Dewey Larson: the Reciprocal Theory of the Universe


Richard Moore

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by Dewey Larson


Ever since the dawn of science, the ultimate objective of the theoreticians in 
the scientific field has been to devise a general physical theory: one in which 
all physical phenomena are derived from a single set of premises. As expressed 
by Richard Schlegel of Michigan State University:

In a significant sense, the ideal of science is a single set of principles, or 
perhaps a set of mathematical equations, from which all the vast process and 
structure of nature could be deduced.

Up to the present time, all of the many efforts along this line have been 
fruitless. It has not even been possible to derive the relations in one major 
physical field from general premises; that is, without making assumptions 
specifically applicable to that particular field and to that field only. But, 
the development of the Reciprocal System of theory has now produced just the 
kind of a thing that Dr. Schlegel describes: a set of basic postulates whose 
necessary consequences are sufficient in themselves to describe a complete, 
theoretical universe.

More than 90% of the conclusions derived from these postulates are in agreement 
with concurrent scientific thought, and are not contested. Thus, the Reciprocal 
is not only a general physical theory; it is a general physical theory that, on 
the basis of present knowledge, is at least 90% correct. It therefore 
constitutes a significant advance in scientific understanding, irrespective of 
the judgment that may ultimately be passed upon the remaining 10% of the 
conclusions derived from the theory.

Under the circumstances, many individuals are interested in making a critical 
examination of the development of thought from the fundamental postulates to the
various conclusions in order to satisfy themselves that this development is, in 
fact, purely deductive. This present work has been designed to facilitate such 
an examination. In the previous publications which introduced the new 
theoretical system it was, of course, necessary to devote much of the text to 
explanation and argument, and even though these works have emphasized the fact 
that all of the conclusions reached in the theoretical development are derived 
solely from a determination of the consequences of the postulates, many readers 
have been unable to follow all of the logical development of the various lines 
of thought. It is probably that this is due, at least in large part, to a 
tendency to expect something of a more esoteric nature‹some magic formula or 
all-embracing mathematical expression‹rather than the simple ³if this, then 
that² type of deductive developmenet by which the theoretical structure has been
constructed. In any event, it has seemed advisable to supplement these previous 
publications with a presentation which will cover the basic portions of the new 
system of theory without explanation or argument, and will concentrate entirely 
on a step-by-step derivation of the pertinent points.

This presentation as it now stands (subject to possible extension later) is 
essentially no more than a sample; it carries the development of theory forward 
only a few steps. But even this very modest start toward a determination of the 
consequences of the postulates already brings us to the point where some of the 
most important features of the physical universe have been duplicated by the 
theoretical features that have emerged. Already, in this very early stage of the
theoretical development, we find that the universe defined by the theory is 
expanding (as the observed universe does). It contains radiation, consisting of 
individual particles (photons) which travel outward at unit speed (the speed of 
light) in all directions from various points of emission, followed a wave-like 
path (in full agreement with the properties of radiation as observed.) The speed
of light, and of radiation in general, in this universe is constant, 
irrespective of the reference system (as it is in the observed universe).

The theoretical universe contains matter, consisting of individual atoms (as the
observed universe does). This matter is subject to gravitation, which acts 
instantaneously, without an intervening medium, and in such a manner that it 
cannot be screened off or modified in any way (just as gravitation does in the 
observed universe, although most theorists close their eyes to these facts 
because they cannot account for them). In this theoretical universe, there are a
specific number of different kinds of atoms with different properties; the 
chemical elements (as in the observed universe). These elements constitute a 
series, each member of which differs from its predecessor by one unit of a 
particular kind, and the series is divided into groups and sub-groups with 
certain group characteristics (all of which is in full agreement with 
observation). There are additional types of units similar to, but less complex 
than, the atoms, which have some, but not all, of the properties of the atoms 
(also in agreement with the observed properties that are currently assumed to 

In the light of this demonstration of how the major features of a theoretical 
counterpart of the observed physical universe‹radiation, matter, gravitation, 
the galactic recession, atomic structure, etc.‹can be derived by a relatively 
simple logical development of the conclusions that are implicit in the 
postulates of the theory, it should not be difficult to understand how the 
theoetical universe can be extended into great detail by further application of 
the same process of following out the logical implications of the postulates and
the conclusions previously derived. Furthermore, it is clear, even at this very 
early stage of the investigation, that this development is capable of resolving 
some of the most serious issues facing current science.

The manner in which the development of the theoretical structure leads to a 
unique set of numerical values for each chemical element‹a series number, and 
three rotational displacement values‹also shows how the mathematical character 
of the theoretical universe emerges side by side with the qualitative 
relationships. Obviously, these sets of numbers are the means by which the 
elements enter into the mathematical aspects of the many physical relations that
appear later in the development, and the simple manner in which they are deduced
from the basic premises should serve as an explanation as to why nothing of a 
more complex mathematical nature than simple arithmetic is needed in the early 
stages of the inquiry.

The fundamental postulates, together with some comments concerning the 
interpretation of the language in which they are expressed, are stated in 
Section 1. The statements that follow are sequential; that is, each is a 
necessary consequence of the statements that have preceded it, either in the 
postulates themselves, or in previous deductions from the postulates. The 
justification for asserting that each specific conclusion is a necessary 
consequence of something that preceded this may not always be obvious, but the 
objective of the present work is to identify the specific items entering into 
the system of deductions leading from the postulates to the various theoretical 
conclusions, and to show how each fits into the deductive pattern. Everything 
which might tend to divert attention from this objective, such as explanation or
argument, has therefore been omitted. In any case where the continuity of 
thought may not be clear reference should be made to previous publications 
describing the theory.

1. The Basic Relations
Conceptual Fundamentals

This theory introduces two new concepts into physical science: the concept of 
physical location, and the concept of scalar motion.

The nature of these new concepts can be illustrated by a consideration of the 
³expansion of the universe² that is postulated in the astronomers¹ latest theory
of the recession of the distant galaxies. As explained by Paul Davies, ³The 
expanding universe is not the motion of the galaxies through space... but is the
steady expansion of space.² Since the galaxies, on this basis, are not moving 
through space, each galaxy remains in what we will call a physical location in 
space. This physical location is moving outward in the context of the stationary
spatial reference system, carrying the galaxy with it. While only the galactic 
motion can be observed, all physical locations necessarily participate in the 
outward motion, irrespective of whether or not they are occupied by galaxies.

Inasmuch as all galaxies, and the physical locations that they occupy, are 
moving uniformly outward from all others, each is moving outward in all 
directions. A motion distributed uniformly over all directions has no specific, 
or inherent, direction; that is, it is scalar. Thus the expansion can be 
described as a positive scalar motion of all physical locations (represented as 
outward in the spatial reference system). Our new theory defines a universe of 
motion in which scalar motion of physical locations is not a unique phenomenon 
confined to the expansion recognized by the astronomers, but is the basic form 
of the motion from which all physical phenomena are derived.

Basic Premises

The basic premise of the theory consist of certain preliminary assumptions, a 
postulate, and a definition.

A. In order to make science possible, some preliminary assumptions of a 
philosophical nature must be made. We assume that the universe is rational, that
the same physical laws apply throughout the universe, that the results of 
experiments are reproducible, etc. These assumptions are accepted by scientists 
as a condition of becoming scientists, and are not usually mentioned in purely 
scientific discourse.

B. We assume that the generally accepted principles of mathematics, to the 
extent that they will be used in this development, are valid.

C. We postulate that the universe is composed entirely of one component, motion,
existing in three dimensions and in discrete units.

D. We define motion as the relation between two uniformly progressing reciprocal
quantities, space and time.

Deductive Development

Each of the following statements is a deduction from the postulate and the 
preceding statements. The objective of the deductive development is to determine
what can exist in the theoretical universe defined by the premises of the 
theory. In most cases it will be evident that the entity or phenomenon that 
theoretically can exist is identical with one that does exist in the actual 
physical universe, and there are no definite conflicts in any case. To the 
extent that the outline has been carried, the theoretical universe is thus a 
correct representation of the observed physical universe.

1. Motion, as defined, is measured in terms of speed, the scalar magnitude of 
the relation between space and time.

2. By reason of the postulated reciprocal relation between space and time, each 
individual unit of motion is a relation between one unit of space and one unit 
of time, a motion at unit speed.

3. We define the primary motions as those which can exist independently of the 
existence of motions of other types.

4. According to our definition, motion involves a uniform progression of both 
space and time. We define a point, or segment, on the line of the space 
progression at a given time as a physical location in space.

