Although the preceding chapters have been devoted to an examination of the fundamentals of physical existence rather than being directed specifically at the astronomical phenomena that are the subjects of our present inquiry, they have nevertheless outlined the general framework of the astronomical world. They have shown that the concept of a universe of motion Ieads directly to an explanation of the existence and general properties of the matter of which stars and galaxies are composed, the gravitation that controls their destinies, and the radiation by means of which our information concerning these objects is obtained. Here, then, we have the foundation for a general astronomical theory.
In dealing with such phenomena as quasars and pulsars, however, we will be concerned not so much with the nature, origin, and behavior of the various constituents of the astronomical universe as with the processes by which these constituents are ultimately destroyed, and the products resulting from their destruction. These processes, we will find, involve destruction of matter itself, and it will therefore be necessary to extend our consideration of the structure of matter to a determination of the limits to which this structure is subject and the nature of the influences that result in the attainment of these limits. For this purpose we will take a brief look at some additional types of motion.
this discussion it will be advisable to make a few comments with respect
to the mathematical aspects of the Reciprocal System of theory. One of
the most significant features of this system is that numerical values
appear at the very start of the theoretical development-the numerical
pattern of the atomic rotations, for example, is the essence of the theory
of atomic structure-and the mathematical development goes hand in hand
with the logical development as the details of the theoretical universe
are gradually clarified. For some purposes, these mathematical relations
are indispensable. In the study of the properties of matter, for instance,
the numerical values of the properties of various substances are the primary
objective, and one of the principal arguments in support of the validity
of the theoretical system is that it is able to produce correct values
from purely theoretical premises, mainly from the rotational displacements
of the different atomic combinations, without recourse to physical
constants obtained from empirical measurements. But for the purposes
of the presentation in this volume the mathematical aspects af the theory
are irrelevant, and in order to keep the text as brief and to the point
as possible, no mathematical discussion has been included. If questions
concerning mathematical issues arise, reference should be made to the
previous books in this series listed opposite the title page.
A significant point about motion is that we do not observe it as it actually exists; we observe it only in the context of some particular reference system. In the preceding chapter, for instance, we noted that the inward motion in space that is imparted to a material aggregate by gravitation cannot be detected in any direct manner. All that we can observe is motion toward some other aggregate. Similarly, we do not observe the scalar motion of the progression in its true character as an outward motion without direction; we see it as an outward motion of the galaxies or other objects to which it applies, but we see these objects receding from us in specific directions. Our reference system thus converts scalar motion into an apparent vectorial motion.
The manner in
which a direction that is not an inherent property of the motion itself
can be imparted to that motion by means of a reference system is well
illustrated by the expanding balloon analogy. Fig. 2 shows a group of
spots on the surface of such a balloon. The motion of these spots is inherently
scalar; all spots are moving outward in all directions. But if we view
this motion in the context of a three-dimensional reference system defined
by the room in which the balloon happens to be located, the inherently
identical motions of these four spots are all different. If spot A is
resting on the floor, then spot B is moving west, spot C is moving north,
while spot D is moving east. Spot A is not moving at all. What has been
accomplished, so far as the motion of a spot like B is concerned, is to
stop the motion in one of the dimensions and thus reduce the original
scalar motion distributed over two dimensions to a one-dimensional linear
We now want to recognize that by meeting this same requirement that the spatial motion in all dimensions but one be zero, a physical object such as an atom or aggTegate of matter can have an inherently vectorial motion, one in which the direction with respect to any three-dimensional system of reference is an inherent property of the motion. We can best define the status of such a motion by considering what is necessary to produce it, if we start with the physical equivalent of nothing at all, a space-time progression in three dimensions. This situation can be represented by a triangular diagram, Fig. 3 (a) , where each vertex of the triangle indicates the speed in one of the three dimensions. The first requirement that must be met in order to reach the defined objective is to reduce the outward motion in each of two dimensions to zero by adding a unit of motion in the inward spatial direction. The resulting motion then has the pattern shown in diagram b. This is the space-time progression as we observe it in the context of our three-dimensional reference system: a uni directional linear motion directly outward from the location of observation. Here we, as observers, are in a position analogous to that of spot A on the balloon, the spot that is fixed in the reference system and thus appears to have no motion.
