Current theoretical physics views time as onedimensional and constituting a kind of quasispace which joins with the three dimensions of space to form a fourdimensional spacetime framework, within which physical objects move onedimensionally. This view has been formulated to help explain some of the new phenomena discovered in the twentieth century, such as the very small, the very large, and the very fast. These phenomena exist outside of our normal everyday world, where Newton’s laws predominate and where space seems to be totally separate from time. However, even with this modern framework, most of the phenomena remain mysteries, in whole or in part.
In contrast, the Reciprocal System of theory, originated by D.B. Larson,¹ postulates that both space and time have threedimensional aspects and join together to form one entity, spacetime or motion, which itself is. threedimensional. Space and time are the two reciprocal aspects of motion and have no properties other than what they have in motion. Here, spacetime or motion is theorized to be the sole component of the universe, not the framework or the background for particles of matter. Matter in the theory is itself a form of rotational motion and may move translationally in more than onedimension coincidentally. To be sure, these ideas are novel and unfamiliar but they do overcome the current difficulties in treating phenomena of the very small, the very large, and the very fast, as will be demonstrated in this paper.
The conventional physical reference system is based on three dimensions of space and one of time. The space is considered to be stationary and the time is considered to be flowing. Within this space, material objects move as a function of time in one dimension in a specific vectorial direction. This onedimension of motion may be resolved into three components, one along each of the three orthogonal axes of the reference system (usually denoted x, y, and z).
In the Reciprocal System, space and time each have the properties of the other. Time is threedimensional, like space, and space progresses, like time. Of course in a gravitationallybound material environment, space appears to be stationary and threedimensional and time appears to be onedimensional and progressing, and so the conventional reference system works for this situation. In a gravitationallybound cosmic (or inverse) environment, where space and time are interchanged, time would appear to be stationary and threedimensional, and space would appear to be onedimensional and progressing. The inverse of the conventional reference system would work in this situation. So, in the Reciprocal System two types of reference systems exist: the first with threedimensions of space and one of time, and the second with three dimensions of time and one of space. The first is applicable to objects which are aggregated in space (as in our ordinary material sector) and the second is applicable to objects which are aggregated in time (as in the cosmic sector). Conventional physical science does recognize antiparticles and antigalaxies but does not stipulate an “antireference system.”
A common mistake of students of the Reciprocal System is to deduce from the above that there are thus six dimensions of the universe, three of space and three of time. This is not so, however. All that actually exists are three dimensions of motion, not three dimensions of space or three dimensions of time individually. Of course, where convenient, we can mentally fix one component, while allowing the other to move. This has the effect of concentrating on one aspect of each of the components while ignoring the others. But it is important not to forget that space and time do not exist separately; they are bound together in units of motion, which are the actual reality.
Outside of our gravitationallybound region, what happens? It is an observed fact in astronomy that distant galaxies are moving away from our galaxy (and all others) at speeds approaching that of light. The current explanation is that this is a result of a hypothetical big bang some 16 billion years ago. But this is not, of course, the explanation of the Reciprocal System. Here, the cause is the space progression, which manifests itself when gravitation is attenuated. It is an effect brought about by the motion of the natural reference system relative to our conventional spatial reference system. The equation for this motion (at the full speed of light) in our sector is
x_{1}² + x_{2}² + x_{3}² = c²t² 
(1)

(where c, of course, is the speed of light). Please note that because the motion is actually scalarly outward only, the imputation of a specific vectorial direction for a particular space unit is arbitrary.
Similarly there is an outward motion of cosmic galaxies relative to a cosmic observer’s galaxy, such motion also approaching the speed of light in the limit. Again, this is not due to some sort of big bang in the cosmic sector; rather it is due to the motion of the natural reference system relative to the threedimensional temporal reference system. At the full speed of light, the equation is:
t_{1}² + t_{2}² + t_{3}² = x²/c² 
(2)