5. Inasmuch as we postulate that the universe is three-dimensional, we may 
represent the scalar progression of space by a line in a stationary 
three-dimensional spatial reference system, measuring the corresponding 
progression in time by means of a scalar device, a clock. In this reference 
system, a positive motion is represented as outward from a reference point, and 
a negative motion as inward. The terms outward and inward will be used in 
preference to ³positive² and ³negative to avoid possible confusion with another 
use of the latter set of terms.

6. The initial point of the progression of an individual unit of motion is zero.
As the distance between two points cannot be less than zero, it follows that the
primary motions are necessarily outward, increasing the distances relative to 
the initial points.

7. This progression is scalar. It is simply outward without any inherent 
direction. Motion outward from the initial point of the progression is therefore
outward from all points of reference.

8. From the foregoing, any two physical locations are progressing outward from 
each other at unit speed; that is, their separation is increasing at the rate of
one unit of space per unit of time.

9. We define the natural system of reference as that system in which the primary
motions do not cause any change in the positions of physical locations.

10. From (8) it follows that the natural system of reference is progressing 
outward at unit speed relative to the spatial system of reference.

11. We identify unit speed as the speed of light.

(The various features of the theoretical universe emerge from the deductive 
development without labels. It is therefore necessary to identify the physical 
phenomena to which they correspond. The correlation is usually quite evident, as
in this instance. In any event, it is self-verifying, as any error would quickly
show up in the subsequent development.)

12. Since the postulate specifies that nothing exists other than discrete units 
of motion, and the natural reference system is a direct consequence of the 
existence of the primary units, this reference system is the framework, or 
background, of the universe of motion, and does not represent any activity in 
that universe. The natural system of reference, as defined, is therefore the 
physical zero, or datum level, from which all physical activity extend.

13. We identify the outward progression of the natural reference system relative
to the stationary system of reference as the ³expansion of the universe² 
reported by the astronomers.

At this point we have arrived, by deduction from our basic premises, at an 
explanation of the general background of the physical universe that is 
essentially in agreement with the astronomers¹ assumption. (Our derivation leads
to a uniform outward speed, rather than a speed that varies with the distance, 
as produced by the kind of an expansion assumed by the astronomers, but this 
difference is easily accounted for, because there is a known force, gravitation,
that acts against the outward motion, with a magnitude varying as an inverse 
function of distance.)

The advantage of deriving this explanation of the universal background from a 
set of general premises, rather than merely assuming its existence, lies in the 
fact that further deductions can be made from these same premises. Instead of a 
single process involving the universe as a whole, the explanation that we have 
just derived from the premises of the theory of the universe of motion 
identifies the expansion as the result of outward scalar motions of individual 
physical locations. This opens the way for the existence of other scalar motions
of the same physical locations, independent motions, as we will call them.

14. Once the primary units of motion are in existence, units of inward scalar 
motion can be superimposed on the outward units. The net magnitude of the two 
motions is zero, and the combination therefore has no physical properties in a 
spatial reference system, but it constitutes a base upon which other 
combinations can be formed.

15. As stated in our definition, motion is a progression. Thus it is not a 
succession of jumps, even though it exists only in discrete units. There is 
progression within the unit, as well as unit by unit, simply because the unit is
a unit of motion (progression). The significance of the discrete unit postulate 
is that discontinuity can occur only between units, not within a unit. But the 
various stages of the progression within a unit can be identified.

16. The continuity of the progression within the units enables the existence of 
another type of scalar motion of physical locations. This is a motion in which 
there is a continuous and uniform change from outward to inward and vice versa; 
that is, a simple harmonic motion. At this stage of the development only 
continuous processes are possible, but a continuous change from outward to 
inward and the inverse is just as permanent as a continuous outward or inward 

17. In the two-unit complete cycle of the simple harmonic motion the net change 
of the spatial position of the physical location is zero. As represented in the 
spatial reference system, the two-unit combination remains stationary in the 
dimension of motion.

18. From (10) it follows that the physical location occupied by that motion 
combination (17) moves outward at the speed of light in a second dimension.

19. The path of the combined progressions then takes the form of a sine curve.

20. We identify such scalar motion combinations as photons. A system of photons 
is electromagnetic radiation.

(This derivation shows why radiation has the properties of a wave as well as 
those of particles. It is composed of particles (discrete units), but the motion
(progression) of these particles is wave-like.)

21. The outward movement of physical locations due to the motion of the natural 
reference system relative to the stationary spatial system carries with it not 
only the photons, but also any other physical entities that occupy such 

(In addition to the photons, there are certain other massless particles that 
have no known motion-producing mechanism, and must therefore remain stationary 
in the natural system of reference, unless acted upon by some outside agency. 
There are also objects‹very distant galaxies‹that do have a motion-producing 
mechanism (gravitation), but are so far away that the gravitational motion 
toward our location has been reduced to negligible levels. All of these objects 
behave exactly as required by the theory; that is, they move outward relative to
the spatial reference system at the speed of light.)

22. There is no inherent relation between the time magnitudes involved in the 
different dimensions of the photon motion. One is the time of the progression of
the natural reference system. The other is independent of this progression. Thus
the frequency of the radiation, the number of cycles per unit of the linear 
progression, can take any value, subject only to the capability of the process 
whereby the radiation is produced.

23. The postulate that the universe is three-dimensional means that three 
independent magnitudes are required for a complete definition of each of its 
basic quantities. Thus three dimensions of scalar motion are possible. In order 
to distinguish these purely mathematical dimensions of motion from the 
dimensions of space, which are geometrical, as well as mathematical, in the 
context of a spatial reference system, we will refer to them as scalar 

24. Only one dimension of motion can be represented in a three-dimensional 
spatial system of reference. Each motion shown in such a system is represented 
by a vector, a one-dimensional quantity having both magnitude and direction, and
any combinations of such motions can be represented by the vector sum, which is 
likewise one-dimensional.

25. A scalar motion has magnitude only, and no inherent spatial direction. It 
therefore has to be given a direction in order to be represented in a spatial 
reference system.

26. To give directions to the members of a system of scalar motions, it is 
necessary to couple one of the moving locations to the stationary reference 
system in such a way that it is represented as motionless. The directions 
imputed to the other motions of the system are then determined by their relation
to this assumed motionless reference point.

(For example, if we designate our galaxy as A, the direction of the motion of 
distant galaxy X, as we see it, is AX. But observers in galaxy B see galaxy X as
moving in a very different direction BX because they use a different reference 
point. This contrasts sharply with the directions of the motions of our ordinary
experience‹vectorial motions‹which are the same regardless of the location from 
which they are being observed. In this vectorial case the direction is the 
property of the motion.)

27. From (25) and (26), it follows that the factors which determine the 
direction of a scalar motion are independent of those which determine the 
magnitude. The direction is a result of the nature and location of the coupling 
of the motion to the reference system. It may be a constant direction, as in the
outward travel of the photons of radiation, or it may be a rotationally 
distributed direction, one that is continually changing.

28. From (27), the translational motion of a photon, instead of being 
unidirectional, as in (18), may be rotationally distributed in the reference 
system. The motion thus distributed, which we will call a scalar rotation, is a 
linear progression with a constant magnitude but a continually changing 

29. From (23), scalar rotation can take place coincidentally in three 
dimensions. From (24), however, it can be represented in a spatial reference 
system only on a one-dimensional basis. The magnitudes of the motions in the 
three dimensions are additive, and can be represented as a total, but the 
directions of the different distributions cannot be combined. The representation
in the reference system therefore indicates the correct magnitude (speed) of the
three-dimensional motion, but shows only the directions applicable to the single
dimension of the motion that is parallel to the dimension of the reference 

30. In the absence of any specific restrictive factor, rotationally distributed 
scalar motions are distributed over all spatial directions. The magnitude of 
such a motion toward a point in any given direction is therefore inversely 
proportional to the second power of the intervening distance.

(This is the origin of the ³inverse square law.² )

31. Inasmuch as the natural reference system progresses outward at unit speed 
relative to the spatial reference system, no further increment of outward speed 
is possible, because of the discrete unit postulate. The net total magnitude of 
a rotationally distributed linear motion must therefore be inward.

32. If the scalar motion is less than three-dimensional, the basic photon will 
move outward as radiation in a vacant dimension, and the motion combination will
disintegrate. In order to be stable, the rotationally distributed motion must 
therefore be three-dimensional.

33. The three-dimensional combination of vibrational and rotationally 
distributed motions appears in the reference system as an identifiable object 
moving inward in all directions. We identify such an object as an atom, or a 
sub-atomic particle. Collectively, the atoms and particles constitute matter.

