A half century ago, P. W. Bridgman, one of America's foremost scientists, pointed out that many of the "basic ideas and concepts to which scientists subscribe "have not been thought through carefully but are held in the comfortable belief...that some one must have examined them at some time". One of the concepts to which this comment by Bridgman is particularly appropriate is that of "motion". Most scientists are apparently willing to go along with Newton's view that motion does not need to be specifically defined because it is "well known to all". But in order to make use of this concept in a scientific context the rather vague general understanding of its meaning that is "well known to all" has to be given some more specific significance. The objective of the present discussion is to show that the qualifications that have been added to the layman's definition of motion in the pursuit of greater specificity are too restrictive, and lead to misinterpretation of a number of basic physical phenomena.
The core of the currently accepted definition is the assertion that motion is a change of position relative to some identifiable object. For present purposes, this statement can be accepted as valid, But present-day physics goes on to assert that in order to define the motion of object A specifically, a frame of reference must be constructed on the reference object B. The location of object A is then specified by a position vector in the reference frame, and its rate of motion is specified by a velocity vector, the time rate of change of the position vector.
Any change that can be defined by such a velocity vector is unquestionably a motion, but the point now at issue is whether this definition is comprehensive; that is, are there motions that cannot be defined in this manner? For an answer to this question let us look first at the astronomical situation. One of the most important astronomical discoveries of modern times is the recession of the distant galaxies. According to measurements of the Doppler shift in the radiation received from these objects, they are all moving radially outward from our galaxy at high speeds. We cannot measure the motion of our own galaxy, but unless we make the assumption that it is the only stationary object in the universe, an assumption that was repudiated by science long ago, our galaxy is receding from all of the others; that is, it is moving outward in all directions. And since it is conceded that our galaxy is not unique, it follows that all of the widely separated galaxies are moving radially outward from each other in all directions.
Attempts have been made to explain the origin of this motion, the currently favored hypothesis being that it is due to a general expansion of the universe. But it does not seem to have been generally realized that the nature of the motion itself is something that also calls for a more comprehensive understanding. So far as can be determined from the scientific literature, the characteristics of the motions of these distant galaxies have not been subjected to any critical investigation, apparently because it has been assumed that the galactic situation is a special case, having no relevance to physical activity as a whole.
The error in this assumption is evident when we note that gravitation is clearly the same kind of motion. This is not readily recognizable under all circumstances, but since the basic nature of a physical phenomenon does not change, we can establish the basic nature of gravitation by consideration of an example in which the extraneous factors that tend to confuse the situation are at a minimum. Let us consider a number of galaxies relatively close together, as they are in a cluster, and approximately the same size. ¥e know that since these galaxies are free to move, they will move inward in all directions toward each other at speeds that conform to a uniform pattern. This motion is identical with that of the distant galaxies, except that it is negative (that is, it reduces the separation between the moving objects) whereas the motions of the distant galaxies are positive. Motion that takes place uniformly in all directions coincident-ally has no specific inherent direction. It is completely defined by a magnitude (positive or negative); that is, it is a scalar motion.
A small-scale example of scalar motion can be seen in the motions of spots on the surface of an expanding balloon, often used as an illustration by those who undertake to explain the nature of the galactic motion. In this case, the motion can be reversed. Spots on the surface of a contracting balloon have a negative scalar motion analogous to that of gravitating objects.
Whenever a new view of a familiar phenomenon is introduced there is a general tendency to assume that it is a product of a new theory or hypothesis, and the question as to the validity of that innovation becomes an important issue. It should therefore be emphasized that the existence of scalar motion is a matter of direct observation, and is independent of any theory. It is one of those observed facts with which all theories must agree in order to be valid. The previous failure to recognize the existence of this type of motion was not due to any lack of empirical evidence, or to any question as to the validity of that evidence. It was purely an oversight, due mainly to the manner in which knowledge in the two physical areas most directly involved has developed. Understanding of gravitation has been developed in terms of force, without a clear recognition of the fact that force, by definition, is a property of motion (a point that will be examined later in this discussion). Meanwhile, the concept of motion as inherently vectorial had remained unchallenged for so long that the deviant characteristics of the galactic motion were not recognized in their true light when discovered.
There has been a general realization that the motion of spots on the surface of an expanding balloon is, in some way, different from the motions of our ordinary experience. It is this realization that has made the use of the balloon for explanatory purposes feasible. But expanding balloons play no significant role in physical activity, and no one has heretofore been sufficiently interested in the physics of these objects to undertake a systematic investigation of the characteristics of their motion. Once it is recognized that gravitation and the recession of the distant galaxies are motions of the same kind, this investigation can no longer be neglected. This finding makes it clear that scalar motion is not something minor and incidental. It is one of the basic features of the physical universe.
