Chapter VIII
Motion in Time
In terms of presentday thinking, motion is regarded
as a processtaking place in space: a change in the spatial relation between
objects. But if space and time are symmetrical, as the reciprocal postulate
requires, then it is equally possible for the temporal relations: between
objects to undergo similar changes, and this process of temporal change
constitutes motion in time.
The factors involved in the concepts of location in space
and location in time have been examined in detail in previous publications,
but since they are essential to an understanding of motion in time, we
will review them briefly here. Let us first consider a distant galaxy,
which at time t_{0} occupies location A in space, and is therefore
receding from our Milky Way galaxy M, in the direction MA. During an interval
t, the recession carries the galaxy outward in this direction to a new
location B. But we know from observation of the nearer galaxies that these
units also have random motions of their own, so that during time t the
galaxy under consideration will have moved an additional distance to some
location C which will not, unless by pure chance, lie on a prolongation
of the line MAB. The actual displacement of the galaxy during time t is
therefore the vector resultant of the distance AB and the distance BC.
We have already identified the recession of the galaxies
as a manifestation of the progression of space, hence in view of the symmetry
between space and time, we may deduce that exactly the same kind of a
situation exists in time. While time is progressing from time location
a to time location b, carrying a galaxyour Milky Way galaxy, let us saywith
it, the random motion of the galaxy in time takes it to some other time
location c, and the total time displacement of the galaxy during this
interval is not the time of the progression alone, but the vector resultant
of this time ab and the random time displacement bc.
The progression of time which carries our galaxy from
time location a to time location b is the quantity which we measure by
means of a clock, and it is commonly called clock time. Since the
progression of space that carries the distant galaxy from location A to
location B is the space equivalent of clock time we may utilize the same
terminology and call it clock space. The random motion of the distant
galaxy from location B to location C takes place in the ordinary threedimensional
space of our everyday experience, and inasmuch as we usually represent
this by some sort of a coordinate system, we may call it coordinate
space. The displacement of our galaxy from time location b to time
location c is the time equivalent of the space displacement BC, and it
takes place in threedimensional time. Again we may use the same terminology
that we apply to space and refer to this as coordinate time.
Because the gravitational motion cancels the motion of
the spacetime progression in our local environment we do not detect the
recession of our own galaxy and the only space that we recognize locally
is coordinate space. When we observe, for instance, that our near neighbor
among the stars, Alpha Centauri, is moving away from us with a radial
velocity of approximately 20 km/see, this is a motion in coordinate space,
the same kind of a motion that we observe in our everyday life. When we
also observe that a galaxy in Ursa Major is moving away from us with a
radial velocity of 15000 km/sec, it would appear on first consideration
that this is exactly the same thing, aside from the substantial difference
in the speed. But in reality there is a very significant difference between
the two motions. The motion of Alpha Centauri that takes it away
from us carries it toward any star located still farther away in
this outward direction. Unless one is familiar with recent astronomical
discoveries, he is quite likely to take the stand that this must necessarily
be true. The fact is, however, that it is not true in the case
of the motion of the distant galaxies. When the Ursa Major galaxy moves
away from us, it is also moving away from all other galaxies,
including those located diametrically opposite from us.
Obviously these are motions of a totally different nature.
The explanation is that the galactic recession is not a motion
in coordinate space, the kind of a motion with which we are familiar.
Aside from a relatively slow motion of a random character, comparable
to the motions which we observe in the galaxies of our local system, the
Ursa Major galaxy remains stationary in coordinate space but it moves
outward in clock space. Our own Milky Way galaxy is doing exactly the
same thing but, of course, we do not recognize our own outward motion
from direct observation. Because of the reciprocal relation between space
and time the galaxies which move outward in clock space are moving inward
in clock time, but here again the motion is outside the range of existing
observational facilities.
In the local environment, where the gravitational motion
exceeds that of the progression, the directions of motion are just the
reverse. While the atoms of matter are moving inward in space under the
influence of gravitational forces and thus gathering into aggregates that
are localized in space, they are coincidentally moving outward
in time in random directions. Hence the material aggregates are not
localized in time; that is, the atoms of a star, for example, are clustered
together in a stable configuration in a relatively small amount of space,
but they are widely dispersed in time with no stable relationships between
units. In our observation of time, therefore, we have no landmarks by
which we can recognize positions in coordinate time, and the existence
of this kind of time therefore remained undetected until it was discovered
theoretically in this present investigation. The temporal relations between
atoms occupying widely separated locations in time are comparable to the
spatial relations between distant galaxies, and the aspect of time that
is recognizable in our local environment is the clock time.
