Progression vs. Gravitation
From the standpoint of our accustomed habits of thought,
one of the most surprising of the conclusions that were derived by the
extrapolation process in Chapter IV is that of a progression of space.
The somewhat intuitive impression that we gain from our everyday experiencean
impression that has been accepted and formalized by present-day physical
scienceis that space is an entity that stays put, whereas
time is an entity that progresses. But now the postulate derived from
an extrapolation of the observed space-time relation tells us that space
also progresses in exactly the same manner as time.
The origin of the progression is evident as soon
as the reciprocal postulate is formulated. If space and time are reciprocally
related, then a single unit of space is equivalent to a single unit of
time, from the scalar space-time standpoint. When the passage of one additional
unit of time causes point A to move forward to A + 1 in time, the equivalence
of the unit of time and the unit of space means that point A has also
moved forward one additional unit of space, to point A + 1 in space.
The general nature of the progression is not as
obvious. Our rather vague psychological impression of the passage of time
suggests a unidirectional movement, from the past and toward the futurethe
River of Time, as it is so often called. But now that we recognize both
space and time as progressing, we have an opportunity to see the progression
in a much clearer light. As pointed out in Chapter IV, the recession of
the distant galaxies is clearly due to the space-time progression, and
this phenomenon therefore gives us a visible illustration of the nature
of the progression of space and, by extension, the nature of the corresponding
progression of time. It is not difficult to get a clear mental picture
of the observed situation in which the galaxies are moving directly outward
from us in all directions, and we need only to imagine this recession
taking place at the velocity of lightwhich it undoubtedly does somewhere
beyond our present observational rangein order to get an understanding
of how the locations in space are continually moving away from
the location which we happen to occupy.
The corrolary to this proposition, the fact that we are
likewise moving away from all other galaxies in the same manner and that
the location which our galaxy occupies is moving outward in all directions
away from all other spatial locations, is somewhat harder to visualize.
It is not easy to conceive of motion taking place in all directions simultaneously.
But unless we wish to take the position that our galaxy alone, among all
of the billions within observational range, occupies a fixed positiona
rather fantastic contentionour galaxy must be moving away
from all others, and hence must be moving in all directions. A motion
in all directions has no specific direction; that is, such a motion
is scalar. The movement is simply from A to A + 1 and on to A + n, both
in space and in time. To illustrate this phenomenon the astronomers commonly
utilize the example of points on the surface of a balloon, which is being
inflated. As the inflation proceeds, the distances between the points
gradually increase; that is, each point moves away from all other points,
and thus moves outward in all directions simultaneously. By visualizing
a similar situation in three dimensions we can obtain a mental picture
of the recession of the galaxies and of the progression of space which
causes the galactic recession.
If we now recognize that time is subject to exactly the
same kind of a progression as space, we can get a new concept to replace
the familiar idea of a River of Time flowing past us unidirectionally.
Instead of a river, we should visualize the equivalent of an expanding
balloon. Each point in time moves outward from all other points just as
each point in the three-dimensional space occupied by the balloon moves
outward from all other points. But we should keep in mind that the balloon
is an incomplete analogy. The progression of time is different in one
important respect: it does not take place in space; it takes place
in time. Each location in time is continually moving outward
away from all other locations in time.
An important consequence of the progression of space-time
is that unit velocity, one unit of space per unit of time, is the condition
of rest in the physical universe, the datum from which all activity begins.
We are so accustomed to measuring from the mathematical zero that this
concept of a finite velocity as the neutral condition will no doubt seem
odd on first consideration, but it is not without precedent. There are
other physical situations in which the neutral point is at some finite
value with meaningful deviations in both directions. For example, there
is the hydrogen ion concentration, measured on the pH scale. If we are
concerned about alkalinity and we find that two solutions have pH values
of 7 and 8 respectively, it might appear to the uninitiated that one solution
is slightly less alkaline than the other. The truth is, of course, that
the solution with the 7 pH is not alkaline at all, as 7 is the neutral
value. This is not an arbitrary point, like the zero on the Centigrade
temperature scale; the pH is mathematically related to the actual hydrogen
ion concentration, and hence represents an actual physical reality. Unit
velocity is a neutral value of the same nature: a true physical datum
with a finite magnitude.