The characteristics of vectorial motion are defined by Newton's laws of motion, and are accurately represented in the conventional reference systems. The first law, which is accepted as a postulate in mechanics, states that an object which is not acted upon by any force moves at a constant speed (which may be zero) in a straight line in the reference system. Such a vectorial motion has a specific direction, and if that direction is defined with respect to one location in the reference system it is thereby defined with respect to all locations in the system. Thus, if object A is moving in the direction AB when observed from point X, it is also moving in the direction AB when observed from any other point Y, providing that the observations are accurate in both cases. Coincident vectorial motion at uniform speed in all directions would result in no net movement, and no change of position in the reference system.
Scalar motion does not conform to these relations. In the examples cited, the motions take place coincidentally in all inward or outward directions (contrary to Newton's first law), and result in changes of position in all of these directions. Such motion has no property other than a magnitude. It is simply an increase or decrease in the separation between identifiable points or objects. Thus it has no inherent relation to the reference system. In order to represent scalar motion in a reference system of the conventional type, a coupling to the reference system, independent of the motion, must be supplied. The direction of the motion, as seen in the reference system, is a property of the coupling, not a property of the motion.
Obviously, a conventional spatial coordinate reference system, which cannot represent coincident motion in more than one direction; is incapable of representing multidirectional scalar motion in its true character. It represents only one component of the total motion, and gives us a distorted picture of that component. If we designate our galaxy as A, the direction of motion of galaxy X, as we see it, is AX, and its position at time t is x1, a location on an extension of the line AX. But observers in galaxy B, if there are any, see it as moving in the very different direction BX, and see its position at time t as x2 a location on an extension of the line BX. Those in galaxy G see the direction as GX and the location at time t as x3, and so on. No one of these directions or positions has any more significance than another. We cannot define a specific point that represents the position of galaxy X in the reference system. The best that we can do is to define a location in the reference system that represents the position of that distant galaxy relative to the location of our Milky Way galaxy.
When we observe the moving system of galaxies from one of these specific locations, we are taking that location as a reference point. In effect, we are coupling the moving point to the reference system, identifying it with a fixed point in that system. The moving galaxy from which the observation is being made is then represented as motionless, while each of the other galaxies in the scalar system, which are actually moving in all directions, is represented as moving only in the direction radially outward from the point of observation. The speeds: of the individual galaxies are similarly misrepresented. Since the rate of increase in the separation between any two galaxies is not altered by the coupling to the reference system, the immobilization of the reference galaxy by the coupling has the effect of transferring its motion to each of the other galaxies in the system.
This finding that the position of an object with a scalar motion similar to that of the distant galaxies can be specifically defined in a spatial reference system only relative to some particular point, and cannot be defined relative to the reference system as a whole, in the manner in which vectorial motion is defined, will no doubt be distasteful to many, perhaps most, scientists, particularly since it opens the door to the possibility that there may be still other limitations on the capabilities of the conventional reference systems. Our everyday activities take place in a fixed three-dimensional space, and it seems to "be a fact of experience that every physical object occupies a specific location in that space. But time and again in the history of science an assumption that once seemed almost axiomatic has had to "be abandoned when additional information became available. The revision of existing ideas about motion that is now required is merely another instance of this same kind. The existence of scalar motion is undeniable, once attention has been called to it. The properties of this type of motion, and the limitations on the ability of the conventional reference systems to represent the positions and motions of the objects that are involved, are therefore empirically established features of physical activity with which all physical theories must come to terms.
Several other aspects of scalar motion are relevant to the present discussion. In the galactic situation, the location of the observer is the reference point, but the reference location for other scalar motion may be, and usually is, determined by other factors. In gravitation, the location of any mass that is stationary in the reference system becomes the reference point for the scalar system of motions of which the motion of that mass is a member. The reference point in the case of the expanding balloon is determined by the placement of the balloon. If it is placed on the floor of a room, the point on the balloon surface that is in contact with the floor is the reference point.
Two basic features of scalar motion are illustrated by the balloon placement. First, the reference point of a scalar- motion is independent of the motion itself, and may "be altered by external factors. The balloon can be moved. Second, the reference point, and the system of motions related to it, may be in motion vectorially. For instance, the balloon may be resting on the floor of a moving vehicle. As can be seen from this illustration, the two types of motion are independent.