But even though the local situation is such that we normally
recognize only clock time and coordinate space, clock space and coordinate
time have some very significant effects under what we consider extreme
conditions. At extreme distances the space progression, the motion in
clock space, manifests itself as the recession of the galaxies. At extreme
velocities the motion in coordinate time manifests itself by the deviations
from Newton’s Laws of Motion that were revealed by the MichelsonMorley
experiment. Under conditions of extremely small space or time separations
there is a replacement of motion in space by motion in time and vice versa
which has some important effects that will be discussed later in this
chapter.
The expression “motion in time,” as it will
be used in this work, refers to motion in coordinate time: a change of
location in three dimensional time analogous in all respects to the change
of location in threedimensional coordinate space which constitutes motion
in space. The total time corresponding to any specific clock time
is the vector resultant of this coordinate time and the corresponding
clock time.
The quantitative measure of motion in space is velocity,
and the mathematical definition of velocity is v = s/t. Here the term
s is a vector quantity representing the displacement in space. The term
t is scalar, since time has no direction in space, and the term v is then
a vector quantity representing the space displacement per unit of time.
The analogous quantitative expression for motion in time is D
= t/s or delta is equal to t divided by s. Here the term t is a
vector quantity representing the displacement in time. The term s is scalar,
since space has no direction in time. The term D
is then a vector quantity representing the time displacement per unit
of space, this being the timeoriented quantity corresponding to velocity
in spaceoriented phenomena.
From the foregoing, the reason for the scalar nature
of the spacetime progression, which is motion in both space and time,
is evident. Since time has no direction in space and is therefore a scalar
quantity so far as motion in space is concerned, and for similar reasons,
space is a scalar quantity so far as motion in time is concerned, it follows
that motion in both space and time cannot have a direction in either
space or time. Hence motion in spacetime is scalar.
We may summarize the conclusions with respect to the
directional characteristics of the various kinds of motion as follows:
In the equations of motion in space, time is scalar.
In the equations of motion in time, space is scalar.
In the equations of motion in spacetime, both space and time are scalar.
Some readers of the previous volumes of this series have
found it difficult to accept the idea that time can be threedimensional
because this makes any time interval a vector quantity and presumably
leads to situations in which we are called upon to divide one vector quantity
by another. As indicated in the foregoing discussion, however, such situations
are nonexistent. If we are dealing with spatial relations, time is scalar
because time has no direction in space. If we are dealing with temporal
relations, space is scalar because space has no direction in time. Either
space or time can be vectorial, but there is no physical situation in
which both are vectorial.
Since the property which we are calling “direction
in time” is something quite distinct from “direction” as
we ordinarily use the term in the sense of “direction in space,”
there might be some good arguments in favor of coining a new name and
not using the word “direction” for this purpose. This would
do doubt contribute toward clarifying such issues as the reason why time
is always scalar in the equations of space motion irrespective of the
number of dimensions which time itself may have. On the other hand, it
should not be difficult to get away from the habit of interpreting “direction”
as meaning “direction in space.” As a matter of fact, we already
recognize that the spatial connotation that we give to the word “direction”
is in many cases fictitious. A scalar quantity is specifically defined
as one, which has no direction, yet we habitually use the word “direction”
and directional terms of one kind or another in speaking of scalar quantities,
or even in connection with items, which cannot be expressed in physical
terms at all. We speak of wages and prices as moving in the same direction,
temperature as going up or down, a change in the direction of our thinking,
and so on. Here we recognize, consciously or unconsciously, that in our
definition of a scalar quantity we are using the term “direction”
in the sense of “direction in space,” whereas when we are talking
about the direction of price change or something similar we are using
the word “direction” without any spatial significance. It should
not require any great mental effort to apply the same viewpoint to temporal
quantities and to recognize that here also the term “direction”
has no spatial significance.
On the other side of the ledger, there are some very
definite advantages to be gained by utilizing the term “direction”
in reference to time as well as in reference to space. Because of the
symmetry of space and time, the property of time that corresponds to the
familiar property of space that we call “direction” has exactly
the same characteristics as the latter, and by using the term “direction
in time” as a name for this property we convey an immediate understanding
of its nature and characteristics that would otherwise take a great deal
of discussion and explanation. All that is then necessary is to keep in
mind that although direction in time is like direction in space,
it is not direction in space.
