The Intermediate Regions
We are now ready to begin a full-scale examination of the only one of the regions into which the universe is divided by the reversals that take place at the unit levels of speed, space, and time, that has not yet been considered. This is an appropriate point at which to review the general situation, and to see just how each of the several regions fits into the overall picture.
As brought out in detail in the preceding pages of this and the earlier volumes, the region that can be accurately represented in a spatial system of reference is far from being the whole of the physical universe. There is another equally extensive, and equally stable, region that is not capable of representation in any spatial reference system, but could 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 either a spatial or a temporal reference system.
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 the 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 space that is involved in a motion falls below the unit level. Here motion in space is not possible, because less than unit space does not exist, but the equivalent of a motion in space can be produced by adding motion in time, since an energy of n/1 (n units of energy) is equivalent to a speed of 1/n. This region within one unit of space, the time region, as we have called it, because all change that takes place within it is in time, is paralleled by a similar space region at the other end of the speed-energy range. Here the equivalent of a motion in time is produced inside a unit of time by the addition of motion in space.
The extent to which our view of the physical universe has been expanded by the development of the theory of the universe of motion can be seen from the fact that the one section of this diagram marked “3d [three-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.
By developing the necessary consequences of the postulates that define the universe of motion, we have identified the nature and properties of the primary entities and phenomena of the three-dimensional region of space and those of the time region. The inverse regions, the three-dimensional region of time and the space region, are unobservable, but since they are exact duplicates of the regions that we have examined in detail, the findings with respect to those observable regions are also applicable, with space and time interchanged, to the two inverse regions. The subdivision that remains to be explored is the transition zone between the two three-dimensional regions identified in the diagram as the scalar zone.
The separation of the two sectors of the universe into distinct regions is a result of the fact that the relation between the natural and conventional reference systems changes at each unit level, because the natural system is related to unity, while the conventional system is related to zero. Since the natural system is the one to which the universe actually conforms, any process, which, 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 relation to the spatial reference system.
Inasmuch as the three scalar dimensions are independent, the maximum speed in each is two units, as shown in Figure 8 (Chapter 6). Thus there are six total units of speed (or energy) between the absolute speed zero and the absolute energy zero. It follows that the neutral point is at three units. At any net speed below this level, the motion of an object, as a whole, is in space. This fact has an important bearing on the nature of the motion. As we have seen in our examination of fundamentals, an object can move either in space, at a speed of 1/n, or in time, at a speed of n/1, but it cannot move in both space and time (relative to the natural datum of unity) coincidentally, since the speed cannot be both above and below unity. As pointed out earlier, it then follows that where motion in time exists as a minor component of a motion that, in total. takes place in space, the motion in time acts as a modifier of the magnitude of the motion in space, rather than as an actual motion in time. In other words, it is a motion in the spatial equivalent of time: a motion in equivalent space.
As indicated in Figure 8, the second unit of translational motion is motion in time, but since the translational motion as a whole is in space as long as it remains below three units, this second unit of motion takes place in equivalent space. Such motion can be represented in the conventional spatial reference system to the extent that the magnitudes that are involved are within the limits of the reference system: zero and unity. As can also be seen from Figure 8 , the motion in the second unit of one dimension, the motion in time (equivalent space), is fully coordinate with the motion in the first unit, and has the same kind of a relation to the natural datum, unity, as the original unit. It therefore substitutes for the original unit, rather than adding to it. The motion in equivalent space in this second unit is similar to the motion in space in the first unit, except that it is inverse, and reduces, rather than increases, the equivalent spatial magnitudes. These magnitudes therefore remain within the limits of the reference system, and can be represented in it, as we see in the case of the reduction in the size of the white dwarf.
On the other hand, when the motion is extended to a third unit, a unit of motion in space, so that there is motion in both a dimension of space and a dimension of equivalent space, the magnitudes are additive, and the increment due to the motion in equivalent space is outside the one-unit limit of the reference system. It follows that this increment cannot be represented in the reference system, although it appears in measurements such as the Doppler shift that deal with total scalar magnitudes, and are not subject to the limitations of the reference system.