No theories or assumptions are involved in the description of the relations between scalar motion and the conventional reference systems given in the foregoing paragraphs. The details of the representation of this type of motion in the reference system are simply a matter of geometry. Thus the conclusions that have been reached are factual, not theoretical or speculative. The results that we obtain by applying these findings to specific physical situations are therefore likewise factual.
We may begin this application by noting that the findings with respect to the representation of scalar motion in the conventional reference systems show that gravitation is an inward scalar motion, not only where the gravitating objects are free to move, so that the motion is observable, but in all cases. Recognition of the generality of this identification has heretofore been blocked by the observation that gravitational effects often originate in objects that are not in motion, as motion is currently defined. This obstacle is now removed by the finding that all gravitating objects are moving inward in all directions, and that the apparent lack of motion in some cases is due to the inability of the reference system to represent scalar motion as it actually exists.
Ordinarily, motion of a mass is produced "by application of a force. The observation that a mass B in the vicinity of another mass A acquires a motion toward A, while mass A acquires a motion toward B, has therefore led to the conclusion that each mass is exerting a force on the other. However, our discussion thus far has dealt only with motions. In order to clarify the role of force in the gravitational process we will need to consider the relation between force and motion. For application in physics, force is defined by Newton's second law of motion. It is the product of mass and acceleration: F = ma. Motion is measured on an individual mass unit basis as velocity-that is, each mass unit moves at this rate-or on a collective basis as momentum, the product of mass and velocity. Momentum was formerly called "quantity of motion", a term that more clearly expresses the nature of this quantity, which is actually the sum of the motions of the individual units. The time rate of change of the motion is dv/dt (acceleration, a) in the case of the individual unit, and m dv/dt (force, ma) when measured collectively. Thus force is a property of a motion, in exactly the same sense as acceleration. It is the time rate of change of the total quantity of motion, the "quantity of acceleration", we could appropriately call it.
The significance of this point, in the present connection, is that a force cannot be autonomous. By definition, it is a property of a motion. Thus wherever we find that a force exists, it follows that there must necessarily be an underlying motion of which the force is a property. This is a positive requirement, with no exceptions. A force cannot originate in a motionless object. Either the object itself, or one or more of its constituents, must be moving in the direction of the force. There cannot be any such thing as a "fundamental force". The so-called fundamental forces are the force aspects of fundamental motions. In the gravitational case we have found that all members of any system of gravitating objects are moving inward toward each other, even if one of them is represented as stationary in the reference system. The gravitational force is the force aspect of this gravitational motion.
Since scalar motion takes place coincidentally in all directions, the magnitude of the mutual gravitational motion of two masses is distributed over the area of a spherical surface with a radius equal to the distance between the masses. The gravitational effect thus varies inversely as the second power of the distance. Where this distance is large in proportion to the amount of mass involved, the effect is negligible. But at the shorter distances each of the constituent units of mass A has an inward gravitational motion toward each of the constituent units of mass B. If both masses are free to move, the representation of the mutual motion in the reference system is divided equally between motion of A and motion of B. If the location of one of these masses is represented as fixed, the entire motion is attributed to the other mass, for reasons explained earlier. It should be noted, however, that the reference system does not represent the total scalar motion, the product of the speed and the number of units involved. It represents the speed only. Thus the motion (measured as speed) of mass B is represented in the reference system as proportional to the total motion AB divided by the mass B; that is, it is proportional to the mass of A.
Here, than, is the explanation of the gravitational field. The question as to the nature of a "field" is a long-standing scientific problem. A typical definition taken from a physics text says that an electric field is "what is in the space around an electric charge that allows one charge to interact with another". As this definition indicates, the field is a phantom. There is no actual evidence that there is anything in this space that could be identified with the hypothetical field. But the currently accepted physical theories require some kind of a medium to transmit gravitational and electromagnetic effects, and it is therefore assumed that there must be something in the space that serves this purpose. For the modern physicist, says Einstein, the field is "as real as the chair on which he sits".
In fact, the only way in which any indication of a gravitational effect in the vicinity of a massive object can be obtained is to introduce a test mass into this apace. This test mass accelerates toward the massive object. But, as brought out in the foregoing discussion, this is not due to anything that exists in the space. Each mass has an inherent scalar motion that carries it inward toward the other.
