## CHAPTER 6## The General PictureTranslation of the mathematical properties of reciprocals into the physical terms applicable to scalar motion, a reciprocal relation between space and time magnitudes, in the preceding chapter revealed that there necessarily exists an inverse sector of the universe in which the scalar motions of our familiar material sector are duplicated in inverse form with space and time interchanged. The phenomena of one dimension of the inverse type of motion can therefore be represented in a three–dimensional temporal reference system corresponding to the three–dimensional spatial reference system in which spatial motion is customarily represented. Our next undertaking will be to extend our consideration of the properties of reciprocals to an investigation of the intermediate regions between the regions represented in the two types of three–dimensional reference systems. For this purpose we will need to consider the manner in which the primary scalar motions are combined. As noted earlier, the photons of radiation have no capability of independent motion, and are carried outward at unit speed by the progression of the natural reference system, as shown in (1), Diagram A. All physical objects are moving outward in the same manner, but those objects that are subject to gravitation are coincidentally moving inward in opposition to the outward progression. The information developed from the investigation of scalar motion does not indicate the exact nature of the gravitating objects, which we identify from observation as atoms and sub–atomic particles, but for present purposes this knowledge is not essential. When the gravitational speed of such an object is unity, and equal to the speed of progression of the natural reference system, the net speed relative to the fixed spatial reference system is zero, as indicated in (2). In (3) we see the situation at the maximum gravitational speed of two units. Here the net speed has reached –1, which, by reason of the discrete unit limitation, is the maximum in the negative direction.
An object moving with speed combination (2) or (3) can acquire a translational motion ín the outward scalar direction. Thís ís the type of motion with which we will be concerned in the remainder of this volume. One unit of the outward translational motion added to combination (3) brings the net speed relative to the fixed reference system, combination (4), to zero. Addition of one more translational unit, as in combination (5), reaches the maximum speed, +l, in the positive scalar direction. The maximum range of the equivalent translational speed in any one scalar dimension is thus two units. As indicated in Diagram A, the independent translational
motions with which we are now concerned are additions to the two basic
scalar motions, the inward motion of gravitation and the outward progressíon
of the natural reference system. The net speed after a given translational
addition therefore depends on the relative strength of the two original
components, as well as on the size of the addition. That relative strength
is a funetion of the distance. The dependence of the gravitational effect
on distance is well known. What has not heretofore been recognized is
that there is an opposing motion (the outward progression of the natural
reference system) that predomínates at great dístances, resultíng ín a
net The outward motion (recession) of the distant galaxies
is currently attributed to a different cause, the hypothetical Big Bang,
but this kind of an ad hoc assumption is no longer necessary. Clarification
of the properties of scalar motion has made it evident that this outward
motion is something in which
Objects, such as the galaxies, that are subject to gravitation,
attain a full unit of net speed only where gravitation has been attenuated
to negligible levels by extreme distances. The net speed at the shorter
distances is the resultant of the speeds of the two opposing motions.