This is a general situation that applies all through
the spacetime relations. The impact of time on our consciousness is vague
and elusive, and it is therefore quite difficult to visualize any concrete
physical situations involving threedimensional time. The most effective
way of grasping the essentials of the participation of time in such situations
is to visualize the corresponding space phenomenon and then recognize
that the time phenomenon is exactly the same except that space and time
are reversed. In order to do this easily and efficiently it is necessary
to utilize the same terms for the corresponding space and time entities,
and this policy has been followed throughout the present series of publications.
As brought out in Chapter V, the developments of this
work, revolutionary as they may be in some of their aspects, have very
little effect on the physical processes and relations of everyday life.
The reason is now apparent. In our everyday experience we are dealing
with motion in space, and the laws and principles governing motion
in space are already firmly established. Any correct theoretical development
must necessarily lead to these same laws and principles. The discovery
of the possibility of motion in time and the formulation of the analogous
laws and principles governing this type of motion has no effect on any
situation where all motion is in space.
But physical science is now penetrating into regions
where motion in time plays an important, often controlling, part in physical
phenomena, and much of the difficulty that the presentday physicist is
encountering in his attempts to systematize knowledge in these regions
is due to his attempt to treat the phenomena in these regions by means
of the relations applicable to motion in space, while the motion with
which he is dealing is actually, in whole or in part, motion in time.
The problem, which Einstein faced in setting up his Special
Theory of Relativity, is typical. In the light of the information that
has been developed in this work we may compare it to the problem that
would confront anyone who knew nothing of the concept of direction and
who attempted to devise a scalar equation to relate speed and velocity.
The latter would, of course, be nothing but another scalar quantity to
anyone who is unaware of the existence of direction, just as the time
entering into a high velocity was to Einstein no different from the time
entering into a low velocity, aside from the difference in magnitude.
Such an investigator would find it entirely possible to devise an accurate
mathematical relation that would apply to some special speedvelocity
situation, in the same way that the Lorentz equations apply to uniform
translational motion, but it is obvious that there can be no general
relation of a scalar character connecting speed and velocity. If a “Special
Theory” of the speedvelocity relation is devised for some special
case, sinusoidal motion, let us say, and the success of the theory in
this particular area leads its originators and supporters to believe that
it can be extended to motion in general, the outcome will inevitably be
either that the attempts are ultimately given up as hopeless, or that
successive ad hoc modifications of the original theory finally
result in a “General Theory” of the speedvelocity relation
which is so vague and confused conceptually and so complex mathematically
that no one can pin it down closely enough to reveal its true character.
A valid general solution of the hypothetical speedvelocity
problem cannot be obtained until someone discovers the threedimensionality
of space and introduces the concept of direction. Similarly no general
solution for Einstein’s problem was possible until this present investigation
discovered the threedimensionality of time and introduced the concept
of motion in time. But in both cases the answer is simple and obvious
as soon as the necessary conceptual foundation has been laid.
Hesse sums up the position in which physics stands without
the concept of motion in time as follows:
The fundamental logical proposition to which all such theories
must conform is that one cannot assert both that the velocity of
light is invariant for all possible reference frames, and that
the geometry of light rays is Euclidean.^{54}
The general and uncritical acceptance of this socalled
“logical proposition” is the factor that has forced physical
theory into the uncomfortable and untenable position that it occupies
today. The truth is that this is not logical at all. It could be logical
only if coupled with a proviso that the existing concepts of the nature
of space, time, and motion must be maintained unchanged, and there is
clearly no physical justification for such a proviso. There has
never been any assurance that these concepts are physically valid; on
the contrary, they are pure assumptions, and the development of the Reciprocal
System has now demonstrated that they are erroneous assumptions.
If they are replaced by concepts that are physically valid, then
it is possible to formulate a logical and selfconsistent alternative
to the Special Theory which does just exactly what Hesse claims is impossible;
that is, it reconciles Euclidean geometry with the constant velocity of
light.
