which in another would be simultaneous with it; (14) the identity in the velocities of light and of the passage of space insures the agreement between the visual or distance space and the contact space, or that of the measuring rod, for parallel spaces, but this is an identity of spatial order of the body as seen and the body as possibly felt or measured; (15) it does not necessarily hold for the body after the light wave left it if that body were moving, for the movement of a body is a determining factor in its location in the cogredient spread or specious present, the assumption being that in the approach to an instant all motion of objects with reference to one another in the field disappears; (16) the mere fact, then, that the body as measurable is assumed to have moved between the moment of the light wave's leaving the object and the wave's reaching the percipient event or individual by definition places it outside this specious present and places us in the position of regarding the field of that specious present as moving with reference to the object; in so far as the objects were regarded as both within and without this specious present the spaces would not be parallel-from one point of view there would be simultaneity and from the other succession; (17) this amounts to saying that the body as seen and as measurable in terms of the elements of physical science will have different temporal and spatial characters and, in consequence, different mass or energy characters, and that these differences will increase with the velocity of the motion of the object of vision; (18) if the velocity reached that of light, the body would be both visible and invisible, that is, such a velocity in a visual world is inconceivable; (19) for velocities less than
(603) that of light the Lorentzian transformations presumably represent the differences in the characters of space, time, and mass which must be ascribed to the object if it is regarded as still lying within the field of the specious present, that is, the instantaneous visual field that is correlated with the contact or measurable spatial order of the percipient event, or individual; (20) this would seem to imply that the Lorentzian transformation gives the temporal, spatial, and mass characters which the object must have to remain in the field where the measurement is made; (21) relativity is itself but one phase of a nature in which there exist perceptual situations which are determined by the relation of individual organisms to their environments, and in which the spatiotemporal extension is subject to the same determination; (22) there is, however, a constant among these different families of durations, that is, the velocity of light which is constitutive of the distance phase of the perceptual situation; (23) whatever other implications are involved in such a constant, it is certain that it could be discovered only by individuals who could place themselves in different perceptual situations and thus reach a nature made up of different families of durations, or different perceptual situations, over against the attitude of correcting not only one's spatial but one's temporal perceptual perspectives; (24) it is only the individual who can imaginatively place himself in an airplane while retaining his position on the ground who can realize that a point for one is a line for the other, or one who can retain the whole uniformly moving landscape from the car window while he watches the telegraph pole leap out of the scene, who can realize that the order of succession is dependent upon the particular cogredient set, or specious present: (25) and, in indicating to him-elf these different -,patiotemporal characters, he also indicates from a position outside of both what is identical in them and thus discovers over against this attitude a nature that is absolute, at least in abstraction from those differences he has been contemplating; (26) such an absolute nature would not lie in an absolute space and an absolute time but would consist of passing events which suc
(604) ceed one another in differing orders dependent upon the differing cogredient sets, or perceptual situations, within which the same events occur, while formulas can be obtained for the translation of the spatiotemporal characters of the event of one spatiotemporal system to those of another to which it also belongs, formulas which contain as a constant coefficient the velocity of light, that is, of that physical process which is constitutive of the order of events in a distance space in all spatiotemporal systems.
We can now return to the earlier statement of perception as affected by futurity. We perceive things at a distance. Their perceptual reality as physical things is the contact character they will have if the act involved in the perception is carried out. This is most fundamentally expressed by their magnitude as determined by a measuring rod. So far as the laws of optics and their implications reveal these contact characters immediately, the character of futurity in the perception approaches zero, and we assume all things seen to have the revealed contact characters at the approximate instant of perception. The fact, however, that the body seen has moved between the moment of forwarding the light wave and the arrival of that wave at the organism dislodges it from the cogredient set in which it lies as perceived and places it in another family of durations. However minute this motion may have been, it has invaded the apparent instantaneousness of the perception. As already indicated, this instantaneousness is only an approach to a limit. There is always in every specious present a passage, and that passage cannot be less than that involved in the velocity of light. By the laws of optics the visual distant object is there as an object answerable to the measuring rod if it resides in an absolute space or in the same family of durations of passing space; but if in the period within which the light wave reaches the eye it has moved on, then its measurable character or content on the assumption of instantaneity with the visual object implies a different visual object, that is, if it was really farther away than it looked, it ought to have looked smaller; and) if we insist on proceeding on
(605) the assumption of instantaneity, we must transform proportionately our account of it in terms of the measuring rod. If there were an absolute timeless space, we could make our spatial estimates entirely in terms of this and could disregard instantaneity; and this has been the assumption of the classical doctrine, based upon the fact that all the distortions of spatial perspectives can, in accordance with the laws of optics, be harmonized with contact experience of the measuring rod, but this ignores the equally ineluctable fact that contact space only exists in its relation to distance space and that distance space in the perceptual world, the only field of experimental science, is hopelessly infected with futurity. The assumption of instantaneity is involved in the jumping-off spot of one act; but, as soon as we are able to see ourselves from the point of view of the moving object, the stationary field of instantaneity begins to flow, and its spatial structure is distorted. There being no position eternally pegged down that could not from another watchtower be seen to move, we come back to the recognition of what has been already affirmed-that the universe is made up of passing events which fall into different perceptual, or spatiotemporal, situations that determine their objects. What the theory of relativity has elicited is that this holds even of the spatiotemporal character of objects in the perceptual world. It has been able to achieve this by sending the scientific imagination behind the fact that the passage of light occupies an appreciable period, for distance space is optical. Thus even the most fundamental spatiotemporal characters of the world at an instant is contaminated with the not-yet. Our grasp of the innermost structure of things is experimental.
It is perhaps not out of place, at the conclusion of this summary statement of relativity in its bearing upon perception, to point out that the selection involved in any cogredient set at an instant is not of a more or less of a spatial spread, for, by implication, the whole universe is there at an instant, but it is an inclusion of certain successive events rather than others. The selection is temporal rather than spatial.