Another unit of motion in opposition to the progression would produce the zero level of the spatial reference system, diagram c. A finite time displacement in the active dimension then generates a linear motion in space, as in diagram d. This is the ordinary vectorial motion of our everyday experience. For present purposes no extended discussion of this type of motion is necessary, but later on we will be interested in what happens when additions of space displacement (or its equivalent) bring the speed up to the maximum limit for motion in space. From the preceding development of theory it is evident that a scalar addition to the speed would then take place, reversing the course previously described, and ultimately, if the additions continue, returning to the neutral level, the condition represented by diagram a.
Thus far we have examined three general types of motion: unidirectional linear motion (scalar and vectorial) , unidirectional rotation, and vibratory linear motion. It is evident that there is one more possible combination, and we now turn to a consideration of the fourth of the general types: vibratory rotation, a rotational motion that periodically reverses direction.
Motion of this type plays only a relatively minor role in our ordinary experience, and, in general, we do not find enough difference between rotational and linear vibrations to justify making any special distinction between the two. At the level of atoms and particles, however, the effects of a rotational vibration are altogether different from those of a linear vibration. The reason is that the atom or sub-atomic particle is basically a rotating unit. The result of adding linear translation or vibration, motion of a different nature, is to move the rotating unit, but rotational vibration is motion of the same general character as that which constitutes the basic structure of the unit to which it is applied, hence the result of adding rotational vibration is to modify the rotating unit.
As brought out in Chapter IV, the three-dimensional rotation of the atom actually consists of a two-dimensional rotation and a onedimensional rotation in the opposite scalar direction. The rotational vibration, which must necessarily oppose the rotation, may therefore be either one-dimensional or two-dimensional. The one-dimensional rotational vibration that exists in the theoretical universe can be identified with the physical phenomenon known as the electric charge. Such charges are easily produced in almost any kind of matter or sub-atomic particle, and can be detached from these units with equal ease. In a low temperature environment such as that on the surface of the earth, the electric charge therefore plays the part of a temporary appendage to the relatively permanent systems of rotational motion.
Addition of two-dimensional rotational vibration to an atom or particle has a similar effect, and since we can identify this effect with the physical phenomenon known as magnetism, we will use the same terminology and will call this rotational vibration a magnetic charge, even though the notion of a charge is somewhat foreign to current thinking in this area.
A charge is normally opposite in space-time direction to the rotation which it modifies, for the same reasons that apply to added motion in general. Thus a rotation with a time displacement normally takes a charge with a space displacement, and vice versa. Charges of the same space-time direction as the rotation do not exist unless they are of a forced character; that is, are originated in response to some outside influence, and where they do appear, their effects are quite different from those of an ordinary charge, as will be seen in an example shortly. Inasmuch as the rotation in the electric dimension may have either space or time displacement, electric charges of both space-time directions are possible. Two-dimensional rotation in the material universe, on the other hand, always has time displacement, simply because it is the rotational combinations with two-dimensional time displacement that we call matter. The normal magnetic charges therefore have the space direction.
The terms positive and negative are in common use with reference to both electricity and magnetism, and in order to avoid introducing additional confusion into a situation that is complicated at best, these terms will be given their usual significance whenever they are used in this work, even though this usage is somewhat inconsistent in the light of the theoretical findings. On this basis an electropositive element (which has an electric time displacement) takes a positive charge (with a space displacement) whereas an electronegative element (which has an electric space displacement) takes a negative charge (with a time displacement) . The accepted usage thus equates the positive and negative designations with the normal sequence of additions to the compound motions, rather than specifying the space-time direction of the displacement, which would, in many respects, be more convenient.
Inasmuch as a charge is a modification of the basic rotation, the number of charges that an atom can acquire, the deg7-ee of ionization, as it is called, is limited by the number of rotational units of the appropriate space-time direction that exist in the atomic structure: the number of units available for modification. Negative ionization is confined to low levels, as the effective negative rotation is never more than a few units. The limit of positive ionization is the atomic number, which represents the net total number of units of rotational time displacement in the atom.