34. We identify mass as a measure of the net magnitude of the rotationally 
distributed scalar motions of matter. We identify the observable inward-directed
effects of this motion as gravitation. The magnitude of the gravitational effect
is therefore directly proportional to the mass.

35. The inward gravitational motion of the atoms results in the formation of 
material aggregates of various sizes. In these aggregates the atomic motions 
(and masses) are independent and additive.

36. The outward motion due to the progression of the natural reference system 
always takes place at unit speed, regardless of the size of the aggregate or the
distance that is involved (8). The net relative motion of any two gravitating 
objects with no additional motions is the algebraic sum of the unit outward 
motion and the inward gravitational motion.

Because of the spherical distribution of the gravitational motion in the 
reference system, the magnitude of the motion of one unit of matter toward 
another is inversely proportional to the square of the intervening distance.

37. At relatively short distances gravitation predominates, and the net motion 
is inward. Since the gravitational motion decreases with distance, while the 
outward progression remains constant, the opposing motions reach equality at 
some greater distance, which we will call the gravitational limit. Beyond this 
distance the net motion is outward, increasing with distance, and approaching 
unity (the speed of light) at extreme distances.

(This theoretical pattern of net speeds is verified observationally by 
measurements of the Doppler shift in the radiation received from the distant 

38. The conventional spatial reference system in conjunction with a clock for 
measuring time represents a physical situation in which the space component of 
the progression of the natural reference system is neutralized by gravitation, 
while the time component progresses at the full normal rate. In this reference 
system, the space progression, as indicated by the motion of a massless object, 
appears as a one-dimensional motion through three-dimensional space.

39. Since we postulate a reciprocal relation between space and time, each of the
deductions expressed in the foregoing numbered statements is also valid in the 
inverse form; that is, with space and time interchanged.

40. We identify the time component of the progression of the natural reference 
system as the ³flow of time² registered on a clock.

41. It follows from (39) that motion in time takes place in three dimensions, in
the same manner as motion in space. The time component of the progression of the
natural reference system (clock time) is a one-dimensional outward motion 
through a stationary three-dimensional temporal system of reference, in which 
independent motions at different speeds and different directions also take 

42. Motion at unit speed causes unit change of position in both the spatial 
reference system and the temporal reference system. It is a motion in time as 
well as a motion in space.

43. When motion takes place in time, the constant progression analogous to clock
time is in space, and would be measured by some kind of a ³space clock.² But the
rates of progression are the same, one unit of space and one unit of time per 
unit of motion. Thus the measurements relative to the ³space clock² are 
identical with those relative to a clock that registers time, if expressed in 
the same units.

44. As noted in (2), the space-time ratio in the units of motion is fixed at 
unity by the reciprocal postulate. It follows that a reduction of speed‹as, for 
instance, by an increase in the distance between gravitating objects‹does not 
alter the ratio of space to time in the effective motion; it reduces the 
proportion of the total motion that is effective in increasing the spatial 
separation of the objects. This effective portion of the motion increases the 
separation by x units of space per one unit of clock time, where x is a 
fraction, and because of the fixed relation between space and time in the 
individual units, also increases the separation in time by x units.

45. Where only one motion is involved, the x units of time are coincident with 
the time progression, and do not enter separately into the determination of the 
speed. But if two objects are both moving, their relative position in space may 
change at a rate exceeding unity by some quantity x. From (44), the change in 
the separation in time then also exceeds unity (clock time) by x. The speed is 
(1+x)/(1+x)=1. Thus, if at least one of the two objects is a photon (or other 
object moving with unit speed), the relative speed is always unity. This agrees 
with statement (8).

(This is the explanation of the observed fact that the speed of light is 
independent of the reference system.)

46. Where motion at a speed greater than unity (motion in time) takes place 
under conditions that preclude actual changes of position in time, this motion 
acts as a modifier of the spatial motion; that is, a motion in equivalent space.
The spatial equivalent of a temporal magnitude x is 1/x.

47. Where scalar motion in space is three-dimensional, the speed in one of the 
dimensions may be greater than unity. But, as indicated in (29), the effective 
magnitude of a combination of motions is determined by the net total of the 
scalar speeds, and because there are two low speed dimensions, the net speed is 
less than unity. In this case, then, the motion in the high speed dimension acts
as a motion in equivalent space, and modifies the magnitude of the change of 
position in space, rather than causing a change of position in time.

48. We identify the material atoms with scalar rotation in equivalent space as 
the atoms of the electronegative elements.

49. We also encounter motion in equivalent space within the units of space. Here
no modification of the normal progression of space can take place (because of 
the discrete unit postulate), but motion can take place in time. Inasmuch as 
this motion within the spatial unit does not alter the position in time of the 
unit as a whole, the changes within the unit that result from the motion are 
observed in equivalent space rather than in actual time.

50. The existence of a spatial unit within which motion has properties quite 
different from those prevailing in the region outside the unit explains the 
discontinuity in physical properties at very short distances that has led to the
development of the quantum theory.

51. The progression of the natural reference system relative to the spatial 
system of reference is always outward, but, as indicated in (10), the natural 
datum level, or physical zero, is at unity, rather than at the mathematical 
zero. Within a unit of space, outward from unity is toward zero. It follows that
the progression within the unit, as seen in the spatial reference system, is 

52. From (31), the gravitational motion is inward. This direction, too, is 
inward relative to the natural datum, unity. Within a unit of space, it is 
therefore outward in the spatial reference system.

53. No stable equilibrium between the atoms or aggregates of matter is possible 
at separations greater than one unit of space. The inward and outward motions 
are equal at the gravitational limit, but this equilibrium is unstable, as the 
change in separation due to any unbalance between the opposing motions increases
the unbalance. Within a unit of space, where the directions of the basic motions
as seen in the spatial reference system, are reversed, the effect of a change in
separation between atoms due to an unbalance of the opposing motions reduces the
unbalance, and eventually results in the establishment of a stable equilibrium.

54. The positional equilibrium in equivalent space that is established within a 
unit of space accounts for the existence of the crystalline state of matter.

2. Atoms

In the first section of this outline, the general characteristics of the motion 
of which the universe is constructed, together with additional information about
the various forms and manifestations of that motion, were deduced from the 
postulates of the theory. With the benefit of this information we are now in a 
position to develop the details of the individual phenomena in the various 
physical fields. We will begin by identifying the possible combinations of 
scalar rotations (atoms and sub-atomic particles) and their individual 
characteristics, including the properties that are represented in the periodic 
table of the elements. As in Section I, each statement is a deduction from the 
postulates of the theory or from one or more of the numbered statements earlier 
in the outline.

55. As noted in (12), the primary motions are the framework, or background, of 
the universe of motion, and do not constitute any physical activity in that 
universe. Physical activity‹that is, meaningful change‹in the physical universe 
results from motions superimposed on the primary motions. We will now want to 
examine the general considerations involved in such combinations of motions. 
First we note that there are no restrictions on the combination of motions of 
the same kind in different dimensions. For instance, rotations in different 
scalar dimensions can combine by rotating around the same central point.

56. The normal progression, both of the natural reference system and of the 
added motions, is a continuous succession (rather than a combination) of units 
of the same kind. As soon as one unit of the progression ends, another one 
begins. But the units in a succession do not necessarily have to be identical. 
For example, the two-unit cycle of simple harmonic motion has the same initial 
and final points as a two-unit segment of unidirectional linear motion, and 
therefore fits into the linear progression. We may generalize this situation, 
and say that compatible units of a different kind of motion can replace units in
the normal progression.

57. It follows from (44) and (56) that compatible units of motion added in a 
dimension of an existing motion will merge with this previously existing motion,
merely altering its magnitude. Formation of a compound motion, a combination 
that retains the distinction between its components, therefore requires the 
addition of an incompatible motion.

58. Except where outside forces intervene, the added motion must oppose the 
original in order to achieve stability. Otherwise there is nothing to hold the 
components together. The opposition reduces the net total magnitude of the 
motion, and since lower numbers are more probable than higher numbers, this 
makes the combination more probable than independent existence of the 

59. A numerical constraint on the combinations is imposed by the discrete unit 
postulate. Addition of two inward units of motion to the unit outward 
progression of the natural reference system produces one net inward unit, the 
limiting value. The maximum linear addition to a motion combination is thus two 

60. Where the motion is n-dimensional, the maximum is two units in each 
dimension, a total of 2n units.

61. Scalar motion is measured in terms of speed (or inverse speed). As we have 
seen, however, the natural datum level is at unity, not at zero. The natural 
speed magnitudes are therefore the deviations from unity. A deviation downward 
from unity, 1/1 to 1/n, has the same natural magnitude, n-1 units, as a 
deviation upward from 1/1 to n/1. In dealing with the basic scalar motions we 
will therefore use the deviations rather than the speeds measured from zero. We 
will call these deviations ³speed displacements,² abbreviated to ³displacements²
where the meaning is clear.