As the distance decreases from the extreme values, the net outward motion
likewise decreases, and at some point, the Aggregates of matter smaller than the galaxies are under the gravitational control of larger units, and do not exhibit the same direct connection between distance and net speed that characterizes the galaxies. The same two opposing basic motions are, however, effective regardless of the size of the aggregate, and the equilibrium to which they lead can be recognized in a number of astronomical phenomena. The globular star clusters are a good example. These clusters are huge aggregates of stars, up to a million or more, in a nearly spherical structure, that are observed in the outlying regions of the larger galaxies. No viable explanation has heretofore been found for the continued existence of such a cluster. Only one force is known to be applicable, that of gravitation, and an equilibrium cannot be established without the presence of some equally powerful antagonist. Rotational forces often play the antagonist role in astronomy, but there is little rotation in these clusters. A dynamic equilibrium, as in a gas, has also been suggested, but a gas sphere is not a stable structure unless it is confined. On the basis of what is now known, the cluster should either dissipate relatively quickly, or collapse into one central mass. It does neither. Since there is no explanation available, the whole issue has been shelved by the astronomers for the time being. The outward progression of the natural reference system now supplies the missing ingredient. Each star is outside the gravitational limits of its neighbors, and therefore has a net outward motion away from them. Coincidentally, however, all stars are subject to the gravitational effect of the cluster as a whole. In a relatively small cluster the inward gravitational motion toward the center is not sufficient to hold the cluster together, but as the size of the cluster increases, the gravitational effect on the outer stars increases correspondingly. In a very large aggregate, such as a globular cluster, the net motion of the outer stars is inward, acting against the outward motion of the inner stars, and confining all stars to equilibrium positions. Once the nature of the cluster equilibrium is understood, it is evident that the same considerations apply to the galaxies, although the rotational forces in these more complex structures modify the results. The existence of the scalar motion equilibrium accounts for some otherwise unexplained properties of the galactic structure. For instance, the minimum observed separation between stars in the outer regions of the Galaxy (aside from that in double or multiple star systems) is more than two light years, an immense distance that is inexplicable without some specific obstacle to a closer approach. The existence of an equilibrium distance similar to that in the globular clusters now provides the explanation. The fact that the stars occupy equilibrium positions rather than moving freely in interstellar space also gives the galactic structure the characteristics of a viscous liquid, which explains a number of effects that have heretofore been difficult to understand, such as the confinement of quantities of high energy matter in the central regions of certain galaxies. The units of translational motion that are applied to
produce the speeds in the higher ranges are outward scalar units superimposed
on the motion equilibria that exist at speeds below unity, as shown in
combination (5), Diagram A. The two–unit maximum range in one dimension
involves one unit of speed, s/t, extending from zero speed to unit speed,
and one unit of inverse speed, t/s, extending from unit speed to zero
inverse speed. At this point it will be convenient to identify inverse
speed as For the benefit of those who may feel that the use of
the term “energy” in this significance is definitely ruled out
by a conflict with the kinetic energy equation, in which the energy varies
as the syuare of the velocity, rather than being inversely related, it
should be noted that the energy does not vary with v Unit speed and unit energy are equivalent, as the space–time
ratio is 1/1 in both cases, and the
In the foregoing paragraphs we have been dealing with
full units. In actual practice, however, most speeds are somewhere between
the unit values. Since fractional units do not exist, these speeds are
possible only because of the reciprocal relation between speed and energy,
which makes an energy of n/1 equivalent to a speed of 1/n. While a simple
speed of less than one unit is impossible, a speed in the range below
unity can be produced by addition of units of energy to a unit of speed.
For reasons that require a theoretical explanation, and are therefore
beyond the scope of this factual presentation, the quantity 1/n is modified
by the conditions under which it exists in the spatial reference system,
and appears in a different mathematical form, usually 1/n In this connection, it may be well to point out that
this work does not undertake to supply the reasons why things are as they
are – that is the task of fundamental theory. Where the reasons are
necessary consequences of known facts, they are, of course, included with
the other factual material, but otherwise the results of observation are
accepted as they are found. In the case now being considered, the second
power expression, 1/n As noted earlier, unit speed and unit energy are oppositely
directed when either zero speed or zero energy is taken as the reference
level. The scalar direction of the equivalent speed 1/n The net effective speed 1–1/n Because of the existence of three speed ranges with different
space and time relationships, it will be convenient to have a specific
terminology to distinguish between these ranges. In the subsequent discussion
we will use the terms Inasmuch as the three scalar dimensions are independent, the two–unit range between zero speed and zero energy applies to each of these three dimensions individually. Thus the total separation between zero speed and zero energy on the full three–dimensional basis is six units of speed (or energy). The midpoint that divides the material (space) sector from the cosmic (time) sector is three units. In practice, however, neither net speed nor net energy exceeds the two–unit level by any significant margin, because of the gravitational effects. This is illustrated in Diagram C, which shows the relations between the speeds and energies of the two sectors.