In this neutral condition, each unit of space is exactly
like all other units of space and each unit of space is equivalent to
a unit of time that is exactly like all other units of time. A unit of
elapsed time, a unit movement in time, is equivalent to a unit movement
in space, hence all locations in space-time are moving away from all other
locations at unit velocity. Since space-time is motion, in the most general
sense of that term, its measure is speed or, as this speed manifests itself
in a spatial or temporal reference system, velocity. Just as we measure
space in centimeters, or some similar unit, and time in seconds, we measure
space-time in centimeters per secondin velocity terms. Unit velocity
is not only the measure of the progression of space-time; it is the measure
of space-time itself. Space-time is a motion: a progression. Aside
from this ceaseless progression, a universe in the neutral condition would
be one vast domain of perfect uniformity in which nothing ever happens
and nothing could happen.
In order that there may be events or phenomena
in the universeanything other than the uniform and featureless
progressionthere must be a deviation from unity: a displacement
of space-time from the unit level. There cannot be any such deviation
in the space-time velocity, since the equivalence of a single unit of
time and a single unit of space holds good for any number of units or
any combination of units. The space velocity or the analogous quantity
in time may, however, experience displacement because of the directional
effects that pertain to space and time individually. If the space direction
of the progression, for example, reverses at the end of a unit, the progression
of space-time is not affected, since space-time is scalar and has no directional
characteristics, but the progression of space now moves back over the
same space unit which it just traversed.
On first consideration it may be hard to understand how
an object which is moving directly away from us can reverse its direction
of motion and still continue moving directly away from us. We realize,
however, that inasmuch as the distant galaxies are all moving directly
away from us, we must be moving directly away from all of them.
Our galaxy M is therefore moving away from galaxy A in the direction AM,
whereas it is also moving in the opposite direction BM directly away from
some galaxy B which is diametrically opposite to A in our field of vision.
It is quite possible, then, for some object to have a motion coinciding
with the recession of our galaxy in the direction AM, and then to reverse
this spatial direction and move in unison with the recession of our galaxy
in the direction BM.
The important point here is that the recession of our
galaxy in the direction AM moves the galaxy outward in space away from
all other galaxies. Consequently any object whose motion coincides with
that of the galaxy is also moving outward away from the distant galaxies;
that is, it is moving outward from all other locations in space. But exactly
the same thing can be said of any object whose motion coincides with that
of the galaxy in the opposite direction BM. This object is also moving
outward away from all other locations is space.
The scalar direction of any motion, the inward
or outward direction toward or away from all other locations, is
thus independent of the spatial direction. In the example we have
been discussing, motion in the direction AM may be either inward or outward,
from the scalar standpoint. The same is true of motion in the direction
BM. This explains how the space-time progression which, in our region
of the universe, always proceeds outward, can, under appropriate circumstances,
reverse its spatial direction.
No special mechanism is necessary in order to accomplish
this reversal. The reciprocal postulate requires the existence of aggregations
of n units of space (or time) in association with single units of time
(or space) and, as indicated in the foregoing discussion, a change of
spatial direction (or temporal direction) is the only means by which such
associations can be formed. Deviations from the normal one to one space-time
ratiodisplacements of space-time, as they are called in this
worktherefore must exist, and directional changes must
take place wherever such displacements occur.
A directional reversal of this kind is an eventa
physical occurrenceand it takes place at a specific spatial or temporal
location. All such locations are subject to the progression; that
is, a space-time location is a thing in motion. The reversed motion thus
becomes detached from the general space-time structure and is carried
along by the progression in a direction perpendicular to the direction
of the original motion. It now becomes a physical entity: an independent
phenomenon pursuing its own course and having a space velocity of its
own, the magnitude of which is determined by the relative frequency of
reversals of space direction and time direction. Space progresses n units
while time progresses m units, and the space velocity is therefore n/m
in this particular phenomenon.
