## CHAPTER 6## The Reciprocal RelationInasmuch as the fundamental
postulates define a universe composed entirely of units of motion, and
define space and time in terms of that motion, these postulates preclude
space and time from having any significance other than that which they
have in motion, and at the same time require that they This general reciprocal relation
that necessarily exists in a universe composed entirely of motion has
a far-reaching and decisive effect on physical structures and processes.
In recognition of its crucial role, the name “Reciprocal” has been applied
to the system of theory based on the “motion” concept of the nature of
the universe. The reason for calling it a “system of theory” rather than
merely a “theory” is that its The reciprocal postulate provides
a good example of the manner in which a change in the basic concept of
the nature of the universe alters the way in which we apprehend specific
physical phenomena. In the context of a universe of matter existing in
a space-time framework, the idea of space as the reciprocal of time is
simply preposterous, too absurd to be given serious consideration. Most
of those who encounter the idea of “the reciprocal of space” for the first
time find it wholly inconceivable. But these persons are not taking the
postulates of the new theory at their face value, and recognizing that
the assertion that “space is an aspect of motion” means exactly what it
says. They are accustomed to regarding space as some kind of a container,
and they are interpreting this assertion as if it said that “container
space is an aspect of motion,” thus inserting When the new ideas are viewed in the proper context, the strangeness disappears. In a universe in which everything that exists is a form of motion, and the magnitude of that motion, measured as speed or velocity, is the only significant physical quantity, the existence of the reciprocal relation is practically self-evident. Motion is defined as the relation of space to time. Its mathematical expression is the quotient of the two quantities. An increase in space therefore has exactly the same effect on the speed, the mathematical measure of the motion, as a decrease in time, and vice versa. In comparing one airplane with another, it makes no difference whether we say that plane A travels twice as far in the same time, or that it travels a certain distance in half the time. Inasmuch as the postulates
deal with space and time in precisely the same manner, aside from the
reciprocal relation between the two, the behavior characteristics of the
two entities, or The most conspicuous property
of space is that it is three-dimensional. On the other hand, it is generally
believed that the observational evidence shows time to be one-dimensional.
We have a subjective impression of a unidirectional “flow” of time from
the past, to the present, and on into the future. The mathematical representation
of time in the equations of motion seems to confirm this view, inasmuch
as the quantity Notwithstanding its general
and unquestioning acceptance, this conclusion as to the one-dimensionality
of time is entirely unjustified. The point that is being overlooked is
that “direction,” in the context of the physical processes which are represented
by vectorial equations in present-day physics, always means “direction
in space.” In the equation It is quite true that this
result would automatically follow if time were one-dimensional, but the
one-dimensionality is by no means a necessary condition. Quite the contrary,
time is scalar in this space velocity equation (and in all of the other
familiar vectorial equations of modern physics; equations that are vectorial
because they involve direction in space) The existing confusion in
this area is no doubt due, at least in part, to the fact that the terms “dimension” and “dimensional” are currently used with two different meanings.
We speak of space as three-dimensional, and we also speak of a cube as
three-dimensional. In the first of these expressions we mean that space
has a certain property that we designate as dimensionality, and that the
magnitude applying to this property is three. In other words, our statement
means that there are three dimensions There is a rather general
tendency to interpret any postulate of multi-dimensional time in this
latter significance; that is, to take it as meaning that There is nothing in the role
which time plays in the equations of motion in space to indicate specifically
that it has more than one dimension. But a careful consideration along
the lines indicated in the foregoing paragraphs does show that the present-day
assumption that we Perhaps it might be well to point out that the additional dimensions of time have no metaphysical significance. The postulates of a universe of motion define a purely physical universe, and all of the entities and phenomena of that universe, as determined by a development of the necessary consequences of the postulates, are purely physical. The three dimensions of time have the same physical significance as the three dimensions of space. As soon as we take into account
the effect of gravitation on the motion of material aggregates, the second
of the observed differences, the Little additional information about either space or time is available from empirical sources. The only items on which there is general agreement are that space is homogeneous and isotropic, and that time progresses uniformly. Other properties that are sometimes attributed to either time or space are merely assumptions or hypotheses. Infinite extent or infinite divisibility, for instance, are hypothetical, not the results of observation. Likewise, the assertions as to spatial and temporal properties that are made in the relativity theories are, as Einstein says, “free inventions of the human mind,” not items that have been derived from experience. In testing the validity of
the conclusion that all properties of As brought
out in Chapter 4, deviations from unit speed,
the basic one-to-one space-time ratio, are accomplished by means of reversals
of the direction of the progression of either space or time. As a result
of these reversals, one component traverses the same path in the reference
system repeatedly, while the other component continues progressing unidirectionally
in the normal manner. Thus the deviation from the normal rate of progression
may take place For example, let us consider
an object rotating with speed 1/n and moving translationally with speed
1/n. The reciprocal relation tells us that there must necessarily exist,
somewhere in the universe, an object identical in all respects, except
that its rotational and translational speeds are both n/1 instead of 1/n.