The two linear scalar units of motion effective in the intermediate region are not restricted to a specific scalar dimension. Consequently they are distributed over all three of these dimensions by the operation of probability. This means that there are eight possible orientations of the units of motion. Motion in actual space is restricted to one of these by the nature of the reference system that defines what is considered to be actual space. Inasmuch as this reference system imposes no restrictions on time, the other seven orientations are available for the motion in the spatial equivalent of time (equivalent space).
ln the absence of any influences tending to favor one orientation over another, the total scalar motion is distributed equally among the eight orientations. However, for reasons that were explained in Volume I, all quantities in equivalent space are two dimensional in terms of actual space. The seven equivalent units are divided between the two dimensions, usually equally. One of the two resulting speed components adds to the speed in actual space. The other does not. Furthermore, the second power relation between the quantities of the two kinds (actual space and equivalent space) leads to a similar relation between the units. Thus the fractional unit of equivalent space comparable to the fractional unit n of actual space is n½. Where the spatial speed is n, the corresponding speed in equivalent space (the distribution in one dimension) is normally 3.5 n½, and the total equivalent spatial speed is n + 3.5 n½.
This quantity, the total equivalent spatial speed, is the total scalar magnitude in the dimension of the reference system, the quantity that is measured by the Doppler shift. Motion in the low speed and intermediate ranges is confined to one spatial dimension, and is limited to the value n, generally represented by the symbol z in this application. Extension of the motion to a second spatial dimension in the ultra high speed range adds the magnitude represented by the term 3.5z½ Thus the Doppler shift of any object moving at ultra high speed is normally z + 3.5z½ This theoretical conclusion will be compared with the results of observation in Chapter 22.
In conventional physical thought the reception of radiation from an object traveling away from our location at a speed greater than that of light would be impossible, even if such speeds exist, which conventional theory denies. The reasoning is that an object moving at such a speed would be traveling faster than the signal that it is emitting. But in the universe of motion any motion at a speed greater than unity (the speed of light) is a motion in time at an inverse speed less than unity. This means that the object is moving slower than light in time. The radiation from an object moving away from us at such a speed therefore reaches us through time rather than through space, if we are appropriately located relative to the moving object.
Although the neutral point between motion in space and motion in time is at three units of equivalent speed, the maximum net translational speed that can be attained is actually two units, because of the gravitational reversal. When the net speed reaches the two-unit level, reversal of the gravitational direction (from motion in space to motion in time) results in a net increase in speed of two units. Any further increase in equivalent speed beyond this two-unit level is accomplished by reduction of the magnitude of the inverse speed; that is, by decreasing the motion in time.
While net speeds exceeding two units take the motion across the sector boundary and out of the observable region, as indicated above, ultra high speeds can exist in the material sector in conjunction with oppositely directed speeds of different origin that keep the net effective speed below the two unit level, at least temporarily. Under these conditions, the distinctive features of ultra high speed motion, such as existence in two spatial dimensions, is applicable to objects that are still within the observable range.
The intermediate, or scalar, zone is separated into two regions by the sector boundary. One of these, from two units of inverse speed to one unit, is on the cosmic side of the sector boundary, and is unobservable. The other, from one unit of speed to two units, is outside the region that can be represented accurately in the spatial reference system (the three-dimensional region of space), but it is within the material sector, and it does have effects on physical magnitudes in that sector. These effects enable us to detect objects moving in the upper speed ranges, and to determine their properties. The results of an investigation of these properties will constitute the subject matter of the remainder of this volume, except for the last two chapters.
The effects of translational speed in the intermediate range, between one and two units, insofar as they apply to aggregates of stellar size, were discussed in Chapter 6. Some similar effects are produced in galaxies, but it will be convenient to consider these after the characteristics of matter moving at ultra high speeds are developed. Examination of these intermediate galactic phenomena will therefore be deferred to Chapters 26 and 27. We will now turn our attention to motion at ultra high speeds, in the range between two and three units.