62. Where quantities are reciprocally related, the choice as to which should be 
called ³positive² is purely arbitrary. It will, however, be convenient to refer 
to the phenomena of our ordinary experience as positive. Since the speeds in our
local environment are below unity, we will call a decrease in speed from 1/m to 
1/n a positive displacement of n-m units, and an increase in speed from m/1 to 
n/1 a negative displacement of n-m units.

63. The photon, as defined in (20), is a vibrating unit that moves outward 
translationally at the speed of light. As noted in (22), the frequency of the 
vibration is limited only by the capacity of the production process. The atom, 
defined in (33) is likewise a vibrating unit with an added linear (scalar) 
motion, but in this case the linear motion is rotationally distributed over all 
directions, and the rotational character of the added motion imposes some 
restrictions on the numerical magnitudes.

64. A one-dimensional scalar rotation (28) of the linear vibrational unit 
generates a two-dimensional figure, a disk. A scalar rotation of the disk around
another axis generates a three-dimensional figure, a sphere. This exhausts the 
available dimensions. The basic scalar rotation of the atom is therefore 

65. While no further rotation of the same kind (inward) is possible, the entire 
combination of motions can be given an outward scalar rotation around the third 
axis. This conforms to the requirements of (57)‹it is a one-dimensional addition
to a two-dimensional motion‹and those of (58)‹it is an outward motion added to 
an inward motion.

66. The vibrational speed displacement of the basic photon may be either 
positive (less than unity) or negative (greater than unity). For the present, we
will consider only those combinations in which the basic vibrational 
displacement is negative. We will call this system of combinations the material 
system. The system based on the positive photon speed will be called the cosmic 

67. From (58) we find that where the vibrational displacement is negative the 
net total rotational displacement must be positive.

68. Where a one-unit positive rotational displacement is applied to a one-unit 
negative vibration, the net total speed displacement (a scalar quantity) is 
zero. This combination of motions has no effective deviation from unit speed 
(the physical datum), and therefore has no observed physical properties. We will
call it the rotational base of the material system. A similar combination with 
positive vibration and negative rotation is the rotational base of the cosmic 

69. For convenience, we will represent the different motion combinations of this
type of sets of numbers representing the speed displacements in the three scalar
dimensions. We will specify only the effective magnitudes of the displacements, 
and we will use the letters M and C to indicate whether the combination belongs 
to the material or the cosmic system. The displacement magnitudes will be 
expressed in the form M a-b-c, where a and b are the effective displacements of 
the two-dimensional rotation, which we will call the magnetic rotation, and c is
the effective displacement of the one-dimensional, or electric, rotation. 
Negative displacements will be enclosed in parentheses. On this basis, the 
material rotational base is M 0-0-0, and the cosmic rotational base is C 0-0-0.

70. To the material rotational base we may add a unit of positive electric 
rotational displacement (that is, one unit of effective one-dimensional scalar 
rotation), producing M 0-0-1, which we identify as the positron. Or we may add a
unit of negative electric displacement, producing M 0-0-(1), which we identify 
as the electron. These are the first members of a series of combinations that we
identify as the sub-atomic particles of the material system.

71. Addition of a magnetic (two-dimensional) displacement unit to the material 
rotational base produces M ‹-‹-0. There are no half units, but a magnetic unit 
occupies both dimensions, and we therefore credit half to each. We identify this
combination as the muon neutrino.

72. At the unit level, the magnetic and electric displacement units are 
numerically equal; that is, 1‹ = 1. Addition of a unit of negative electric 
displacement to the muon neutrino therefore produces a combination with a net 
total rotational displacement of zero. We identify this combination, M ‹-‹-(1), 
as the electron neutrino (hereinafter referred to simply as the neutrino).

73. Geometrical considerations indicate that two photons‹in different scalar 
dimensions‹can rotate around the same central point without interference as long
as the rotational speeds are the same, thus forming a double structure. Any 
rotational combination with two or more net units of rotational displacement can
take the double structure.

74. This introduces a new situation: the existence of competing structures. The 
aim of our development of the consequences of the postulates of the theory of 
the universe of motion is to determine what can exist in that theoretical 
universe. Thus far we have been able to identify an existing feature of the 
observed physical universe corresponding to each of the entities and phenomena 
that we have found that can exist in the theoretical universe. From now on we 
will have to consider the possibility that the existence of certain structures 
may preclude the existence of competing structures. The result of the 
competition in each case is a matter of relative probability. Where the 
probabilities are nearly equal, the structures may coexist. Otherwise, the 
structure that is most probable (in a given set of circumstances), is the only 
one that exists under those circumstances, other than momentarily.

75. The double rotational structure is more compact, and therefore more 
resistant to disruption than the equivalent single structures. This gives it a 
sufficient margin of probability to preclude the existence of any significant 
quantity of the competing single structures (unless external forces intervene).

76. We identify the double rotational combinations as atoms.

77. The combination ‹-‹-1 has a total net rotational displacement of 2, and is 
excluded by (75). The two-unit magnetic structure M 1-1-0, and its positive 
derivative M 1-1-1, which have net displacements of 2 and 3 respectively, are 
likewise excluded for the same reason. But the negative derivative M 1-1-(1) can
exist as a particle, since its net displacement is only one unit. We identify it
as the proton.

78. A double rotating system with only one net unit of displacement can be 
formed by a combination of a rotation of the proton type, M 1-1-(1), and a 
rotation of the neutrino type, M ‹-‹-(1). We identify this combination, M 
1‹-1‹-(2), as the mass 1 isotope of hydrogen. Since the second rotation has a 
net displacement of zero, the probability difference between this double 
structure and the equivalent single structure, the proton, is small. These 
structures therefore coexist under appropriate conditions.

79. If the cosmic neutrino type of rotation, C (‹)-(‹)-1 is substituted for the 
material neutrino type of rotation in this double structure, the combination has
net total displacements of M ‹-‹-0. We identify it as the neutron.

80. Because of some significant differences between atoms and sub-atomic 
particles, we will use a different system of notation in representing the atomic
combinations. This notation will show the total speed displacement in each 
dimension (including the initial non-effective unit), will use a double unit, 
and will omit the letter symbols M and C, which are unnecessary when the initial
unit is included.

81. To convert the rotational displacement of the mass 1 hydrogen atom from the 
sub-atomic notation, M 1‹-1‹-(2), to the atomic notation, we divide by 2, 
obtaining 1-‹-(1), and then add the initial unit, the result being 1‹-1-(1). The
net effective displacement, in terms of the double unit is ‹.

82. An additional single unit of displacement brings the total to 2-1-(1). We 
identify this combination as the mass 2 isotope of hydrogen. This is the first 
of the complete two-rotation combinations (those with effective rotational 
displacement in both rotations). It is therefore given the atomic number 1.

83. One positive displacement unit (atomic basis) added to mass 2 hydrogen, 
2-1-(1), neutralizes the negative electric rotation, and produces 2-1-0. We 
identify this combination as helium, atomic number 2.

84. Successive additions of units of positive electric displacement, or the 
equivalent, to the helium atom, produce the other members of a series of atomic 
combinations, the series of chemical elements.

85. Inasmuch as the two-dimensional (magnetic) rotation is the basic rotation of
the atom, as indicated in (64), the magnetic rotation takes precedence over the 
electric rotation where both are possible. It follows that some of the additions
to the atomic series involve magnetic displacement in lieu of electric 
displacement. If we let n represent the number of double magnetic units of 
displacement (units of atomic number), the corresponding number of single 
magnetic units is 2n. When acting jointly in a motion combination, x magnetic 
units are equivalent to x‹ one-dimensional (electric) units. The 2n single 
magnetic units are therefore equivalent to 4n‹ single electric units. Dividing 
by 2 to convert the double units of the atomic system, we find that n magnetic 
displacement units in an atom are equivalent to 2n‹ electric displacement units.

86. Successive additions of magnetic displacement go alternately to the two 
magnetic dimensions, since small numbers are more probable than larger numbers. 
One magnetic unit added to helium, 2-1-0, produces 2-2-0, which we identify as 

87. Helium already has one effective magnetic displacement unit in each magnetic
dimension. Thus the increase from 2-2-0 involves a second unit in one of the 
dimensions. From (85), this second magnetic unit is equivalent to 2 ‹ 2‹ = 8 
electric units. It should be noted that this is the electric equivalent of the 
second unit, not the sum of the two units. The reason is that the progression in
the region inside unit space takes place in time only, and the succession of 
values is 1/1, 1/2, 1/3, 1/n. The number of time units involved is 1,2,3,...n. 
Thus the value 2 applies to the second unit only, not to the total of the first 
two units.