Electric ionization may be produced by any one of a number of agencies, inasmuch as the requirement for this process is essentially nothing more than the availability of sufficient energy under appropriate conditions. In the universe at large the predominant process is thermal ionization. Thermal or heat energy is linear motion of rnaterial particles, and it is therefore space displacement. In the ionization process this linear space displacement is transformed into rotational space displacement: positive charge. As the temperature increases, more and more space displacement becomes available for ionization, and the degree of ionization rises until the atom finally reaches the point where it is fully ionized; that is, each of its units of time displacement has acquired a positive charge.
If the temperature of the fully ionized atom continues to rise, a destructive limit is ultimately reached at the point where the total space displacement, the sum of the ionization and the thermal energy, is equal to the time displacement of one of the magnetic rotational units. Here the oppositely directed rotational displacements neutralize each other, and both revert to the linear basis, destroying this portion af the atomic structure. Since the maximum ionization increases with the atomic number, the amount of thermal energy required to bring the total space displacement of a fully ionized atom up to the destructive limit is less for the heavier atoms, and the effect is to establish a temperature limit for each element that is inversely related to the atomic number. As the temperature of an aggregate rises, the heaviest elements are therefore the first to disintegrate.
The electric charge has always been regarded as one of the more mysterious natural phenomena, and the question as to just what it is and how it originates was a very live issue until the modern physicists solved the problem by the assertion that the question has no answer; that we will simply have to accept the charge as one of the given items in nature. Some may find it difficult, therefore, to adjust to the idea that there is actually nothing mysterious or esoteric about an electric charge; that it is simply a kind of motion. But it should be realized that we are already committed to this viewpoint just as soon as we accept the concept of a universe of motion. In such a universe all entities and phenomena are manifestations of motion, and tlie only question remaining to be answered with respect to the electric charge is just what kind of a motion it is.
As soon as we resolve this question, and arrive at an understanding that the electric charge is a one-dimensional rotational vibration, it becomes evident that a two-dimensional rotational vibration of the same nature must also exist, and that this is a magnetic charge. The fact that certain substances can be magnetized-that is, put into a state in which their magnetic behavior is analogous to the electric behavior of a charge-is well known, but the motion of an electric charge produces similar magnetic effects, and the physicists have therefore assumed that all magnetic phenomena are due to moving charges. In the light of the new information as to the nature of charges, it is evident that the same factors which produce one-dimensional (electric) ionization are also capable of producing two-dimensional (magnetic) ionization, and this magnetic ionization is therefore present wherever conditions are favorable.
As it happens, positive magnetic ionization (space displacement) which corresponds to the very common positive electric ionization, and which is normal for a material atom with its net time displacement, plays only a minor role in terrestrial phenomena, although it is more of a factor in some other locations. The reason for this seeming anomaly is the existence of a process which leads to the production of negative magnetic ionization in such quantities that the positive ionization is normally precluded. For an explanation of this process we return to the subject of sub-atomic particles.
hydrogen, with displacements 2-1- (1) , is the first rotational combination
with an effective displacement in both rotational systems, and is therefore
the first of the material elements, a series of simpler units-particles-may
be formed by addition of electric space or time displacement to the rotational
base and to the neutron. The particles thus derived are as follows:
As indicated in the preceding discussion, and as the displacement values in the tabulation clearly show, the sub-atomic particles are compound motions of the same general character as the atoms of matter, but do not have the effective displacement in the two rotating systems that is the characteristic property of matter. The electron, for instance, has no displacement at all (above the 1-0-0 datum) in the magnetic dimensions, and its only significant feature is one unit of space displacement in the electric dimension. In the uncharged state this particle is essentially nothing but a rotating unit of space. As such it cannot move through open space, since the relation of space to space is not motion, but it can move through matter, as matter has a net time displacement. Within matter moving electrons are known as current electricity. Like any other rotating unit, the electron (with rotational space displacement) is able to acquire an electric charge, in this case negative (time displacement) . In the charged state the particles are neutral from the space-time standpoint, and can therefore move freely in either matter or space.
The particle which is of particular interest in the present connection is the neutrino. The displacements of this particle, as given in the tabulation, are 1-1- (1) , which means that the net effective displacement of this combination is zero. With both one-dimensional and two-dimensional rotations, the neutrino is capable of taking either an electric or a magnetic charge, but on the basis of probability considerations the magnetic charge takes precedence, and under appropriate conditions the particle acquires a one-unit positive magnetic charge. This is a unit space displacement, and since the neutrino is otherwise featureless, the charged neutrino is essentially nothing but a mobile unit of space similar, in this respect, to the uncharged electron. Like the latter, it can move freely in matter, but is barred from motion through space, simply because the relation of space to space is not motion.