A brief summary of the detailed explanations of this
situation that have been published elsewhere can be given with the aid
of the diagram, Fig.1. Let us assume that a ray of light from a distant
source S passes from A to B and from A’ to B’ in two parallel
systems. Then let us assume that the systems AB and APB’ are in motion
in opposite directions as shown, and are in coincidence as the light ray
passes A and A’. Because of the motions of the respective systems,
point B will have moved to some point C closer to A by the time the light
reaches it, whereas B’ will have moved to some more distant point
C’. Yet if the results of the MichelsonMorley experiment are to
be believed, the velocity of the incoming ray at C is identical with the
velocity of the incoming ray at C’; that is, the velocity of light
is independent of the reference system.
Fig.1
The interpretation that has been placed on the
results of this experiment by the physicists is that the time required
for the light ray to pass from A to C is the same as the time required
to pass from A’ to C’. From a common sense viewpoint this conclusion
is absurd, and the feeling of discomfort which most laymen, and many scientists,
experience on contact with Relativity theory is basically due to the fact
that Einstein made this contradiction of common sense the cornerstone
of his theory. With the benefit of the discussion earlier in this chapter,
it is now evident that the physicists’ interpretation of the MichelsonMorley
experiment is wrong, and that the conflict with common sense was wholly
unnecessary. The time AC is not the same as the time A’C’. It
is only the clock time that is the same in both systems, and the
clock time is only one component of the total time.
In our observations of the distant galaxies we can ignore
the random motion of these objects–the motion in coordinate space–because
it is so small that its effect is negligible compared to the effect of
the motion of the recession–the motion in clock space. But if this
random motion were taking place at a velocity in the neighborhood of that
of light, the situation would be quite different. This motion in coordinate
space would then have a very appreciable effect on the total displacement
of the galaxy during any interval of observation and we could no longer
ignore it.
Similarly, the change in temporal location–the displacement
in coordinate time–at the relatively low velocities of our ordinary
experience is negligible in comparison with the time of the progression–the
clock time–and we can disregard it. But here again, this ceases to
be true at the velocity of light. At high velocities the coordinate time
has a finite magnitude, and the total time, the time that actually enters
into physical relations, is the vector sum of the clock time and the coordinate
time. The total time required for the light ray to pass from A to C in
the moving system is the clock time ab minus the coordinate time cb, or
ac, and the velocity is the space displacement AC divided by the net total
time act The total time for the ray to pass from A’ to C’ is
the sum of the clock time a’b’ and the coordinate time b’c’,
or a’c’, and the velocity is the space displacement A’C’
divided by the total time a’c’. The velocity of light is thus
AB/ab for a system at rest, AC/ac in the system moving toward the light
source, and A’C’/a’c’ in the system moving away from
the light source.
Inasmuch as one unit of time is equivalent to one unit
of space, according to the postulates of the Reciprocal System, this means
that the velocity of light is unity–one unit of space per unit of
time–in all three cases. And the theory further tells us that this
velocity cannot be other than unity under any circumstances, because a
light photon has no motion of its own. The photon stays permanently in
the same spacetime unit in which it originates and is carried along by
the progression of spacetime itself. The progression moves one unit of
space per unit of time simply because one unit of space is one unit of
time and the equivalence of unit space and unit time is the progression.
Even in passing through matter, where the measured light velocity
is less than unity, the true velocity still remains one unit of
space per unit of time. The factors, which cause the measured velocities
to diverge from unity under these conditions, will be considered in a
subsequent chapter.
As can be seen from the foregoing explanation, the concept
of motion in time, which is one of the necessary consequences of the postulates
that were derived by extrapolating the observed properties of space and
time, solves Einstein’s problem, the problem posed by the results
of the MichelsonMorley experiment, in an easy and natural way without
any distortion of established physical principles. Notwithstanding Hesse’s
statement that the constant velocity of light is logically incompatible
with Euclidean geometry, this solution of the problem, number six in our
list of Outstanding Achievements; is completely in harmony with both.
In spite of the general belief that the MichelsonMorley results cannot
be explained without giving up the idea of absolute space and time, Einstein’s
positive assertion, on the same grounds, that “moving rods must change
their length, moving clocks must change their rhythm,”^{88} and all of the chorus of similar
statements throughout scientific literature, the findings of the Reciprocal
System are entirely consistent with both the constant velocity of light
and the existence of absolute magnitudes of space and time.