Although we have been dealing only with reversals thus
far, it will be noted that in making some of the general statements in
the preceding paragraphs it was necessary to use the term change
rather than reversal of direction. The reason is that there
is no requirement of an immediate reversal. A gradual change of direction
by means of a rotational movement will accomplish the same result. However,
a direct generation of rotation from the neutral condition, in which nothing
exists but the uniform progression of space-time, is impossible simply
because there is nothing to rotate. The first effect of a displacement
applied to the neutral situation is therefore to cause vibrational motion.
The vibrating unit then progresses translationally as has been explained.
When this vibrating unit is viewed from a reference system that does not
progress, the combination of an oscillation in one dimension with a unidirectional
progression in a perpendicular dimension takes the form of a sine curve.
If a number of such oscillating units are generated at
the same space-time locationthat is, are generated simultaneously
at the same space locationtheir unidirectional progression always
takes place in the outward scalar direction, but outward from the scalar
standpoint is indeterminate from the standpoint of spatial direction,
and the progression of any individual unit can therefore take any
spatial direction. Since all directions are equally probable, the mathematical
principles of probability, whose validity was assumed as a part of the
Second Fundamental Postulate, tell us that the individual progressions
of the units will be distributed equally over all spatial directions.
The first phenomenon that we develop from the Fundamental Postulates is
therefore one in which oscillating space-time units originate at various
locations in space-time and move outward in all directions from these
locations at unit velocity, one unit of space per unit of time.
The various entities that emerge as constituents of the
theoretical RS universe as the development proceeds will, of course, appear
without labels, but it will not usually be difficult to identify the corresponding
feature of the observed physical universe. In this case it is obvious
that the oscillating units which we have been describing are photons
of light or other electromagnetic radiation. The process of emission and
movement of these photons is known as radiation, the space-time
ratio of the oscillation is the frequency of the radiation, and
unit velocity is the velocity of electromagnetic radiation or, as it is
more commonly termed, the velocity of light, customarily represented
by the symbol c.
Here, then, is the first of those Outstanding Achievements
of the Reciprocal System, which deserve special emphasis. The foregoing
description of the nature of the photon furnishes a complete and logical
explanation of the seemingly paradoxical behavior of radiation in which
it sometimes acts as a particle and sometimes as a wave—one of the most
baffling enigmas of modern physics: the vexed antinomy of corpuscles
versus waves which contemporary physics faces and which the term
complementarily merely hides without removing,78 as Capek describes it. The photon
acts as a particle in emission and absorption because it is a single independent
unit; it travels as a wave because the combination of a linear oscillation
and a translatory movement in a perpendicular direction produces a wave-like
One of the most significant features of the Reciprocal
System is that the explanations, which it produces for basic physical
phenomena, are extremely simple. Instead of explaining why seemingly
complicated phenomena are complex and perplexing, this system removes
the complexity and reduces the phenomena to simple terms. The space-time
progression and the galactic recession, which it produces, occur because
one unit of space is equivalent to one unit of time. The photon originates
by a periodic reversal of the direction of one of the components of space-time.
Both of these are about as simple as any physical explanation can be.
Now we find that the answer to the seemingly insoluble wave-particle problem
is equally simple. To the question: Is the photon a wave, a particle,
some hybrid that could be called a wavicle, or is it one of
the ghostly denizens of the half-world of the quantum theories?, we are
able to reply: The photon is a particle (that is, a discrete physical
entity) which travels as a wave. On this basis the reason why radiation
can have wave-like properties such as that of polarization even though
it consists of discrete particles is obvious.
The same simple explanation of the nature of the photon
can also be credited with Outstanding Achievement Number Two: the answer
to the problem of how the energy of radiation is transmitted from one
object to another distant object without any connecting medium between
the two. Such answers must be innovations; if they could be obtained from
existing lines of thought there would be no problems. Furthermore, if
they are to be simple answers to problems of long standing, they must
have some rather surprising aspects, as it is not at all likely that answers
within the bounds of accepted thinking would have remained hidden so long,
particularly in view of all of the effort that has been applied to searching
for them. In the case of the wave-particle problem, no one has previously
realized that the photon, as observed, might be more than a photon; that
is, it might be a photon in conjunction with something else. But as soon
as we look at the situation in this light, it is apparent that we have
arrived at a simple solution of the difficulty.