Again, the assigned vectorial directions are arbitrary, since this is actually a scalar motion outward in all directions.
The two major sectors of the universe, the material sector and the cosmic sector, each with their appropriate reference system, are stable. In between these two sectors is an unstable transition zone, which cannot be represented properly by either reference system.
In the material sector, the velocities of ordinary phenomena are below that of the speed of light. In the cosmic sector the inverse velocities of ordinary cosmic phenomena are below that of the speed of light. Hence the speed of light is the dividing line between the two sectors, and, in fact, the photons are not actually part of either sector, but at the boundary. They have no independent motion (other than their vibration) and so remain in the same spacetime location, which is carried outward by the spacetime progression (in a perpendicular direction) with respect to the conventional space or time reference system. From the standpoint of a gravitationallybound cosmic aggregate, the photons appear to be moving outward in all coordinate time directions. Actually, however, the photons remain stationary in the natural reference system; the matter particles are moving inward in space and the cosmic particles are moving inward in time, and so the opposite motions are imputed to the photons.
Because motion can be threedimensional, the actual separation between the two major sectors of the universe is scalar unit speed in all three dimensions, or 3c. Each of the three dimensions is limited to a maximum of one unit of speed and if motion were limited to one dimension we would agree with current physics that nothing could travel faster than the speed of light. However, because the motion is not so limited, the actual limit is 3c. Notice that we are summing the value of speed of each dimension. These are, after all, scalar quantities, which can only be added or subtracted. It is not possible to add vectorially the motions in the different dimensions of multidimensional motion! The sequence of additions of units of speed are: first one unit, in dimension l; then the second unit, in dimension 2; and finally the third unit, in dimension 3.
In our sector, velocity is measured as s/t. In the cosmic sector it is t/s. To material observers, photons appear to move through space; to cosmic observers, photons appear to move through time. Both observers see photons as being the upper limit of speed (or energy). Many beginning students of the Reciprocal System conclude that when we talk about motion at speeds faster than that of light, we are referring to rate of change of position in space. But this is not so. At speeds above the speed of light the rate of change applies to change of position in time, which moves objects further apart in time, or (equivalently) moves objects closer together in space.
According to the Reciprocal System, motion exists only in discrete units, so the question arises, how can we have fractional units? Obviously the velocities on Earth are only a tiny fraction of the speed of light, so how can this be? Recall that the theory requires that we start with one unit, not from zero units. This one unit of motion is equal to one unit of energy, because of the reciprocal relation between space and time. To achieve effective translational speeds below unity we simply subtract the appropriate number of energy units from one. The equation in natural units is
v = 11/x 
(3)

where x is the number of onedimensional energy units (with dimensions t/s). Note that as x is increased the speed is increased, and in the limit reaches 1 (or c). In the time region, the region inside unit space, the numerical value of the energy term must be squared, for reasons given by Larson.² So the equation actually is
v = 1(1/x)² 
(4)

Suppose x has the value n. Motion at this speed often appears in combination with a motion 11/m² that has the opposite vectorial direction. The net result is
vH = 1/n²1/m)² 
(5)