In addition to the complete inversions, there are also structures of an
intermediate type in which one or more components of a complex combination
of motions are inverted, while the remaining components are unchanged.
In the example under consideration, the translational speed may become
n/1 while the rotational speed remains at 1/n, or vice versa. Once the
normal (1/n) combination has been identified, it follows that both the
completely inverted (n/1) combination and the various intermediate structures
exist in the appropriate environment. The general nature of that environment
in each case is also indicated, inasmuch as change of position in time
cannot be represented in - a spatial reference system, and each of these
speed combinations has some special characteristics when viewed in relation
to the conventional reference systems. The various physical entities and
phenomena that involve motion of these several inverse types will be examined
at appropriate points in the pages that follow. The essential point that
needs to be recognized at this time, because of its relevance to the subject
matter now under consideration, is the This is a far-reaching discovery of great significance. In fact the new and more accurate picture of the physical universe that is derived from the “motion” concept differs from previous ideas mainly by reason of the widening of our horizons that results from recognition of the inverse phenomena. Our direct physical contacts are limited to phenomena of the same type as those that enter into our own physical makeup: the direct phenomena, we may call them, although the distinction between direct and inverse is merely a matter of the way in which we see them, not anything that is inherent in the phenomena themselves. In recent years the development of powerful and sophisticated instruments has enabled us to penetrate areas that are far beyond the range of our unaided senses, and in these new areas the relatively simple and understandable relations that govern events within our normal experience are no longer valid. Newton's laws of motion, which are so dependable in everyday life, break down in application to motion at speeds approaching that of light; events at the atomic level resist all attempts at explanation by means of established physical principles, and so on. The scientific reaction to this state of affairs has been to conclude that the relatively simple and straightforward physical laws that have been found to apply to events within our ordinary experience are not universally valid, but are merely approximations to some more complex relations of general applicability. The simplicity of Newton's laws of motion, for instance, is explained on the ground that some of the terms of the more complicated general law are reduced to negligible values at low velocities, and may therefore be disregarded in application to the phenomena of everyday life. Development of the consequences of the postulates of the Reciprocal System arrives at a totally different answer. We find that the inverse phenomena that necessarily exist in a universe of motion play no significant role in the events of our everyday experience, but as we extend our observations into the realms of the very large, the very small, and the very fast, we move into the range in which these inverse phenomena replace or modify those which we, from our particular position in the universe, regard as the direct phenomena. On this basis, the difficulties that have been experienced in attempting to use the established physical laws and relations of the world of ordinary experience in the far-out regions are very simply explained. These laws and relations apply specifically to the world of immediate sense perception, phenomena of the direct space-time orientation, and they fail in application to any situation in which the events under consideration involve phenomena of the inverse type in any significant degree. They do not fail because they are wrong, or because they are incomplete; they fail because they are misapplied. No law–physical or otherwise-can be expected to produce the correct results in an area to which it has no relevance. The inverse phenomena are governed by laws distinct from, although related to, those of the direct phenomena, and where those phenomena exist they can be understood and successfully handled only by using the laws and relations of the inverse sector. This explains the ability of the Reciprocal System of theory to deal successfully with the recently discovered phenomena of the far-out regions, which have been so resistant to previous theoretical treatment. It is now apparent that the unfamiliar and surprising aspects of these phenomena are not due to aspects of the normal physical relations that come into play only under extreme conditions, as previous theorists have assumed; they are due to the total or partial replacement of the phenomena of the direct type by the related, but different phenomena of the inverse type. In order to obtain the correct answers to problems in these remote areas, the unfamiliar phenomena that are involved must be viewed in their true light as the inverse of the phenomena of the directly observable region, not in the customary way as extensions of those direct phenomena into the regions under consideration. By identifying and utilizing this correct treatment the Reciprocal System is not only able to arrive at the right answers in the far-out areas, but to accomplish this task without disturbing the previously established laws and principles that apply to the phenomena of the direct type. In order to keep the explanation
of the basic elements of the theory as simple and understandable as possible,
the previous discussion has been limited to what we have called the direct
view of the universe, in which space is the more familiar of the two basic
entities, and plays the leading role. At this time it is necessary to
recognize that because of the Locations in time cannot be represented in a spatial reference system, but, with the same limitations that apply to the representation of spatial locations, they can be represented in a stationary three-dimensional temporal reference system analogous to the three-dimensional spatial reference system that we call extension space. Since neither space nor time exists independently, every physical entity (a motion or a combination of motions) occupies both a space location and a time location. The location as a whole, the location in the physical universe, we may say, can therefore be completely defined only in terms of two reference systems. In the context of a stationary