The innovation that solves the problem of how radiation
is transmitted through empty space is one of an even more surprising character.
The answer here is that radiation is not transmitted at all. The photon
remains permanently in the same space-time location in which it
originates, but space-time itself progresses, carrying the photon with
it, and the photon is therefore able to act on any objects which are not
carried along by the progression and which are therefore encountered en
route. For an explanation of the nature of these objects, let us now return
to the subject of rotation.
Once the photon has come into being, the previous obstacle
to the existence of rotational motion has been eliminated, since there
is now an object that can rotate, and our next step in the
development of the theoretical RS universe will be to examine the characteristics
of this rotation. First, let us bear in mind that the photon, the object
which we are going to rotate, is itself a motion, so that when we rotate
the photon what we are actually doing is generating a compound motion.
We cannot do this by simple addition, as a total magnitude exceeding that
of the progression would result in a directional reversal, and would give
rise to vibration rather than rotation. The photon can, however, rotate
in the opposite scalar direction or, strictly speaking, since rotation
has no meaning from a scalar standpoint, it can rotate in space or time
in such a manner that the corresponding space-time movement is in the
scalar direction opposite to that of the progression. Inasmuch as the
space-time progression is linearly outward in space, this means that the
scalar effect of the rotational motion is linearly inward in space.
Another requirement is that the magnitude of the rotational
motion must be greater than that of the progression. One unit of inward
motion would simply cancel the one unit outward movement of the progression
and create the rotational equivalent of nothing at all. Less than one
unit is not possible, as fractional units do not exist. Hence the magnitude
of the rotational motion must be greater than unity. We find, then, that
when the photon acquires a rotation it reverses its space-time direction
and travels backward along the line of the progression, moving inward
from its own location toward all other spatial locations.
Again we have no difficulty in identifying the corresponding
phenomena in the observed physical universe. The rotating photons, with
the exception of certain incomplete units that we will discuss later,
are atoms. Collectively the atoms constitute matter, and
their inward movement is gravitation.
As a rough analogy, we may visualize a moving belt, traveling
outward from a central location and carrying an assortment of cubes and
balls. The outward travel of the belt represents the progression of space-time.
The cubes are analogous to the photons of radiation. Having no independent
mobility of their own, they must necessarily remain permanently at whatever
location on the belt they occupy initially, and they therefore move outward
from their point of origin at the full velocity of the belt. The balls,
however, can be caused to rotate, and if the rotation is in the direction
opposite to the travel of the belt and the rotational velocity is high
enough, the balls will move inward instead of outward. These balls represent
the atoms of matter, and the inward motion opposite to the direction of
travel of the belt is analogous to gravitation.
The analogy is, of course, incomplete. It cannot portray
a strictly scalar motion, and consequently the mechanism whereby the rotation
of the balls causes them to move inward translationally is not the same
as that which causes the inward motion in the actual atomic situation.
The analogy is also unable to demonstrate movement in all directions.
Nevertheless, it does show quite clearly that under appropriate conditions
a rotational motion can cause a translational displacement, and it also
gives us a rough picture of the general relations between the space-time
progression, gravitation, and the travel of the photons of radiation.
Unlike the space-time progression, which originates everywhere,
and therefore remains constant irrespective of location, the gravitational
motion originates at the location, which the atom happens to occupy. Since
the atom is moving in opposition to the space-time progression it is continually
passing from one space-time unit to another. The spatial direction corresponding
to this scalar inward motion is indeterminate, and inasmuch as this direction
is continually being redetermined because of entry into another unit of
space-time, the effect of the probability laws is to distribute the motion
equally over all directions. The fraction of the total motion directed
toward any area A at distance d is then determined by the ratio of this
area to the total surface area of a sphere of radius d. This ratio is
inversely proportional to d2, hence the gravitational motion decreases
with distance in accordance with the familiar inverse square law.