This is clearly recognized as the Rydberg relation (in natural units) that defines the spectral frequencies of atomic hydrogen—the possible speeds of the hydrogen atom. Other elements have similar relations for their thermal motion. The important point is that translational motion is quantized; it is not a continuum. To this extent, we can agree with current theory.
Because of the ability of adding or subtracting energy units to the three basic speed ranges, we can have speeds of 1  1/x, 2  1/x, and 3  1/x. Larson denotes the speed range 1  1/x “low speed”; the speed 2  1/x, “intermediate speed”; and the speed 3  1/x, “high speed.” Because of the onedimensional nature of energy, it is not possible to go from one speed range to the next by simply adding more energy. The only way to accomplish this is by direct addition of units of speed. And the only way that can be accomplished is by huge stellar or galactic explosions.
In a Type I supernova explosion (caused when the temperature limit of the iron group of elements is reached) part of the material moves outward in space at speeds less than that of light and part moves outward in time (or inward in space) at speeds in the intermediate range. This results in a very dense compact star, a white dwarf, stationary in space, surrounded by a cloud of dust and gas moving spatially outward. Eventually the speeds of the particles of the white dwarf fall below that of unit speed (or c) and the white dwarf begins to expand in space, eventually becoming a normal star on the main sequence. The dust cloud recondenses into a red giant star, which also eventually returns to the main sequence.
A Type II supernova is even more powerful. Here the explosion results in high speed motion of the compact star away from the scene, together with the usual cloud of dust and gas. This compact start, or pulsar, is similar to the white dwarf, except that it has an additional translational motion in the high speed range (or third dimension of motion). Once the effect of gravitation is attenuated (and the net speed goes above two units) the pulsar will leave our sector and move into the cosmic sector, where the processes of that sector will disintegrate the spatial aggregate and recondense it in time by means of cosmic gravitation. It will thus disappear from our view.
In the central regions of the largest galaxies, the spheroidal galaxies, consisting of 10^{12} to 10^{13} stars, the matter is at the upper limit of age. Instead of isolated Type II supernova explosions, a whole chain reaction of such explosions occurs, resulting in galactic fragments (between 7 x 10^{7} to 2 x 10^{9} stars) being ejected. The fragments ejected at upperrange speeds are the quasars; those at low or intermediate speeds are the radio galaxies. Note that although the quasar itself is moving at high speed, the particles of which it is composed are moving at intermediate speed, hence the compact structure.
The Reciprocal System of theory explains many of the puzzling characteristics of quasars. One such characteristic is the observed double image of some quasars. Larson explains this as follows:
Scalar motion does not distinguish between the direction AB and the direction BA. The lateral recession outward from point X is therefore divided equally between a direction XA and the opposite direction XB by the operation of probability. Matter moving translationally at upper range speeds thus appears in the reference system in two locations equidistant from the line of motion in the coincident dimension (the optical line of sight, in most cases).³
Hence there is no need for such a hypothesis as a “gravitational lens.”
Initially the explosion speed of the quasar is applied to overcoming the effect of gravitation, and thus there is a rapid change of position in the reference system. As gravitation is gradually overcome, the net speed increases, but the rate of change of position decreases, because the speed in the explosion dimension is not visible in the reference system. However, the speed in the explosion (high speed) dimension can be detected by the shift in frequency toward the red of the radiation coming from the quasar and received on Earth. This Doppler shift is a measure of the scalar sum of the outward motions of the quasar, both that due to the recession and that due to the explosion speed. It is a direct speed measurement, and the relative adjustment factors do not apply to it. Hence values greater than 1 actually do mean speeds greater than c, which is what the Reciprocal System requires. Thus the quasars are not nearly as distant as the current cosmological explanation of the quasars’redshifts suggests.
Another unusual characteristic of the quasars is their seemingly impossible great energy generation. But the conventional assumption is that this energy is carried away in all three dimensions by radiation. In the Reciprocal System, the radiation that comes from an object at the upper range of speed is distributed twodimensionally. As Larson states:
If we find that we are receiving the same amount of radiation from a quasar as from a nearby star, and the quasar is a billion (10^{9}) times as far away as the star, then if the quasar radiation is distributed over three dimensions, as currently assumed, the quasar must be emitting a billion billion (10^{18}) times as much energy as the star. But on the basis of the twodimensional distribution that takes place in equivalent space, according to the theory of the universe of motion, the quasar is only radiating a billion (109) times as much energy as the star,... which is equivalent to no more than a rather small galaxy.^{4}
Larson calculates^{5} that the explosion redshift is a function of recession redshift and normally takes the value 3.5 z^{½}. The quasar will begin converting to the cosmic status when this speed reaches a value of 2.0. The corresponding redshift is then 0.3265, and the total quasar redshift (the sum of the recession redshift and the explosion redshift) is 2.3265. According to the observers, there is a sudden cutoff in the distribution of quasars above a Doppler shift of 2.2, which is consistent with the theory. (By probability there will be a few quasars that linger on for higher redshifts).
The boundary between the two major sectors of the universe is thus quite unstable, as it is filled with material quasars and pulsars and cosmic quasars and pulsars, all in the process of moving to the opposite sector. It is also filled with material white dwarfs and cosmic white dwarfs which will eventually return to being normal stars in their respective sectors. The boundary here is a speed or energy boundary. There is another boundary within each sector at unit distance or unit time. In the material sector, the region inside unit distance represents and important subdivision; in the cosmic sector, the region inside unit time also represents an important subdivision. Reversals of motion occur at these unit distance or time boundaries just as they do at the unit velocity or energy boundaries.
Inside unit space, only motion in time is possible, because fractional space units do not exist. But the motion in time may be expressed in equivalent space units by means of the reciprocal relation. Similarly, inside unit time, only motion in space is possible, because fractional time units do not exist. This motion in space may also be expressed in terms of equivalent time units by means of the reciprocal relation.
Inside unit distance or time, the spacetime progression and gravitation reverse directions. The progression is always away from unity and gravitation always toward it. So outside unit space or time, the progression moves the very large spheroidal galaxies apart; inside unit space or time, the progression moves the atoms of matter or cosmic matter close together, in opposition to gravitation, which in this region is a force of repulsion. Atoms of matter or cosmic matter can thus reach equilibrium positions in the solid state at the locations where the two forces reach equality. There is thus no need for the ad hoc electrical forces of conventional theory, which, in any case, supply only one of the two necessary forces for equilibrium.
I have thus shown, in brief, that the Reciprocal System of theory, based on the novel concept of three dimensions of motion, with space and time being reciprocally related, can handle some of the current problems in physics: those phenomena involving the very small, the very large, and the very fast. The very small, the atoms and the subatoms, are subject to the relations that apply inside unit space or unit time, where the roles of the progression and gravitation are reversed from what they are in the timespace (material) or spacetime (cosmic) regions. The very large, the spheroidal galaxies, are moving away from each other at speeds approaching that of light because of the spacetime progression and the attenuation of gravitation at great distances. After many billions of years of aggregation, these galaxies are now in the process of discombobulating—emitting jets of high speed gases, quasars, and radio galaxies—because their matter has reached the upper limit of age. The very fast, the quasars, have extraordinarily high redshifts because they are moving at speeds faster than light and they will ultimately disappear into the cosmic sector.
References
 D. Larson, Nothing But Motion, Portland, Oregon: North Pacific Publishers, 1979, p. 30.
 D. Larson, The Structure of the Physical Universe, Portland, Oregon: North Pacific Publishers, 1959, p. 19.
 D. Larson, The Universe of Motion, Portland, Oregon: North Pacific Publishers, 1984), p. 301.
 D. Larson, Ibid., pp. 287288.
 D. Larson, Ibid., p. 210.