As has been explained, the scalar speed of mass B toward mass A (the quantity represented in the reference system) is independent of the mass of B. It is determined by the magnitude of the mass A and the distance between the masses. Thus each point in the space surrounding mass A can be characterized by a magnitude representing the gravitational speed that a mass would have if it were located at that point. However, the actual speed of such a mass always includes an additional component of a vectorial nature, unless the mass has been in free fall all the way from a great distance. It is therefore convenient to take a different property of the motion, the force (total acceleration), rather than the speed, as the acceleration is a result of the geometry of the scalar motion, and is independent of the accompanying vectorial motion. Each of the spatial locations surrounding mass A can be assigned a magnitude and a direction, representing the gravitational force that would be exerted on a unit mass, if one were present. The ensemble of all of these vectors is the gravitational field of mass A.
We thus see that the field is not a tangible physical entity. It might be compared to a set of steam tables. We can refer to these tables and determine the heat content of the steam in a boiler at certain specific levels of temperature and pressure. But this does not tell us anything about the conditions that actually exist in the boiler. It may not even contain any steam. The tables merely tell us what the heat content would "be if certain conditions did exist. Similarly, the tabulations of "field strength" (usually, but not necessarily, expressed graphically) tell us only what forces would be experienced at specific locations if masses happened to occupy those locations. The force field has no more physical existence than the steam tables.
The foregoing explanation of the origin of the forces that appear to be exerted on distant objects also provides the answer to the longstanding problem of action-at-a-distance. Newton's gravitational law appears to call for direct action of one mass on another, regardless of their spatial separation, but many scientists are strongly opposed to the idea that a force can be exerted without a physical contact of some kind. The prevailing opinion has therefore been that the force must be transmitted through some kind of a medium, notwithstanding the total lack of evidence to support such an assumption. The need for this hypothetical medium is now eliminated by the finding that each object in a gravitational system has an inherent negative (inward) scalar motion, and is therefore approaching all other objects in the system because they are moving inward in the same manner.
When the gravitational situation is thus clarified it becomes evident that the forces due to electric charges and the corresponding magnetostatic phenomena (magnetic charges, we may call them) are likewise properties of hitherto unrecognized scalar motions. Observationally, these motions differ from the gravitational motion only in those respects in which scalar motion in general is variable; that is, the motions may differ in magnitude, they may be either positive or negative, and the nature of the coupling to the reference system may vary. Here, again, the absence of observable motion at the point of origin of the force is due to the fact that the location of the charge is the reference point at which the representation of the motion in the reference system is frozen by the coupling of the moving scalar system to the fixed reference system.
The existence of these different types of scalar motion raises the question as to why the apparent interactions are limited to motions of the same kind; why electric charges interact (or appear to interact) only with electric charges, and so on. The answer can be found in the mutual nature of scalar motion. Since the motion of A relative to B, and the motion of B relative to A, are merely two different ways of representing the same motion in the reference system, it follows that a scalar motion AB cannot take place unless the individual motions of A and B are of the same scalar type. There is no interaction between a charge and a mass.
This same property of scalar motion also accounts for the fact that we are able to observe the gravitational motion of a mass only in the direction of other masses, although the motion actually takes place in all directions. Before we can arrive at a complete explanation of this situation, however, it will be necessary to give some consideration to the question as to the existence of an absolute system of reference. The prevailing scientific opinion concurs with Einstein's assertion that there is no absolute reference system, although there is some uneasiness about the rotational situation and about the significant role that the system based on the average positions of the fixed stars seems to play in physical activity. But the conclusion that there is no absolute system of reference is based on arguments that apply only to vectorial motion. What we now want to know is whether an absolute system of reference can be defined for scalar motion.
An absolute system of reference is one in which an object that is, in fact, motionless is represented in its true condition as stationary. We can further say that any object which has no inherent capability of movement in the reference system, and has: not been acted upon by any outside agency, is, in fact, motionless. It has not been possible, thus far, to find any objects that qualify as motionless from the vectorial standpoint. But at least three classes of objects can be identified, on the basis of the foregoing criterion, as having no scalar motion. These are (l) photons of radiation, (2) neutrinos and other massless particles, and (3) galaxies at extreme distances where the effect of gravitation is negligible.
Of course, there is always the possibility that our observations may not be giving us the complete picture, and that one or more of these classes of objects is subject to some unrecognized type of scalar motion. However, this possibility is ruled out by the fact that all three classes of objects follow exactly the same pattern. All of the objects identified as motionless from the scalar standpoint move outward at the speed of light relative to the conventional system of reference. Since these objects are necessarily stationary in the absolute system of reference, it follows that this absolute system of reference for scalar motion is moving outward at the speed of light relative to the conventional reference system.