Neutrinos are produced in substantial quantities in some common physical processes, and since they move freely through either space or matter when in the uncharged condition, because their net displacement is zero, each body in the universe is subjected to a continuous flux of neutrinos in much the same way that it is subjected to a continuous bombardment by photons of radiation. Occasionally one of these neutrinos acquires a charge in passing through matter, and when this occurs the neutrino is trapped and cannot escape. The concentration of charged neutrinos in matter therefore builds up as the material grows older.
The difference between the situation of the charged neutrino and that of the uncharged electron should be specifically noted. While these two particles are analogous to the extent that each is a unit of space and hence can move only through matter, the uncharged electron can escape from this limitation by acquiring a charge, and a continued build-up of the concentration of these electrons also builds up forces which tend to produce the required charge, and will ultimately do so. The charged neutrino, on the other hand, can escape only by losing its charge, and since here also a continued increase in the concentration of these particles builds up forces tending to produce charges, the possibility of losing a charge becomes more remote as the concentration increases.
In order to appreciate the significance of this build-up, it is necessary to recognize that the reciprocal relation between space and time makes any motion of a particle with reference to the atom in which it is located equivalent to a reciprocal motion of the atom with respect to the particle. Inasmuch as these motions are equivalent, they reach an equilibrium. In the situation we are now considering, the rotational vibration of the neutrinos is equivalent to and in equilibrium with a reciprocal rotational vibration of the atoms in which these neutrinos are located. Since the charge of the neutrino is a magnetic space displacement, its presence causes the atom to acquire a magnetic charge with a time displacement. This is opposite in space-time direction to the usual magnetic charge, a seemingly minor point of difference, but one which, in this case, has some farreaching consequences.
The ordinary magnetic charge is foreign to the material environment, a two-dimensional space displacement in a structure whose very essence is a net time displacement, and it therefore plays only a relatively minor part in the phenomena of the material universe. The reciprocal of this charge, on the other hand, is a motion identical with the basic two-dimensional rotation of the atom, except that it is vibratory rather than unidirectional. Consequently, it adds to, and, in a sense, merges with, the atomic rotation, and has the same general effect as an equivalent addition of rotational time displacement.
Instead of exhibiting a behavior of a different kind, such as that which distinguishes an ion or a magnetized particle from a normal atom or particle, the two-dimensional charge due to the presence of the charged neutrino simply adds to the magnitudes of the normal properties of the atoms. For this reason we will not use the term magnetic charge in referring to this motion, but will call it a gravitational charge. The most conspicuous effect of the gravitational charge is to increase the mass of the atom. As noted earlier, the unit of magnetic rotation employed for convenience in the description of the structures of the atoms is equivalent to two natural units, and tbe unit of gravitational charge, which is a natural unit, is therefore one-half unit on the rotational scale. The atomic weight of the normal atom is twice the atomic number Z, and each unit of gravitational cliarge G adds one atomic weight unit. The number of units of charge that an atom may acquire is variable, and each normal atom of atomic weight 2Z is therefore accompanied by a series of isotopes with atomic weight 2Z +G.
In our local environment the various isotopes of each chemical element usually occur in fixed proportions, and the average isotopic weight of the element is recognized as the atomic weight of that element. It is evident from the foregoing discussion, however, that the existing isotopic proportions are not inherent in the structure of matter itself but are results of tbe magnetic ionization level prevailing in the local environment. In a location where the magnetic ionization level is different, the isotopic proportions will also be different.
We can deduce from the theoretical principles involved that in very young matter, where the magnetic ionization level is zero, there are no isotopes, and the atomic weight of each chemical element is its rotational value 2Z. Here, all of the rotational combinations (elements and sub-atomic particles) that are possible, all the way from the electron to element 117, are stable. In this young matter heavier elements are continually being built up from lighter ones by a process of neutron capture, and there is no destruction or degradation of an element once produced, unless the limiting atomic weight 236 (the atomic weight of the unstable element 118) is reached.