The middle line in this diagram (number 3) shows the total speeds and energies (in parentheses), with 3 units of either speed or energy as the midpoint. Where gravitation is absent, as it is (on the individual mass unit basis) at any distance above that corresponding to unit speed, or any inverse distance above that corresponding to unit energy (lines 2 and 4), the effective speeds are the same as in line 3. The upper (1) and lower (5) lines show the net values with gravitation included. The significance of this diagram is that it demonstrates that the effective maximum net speed (or energy) is not three units, the midpoint between zero speed and zero energy, but two units. We know from observation that at the normal (low) speeds of the material sector the spatial density of matter is great enough to subject all aggregates to gravitational effects. In view of the reciprocal relation, we can deduce that the same is true of the density in time in the cosmic sector. Motion in space does not change the density in time, and vice versa. It follows that when the net spatial speed (translational less gravitational) reaches 2 units (line 2), gravitation in time becomes effective, and the motion is at the (3) level on the energy basis (line 5). Summarizing the foregoing discussion, we may say that
the physical universe is much more extensive than has hitherto been realized.
The region that can be accurately represented in a spatial frame of reference
is far from being the whole of the universe, as conventional science assumes
that it is. There is another equally extensive, and equally stable, region
that is not capable of representation in any spatial reference system,
but can be correctly represented in a three–dimensional temporal
reference system, and there is a large, relatively unstable, transition
zone between the two regions of stability. The phenomena of this transition
zone cannot be represented accurately in Furthermore, there is still another region at each end
of the speed–energy range that is defined, not by a unit speed boundary,
but by a unit space or time boundary. In large–scale phenomena, motion
in time is encountered only at high speeds. But since this inversion from
motion in space to motion in time is purely a result of the reciprocal
relation between space and time, a similar inversion also occurs wherever
the magnitude of the As we have just seen, in connection with the combination of speeds and energies to produce net speeds below unity, the mathematical expression of the speed equivalent of an energy magnitude may take a form that differs from the expression of the corresponding speed. This difference in the mathematics, together with the substitution of energy for speed, accounts for the difficulty, mentioned in Chapter 3, that conventional physical theory is having in defining the phenomena of the realm of the very small in “real” terms. With the addition of these two small–scale regions to those described above, the speed regions of the universe can be represented as in Diagram D.
The extent to which our view of the physical universe has been expanded by the identification of the properties of scalar motion can be seen from the fact that the one section of this diagram marked “3d (thr~e–dimensional) space” is the only part of the whole that has been recognized by conventional science. Of course, this is the only region that is readily accessible to human observation, and the great majority of the physical phenomena that come to the attention of human observers are phenomena of this three–dimensional spatial region. But the difficulties that physical science is currently encountering are not primarily concerned with these familiar phenomena; they arise mainly from attempts that are being made to deal with the universe as a whole on the basis of the assumption that nothing exists outside the region of three–dimensional space. Our results show that the principal problems now confronting physics and astronomy stem from the fact that observation and experiment have penetrated into these regions that are beyond the scope of the three–dimensional space to which present–day theorists are limiting their vision. The phenomena and entities of the hitherto unrecognized regions of the physical universe interact with those of the region of three–dimensional space only at widely scattered locations. We therefore encounter them one by one at apparently unrelated points. For a full appreciation of their significance it needs to be realized that all of these seemingly isolated items are constituent elements of a vast physical system that is mainly beyond the reach of our physical facilities. The concept of phenomena that either cannot be represented accurately, or cannot be represented at all, within a three–dimensional spatial system of reference, will no doubt be unacceptable to many individuals who are firmly committed to the long–standing belief that the region defined by such a system is the whole of physical existence. But this is simply another case of anthropomorphism, not essentially different from the once general conviction that the earth is the center of the universe. Nature is under no obligation to conform to the manner in which the human race perceives physical events, and in order to enable continued progress toward better understanding of natural processes it has been necessary time and time again to transcend the limitations that men have tried to impose on physical phenomena. Extension of physical theory into regions beyond representation in the conventional spatial reference systems is a drastic change, to be sure, but the fact that such an extension turns out to be required should not surprise anyone who is familiar with the history of science. As indicated in Diagram C, when the distance exceeds 1.00, the gravitational limit, and gravitation is consequently eliminated, the limiting value of 2–x is at the sector boundary. Any further addition to the speed results in entry into the cosmic sector. It is