Here again, as in so many other situations that have
been discussed in the several volumes of this series, previous investigators
have simply failed to examine possible alternatives. It is true that in
this case the correct alternative was more effectively hidden below many
layers of longstanding habits of thought than in most other instances,
and overlooking it was more a matter of inadvertence than a deliberate
ignoring of unpopular alternatives, as in some other instances, but failure
to be on the alert for alternatives is a serious defect in scientific
practice. The consequences of error are always the same. Nature rewards
only the correct answers; it gives no credit for effort, nor does it make
allowances for extenuating circumstances. The plain truth is that the
physicists should have recognized the possibility of a more satisfactory
alternative to the Special Theory, irrespective of whether or not they
were able to formulate anything acceptable, and a substantial part of
the immense amount of effort that has been wasted in a futile attempt
to patch up the weak spots in that theory should have been applied to
searching for such an alternative. Failure to find the correct
answer is, of course, excusable–even the most diligent efforts by
the most competent individuals do not always reach their goals–but
failure to look for the correct answer, because of unwillingness
to admit that currently accepted ideas could be wrong, is a fair
target for criticism.
The revolutionary change in outlook that accompanies
the application of the concept of motion in time to the Relativity problem
is typical of the way in which this concept clears up confusion and contradictions
in all of the farout regions: the realm of the very small (atomic physics
and quantum theory), the realm of the very fast (gravitation and Relativity
Theory), and the realm of the very large (astronomy and cosmology). All
through these areas hitherto complex and difficult problems are reduced
to simple and understandable terms when they are viewed in the context
of the new conceptual structure.
Phenomena at the atomic level have been particularly
baffling to the physicist. From the very first, those who sought to formulate
theories and mathematical formulae to represent atomic processes have
found it necessary to abandon established physical principles and to base
their theoretical developments on ad hoc assumptions and specially
devised principles of impotence. In spite of the unparalleled freedom
of thought thus attained (or perhaps, more accurately, because
of it) the theories which the physicists have developed have encountered
serious difficulties at every turn, and have never been adequate to meet
the constantly growing demands upon them. The experimental branch of physics
is continually discovering new phenomena and new characteristics of previously
known phenomena, which the theoretical branch did not anticipate and cannot
reconcile with their existing theories. Each experimental advance thus
requires a wholesale modification of these theories and a new batch of
ad hoc assumptions.
The difficulties in which current atomic theory is now
enmeshed were discussed in detail in The Case Against the Nuclear
Atom, but that work was purely a critique of existing thought in
the atomic field and it did not offer any new explanations of the matters
at issue. The preceding discussion has now laid the foundation for a new
theoretical understanding of motion in the atomic region.
Fig.2
Let us consider an atom A in motion toward another atom
B through free space (Fig.2). According to accepted ideas, atom A will
continue to move in the direction AB until the atoms, or the force fields
surrounding them, if such fields exist, are in contact. The postulates
of the Reciprocal System specify, however, that space exists only in units,
hence when atom A reaches point x, one unit of space distant from B. it
cannot move any closer to B in space. It is, however, free to change
its position in time relative to the time location occupied by atom B.
The reciprocal relation between space and time makes an increase in time
separation equivalent to a decrease in space separation, and while atom
A cannot move any closer to atom B in space, it can move to the equivalent
of a spatial position that is closer to B by moving outward in coordinate
time. When the time separation between the two atoms has increased to
n units, space remaining unchanged, the equivalent space separation, the
quantity that will be determined by the usual methods of measurement,
is then 1/n units. In this way the measured distance, area, or volume
may be a fraction of a natural unit, even though the actual one, two,
or threedimensional space cannot be less than one unit in any case.
So far as the interatomic distance itself is concerned,
it is not very material whether this is an actual spatial separation or
merely the equivalent of such a separation, but the fact that the movement
of the atoms changes from a motion in space to a motion in time at the
unit level has some important consequences from other standpoints. For
instance, the spatial direction AB in which atom A was originally moving
no longer has any significance inside unit distance, as the motion in
time which replaces the previous motion in space has no spatial direction.
It does have what we choose to call a direction in time, but this temporal
direction has no relation at all to the spatial direction of the previous
motion. No matter what the spatial direction of the motion of the atom
may have been before unit distance was reached, the temporal direction
of the motion after it makes the transition to motion in time is
determined purely by chance.