Extension of motion to this higher speed range results in the production of some new and different classes of astronomical phenomena. We will examine the most significant of these phenomena individually in the pages that follow, but in order to lay a foundation for the subsequent discussion, and to emphasize the unitary character of the theory that will be applied to an understanding of the individual items, the general aspects of ultra high speed motion, as derived from the postulates that define the universe of motion, will be developed at this point, where they can be considered independently of the particular conditions that surround the specific applications.
In order to produce speeds in this ultra high range it is, of course, necessary that there be explosive phenomena that are more violent than the Type I supernovae. We will have no difficulty in identifying such phenomena. While the ultra high speed range is a full unit greater than the intermediate range of speeds produced by the Type I explosion, the availability of the direct process of adding units of speed, as discussed in Chapter 14, makes the required addition to the violence of the explosion much smaller than would be indicated by the effects of energy addition in the range below unit speed.
We saw in Chapter 6 that when the Type I supernova explosion occurs, the material in the central regions of the star is blown outward in time, producing a white dwarf star. A more violent explosion that accelerates the fastest of the explosion products to ultra high speeds has the same kind of an effect on the matter in the central regions, except that it adds an outward translational motion in a second dimension of space to the outward (inward from the spatial standpoint) expansion in time. This explosion product is another white dwarf, differing from the white dwarfs discussed in the earlier chapters, in that it is moving outward at a high rate of speed.
At the time of origin, the explosion product is subject to gravitational forces—that is, to motion in the inward direction—and even though the explosion speed is in the 3 - 1/n2 range, the net speed is below two units, and the moving object is observable. As this object travels outward, the gravitational effect is gradually reduced, and unless external forces intervene, the net speed eventually reaches the two-unit sector limit. Further reduction in the gravitational component then takes the net speed across the boundary and into the cosmic sector. At this boundary, gravitation begins operating in time rather than in space. The constituents of this aggregate then move outward from each other in space because of the progression of the natural reference system, now no longer offset by inward gravitational motion. Coincidentally, the process of aggregation in time begins. Ultimately the aggregate in space ceases to exist, and its constituents aggregate in time.
The normal fate of the ultra high-speed products of the most violent supernova explosions is thus ejection from the material sector. But unlike the intermediate region white dwarf, whose destiny is foreordained, the ultra high-speed product may deviate from the normal pattern. Elimination of gravitation in space does not affect the other influences that tend to reduce the speed of the moving material object, particularly the resistance due to the presence of other matter in the line of travel. Instead of continuing to increase, as gravitation in time becomes increasingly effective, the speed of this object may, under certain conditions, reach a maximum at some point above the two-unit level, and then decrease, eventually dropping back into the region of motion in space. Such objects return to the low speed range in essentially the same condition in which they left it. They have never ceased to be material aggregates. Only a very limited range of initial explosion speeds will produce this kind of a result, but it is common enough to give rise to a distinct class of phenomena that will be examined in Chapter 19.
As we have seen, motion at intermediate speed adds an expansion to the original translational motion of a material object. Ultra high speed adds another unit of motion, which takes the form of a translational motion of the expanding object. The fast-moving white dwarf that we are now considering is expanding in time, like any other white dwarf, and moving translationally in a scalar dimension of space other than the dimension of the spatial reference system. But there is no reason why the combination of the two added scalar motions must necessarily take place in this manner. Other things being equal, it is just as possible for the expansion to take place in the second dimension of space, and the translational motion of the expanding object to be in time.
In the central regions of an exploding star, the white dwarf type of product is favored because the compressive forces produced by the explosion act on matter that is already highly compressed, and is so situated geometrically that it cannot relieve any of the pressure by outward motion. The entire action is therefore inward in space, which is equivalent to outward in time. In the outer regions of the star the initial compression is less, and much of the explosion pressure can be absorbed by motion of the matter against which the pressure acts. Here the general direction of the action is outward. These conditions are favorable for production of the alternate type of combination of motions, that in which the expansion is in space and the translation is in time.
Expansion in space is equivalent to contraction in time, and vice versa. Thus, in either of the alternative motion combinations the expansion produces a compact object. Expansion in time, as in the white dwarf, produces a compact object in space. This object then moves linearly in space. The constituents of the object are moving in time; the object as a whole is moving in space. In the alternate motion combination, the constituents of the compact object are moving in space, while the object as a whole is moving in time.