As the foregoing discussion indicates, gravitation is
a movement of the atom inward toward all space-time locations other than
the one, which it occupies (momentarily). Thus it is inherently a motion
of the individual atom or material aggregate relative to the general space-time
framework. However, the only way in which we can recognize such a motion
is by reference to some observable aggregate of matter, and since that
aggregate also has a similar gravitational motion inward in space-time,
what we actually observe is that the two material aggregates are moving
inward toward each other. Quite naturally this has been interpreted as
indicating that the two masses are exerting forces of attraction upon
each other, and the great problem of gravitation has been to account for
the observed characteristics of these forces, which are most
extraordinary and totally unlike those of forces encountered elsewhere
in the physical realm. How can it be possible for one mass to exert a
force upon another distant mass instantaneously, without an intervening
medium, and in such a manner that the force cannot be screened off or
modified in any way?
The total inability of modern science to make any headway
toward an answer to this question has been so discouraging to the scientific
profession that it no longer tries to find the answer. The current practice
is to ignore the observations and to base gravitational theory on assumptions
which are in direct contradiction to the observed facts. Even though all
practical gravitational calculations, including those at astronomical
distances, are carried out on the basis of instantaneous action, without
introducing any inconsistencies, and even though the concept of a force
which is wholly dependent upon position in space being propagated through
space is self-contradictory, the theorists take the stand that since they
are unable to devise a theory to account for instantaneous action, the
gravitational force must be propagated at a finite velocity, all
evidence to the contrary notwithstanding. And even though there is not
the slightest independent evidence of the existence of any medium in
space, or the existence of any medium-like properties of space,
the theorists also insist that since they are unable to devise a theory
without a medium or something that has the properties of a medium, such
an entity must exist, in spite of the negative evidence.
As usually happens when men are driven, in the depths
of their frustration, to the desperate step of denying the facts, all
this has accomplished nothing. Gravitation is still an enigma
or a mystery to the present-day scientist, and there is no
indication that it is becoming any less enigmatic or less mysterious.
Nor is any blue sky visible on the far horizon. Sir John Cockcroft summarizes
the current (1964) outlook as follows: It will probably be a long
time before we can bring the gravitational forces within a general theory,
since there is at present no progress in this direction.79
The answer, which the Reciprocal System now provides
for this difficult gravitational problem is Outstanding Achievement, Number
Three. The explanation in the preceding paragraphs not only tells us how
gravitation originates and why it is an inherent property of matter, but
also accounts for all of the seemingly strange properties of gravitation
in the exact form in which they are observed. And here again a surprising
innovation emerges. The new system does not explain how one mass can exert
a force on another distant mass instantaneously and without an intervening
medium; it tells us that the reason for all of these peculiar properties
is that gravitation is not an action of one mass upon another at all.
Each mass unit is pursuing its own individual course entirely independent
of all other masses, and the phenomenon that appears to be a mutual attraction
is actually the result of the inherent nature of the individual motions.
The gravitational motion of each mass is an inward scalar motion in opposition
to the space-time progression, and it carries the mass inward in space-time.
Since all other masses are similarly moving inward in space-time, each
mass moves toward all other masses. Such a motion needs no medium, nor
does it require a finite time for propagation; the inward motion is an
inherent property of the atoms and there is no propagation.
We must now qualify the previous statement that the magnitude
of the rotational motion of the atom is greater than that of the space-time
progression by noting that this statement applies specifically to the
situation at unit distance. Within this distance the net inward motion
(or equivalent) becomes still greater because of the effect of the inverse
square relation, outside this distance the net inward motion decreases
for the same reason, and at some point in this outer region an equilibrium
between the inward gravitational motion and the outward motion of the
space-time progression is reached. Beyond this point the net movement
is outward, the outward excess increasing as the distance becomes greater.
Where an aggregate of matter is involved rather than a single atom, the
gravitational motion is proportional to the mass, for reasons that will
be explained in Chapter XII, and the point of equilibrium, the gravitational
limit, as we will call it, is therefore a function of the mass.