Any kind of action originating in the region where all
motion is in time is also subject to significant modifications if it reaches
the unit boundary and enters the region of space motion. For example,
the connection between space motion and time motion is scalar” and
consequently only one dimension of a twodimensional or threedimensional
motion can be transmitted across the boundary. This point will have an
important bearing on one of the phenomena that will be discussed later.
Another important fact is that the effective direction
of the spacetime progression reverses at the unit level. Outside unit
space the progression carries all objects outward in space away from each
other. Inside unit space only time progresses and since an increase in
time, with space remaining constant, is equivalent to a decrease in space,
time progression in this region, the time region, as we will call
it, moves all objects to locations which, in effect, are closer together.
The gravitational motion always opposes the progression and hence the
direction of this motion also reverses at the unit boundary. As it is
ordinarily observed in the timespace region, the region outside
unit distance, gravitation is an inward motion, moving objects closer
together. In the time region it acts in the outward direction, moving
objects farther apart.
On first consideration it may seem illogical for the
same force to act in opposite directions in different regions, but from
the natural viewpoint these are not different directions.
As brought out in Chapter VI, the natural datum is unity, not zero, and
the progression therefore always acts in the same natural direction:
away from unity In the timespace region away from unity is also away
from zero, but in the time region away from unity is toward zero. Gravitation
likewise has the same natural direction in both regions, in this case
toward unity.
It is this reversal of direction at the unit level, which
enables the atoms to take up equilibrium positions and form solid and
liquid aggregates. No such equilibrium can be established where the spacetime
progression is outward, because in this case the effect of any change
in the distance between the atoms resulting from an unbalance of forces
is to accentuate that unbalance. If the inwarddirected gravitational
force exceeds the outwarddirected progression, an inward motion takes
place, making the gravitational force still stronger. Conversely, if the
gravitational force is the smaller, the resulting motion is outward, which
further weakens the already inadequate gravitational force. Under these
conditions there can be no equilibrium.
In the time region, however, the effect of a change in
relative position opposes the unbalanced force, which caused the change.
If the gravitational force (outward in this region) is the greater, an
outward motion takes place, weakening this gravitational force and ultimately
reducing it to equality with the constant inwarddirected force of the
progression. Similarly, if the force of the progression is the greater,
the movement is inward, and this increases the gravitational force until
equilibrium is reached.
This is a most important finding: one that is unquestionably
entitled to be designated as Outstanding Achievement Number Seven. The
equilibrium that must necessarily be established between the atoms of
matter inside unit distance in the RS universe obviously corresponds to
the observed interatomic equilibrium that prevails in solids and, with
certain modifications, in liquids. Here, then, is the explanation of solid
and liquid cohesion that we derive from the Reciprocal System: the first
comprehensive and completely selfconsistent theory of this phenomenon
that has ever been formulated. The mere fact that it is far superior in
all respects to the currently accepted electrical theory of matter is
not, in itself, very significant, inasmuch as the electrical hypothesis
is definitely one of the less successful segments of presentday physical
theory, but a comparison of the two theories should nevertheless be of
interest from the standpoint of demonstrating how great an advance the
new theoretical system actually accomplishes in this particular field.
The first item to be noted is that we are not replacing
the electrical theory of matter with another “theory of matter.”
The Reciprocal System is a complete general theory of the universe; it
contains no hypotheses other than those relating to the nature of space
and time and it produces an explanation of solid cohesion in the same
way that it derives logical and comprehensive explanations of other physical
phenomena, simply by development of the consequences of the spacetime
postulates. We therefore do not have to call upon any additional force
of a hypothetical nature to account for the cohesion; the same thing that
makes the atom an atom–the rotation in three dimensions–accounts
for both the inward force of gravitation in the region outside unit distance
and the existence of the interatomic equilibrium inside this distance.
Another significant point is that the new theory identifies
both of the forces that enter into the interatomic equilibrium.