The reference system that represents a motionless object in its true motionless condition is likewise the correct reference system for objects that are, in fact, moving. Thus the absolute system of reference that has been defined is the natural reference system for scalar motion, the one to which the physical universe actually conforms. Every physical object is being carried outward at the speed of light by the movement, or progression, of the natural reference system relative to the conventional system of reference.
Why, then, do most physical objects "stay put", and only the exceptional ones move outward in the manner of the photons? The answer clearly is that all objects with mass are moving inward gravitationally in opposition to the outward progression of the natural reference system. The observed scalar motion is the net resultant of the two opposing motions. At the very short distances of our ordinary experience the outward progression of the natural reference system, which is constant, is negligible compared to the inward gravitational effect, which is inversely proportional to the second power of the distance. However, as the distance increases the gravitational motion decreases, and at a certain very great distance (which is a function of the mass, and is in the neighborhood of two million light years for objects as massive as the larger galaxies) it reaches equality with the outward progression. Beyond this point each galaxy has a net outward motion, increasing toward the speed of light as the distance becomes greater and the gravitational effect decreases still further. Here, then, is the explanation, not only of the recession of the distant galaxies, but also of the inward motion of most of those that are relatively close together.
The finding that there is a hitherto unrecognized motion (and force) of general application illustrates the importance of expanding the currently existing concept of the nature of motion to take scalar motion into account. As brought out in the preceding paragraph, the clarification of the fundamental situation automatically provides the explanation of the recession of the distant galaxies, and eliminates the need to assume the existence of some process such as a universal expansion or a Big Bang to account for the outward motion. Furthermore, the same relations between the opposing motions are also effective in application to the shorter distances and smaller masses, and explain many hitherto poorly understood physical phenomena, including such items as the immense distances between stars, and the structure of the globular clusters.
Identification of the outward progression of the natural
reference system enables us to complete the explanation of the lack of observational evidence of gravitational motion toward locations in space that are not occupied by objects with mass. A point in a spatial reference system obviously has no capability of independent motion. However, as we have found, this point is being carried outward by the motion of the natural reference system relative to the conventional system of reference. The inward motion of gravitation operates against this outward progression up to a speed level equal to the speed of this progression. Because of the mutual character of scalar motion, the effective gravitational speed toward the unoccupied location in space cannot exceed the limiting speed of the point in the reference system. The excess gravitational motion is unobservable (another instance in which the conventional reference system is incapable of representing scalar motion in its entirety). Since the effective inward and outward motions are equal, there is no net change of relative position, and the gravitational motion toward the unoccupied location is unobservable.
The mutual gravitational motion of two masses is not subject to any limitation, and the full net speed of both participants is effective in changing their observable positions in the reference system. Here we have the answer to the frequently asked question, How does mass A know that it must change the direction of its gravitational force when mass B moves from location X to location Y? The answer is that mass A is moving gravitationally in all directions at all times, whether or not other masses are present. Its motion toward mass B, and therefore also toward location X, occupied momentarily by mass B, is observable, whereas its motion toward unoccupied location Y is unobservable. If mass B moves to location Y, the previously observable motion of mass A in the direction AX becomes unobservable, while the previously unobservable motion in the direction AY becomes observable. This is not a unique situation. It is typical of the results of the unidirectional representation of multidirectional scalar motion in the conventional spatial reference systems. The same kind of a pattern can be seen, for instance, in the galactic recession. Galaxy X is moving outward in all directions. When it is viewed from galaxy A, the motion in the direction AX is observable, while that in the direction BX is unobservable. But if the observer moves to galaxy B, the previously observable motion in the direction AX becomes unobservable, whereas the previously unobservable motion in the direction BX becomes observable.
Returning to the question to which this discussion is addressed, Are there motions that are not included within the physicists' definition of this term, the answer is definitely Yes! The accepted definition requires motion to be vectorial-that is, to have both magnitude and direction-whereas, in fact, the basic motions of the universe are scalar; they have magnitude only. The directions, in the context of the conventional reference systems, that are attributed to those that are actually recognized as motions are properties of the coupling of the scalar motion to the reference system, not properties of the motions.
As would be expected where a basic concept is modified, recognition of the existence of scalar motion has some far-reaching consequences. Some of these have been identified in the foregoing pages. However, the discussion has been limited to the immediate and direct results of the revision of the motion concept, in order to make it unnecessary to introduce anything from theoretical sources. Since the existence of scalar motion is an observed fact, these immediate consequences of that existence are likewise purely factual.
Dewey B. Larson