spatial reference system the motion of an absolute location, a location
in the natural reference system, as indicated by observation of an object
without independent motion, such as a photon or a galaxy at the observational
limit, is linearly outward. Similarly, the motion of an absolute location
with respect to a stationary temporal reference system is linearly outward
in time. Inasmuch as the gravitational motion of ordinary matter is effective
in space only, the atoms and particles of this matter, which are stationary
with respect to the spatial reference system, or moving only at low velocities,
remain in the same absolute locations in time indefinitely, unless subjected
to some external force. Their motion in three-dimensional time is therefore
linearly outward at unit speed, and the time location that we observe,
the time registered on a clock, is not the location in any temporal reference
system, but simply the The best way to get a clear picture of the relation of clock time to time in general is to consider the analogous situation in space. Let us assume that a photon A is emitted from some material object X in the direction Y. This photon then travels at unit speed in a straight line XY which can be represented in the conventional fixed spatial reference system. The line of progression of time has the same relation to time in general (three-dimensional time) as the line XY has to space in general (three-dimensional space). It is a one-dimensional line of travel in a three-dimensional continuum; not something separate and distinct from that continuum, but a specific part of it. Now let us further assume
that we have a device whereby we can measure the rate of increase of the
spatial distance XA, and let us call this device a “space clock” , Inasmuch
as all photons travel at the same speed, this one space clock will suffice
for the measurement of the distance traversed by Because objects at rest in
the stationary spatial reference system, or moving at low velocities with
respect to it, are moving at unit speed relative to any stationary In application to motion in
space, the total time, like the clock registration, is a scalar quantity.
Some readers of the previous edition have found it difficult to accept
the idea that time can be three-dimensional because this makes time a
vector quantity, and presumably leads to situations in which we are called
upon to divide one vector quantity by another. But such situations are
non-existent. If we are dealing with spatial relations, time is scalar
because it has no spatial direction. If we are dealing with temporal relations,
space is scalar because it has no temporal direction. Similarly, scalar rotation
and its gravitational (translational) effect take place An important result of the fact that rotation at greater-than-unit speeds produces an inward motion (gravitation) in time is that a rotational motion or combination of motions with a net speed greater than unity cannot exist in a spatial reference system for more than one (dimensionally variable) unit of time. As pointed out in Chapter 3, the spatial systems of reference, to which the human race is limited because it is subject to gravitation in space, are not capable of representing deviations from the normal rate of time progression. In certain special situations, to be considered later, in which the normal direction of vectorial motion is reversed, the change of position in time manifests itself as a distortion of the spatial position. Otherwise, an object moving normally with a speed greater than unity is coincident with the reference system for only one unit of time. During the next unit, while the spatial reference system is moving outward in time at the unit rate of the normal progression, gravitation is carrying the rotating unit inward in time. It therefore moves away from the reference system and disappears. This point will be very significant in our consideration of the high-speed rotational systems in Chapter 15. Recognition of the fact that each effective unit of rotational motion (mass) occupies a location in time as well as a location in space now enables us to determine the effect of mass concentration on the gravitational motion. Because of the continuation of the progression of time while gravitation is moving the atoms of matter inward in space, the aggregates of matter that are eventually formed in space consist of a large number of mass units that are contiguous in space, but widely dispersed in time. One of the results of this situation is that the magnitude of the gravitational motion (or force) is a function not only of the distance between objects, but also of the effective number of units of rotational motion, measured as mass, that each object possesses. This motion is distributed over all space-time directions, rather than merely over all space directions, and since an aggregate of n mass units occupies n time locations, the total number of space-time locations is also n, even though all mass units of each object are nearly coincident spatially. The total gravitational motion of any mass unit toward that aggregate is thus n times that toward a single mass unit at the same distance. It then follows that the gravitational motion (or force) is proportional to the product of the (apparently) interacting masses. It can now be seen that the comments in Chapter 5, with respect to the apparent change of direction of the gravitational motions (or forces) when the apparently interacting masses change their relative positions are applicable to multi-unit aggregates as well as to the individual mass units considered in the original discussion. The gravitational motion always takes place toward all space-time locations whether or not those locations are occupied by objects that enable us to detect the motion. A point that should be noted
in this connection is that two objects are in effective contact if they
occupy adjoining locations in Scientific history shows that physical problems of long standing are usually the result of errors in the prevailing basic concepts, and that significant conceptual modifications are a prerequisite for their solution. We will find, as we proceed with the theoretical development, that the reciprocal relation between space and time which necessarily exists in a universe of motion is just the kind of a conceptual alteration that is needed to clear up the existing physical situation: one which makes drastic changes where such changes are required, but leaves the empirically determined relations of our everyday experience essentially untouched. |