As has been emphasized repeatedly in all of the volumes of this work, the conventional fixed spatial reference system is severely limited in its ability to represent the motions that take place in the universe. Many kinds of motion cannot be represented in this system at all, and others cannot be represented accurately. The linear outward motion in the second scalar dimension of space is incapable of representation, as is all motion in actual time. But where aggregates expanding at the upper range speeds are observable in the reference system, the speed magnitudes are reflected in the dimensions of these aggregates. We have already seen how this effect accounts for the extremely small-observed size of the white dwarf. Now we will need to recognize that expansion into a second scalar dimension of space produces the same kind of a result in the inverse manner; that is, the moving object appears in greatly extended form in the spatial reference system.
Some of the change of position due to the unobservable ultra high speeds is represented in the reference system in an indirect manner. In the initial stage of the outward motion of the ultra high-speed explosion product, much of the explosion speed is applied to overcoming the inward gravitational motion of this object. Inasmuch as that gravitational motion has altered the position (in the reference system) of the matter that now constitutes the explosion product, elimination of the gravitational motion results in a movement of this matter back to the spatial position that it would have occupied if the gravitational motion had not taken place. Since it reverses a motion in the reference system, this elimination of the gravitational change of position is observable in that system, even though the change of position due to the motion that produced this effect, the ultra high speed motion in time or in a second scalar dimension in space, is itself unobservable.
The gravitational retardation of the speed is at a maximum at the time of e ejection, and decreases thereafter, reaching zero at the point where the explosion-generated motion arrives at the unit speed level. Thus the greater the net speed of the explosion product, the smaller the resulting change of position in the reference system. Here we have another of the many findings of this present investigation that seem nothing short of preposterous in the light of current scientific thinking. But again, as in the previous instances of a similar nature, we will find that the validity of this conclusion is verified in a number of astronomical applications.
Inasmuch as the spatial motion component of the ultra high-speed motion is in a second scalar dimension, it is perpendicular to the normal dimension of the reference system. This perpendicular line cannot rotate in a third dimension because the three-dimensional structure does not exist beyond the unit speed level. Thus the representation of the motion in the reference system is confined to a fixed line. Consequently the first portion of the expansion of this ultra high-speed aggregate is linear rather than spherical. The spherical expansion cannot begin until the net speed reaches the unit level and the linear movement has ceased.
As we saw in our examination of the fundamentals of scalar motion, this type of motion does not distinguish between the direction AB and the direction BA, since the only inherent property of the motion is a magnitude. Unless external influences intervene, any linear motion originating at a given point is therefore divided equally between two opposite directions by the operation of probability. In its initial stages the expanding cloud of ultra high speed particles thus takes the shape of two oppositely directed cylindrical streams of matter (jets, in the language of the observers) moving outward from the point of origin.
In the next stage, after the head end of the jet has reached the linear limit, and spherical expansion has begun, each half of the expanding cloud is a weaker and more irregular jet, or stream, of matter, with a knob on the outer end. In its unmodified form, the expanding object as a whole has what is called a dumbbell shape during this stage. In the last stage, the jet has disappeared, and there are now two spherically expanding clouds of ultra high-speed matter, each centered at one of the limits of the linear expansion.
In many instances the physical situation is such that expansion in one of the two directions is prevented, or at least impeded. In that event, the result is a single jet, sometimes accompanied by a small counter jet. In other cases, obstructions, or motions of the expanding object in the dimension of the reference system during the period of expansion, modify the shape and direction of the jet, even to the extent, as we will see in the next chapter, of altering the structure to the point where it is no longer recognized as a jet.
The two alternative expansion patterns of these ultra high speed explosion products, as viewed in the context of the spatial reference system—one a small, dense, and inconspicuous object, the other an enormous double cloud of widely dispersed matter spread over an immense volume of space—are so radically unlike that without a theoretical understanding of their nature and origin one would not suspect that they are related in any way. But, as we have just seen, they are simply two manifestations of the same thing: the result of ultra high-speed motion, a form of motion that involves both expansion and linear movement. In one case the expansion takes place in time, and the linear motion in space. In the other the roles of space and time are reversed; the expansion takes place in space and the linear motion in time. The expansion in time produces an object that is extremely small from the spatial standpoint. The expansion in space produces one that is extremely large spatially.