If this matter is now transferred to a region of higher ionization level, such as the surface of the earth in its present condition, some of the atoms acquire gravitational charges. From theoretical considerations it has been determined that at any given magnetic ionization level, the normal increase in mass due to the acquisition of gravitational charges in the process of attaining equilibrium with the charges of the neutrinos varies as the square of the atomic weight of the uncharged atom. A quantitative evaluation, previously published, also reveals that at a one-unit ionization level, which is the level of the local environment, the normal atomic weight increment varies from practically zero for the lowest elements to 3 for element 20, 10 for element 40, 23 for element 60, 41 for element 80, 54 for element 92, and so on. When the 54 increment is added to the 184 atomic weight of the normal atom of element 92, the total becomes 238, which is above the 236 limit. In this local environment, therefore, element 92, uranium, and all above it are theoretically unstable, and disintegrate by ejection of mass. Some of the elements immediately below number 92 can also exceed the stability limit because of a probability distribution factor similar to that which permits evaporation at relatively low average temperatures.
This disintegration process which takes place in the theoretical universe can obviously be correlated with the observed phenomenon that we call radioactivity. On first consideration, however, there appears to be a discrepancy between the theoretical characteristics of the process and those which are actually observed. The derivation of the theoretical disintegration clearly requires it to be an explosion; a single event initiated as soon as an aggregate reaches the stability limit and continuing until the process is complete. The observed radioactivity, on the other hand, seems to be a series of independent events occurring at random within the aggregate and often extending over a very long period of time. The half-life of some of the isotopes of uranium, for instance, runs into millions of years.
In the context of present-day physics these two descriptions are wholly irreconcilable, but in the Reciprocal System the radioactive explosion is simply the inverse of an ordinary explosion; that is, it is the same process with space and time interchanged. In an ordinary explosion, the action begins at one or more points in the aggregate and is propagated outward in space from these points at a high space velocity. Each atom of the aggregate remains in its original state until the progress of the action reaches the location in space which this atom occupies, whereupon either the atom or the molecule suddenly disintegrates. The explosion as a whole therefore takes the form of a series of individual explosions at different locations in space, initiated successively by an agency propagated through space at a finite velocity.
In a radioactive explosion, the action begins at one or more points in the aggregate and is propagated outward in time from these points at a high inverse velocity (that is, slowly) . Each atom of the aggregate remains in its original state until the progress of the action reaches the location in time which this atom occupies, whereupon it suddenly disintegrates. The explosion as a whole therefore takes the form of a series of individual explosions at different locations in time initiated successively by an agency propagated through time at a finite inverse velocity. Aside from substituting time for space, this description of the radioactive explosion is identical with the preceding description of the ordinary explosion.
As the foregoing discussion brings out, radioactivity, as we observe it, is a result of a past increase in the magnetic ionization level. The accumulation of neutrinos is continuous and irreversible, hence future increases in this level will lead to radioactive disintegration of successively lighter elements. Just as the existence of a maximum value of the combined electric ionization and thermal energy establishes a temperature limit for matter, the existence of this maximum magnetic ionization establishes an age limit.
The chapters that follow will consider the processes that cause certain aggregates of matter to exceed the age and temperature limitations, and the nature of the consequences that ensue. In preparation for these discussions we will now take a brief look at some kinds of motion that were passed over lightly in the preceding pages because they play little or no part in the familiar physical phenomena of everyday life.
It was noted in Chapter IV that the combinations of rotational motion which were identified as atoms could be either linear space displacements rotating with time displacement or linear time displacements rotating with space displacement, but that the latter do not constitute matter. We are now interested in the question as to just what they do constitute. There can be no doubt on this score. Inasmuch as they are exact duplicates of the atoms of matter except that space and time are interchanged, it is obvious that they are atoms of the inverse type of matter, related to ordinary matter in the same way that a positive charge is related to a negative charge. We might refer to them as inverse matter or reciprocal matter, but there are many criteria of inversion that are quite different from space-time direction, and in order to be specific it has seemed advisable to use a more distinctive term. The designation cosmic will therefore be applied to all phenomena of the inverse type that are not (like positive charges, for example) common features of the material sector of the universe. The atoms of the inverse type constitute cosmic matter. The term anti-matter is in common use, but it implies the negative rather than the inverse of ordinary matter, and it is therefore inappropriate.