88. The first four additions of electric displacement units to helium produce 
the following series of elements:


89. As long as the magnetic displacement‹the major component of the atomic 
rotation‹is positive, the electric displacement‹the minor component‹can be 
negative without violating the requirement (67) that the net total rotational 
displacement of a material atom must be positive. Carbon can therefore exist 
with the alternate displacements of 2-2-(4). Here the Neon type magnetic 
rotation with net displacement 10 is combined with 4 negative electric 
displacement units, for a net positive total of 6, the same as the net 
displacement of the 2-1-4 combination. The probability difference between these 
two combinations is small, and both are found observationally. Beyond Carbon the
probabilities favor the smaller negative electric displacement. The normal forms
of the next three elements are therefore:


90. Another group of eight elements follows, bringing the second magnetic 
dimension up to two effective displacement units at Argon, 3-2-0. A further 
one-unit increase raises the effective displacement level to 3 units in one of 
the magnetic dimensions. The third magnetic unit is equivalent to 2 ‹ 3‹ = 18 
electric units. Two 18-unit groups of elements therefore follow, increasing the 
displacements first to 3-3-0 (Krypton, element 36) and then to 4-3-0 (Xenon, 
element 54). Finally, there are two groups of 2 ‹ 4‹ = 32 elements each. The 
first of these carries the series of 4-4-0 (Radon, element 86). The second would
reach 5-4-0 (element 118), but here another factor intervenes.

91. From (60), the maximum three-dimensional scalar rotation has a magnitude of 
eight units. The significance of this is that at a speed displacement of eight 
net units, the rotationally distributed progression reaches the same scalar 
location, the end of the spatial unit, that a linear progression reaches in the 
same time interval. The next unit of the progression then begins without any 
limitation on the nature of the coupling to the reference system. In the absence
of such a limitation, the motion takes the most probable form, a unidirectional 
linear progression. This means that at element 118, where the rotational 
displacements are 5-4-0, and there are a total of eight effective magnetic 
displacement units (four in each dimension), the rotational combination of 
motions disintegrates and reverts to the linear basis. The series of chemical 
elements therefore terminates at element 117.

92. Because the succession of speed displacements follows the definite pattern 
outlined in (84) to (91), each element can be characterized by a unique set of 
numbers (subject to some modification under special circumstances). These are 
the values that enter into the various equations which determine the magnitudes 
of the different properties of the elements and their combinations.

93. Each successive element in the atomic series adds one double unit of 
positive three-dimensional rotational speed displacement to the combination of 
motions (the atom). In (34), three-dimensional speed displacement, positive in 
the material system, was identified as mass. The atomic mass is expressed in 
terms of atomic weight, the unit of which is half the rotational mass 
corresponding to the atomic number. The rotational mass of an atom of atomic 
number n is thus 2n atomic weight units.

94. When physical quantities are resolved into component quantities of a 
fundamental nature, these component quantities are called ³dimensions.² Since we
postulate that the physical universe is composed entirely of units of motion, a 
relation between space and time, the dimensions of all physical quantities (in 
this sense of the the term) can be expressed in terms of space and time only. 
From (34), the three-dimensional gravitational motion of the atoms of matter has
the dimensions s‹/t‹, where s and t are space and time, respectively.

95. In order to change the spatial position of an atom, or an aggregate of 
atoms, an outward motion must be applied against the inward scalar motion of the
atom. That inherent inward motion then acts as a resistance to the applied 
outward motion. In this capacity as a resistance, or inertia, the mass acts as 
the inverse of a three-dimensional speed, with the dimensions t‹/s‹. In 
practice, gravitation is measured in terms of force, a derivative of inertia, 
rather than in terms of speed. Both the gravitational and the inertial relations
are therefore expressed in terms of the t‹/s‹ magnitudes.

(This explains why measurements of the ³gravitational mass² and the ³inertial 
mass² arrive at the same result.)

96. Having established the space-time dimensions of mass, we can now define the 
dimensions of the other physical quantities of the mechanical system. The 
product of mass and speed, momentum, is t‹/s‹ ‹ s/t = t‹/s‹. The product of mass
and the second power of speed, energy, is t‹/s‹ ‹ s‹/t‹ = t/s. Acceleration, the
time rate of change of speed, is s/t ‹ 1/t = s/t‹. Force, the product of mass 
and acceleration, is t‹/s‹ ‹ s/t‹ = t/s‹.

97. Physical phenomena with the same dimensions have the same general status in 
physical interactions, and are interchangeable. For example, all phenomena with 
the dimensions t/s are equivalent to energy, and can be converted to kinetic 
energy by appropriate processes.

3. Electricity and Magnetism

In this section, we examine the application of the general physical principles 
developed in Section One to the basic phenomena of another physical field. The 
field selected for examination in Section Two was chosen to show how the 
quantitative relations emerge easily and naturally from the mainly qualitative 
general principles and relations. Now in this third section, we demonstrate the 
ability of the theory of the universe of motion to clarify the theoretical 
relations in a field that has heretofore been subject to much confusion. As in 
the preceding sections, each statement is a deduction from the postulates of the
theory or one or more of the numbered statements earlier in the outline.

98. The only difference between the effective component of the electron, M 
0-0-(1), and the rotational base, M 0-0-0 (69), is one unit of rotational space 
displacement. It is therefore a rotational combination with the dimensions of 

(The term ³electron,² as used in this outline refers to the particle defined in 
(70). Similar particles carrying charges will be identified as ³charged 
electrons.² )

99. As noted in (97), different physical phenomena with the same space-time 
dimensions have the same status in physical interactions. From the general 
physical standpoint, the electron is therefore equivalent to a unit of what we 
may call extension space, the ³space² of our ordinary experience.

(The idea of the equivalent of ordinary space is new to science and may be 
conceptually difficult for some scientists, but it is the same kind of a concept
as the idea of the equivalent of ordinary kinetic energy that we have all become
accustomed to. For example, if we wish to put a rocket into orbit, what we have 
to do is to accelerate it to a certain speed; that is, give it a certain amount 
of kinetic energy. But, in addition, we must provide enough fuel energy to 
compensate for the difference in the energy of position‹potential energy‹and 
lift the rocket against the earth¹s gravity. This potential energy is not 
³kinetic energy,² but it is ³energy,² and in relations involving energy in 
general it is the equivalent of kinetic energy. Similarly, electron space is not
³extension space,² but it is ³space,² and in relations involving space in 
general it is the equivalent of extension space.)

100. From (67), the net speed displacement of the atoms of ordinary matter is 
positive; that is, in terms of effective units there is an excess of time over 
space. The electron can therefore move through matter, as the relation of space 
(electrons) to time (matter) constitutes motion, according to the postulates of 
the theory of the universe of motion. It cannot move thru space, relative to the
natural reference system, as the relation of space (electrons) to extension 
space does not constitute motion.

101. We identify the movement of electrons through matter as current 
electricity. It should be noted that the current moves through the matter, not 
through the spaces between the atoms, as has been assumed.

102. The movement of space (electrons) through matter is identical, except in 
scalar direction, with the movement of matter through extension space. Thus 
quantities involved in these motions, and the relations between them, are thus 
the same in both cases. We may characterize the relations involved in the 
movement of space through matter as the mechanical aspects of electricity.

103. Since the scalar direction of gravitation (a movement of matter through 
space) is inward (34), it follows from (102) that the scalar direction of 
current electricity is outward.

104. The electrons (effective dimensions s) are units of electric quantity, q. 
The rate at which the electrons move through matter (quantity per unit time) is 
the electric current, I, with dimensions s/t, equivalent to those of speed. 
Electrical force, or voltage, V, has the general force dimensions t/s‹. The 
product of voltage and current is power, P, with dimensions t/s‹ ‹ s/t = 1/s. 
The product of power and time is electrical energy, or work, W, dimensions 1/s ‹
t = t/s. The mass taking part in the current flow is not a constant quantity, 
but depends on the duration of the current. The mass per unit time, dimensions 
t‹/s‹ ‹ 1/t = t‹/s‹, is therefore a significant quantity in current electricity.
We identify it as resistance, R.