In the pages that follow we will examine a variety of astronomical phenomena that belong in this category, and we will find that, notwithstanding their apparent dissimilarities, they can all be explained on the basis of the theory set forth in the preceding paragraphs. Each of the particular applications has some special features that are peculiar to the existing situation. This has the effect of confusing the essential issues, as they tend to be buried under a mass of detail that has little, if any, relevance to the basic elements of the phenomena that are involved. Furthermore, the prevailing view of the particular situation is, in most cases of the kind we are now considering, incorrect in some significant respects, and it is hard for those accustomed to these currently accepted ideas to avoid being influenced by them. It is therefore advantageous to consider the essential issues on an abstract basis, as we are doing in this chapter, without the complications that accompany the specific applications, and to establish the theoretical relations on a firm basis before undertaking to apply them to the individual cases to which they are applicable.
One more feature of the intermediate regions that should have attention from the standpoint of fundamental theory before beginning consideration of the observable phenomena of this region is the nature of the thermal radiation from objects moving with upper range speeds. As we saw in the earlier volumes, this thermal radiation originates from linear motion of the small-scale constituents of material aggregates in the dimension of the spatial reference system. The effective magnitude of this motion is measured as temperature.
Inasmuch as motion at intermediate speeds is in the same scalar dimension as the motion at speeds below unity, the vibrational motion that produces the thermal radiation continues into the upper speed ranges. But because of the reversal at the unit speed level, the temperature gradient in the intermediate region is inverse; that is. the maximum intensity of the thermal vibration, and the resulting radiation, is at the unit speed level, and it decreases in both directions. In this intermediate region, an increase in speed (equivalent to a decrease in inverse speed) decreases the thermal radiation.
Furthermore, the radiating units of matter are confined within one unit of time at the upper end of the intermediate temperature range (the lowest inverse temperatures), just as they arc confined within one unit of space at the lower end of the normal temperature range. This alters the character of the observed radiation. As brought out in the earlier volumes, and reviewed in Chapter 6, speeds less than unity can be attained only by addition of units of the inverse quantity, energy. The result of such an addition is a speed of 1 - 1/n2, where n is the number of units of energy. A wider range of values is then possible by means of combinations of the form ( 1 - 1/n2) - ( 1 - 1/m2). When an atom moves independently, as it does in the true gaseous state, it can only move with certain specific speeds, the speeds that are defined by the foregoing equation with the applicable values of the energy components m and n. Thus each kind of atom (each element) has a specific set of possible radiation frequencies, and a line spectrum.
The radiation is emitted from the atom at these same frequencies regardless of the physical state of the aggregate in which the atom exists, but at the low end of the ordinary temperature range, where matter is in the solid or liquid state, the thermal motion of the atom takes place entirely within one unit of space. The radiation originating from this motion has to be transmitted across the boundary between the region inside the unit boundary, the time region, to the outside region where it is observed. For reasons that have been explained in detail in the earlier volumes, this radiation is distributed in direction, and over a range of frequencies, in the inter-regional transmission process. This radiation therefore has a continuous spectrum.
The same situation prevails in the intermediate region, if it is viewed in terms of inverse speeds and temperatures. When expressed in terms of the speeds and temperatures of the low speed region, the relations in the intermediate region are inverse. The radiation at speeds just above unity comes from atoms that are still in the gaseous state, and are moving freely in time. This radiation, like that in the corresponding range on the lower side of the unit level, has a line spectrum. As the speed increases still further, the intensity of the radiation decreases, just as it does at speeds farther from unity in the low speed region. At a critical level of inverse temperature and pressure the atom drops into the space region, the region inside unit time; that is, the aggregate of these atoms condenses into the inverse solid state. The optical radiation from this region, likes that from the time region where ordinary solids are located, has a continuous spectrum.