Anti-matter has been a favorite subject of speculation in recent years, both in serious scientific literature and in science fiction. The identification of certain anti-particles (not aII of which are cosmic , on the basis of our definition) has, of course, given this speculation a tangible, if somewhat shaky, factual basis, as the conversion of particles of matter and their anti-particles to energy on contact with each other suggests that such contact might provide a powerful energy source. The favorite energy generation device of the science fiction heroes is one which converts matter into energy by allowing it to contact anti-matter at a controlled rate. The astronomers have been equally intrigued with the idea, and are postulating the existence of anti-matter processes wherever the generation oŁ large amounts of energy appears to be going on, and are even speculating that some of the galaxies that can be observed are composed of anti-matter rather than oŁ ordinary matter.
No doubt both the astronomers and the science fiction devotees will be unhappy with what the Reciprocal System has to say about the so-called anti-matter. The inverse matter, cosmic matter, as we are calling it, is subject to inverse, or cosmic, gravitation. This is not inverse in the sense that the atoms move outward rather than inward in space; it is inverse in the sense that the atoms move inward in time rather than in space. Under the influence of this inverse as if force, the cosmic atoms form aggregates, just as material atoms do, but these aggregates are localized in time, not in space. The constituent atoms of each aggregate are contiguous in time, but they are widely dispersed in space. We therefore encounter them in space not as galaxies, or even as aggregates of a size appropriate for fueling a space ship, but as an occasional single atom. The anti-matter energy generators will have to be put on the shelf along with the antigravity devices.
Like many other
interesting subjects, the phenomena in which features of the cosmic sector
of the universe impinge on our material sector are outside the scope of
this presentation, but an understanding of the general relation between
the two sectors will be helpful in connection with some of the issues
that will be explored later. For the purpose of clarifying this relationship
we will begin with ordinary vectorial motion in space, as represented
by diagram d of Fig. 3, and by means of similar diagrams we will follow
the course of events as space displacement, or its equivalent, is added
to the motion. The previous discussion carried this process up to the
point where the motion reached the neutral level, or physical zero, the
point where there is no motion other than the space-time progression.
The first three diagrams in Fig. 4 therefore reverse the process outlined
in Fig. 3. First the equivalent space displacement is increased by reduction
of the time displacement until the limit of vectorial motion is reached
at unit velocity. Scalar space displacement is then added (diagram b)
until the neutral condition is reached (diagram c) . The point of this
present explanation is that because of the reciprocal relation between
space and time, the whole process is repeated in a reciprocal manner in
the region beyond the neutral level. Availability of sufficient additional
space displacement enables reducing the two inactive dimensions to zero
motion in time, represented by the symbol 6. To facilitate this process,
the displacement in the active dimension reverts to the scalar time basis,
diagram d, releasing
space displacement to meet part of the requirements of the conversion of the inactive dimensions. Later addition of more space displacement replaces the amount diverted from the active dimension, and ultimately the speed in this dimension passes the unit level, and vectorial motion in time begins, as in diagram e. This is the normal motion of the cosmic sector, the motion of atoms and aggregates of cosmic matter.
Summarizing the foregoing, we may say that at very low levels of space displacement (equivalent to high levels of time displacement) the spatial speed in two dimensions is zero and that in the third is below unity. Here vectorial motion in space is possible. At very low levels of time displacement (equivalent to high levels of space displacement) the temporal speed in two dimensions is zero and that in the third is below unity. Here vectorial motion in time is possible. Between these two extremes there is a scalar range; that is, after the speed in space reaches unity, any further addition of space displacement-as, for instance, by release of energy in an explosionresults in a scalar addition to the previous motion. If this addition is large enough to increase the scalar speed to a point beyond the neutral level, conversion to motion in time ultimately takes place, as interactions in this zone reduce the inverse speed toward the average level of motion in time. The same considerations apply, in reverse, to motions in time which are raised to high inverse speeds by release of large amounts of inverse energy. If the neutral point is passed, conversion to motion in space ultimately results.
These points will have considerable significance in connection with the discussion in the subsequent pages, as much of the subject matter from this point on will be concerned with violent explosions and their consequences.