We could include the distance factor in the analogy of
the moving belt by devising some means of varying the speed of rotation
of the balls with the distance from the central point. Under this arrangement
the closer balls would still move inward, but at some point farther out
there would be an equilibrium, and beyond this point the balls would move
The reason for the great difference between the view
that we get of time and the view that we get of space in our everyday
experience is now evident. The progression of time is unchecked in our
local environment and this progression so far overshadows any other change
in time location that it is the only aspect of time, which we observe.
Space actually progresses outward at the same rate as time, but the outward
motion which the space progression imparts to objects existing in this
local environment is more than counterbalanced by the inward movement
due to gravitation, and the net result is that what we seem to see is
a stationary space in which most physical objects, aside from the photons
of radiation, have relatively low velocities of a random character. Gravitation
is thus the controlling factor in our view of the universe. In the local
region where it overpowers the progression, we get a picture of a relatively
stable environment; at great distances where the gravitational motion
is small and the progression is dominant we get an entirely different
picture: one in which all objects are moving apart at enormous speeds.
In view of the important role, which the galactic recession
plays in cosmology, we are justified in characterizing the explanation
of this recession that is provided by the new system as Outstanding Achievement
Number Four. However, the existence of a gravitational limit, within which
there is a net inward gravitational motion and outside of which there
is a net outward progression, explains a great deal more than the recession
of the distant galaxies. For one thing, it reconciles the seemingly uniform
distribution of matter in the universe with Newtons Law of Gravitation
and Euclidean geometry. One of the strong arguments that has been advanced
against the existence of a gravitational force of the inverse square type
operating in a Euclidean universe is that on such a basis The stellar
universe ought to be a finite island in the infinite ocean of space,80 as Einstein puts it. Observations
indicate that there is no such concentration. As far as we can tell, the
galaxies are distributed uniformly or nearly uniformly throughout the
immense region now accessible to observation, and this is currently taken
as a definite indication that the geometry of the universe is non-Euclidean.
It is now clear that the flaw in this argument is that
it rests on the assumption that gravitation is effective throughout space.
This present work shows that this assumption is incorrect, and that there
is a net gravitational force only within the gravitational limit of the
particular mass under consideration. On this basis it is only the matter
within the gravitational limit that should agglomerate into a single unit,
and this is exactly what occurs. Each galaxy is a finite
island in the ocean of space within its gravitational limit. The
existing situation is thus entirely consistent with Newtonian gravitation
operating in an Euclidean universe, which is the situation envisioned
by the Reciprocal System.
The existence of the gravitational limit also solves
the problem of how the galaxies could form in the first place, a question,
which the cosmologists have been unable to answer. As Gold and Hoyle describe
the situation: Attempts to explain both the expansion of the universe
and the condensation of galaxies must be very largely contradictory so
long as gravitation is the only force field under consideration. For if
the expansive kinetic energy of matter is adequate to give universal expansion
against the gravitational field it is adequate to prevent local condensation
under gravity, and vice versa.81 In the RS universe gravitation
is not the only force involved, and the existence of an equilibrium
point within which the motion of matter is inward and beyond which it
is outward accounts in an easy and natural way for both the aggregation
of matter into galaxies and the recession of the distant galaxies.
The answer to the dilemma described by Gold and Hoyle
could well be considered another of the outstanding achievements of the
new system, but the limitations which have had to be imposed on the scope
of this volume will prevent going into sufficient detail to clarify the
nature of the process of galaxy formation, as it occurs in the RS universe,
and this subject will therefore be omitted from the list. It should be
understood in this connection that this list is not intended as a complete
catalog of the major achievements of the Reciprocal System; it is merely
a selection of the most significant items from among those included in
the subject matter of this particular volume.
A full development of the other consequences of the existence
of gravitational limits is also beyond the scope of this present volume,
but it should be mentioned that these limits apply to all aggregates of
matter and not only to the galaxies. Inasmuch as the smaller aggregates
are under the gravitational control of the larger units such as the galaxies,
the effect of the gravitational limits is somewhat modified in application
to the smaller masses, but nevertheless, the existence of these limits
has many significant results, some of which have been explored in previous