105. To demonstrate the identity of the electric current relations (motion of 
space through matter) with those of the mechanical system (motion of matter 
through space), we may compare the energy equations. Kinetic energy is ‹mv‹, 
space-time dimensions t‹/s‹ ‹ s‹/t‹ = t/s. Electrical energy is RtI‹, dimensions
t‹/s‹ ‹ t ‹ s‹/t‹ = t/s. Another mechanical expression for energy is force times
distance, Fs = t/s‹ ‹ s = t/s. The analogous electrical expression is voltage 
times electrical quantity, Vq = t/s‹ ‹ s = t/s. In both cases the equations are 
identical, except for the terminology.

106. Since they are phenomena of the same kind, the flow of electrons through a 
conductor is analogous to the flow of gas molecules through a pipeline. A 
constant force (voltage) differential causes a steady flow of current.

(This agrees with observation. Existing theory ascribes the flow to a difference
in electrostatic potential, which it does not distinguish from voltage. But such
a potential difference applied to the charged electron which is assumed to be 
the moving entity would result in an accelerated motion. Present-day science has
no explanation for this contradiction.)

107. From (33), the scalar motion that constitutes the atom of matter is 
three-dimensional and inward. The one-dimensional outward movement of electrons 
(units of space) through matter, or through a gravitational field, therefore 
neutralizes a portion of the gravitational motion and leaves a scalar motion 
remnant in two dimensions. The physical effects of this residual motion are 
known as electromagnetism. As would be expected, they are similar to those of 
gravitation, except for the differences introduced by the two-dimensionality.

108. The residual motion in two dimensions is perpendicular to the dimension of 
the motion that is neutralized; that is, perpendicular to the electric current.

(This provides the explanation of the unique direction of electromagnetism that 
has heretofore been an unexplained anomaly).

109. As the residue of the inward gravitational motion, the electromagnetic 
motion is necessarily inward. However, the orientation of the scalar direction 
³inward² with respect to the spatial reference system is reversed when the 
direction of the current is reversed.

(Conductors carrying current in the same direction move toward each other, while
conductors carrying currents in opposite directions move away from each other.)

110. There is no two-dimensional analog of the electric current because the 
material system contains no negative magnetic particle. But the equivalent of a 
magnetic current, a two-dimensional motion through matter, can be produced by 
various means, such as mechanical movement of a conductor in a magnetic field. 
This two-dimensional motion neutralizes a portion of the three-dimensional 
motion of the matter, and leaves a one-dimensional residue. If a conductor is 
appropriately located, this residue manifests itself as an electric current. The
process of producing a current by this means is known as electromagnetic 

111. As noted in (1), motion in general is measured in terms of speed. When 
represented in a spatial reference system, the motion acquires a direction, and 
speed becomes velocity. The introduction of directions does not affect the 
dimensional relations. All of the previous dimensional conclusions stated in 
terms of speed are equally valid in terms of velocity.

112. From (111) and (96), the product of mass and velocity, momentum, has the 
dimensions t‹/s‹. This quantity was formerly called ³quantity of motion,² an 
expression which more clearly indicates its nature. It is actually a measure of 
the total motion of the mass, which consists of n mass units, each having the 
quantity of motion measured by the velocity. The time rate of change of velocity
is acceleration. The time rate of change of the product of mass and velocity, 
the ³quantity of motion,² is force. Thus force is, by definition, the same kind 
of a property of motion as acceleration. We could appropriately call it 
³quantity of acceleration.²

113. Since force is by definition (112), a property of motion, it follows that a
force cannot be autonomous. The so-called ³fundamental forces of nature² are 
necessarily properties of fundamental motions.

114. The same considerations apply to the electrostatic force, which, from 
(112), must also be the force aspect of an electric motion. For an understanding
of this motion we return to the question as to the types of scalar motion that 
can exist in the theoretical universe. Thus far we have encountered three 
general types: 1) Unidirectional linear motion; 2) Vibrational (simple harmonic)
motion, which is linear motion with a continuous change from inward to outward, 
and vice versa; 3) Scalar rotation, which is a uniform rotationally distributed 
scalar motion.

Obviously, there is a fourth possibility, a scalar rotational vibration; that 
is, a rotationally distributed scalar motion with a continuous change from 
inward to outward and vice versa, a rotational simple harmonic motion.

115. An independent rotational vibration cannot exist, as there would be nothing
to confine the progression to the rotational path, and it would revert to the 
more probable linear status. But a unit of rotational vibration can be combined 
with a unit of rotation. The inward phase of the rotational vibration is 
coincident with the corresponding rotation, and has no physical effect. The 
outward phase is an effective rotationally distributed scalar motion opposing 
the atomic rotation in the dimension, or dimensions, of the rotational 
vibration. It thus conforms to the requirement for stability, as expressed in 

116. From (57), the rotational vibration must not be of the same general nature 
as the rotation to which it is applied. The effect of this restriction is to bar
three-dimensional rotational vibration. The added rotational vibrations may be 
either one-dimensional or two-dimensional.

117. We identify a rotational vibration as a charge, and a one-dimensional 
charge as an electric charge.

(Inability to identify any motion connected with the electric charge is one of 
the reasons why the theorists have accepted the force exerted by the charge as 
fundamental, even though this conflicts with the definition of force, as noted 
in (112). The explanation, as indicated above, is that the charge itself is the 

118. From (115), the charge must have a carrier, an atom or particle. 
Independent charges do not exist.

119. From (117), the space-time dimensions of the electric charge are t/s; that 
is, the charge is dimensionally equivalent (97) to energy.

(The equivalence is demonstrated by the fact that charge and kinetic energy are 

120. Electric charges may be either positive or negative, but the total 
displacement is smaller, and therefore more probable, if the displacement of the
charge is opposite to that of the rotation. Consequently, a positive rotation 
takes a negative charge, and vice versa. But in current practice the rotational 
combinations are designated as positive (or electropositive) if they normally 
take positive electric charges, and negative (or electronegative) if they 
normally take negative electric charges. It is not feasible to try to change 
this firmly established practice, so the usual terminology will be applied in 
the statements that follow, with the understanding that the significance 
appertaining to the terms ³positive² and ³negative² elsewhere in this outline is
reversed in application to electric charge.

121. From (26), we find that in order to represent a scalar motion in a fixed 
spatial reference system it is necessary to identify a reference point.

122. The motion of a positive charge (a high speed rotational vibration) is 
outward from a negative reference point toward more positive values, including 
the positive reference points. That of a negative charge (a low speed rotational
vibration) is outward from a positive reference point toward more negative 
values, including the negative reference points.

(The reference system cannot distinguish between positive and negative reference
points. This is another of the difficiencies of the conventional spatial 
reference system.)

123. From (122), two positive charges move outward from the same reference 
point, and therefore outward from each other (7). Two negative charges do 
likewise, but a positive charge moves outward from a negative reference point 
toward all positive reference points, including the reference point of the 
negative charge, and therefore toward the negative charge. Thus, like charges 
repel each other, while unlike charges attract.

124. These scalar directions of the electrostatic forces are opposite to those 
of the corresponding electromagnetic forces (109); that is, like electric 
charges repel, whereas like currents (those moving in the same vectorial 
direction) attract.

(This agrees with the theoretical scalar directions of these two types of 
motion, which are opposite. The electromagnetic motion (109) is inward, while 
the electrostatic motion (115) is outward.)

125 An electric charge can be applied either against the electric rotation or 
against one dimension of the magnetic rotation. All atoms and sub-atomic 
particles of the material system, except the electron, have at least one 
effective positive displacement unit. With the one exception, all of them can 
therefore take positive charges. Negative charges are confined to the sub-atomic
particles with negative electric displacement, and to the electronegative 
elements with electric displacement of 4 or less. Those with higher 
displacements are usually excluded by the greater probability of positive 
charges based on the lower magnetic displacements.

126. Application of an electric charge to the electron neutralizes the net 
negative displacement of the particle. As a neutral particle, containing both 
positive and negative components, the charged electron is able to move either 
through matter (predominantly time) or through space. The charged electrons move
through matter in the same manner as their uncharged counterparts; that is, they
move freely through good conductors, less easily through poor conductors, and 
are blocked or impeded by insulators. We identify the various phenomena involved
in the production and movement of these charged electrons as static electricity.

127. Electric charges may also be applied to atoms (existing individually or in 
combinations), which are then known as ions. As noted in (115), each unit of 
rotational vibration combines with a unit of rotation. The maximum degree of 
ionization (number of applied charges) is therefore equal to the net rotational 
displacement. negative ionization is confined to the most electronegative 
members of each rotational group, and is limited to the magnitude of the 
negative electric displacement of each atom. Positive ionization can take place 
up to the number of net positive rotational displacement units in the atom (the 
atomic number). An atom in this limiting condition is said to be completely 

128. A charge (rotational vibration) may be two-dimensional, rather than 
one-dimensional. In that case, it constitutes a magnetic charge. Material 
objects carrying magnetic charges are known as magnets. Where the charge 
persists for a substantial period of time, the term permanent magnet is applied.