One of the major defects of the electrical theory is that it only provides
one force, the hypothetical electrical force of attraction, whereas two
opposed forces are required to explain the observed situation. Originally
it was assumed that the atoms were impenetrable and that the electrical
forces simply held them in contact, but presentday experimental knowledge
of compressibility and other properties of solids has demolished this
hypothesis and it is now evident that there must be what Karl Darrow calls
an “antagonist” to counter the attractive force, whatever it
may be, and produce an equilibrium. Physicists have been unable to find
any such force and, as Darrow says, they take refuge in evasion, and “manage
to avoid the question, by using “words not conveying directly the
notion offorce.”^{89}
A particularly important advantage of the Reciprocal
System is that it utilizes the same mechanism for the cohesion
of all substances. The basic hypothesis of the electrical theory–that
of a force of attraction between a hypothetical positively charged constituent
of the molecule and a hypothetical negatively charged constituent–is
applicable only to a restricted class of solid substances and it is necessary
to call upon weird ideas such as “shared electrons” to replace
the basic hypothesis where the latter is clearly inapplicable. Even with
this extraordinary kind of latitude, the theory is still in serious trouble.
It is freely admitted, for instance, that there is still no plausible
explanation for the cohesion of metallic aggregates. The superiority of
an allinclusive theory is obvious.
The directional characteristics of the interatomic
forces are also explained in an easy and natural way by the Reciprocal
System, whereas the electrical theory has practically nothing to contribute
in this respect. Inasmuch as the atomic forces, according to the new system,
result from rotation in three dimensions, and each dimension has its own
specific rotational velocity, it is evident that a change in the interatomic
orientation will alter the force, which the atom exerts on its neighbor.
Although the foregoing items add up to a very impressive
total, the greatest triumph of the new system in this particular area
is mathematical. By means of methods outlined in Chapter XV it is possible
to determine the magnitudes of the rotational motions in each of the three
dimensions of the atoms of the different chemical elements and the magnitudes
of the corresponding directional forces. Equating these forces to the
constant force of the spacetime progression and solving for the equilibrium
distance then gives us the interatomic distance or distances for each
element or compound. As shown in The Structure of the Physical Universe,
where these calculations are carried out in detail, there are uncertainties
in the structures of the more complex substances that cause the result
to take the form of a set of possible values in each instance rather than
a specific figure, but for the simpler substances the calculated distance
is definite and unequivocal, and in all of these cases it agrees with
the experimental results within the margin of uncertainty of the latter.
Additional studies, as yet unpublished, show that this agreement between
the theoretical and experimental values holds good not only at normal
pressures but also throughout the entire experimental pressure range,
up to 100,000 atm. static pressure and to several million atmospheres
by the recently developed shock wave techniques.
These results, the quantitative as well as the qualitative,
are derived solely from the postulates concerning the nature of space
and time, without any additional assumptions or any reference to the data
of observation. Development of the consequences of the postulates reveals
that there must exist certain combinations of rotational and vibrational
motion, that the possible combinations of this type form a series in which
each successive member possesses one more net unit of motion than its
immediate predecessor, that, for example, a unit of number 19 in this
series will form an equilibrium structure with other units of the same
kind, in which each individual is separated from its immediate neighbors
by the equivalent of 1.541 natural units of distance, and that number
19 will also combine with number 35 in the series, and the resulting 1935
combination will form an equilibrium structure in which each individual
is the equivalent of 1.133 natural units distant from its nearest neighbor.
All of the foregoing is purely theoretical and entirely
independent of anything that may exist in the actual physical universe.
It is simply a description of conditions and mathematical relations, which
are necessary consequences of the Fundamental Postulates of the Reciprocal
System and which therefore, must exist in the theoretical RS universe.
But having come this far, we can now compare these features of the RS
universe with the corresponding features of the observed physical universe.
When we do this we find an exact agreement all the way down the line.
The units of compound motion are atoms of matter, the series of these
combinations is the series of chemical elements, numbers 19 and 35 in
this series are the elements potassium and bromine respectively, their
combination is potassium bromide, and the equilibrium structures which
are formed are solid aggregates of these substances. By making some one
measurement, either of an actual interatomic distance or of an appropriate
combination of basic physical constants, we can identify the ratio of
conventional units (Angstrom units) to natural units of distance as 2.914.
Applying this ratio to the interatomic distances calculated theoretically,
we obtain 4.49 for potassium and 3.30 for potassium bromide. Representative
values from experiment are 3.29 for potassium bromide and 4.50 to 4.54
for potassium.
This, then, is another demonstration that the theoretical
RS universe derived from the postulates of the Reciprocal System is identical
with the observed physical universe: a demonstration which is particularly
significant in that it involves a long chain of theoretical deductions,
which are in complete agreement with the observed facts at every step
of the way, and which ultimately lead to specific numerical values which
can be compared directly with the corresponding experimental results.