possible, however, for an object to acquire a translational speed of 3–x and still remain in the material sector until the opposing gravitational motion is reduced to the point where the net total speed of the object reaches two units. Thus far we have been considering the successive units of speed purely as magnitudes. On this basis, they are all equivalent. As we saw in Diagram B, however, the second unit in each scalar dimension is a unit of energy, rather than a unit of speed. lt is equivalent to a unit of speed in magnitude, but in relation to zero speed it is inverse, and opposite in direction. Motion in this speed range is in time. The effect of the reversal at the unit level is to divide the two sectors of the universe into regions in which the relation between the natural and arbitrary spatial reference systems changes at each regional boundary. Since the natural system is the one to which the universe actually conforms, any process that, in fact, continues without change across a regional (unit) boundary reverses in the context of the arbitrary fixed spatial reference system. Each region thus has its own special characteristics, when viewed in the context of the spatial reference system. The observed characteristics of motion in the intermediate region, for instance, are quite different from those of motion in the speed range below unity. However, the differences are introduced by the connection to the reference system; they are not inherent in the motions. So far as the scalar motion itself is concerned, these are two one–unit positive magnitudes of the same nature. The fact that one of these motions takes place in space, and the other in time, is a result of their relation to unity, the natural datum, or zero level. A speed 1–x is less than unity, and it causes a
change of position in space, without effect on position in time (relative
to the natural datum). A speed of 2–x, in the intermediate range,
is greater than unity, and it causes a change of position in time. Further
addition of speed, bringing the motion into the 3–x range, the uJtra
high speed range, puts it over the one–dimensional limit of two units,
and into the spatial unit of a second dimension. Such a motion is outward
in space in the second dimension, while it continues outward in time in
e first dimension. As noted earlier, coincident motion in both space and
time is impossible. But we have seen that a motion with energy n/1 in
time is equivalent to a motion with speed 1/n in space. As long as the
gravitational effect is strong enough to keep the net total speed below
the sector limit of two units, the motion as a whole continues on the
spatial basis. The motion in time that takes place in the 2–x and
3–x speed ranges while the net speed is below two units is therefore
a motion in The upper speed ranges are duplicated on the energy side of the neutral level. Corresponding to the intermediate speed range is an intermediate energy range, with energy 2–x, where x is the fractional energy eyuivalent of n units of speed. In this energy range, the motion as a whole continues on the time basis as long as the net total energy remains below the two–unit level. The motion in space that takes place in this 2–x energy range is therefore a motion in equivalent time. Similarly, a motion component in the 3–x energy range, which involves motion in time in one dimension and motion in space in a second dimension, continues as a motion in ecluivalent time as long as the net total energy remains below the level at which gravitation begins acting in space. Like the phenomena of the low energy range, the region
of threedimensional time, the events taking place in the two upper Some general comments about the contents of this present
chapter are in order. First, it may seem that the large number and broad
scope of the conclusions that have been reached are out of proportion
to the base from which it is asserted that they are derived, inasmuch
as the stated objective was to derive them from the mathematical properties
of reciprocals. It should be remembered, however, that the point brought
out in Chapter 5 was that application of these mathematical properties
to The second point that warrants some consideration is
the logical status of the conclusions that have been reached with respect
to the phenomena of the regions intermediate between the region represented
in the conventional spatial reference system and the corresponding inverse
region. It has been found empirically that certain things (using the term
in a broad sense to include both entities and phenomena)
In any event, whether we can assert that some physical
objects actually do attain speeds in the intermediate and ultra high ranges,
or whether the most that we can legitimately say is that they can attain
such speeds, what we need to do in order to bring speeds of this magnitude
into the factual picture that we are developing in this work is to identiJv’
physical objects whose properties coincide with the properties of objects
moving at speeds in excess of that of light. lt is evident that such objects,
if they exist, are astronomical. This introduces some difficulties into
the identification process. The amount of observational information about
astronomical phenomena is, in many cases, severely limited. “What
is a quasar? No one knows,” In order to compensate for the scarcity of reliable information
about the nature and properties of the individual astronomical entities,
the identifications based on comparison with this information will be
supplemented by identification of entire In the course of this identification process, however,
we will advance our understanding of the intermediate speed region a step
farther than was possible in the preceding discussion. The physical entities
that we will identify as moving at speeds greater than unity are active
participants in large–scale physical activity. Thus, in examining
and identifying these entities we will also be deriving a general picture
of the large–scale |