129. Because of the orientation effect noted in (109) which applies to all 
two-dimensional scalar motion‹the scalar direction (inward or outward) of the 
motion that constitutes the magnetic charge reverses with the direction relative
to the reference system. Thus, a magnetic charge exerts an attractive force on a
similar charge in one vectorial direction, and a repulsive force on one that is 
located in the diametrically opposite direction.

130. The force exerted by a magnet is the net total of the magnetic forces of 
the individual magnetic charges on the atoms. Each magnet therefore has two 
centers or poles at which the net magnetic forces in the opposite directions are
at a maximum.

131. From (130) it can be seen that while a magnetically charged object has only
two poles, if that object is separated into parts, each part also has two poles.

132. The existence of magnetic monopoles is excluded by (131).

(Present-day physical theory requires the existence of positive and negative 
monopoles analogous to positive and negative charges, and continuing attempts 
are being made to find such phenomena, without success.)

133. As in the case of positive and negative electric charges, and for the same 
reasons (123), like poles repel each other, while unlike poles attract.

134. Inasmuch as the magnetic charge is the two-dimensional analog of the 
one-dimensional electric charge, it has the space-time dimensions t‹/s‹. The 
dimensions of the quantities involved in magnetostatics, the phenomena of 
magnetic charges, are therefore related to those of the corresponding 
electrostatic quantities (where analogous quantities exist) by the factor t/s.

135. This relation (134) enables us to make a positive identification of the 
dimensions of the magnetostatic quantities. Magnetic charge, t‹/s‹, is not 
recognized under that name in current scientific thought, but an equivalent 
quantity, magnetic flux, which has these dimensions, is utilized in many of the 
same applications. The unit of magnetic flux in the SI system is the weber, 
which is equal to a volt-second, dimensions t/s‹ ‹ t = t‹/s‹. The analog of 
electric potential, t/s‹, is magnetic potential, also called vector potential, 
to distinguish it from some other quantities which have, or are thought to have,
the characteristics of potential. The dimensions of magnetic potential are t/s‹ 
‹ t/s = t‹/s‹.

The SI unit is the weber per meter, t‹/s‹ ‹ 1/s = t‹/s‹. Corresponding to 
electric field intensity, t/s‹, is magnetic field intensity, t/s‹ ‹ t/s = t‹/s4.
This quantity is defined as magnetic flux per unit area, on which basis the 
space-time dimensions are t‹/s‹ ‹ 1/s = t‹/s4. Thus, all of these magnetic 
quantities have dimensions equal to the dimensions of the corresponding electric
quantities multiplied by the factor t/s, as required by the theory.

136. In a number of other cases, the dimensions currently assigned to the 
magnetic quantities do not agree with those derived from theory in the foregoing
manner. Here, the currently accepted dimensional assignments have been based on 
empirical observations, and the accurate dimensional analysis that is now 
possible shows that the observations have been improperly interpreted.

137. For example, observations show that magnetomotive force (MMF) is related to
the current, I, by the expression MMF = nI, where n is the number of turns in a 
coil. Since n is dimensionless, this relation indicates that the dimensions of 
MMF are the same as those of the electric current. The unit of MMF is therefore 
taken as the ampere, dimensions s/t. But MMF has the characteristics of a force 
(as the name implies), and the dimensions should be those of magnetic potential,
t‹/s‹. The dimensional study shows that the discrepancy is due to the fact that 
the analog of electric resistance, the permeability, dimensions t/s ‹ t‹/s‹ = 
t‹/s4, enters into the physical relation, and this relation is actually MMF = 
mnI, where m is the permeability. The presence of this quantity is not detected 
by the usual mathematical analysis, as it takes the unit value in most magnetic 
applications, and has no numerical effect.

138. When the magnetic relations are corrected by introducing the permeability, 
and making the necessary adjustments to remove some other errors, the entire 
system of magnetic quantities is brought into agreement with the mechanical and 
electrical dimensions. This completes the identification of a comprehensive and 
entirely consistent system of dimensional relations covering the full range of 
physical phenomena.

(The demonstrated ability to express the dimensions of all physical quantities 
in terms of space and time is not only a powerful tool for analyzing physical 
relations, but also provides an impressive confirmation of the validity of the 
postulate that the physical universe is composed entirely of these two 

139. The most serious error about conventional electric and magnetic theory 
revealed by the dimensional analysis, is the lack of distinction between 
electric quantity and electric charge that has resulted from the assumption that
the electric current is a movement of charges. In present-day practice, both 
charge and quantity are measured in the same units‹coulombs in the SI system. 
But the interconvertibility of electric charge and kinetic energy (97) 
definitely shows that charge has the energy dimensions, t/s, while the relations
cited in (104) demonstrate just as definitely that electric quantity has the 
dimensions of space, s, as required by the theory of the universe of motion.

140. From (139) it follows that there are two distinct kinds of electric and 
magnetic phenomena: (1) the electric current and electromagnetism, in which the 
basic entities are units of electric quantity (dimension s), acted upon by 
forces due to voltage differences, and (2) the phenomena classed as 
electrostatic and electromagnetic, the basic units of which are units of 
electric charge (dimension t/s) and magnetic charge (dimension t‹/s‹), acted 
upon by forces due to potential differences.

141. Electric charges moving through matter or through a gravitational field are
carried by particles or atomic constituents with rotational characteristics 
similar to those of the particles. The movement of these carriers produces 
electromagnetic effects, while the charges that are being carried produce 
electrostatic effects.

142. From (141), an aggregate of charged electrons has both a voltage and a 

(This explains the operation of such devices as the Van de Graaf generator, in 
which charged electrons at a low potential flow into a storage sphere in which 
the potential may be very high. A flow in this direction would be impossible if,
as asserted by present-day theory, only one force, electric potential, is 
operative. But the foregoing development of theory shows, that there are 
actually two forces involved, and the direction of flow depends on the voltage 
differential, not on the potential difference. The voltage in the storage sphere
is determined by the electron concentration, and may be low, even when the 
potential is in the million volt range.)

4. Astronomical Implications

In the preceding Sections, we have presented a step-by-step deduction from the 
fundamental Postulates of the Reciprocal System of theory of the phenomena of 
the physical universe pertaining to the atomic domain. In this Section, we carry
forward these deductions to the astronomical field and show how phenomena, some 
of which have not had proper explanations in conventional theory, emerge 
logically from these deductions. This Section, therefore, serves to demonstrate 
the general nature of the Reciprocal System of theory.

143. At this point, we will need to take into account the concentration of 
energy in the vicinity of matter subject to electrical ionization, and some 
consideration of the nature of this concentration will be required. As long as 
atoms or aggregates are free to move unidirectionally, there can be no 
significant spatial (volumetric) concentration of their kinetic energy. Such a 
concentration is accomplished by containment. Initially, the spatially 
restricted motion, thermal motion, as we will call it, is contained within the 
individual units of space. When the energy level is high enough to permit the 
atoms to escape from the spatial units, a force, exerted either by the walls of 
a container, or otherwise, is required for containment.

144. The level of containment outside unit space is measured by the pressure, 
the force per unit area, dimensions t/s‹ ‹ 1/s‹ = t/s4. The product PV of the 
pressure and the volume is the energy of the contained thermal motion, 
dimensions PV = t/s4 ‹ s‹ = t/s. We identify the thermal energy level as the 

145. From (144), it follows that atoms of matter that are not confined, and 
therefore not subject to any pressure, cannot have temperatures above the very 
low levels at which they are able to escape from the individual spatial units. 
Free translational motion of an aggregate of matter likewise has no temperature 
effect. The motion of this aggregate as a whole is independent of the thermal 
motion of its constituents.

(Temperatures of millions of degrees are currently reported as applying to 
individual atoms and molecules in the vicinity of certain astronomical objects. 
From the foregoing, it follows that these temperature estimates are erroneous. 
Temperatures of unconfined matter are in the range of a few degrees, not in 
millions of degrees.)

146. Ionization is produced by a transfer of speed displacement to rotational 
vibration from some other form of motion, under appropriate circumstances. 
Thermal motion is one such source. The degree of ionization of the atoms of an 
aggregate increases with the temperature of the environment in which the 
aggregate is located, and at extremely high temperatures all elements are 
completely ionized.

147. From (95), the translational motion of masses, including the confined 
thermal motion, is outward. From (115), the electric ionization is also outward.
Thus a further increase in temperature beyond the level of complete ionization 
ultimately brings the atoms up to a limiting level at which the sum of the 
outward ionization and the outward thermal motion is equal to unity. This unit 
outward motion then neutralizes one unit of the inward rotational motion. As 
indicated in (91), both units revert to the linear status, converting the 
rotational vibration and a unit of the rotation to kinetic energy. mass t‹/s‹ 
becomes energy t/s.

148. The conversion factor relating a unit of mass to a unit of energy has the 
dimensions s‹/t‹ (the dimensions of the second power of speed) and unit 
magnitude. The energy equivalent of a mass is therefore the product of the mass 
and the second power of unit speed (the speed of light).

149. As to the question of the result of further additions of thermal motion 
beyond the limiting point defined in (147) (the destructive temperature limit of
the particular element under consideration), we must first return to (59), where
we deduced that the maximum addition to the speed of a motion combination in any
one dimension‹that is, the amount that can be added to a zero base‹is two units.
In these terms of reference, the range is from zero to +2. In terms of 
displacement from the natural datum at unity, the range is from +1 to -1 (or 
from -1 to +1, as the identification of the conventional zero with +1 rather 
than -1 is purely arbitrary). The first added unit of speed eliminates the unit 
of speed displacement (+1), and the second adds a unit of time displacement 

150. Since there are no fractional units of speed, the reduction of linear 
speeds to levels below unity in the manner described in (44) can be accomplished
only by introduction of units of inverse speed. This is motion in time, but the 
atom is moving gravitationally in space in the other two scalar dimensions, and 
the net total scalar motion is therefore in space. It follows, in accordance 
with (47), that the increments of motion in time in the range between zero and 
unit speed act as motion in equivalent space.

151. Elimination of displacement in space (increase of speed) can continue only 
up to the unit speed level, at which point all displacement has been canceled. A
speed greater than unity therefore cannot be attained by means of this process.

(This is the explanation of the observed inability to accelerate material 
objects to speeds in excess of the speed of light by application of electrical 

152. As noted in (151), the limit at the unit level is on the capability of the 
process, not on the speed itself, and it does not preclude an increase in the 
speed above the unit level by means of a different process. Where speed is 
available in full units, it may be added directly, up to the absolute limit, 
which, as stated in (59), is two one-dimensional units. Because an increment of 
speed above unity is a scalar motion in time (equivalent space), the extension 
of the linear motion in space into the second unit is distributed over all three
time dimensions. As in the rotational situation of (91), the existence of 
three-dimensional units of speed then makes intermediate speeds between unity 
and two full linear units possible.

153. The aggregation of matter under the influence of gravitation noted in (34) 
applies to objects of all sizes. Because of the diversity of conditions there is
no uniform aggregation pattern, but since gravitation is omnipresent, the 
average mass of all major classes of physical objects necessarily increases with
advancing evolutionary development‹with the evolutionary age, we may say.

154. The process of aggregation results in the conversion of gravitational 
motion into thermal motion (heat). Coincidentally, there is a loss of heat from 
the surface of each aggregate, due to radiation. But the mass, which determines 
the rate of heat production, other things being equal, increases more rapidly 
than the surface area. The temperature of a large aggregate is therefore a 
function of the mass, as long as the aggregation process continues.

155. Extremely high temperatures are reached only in very large aggregates of 
matter. If the aggregate is large enough to reach the destructive temperature 
limit of the heaviest element present, this activates the process of conversion 
of mass to thermal energy described in (147). We identify such an aggregate as a

156. Since the maximum degree of electric ionization of an element is equal to 
its atomic number (127), the heavier elements have a greater content of 
ionization energy, and therefore require less thermal energy to reach the 
destructive temperature limit, the temperature at which the total of these two 
energy components attains the unit level (149). If the stellar temperature 
continues rising, the elements reach their destructive limits in the inverse 
order of their atomic numbers.

157. The principle that small numbers are more probable than larger numbers 
applies to the formation of the elements (with some modifications due to other 
factors). The heaviest elements are therefore present in the stars only in 
relatively small concentrations, and the energy released in their destruction is
dissipated by radiation from the stellar surfaces. As successively lighter 
elements reach their destructive limits, the concentration of the individual 
element arriving at the limit increases, and eventually this process reaches an 
element that is present in quantities that produce more energy than the 
radiation mechanism can handle. The excess energy then blows the star apart in a
gigantic explosion. We identify the overabundant element as iron, and the 
explosion as a Type I supernova.

(Here the development of the theory leads directly to an explanation of a 
phenomenon for which no generally accepted explanation has been derived from 
astronomical theory.)

158. From (154), the temperature limit of a star is also a mass limit. From 
(153), the attainment of this mass limit is a result of advanced evolutionary 
age. The stars that explode as Type I supernovae are therefore mature stars of 
approximately the same mass. Thus all Type I supernovae have the same general 

(The astronomers agree that all Type I supernovae are very much alike, but they 
have no explanation for the similarity.)

159. When the energy released in the supernovae explosion is added to the 
already high thermal energy level of the surviving portions of the interior 
structure of the star, a substantial portion of the explosion products are 
accelerated to speeds in excess of unity, in the manner explained in (152). From
(46) and (47), the motion of these products takes place in the spatial 
equivalent of outward motion in time, which is inward in equivalent space. The 
aggregate of these very high speed products thus undergoes a drastic spatial 
contraction, and appears to observation as a small star with a density vastly 
greater than that of any aggregate of matter existing in the terrestrial 
environment. We identify this high density aggregate as a white dwarf star.

160. In ordinary stars (those with component speeds below unity) of a given 
class, the more massive stars are the larger; that is, they occupy a greater 
amount of three-dimensional space. From (46), the more massive white dwarf stars
occupy the spatial equivalent of a greater amount of three-dimensional time, 
which is less equivalent space. According to the theory of the universe of 
motion, the more massive white dwarf stars are therefore smaller than the less 
massive ones.

(This deduction is confirmed by observation.)

161. In ordinary stars the spatial density gradient from the surface to the 
center of the star is positive; that is, the center is the region of greatest 
density. From (46), the temporal density gradient of a white dwarf star is also 
positive, which means that the center of the star is the region of greatest 
density in time, or least density in the corresponding equivalent space. Thus 
the spatial density gradient is greatest at the surface, and the lowest at the 

162. Little or no translational motion in space is imparted to the white dwarf 
by the supernovae explosion. It therefore remains in the spatial region heavily 
populated with low speed explosion products, and accretes a substantial amount 
of these products by reason of its gravitational effect. The surface layers of 
the younger white dwarfs thus have a composition similar to that of their 
environment: predominantly hydrogen, with a minor amount of helium, and minute 
amounts of other elements. Because of the inverse density gradient (161), the 
hydrogen moves downward preferentially toward the center of the star, leaving 
the surface layers of the older white dwarfs enriched in helium.

(This, too, is confirmed by observation. A substantial proportion of the white 
dwarfs are reported to have helium-rich surface layers, extending up to ³nearly 
pure helium atmospheres.² Current astronomical theory has no explanation of this
reversal of the normal density relations.)

163. In the supernovae explosion (157), the speeds imparted to the outer 
portions of the exploding star are less than unity. These explosion products 
therefore expand outward in space. Their motion is, however, subject to 
resistance from dispersed matter in the environment, and to the gravitational 
effect of the exploding aggregate as a whole, including the white dwarf that 
does not participate in the outward movement. These opposing forces ultimately 
terminate the expansion and initiate a contraction. Thus most of the ejected 
matter is eventually recondensed into a star. The typical product of a Type I 
supernovae is therefore a double star system consisting of a diffuse A component
on or above the main sequence and a dense B component (white dwarf or system of 
planets) below the main sequence.

(This deduction from the premises of our theory requires the existence of double
star systems as a direct consequence of the nature of the supernovae process, 
and explains why so many of these systems consist of dissimilar objects. The 
present state of astronomical knowledge in this area is described by the 
following quotation from a current astronomy textbook: ³Our hopes of 
understanding all stars would brighten if we could explain just how binary and 
multiple stars form... Unfortunately we cannot.² )

164. Any explosive event comparable in intensity to a Type I supernovae ejects 
some products at speeds greater than unity. The explanation given in (159) for 
the extremely high density of the white dwarfs is equally applicable to these 
other high speed products.

(This accomplishes a significant simplification of astronomical theory, as the 
currently accepted explanation of the white dwarf density cannot be extended to 
such extremely dense objects as quasars, pulsars, x-ray emitters, and dense 
galactic cores, and separate explanations have had to be developed for the 
density of each of these types of objects.)

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