Reciprocity XXV #2, Autumn, 1996
For centuries on mankind has held implicitly the view that we live in a universe of matter contained in space and time. All scientific theories hitherto have been built on this paradigm. Now Larson introduces the new paradigm that motion is the basic and sole constituent of the physical universe, and space-time is the content—not the container—of the universe. We review in this article some of the highlights of his theory, the Reciprocal System, which he develops from the new paradigm.
The objective of this article is to introduce to the physical theory being called The Reciprocal System. Its originator, Dewey Larson, starting from two Postulates as regarding the nature of the basic constituents of the physical universe, and the mathematics applicable thereto builds a cogent theoretical structure that lays claim to a general theory. As it is impossible to outline the whole theory in the short space of an article, attempt has been made to present only those salient features that do not require lengthy explanation and have a broad-enough scope to enable the interested reader to appreciate its potentialities. More esoteric features of the Theory have been intentionally omitted from this preliminary treatment. They are, of course, available in the published works of Larson1-7.
The view that the physical universe is made up of basic units of matter, embedded in a framework of space and time, has been held by the common man and the scientist/philosopher for over the entire period of recorded history. Every new century has brought new and revolutionary ideas about the Universe that shook and changed our earlier views, but the concept of matter contained in a space-time background has remained unquestioned. Larson finds that it is this concept—which we shall call the concept of the universe of matter—that stood in the way of development of a truly general physical theory, one that explains all domains of physical facts—from the atomic to the astronomical—from the same set of fundamental premises. He has carried out the needed review of the concepts of space and time and finds that the introduction of the new paradigm, that the fundamental and the sole constituent of the physical universe is motion, leads us to the understanding of all the physical phenomena, and makes possible the construction of the long-sought after general theory.
To be sure, there have been earlier thinkers who attempted to build a general theory basing on motion as the fundamental constituent. Larson points out that the lack of success in all earlier attempts was due to the fact that these thinkers failed to realize the crucial point that in a universe based on motion (which is a relation of space and time), space and time cannot have independent existence (or definition), that they cannot be regarded as a background (or ‘container’) for themselves. No matter whatever conceptual reforms these thinkers have introduced into physical theory they all alike continued to subscribe to the container view of space and time, and blocked themselves from true progress.
The first of the two fundamental Postulates of the Reciprocal System from which Larson derives every aspect of the physical universe is
“The physical universe is composed entirely of one component, motion, existing in three dimensions, in discrete units, and with two reciprocal aspects, space and time.” (Cf. SD, ii, p.260; ML, p341)
Larson considers speed, which is the relation of space and time, s/t, as the measure of motion and points out that a unit of speed is the minimum quantity that can exist in the universe of motion, since fractional units are not permitted by the Postulate of his theory. Since one unit of speed is the minimum quantity admissible, (cf. ML, pages 135-7, 155, 163) both space and time have to be quantized: unit speed must therefore be the ratio of a unit of space to a unit of time, each of which is the minimum possible quantity. Certain corollaries follow.
Firstly, we see that space and time are reciprocally related to speed: that doubling the space with constant time, for example, has the same effect on speed as halving the time at constant space. As a recognition of the far-reaching significance this reciprocal relation holds for the explanation of all the physical facts Larson names his theoretical structure The Reciprocal System of theory.
At unit level, not only one unit of space is like all other units of space but also a unit of space is equivalent to a unit of time. Larson postulates a total uniformity in the properties of space and of time, except for the fact that they are reciprocal aspects of motion. Thus he concludes that time is three-dimensional as space is, and that space also progresses like time does.
At this juncture it may be pointed out that in order to understand (or evaluate) the new ideas engendered by the new paradigm, namely that the physical universe is a universe composed of units of motion (speed), it is necessary to view them in their new context. On the other hand, the most frequent mistake committed by the novice is to view the new concepts from the habituated viewpoint of the previous paradigm, that the universe is a universe of matter, embedded in a framework of space and time. Such an attempt leads one, often, to seemingly absurd, impossible or incredulous conclusions. To avoid slipping back involuntarily into the old and inadmissible frame of mind, while evaluating the Reciprocal System theory is one of the most difficult tasks that a critic has to accomplish constantly.
Now it is important to recognize that there is absolutely nothing space-like in the three dimensions of time: they are entirely temporal parameters. The common belief that time is one-dimensional is an unwarranted conclusion drawn from the fact that time enters our experience as a scalar quantity. The real reason why time appears as a scalar quantity in the equations of motion lies in the fact that no matter how many dimensions of time do exist, they have nothing to do with directions in space.
The idea that space progresses like time does might look more weird than the idea of multi-dimensional time. Our immediate experience is that of stationary space. But history has repeatedly shown that our immediate experience of space has always proved to be a bad guide in understanding the true nature of the universe. We first thought that the earth is flat. Then we made the mistake of thinking our earth to be the center of the universe and ended up in the maze of epicycles. Larson draws our attention to the fact that the increased scope of our scientific observations has brought us to the point where too many epicycles have once again been accumulated in the field of science in the form of unresolved old questions, fresh new puzzles and ever-increasing complexity of physical theory. He questions whether our anthropocentric view of space is not the culprit once again that is barring the progress. He points out that our experience of space as stationary is valid only locally (that is, in the context of a gravitationally bound system). The true nature of space is to progress, to expand ceaselessly outward. Wherever gravitation (an inward motion) becomes negligible, weakened by distance, the inherent progression of space becomes apparent. The observed recession of the distant galactic systems stems directly from this space progression, not from any hypothetical ‘big bang.’ In fact, the observed Hubble’s law could be derived from the postulates of the Reciprocal System.
Since a universe of motion cannot exist without the existence of motion, the most primitive condition of the universe is the steady progression of space coupled with the progression of time: in other words, a motion at unit speed. (Cf. ML, page 135, 246 & 341) Beginners usually encounter here the difficulty of imagining the existence of motion without it being the motion of anything. But a little reflection should show that in a universe of motion the most fundamental constituent is motion, and all ‘things’ are derivatives of motion. Since every space unit is like every other space unit, and every unit of time is like every other unit of time, such a condition appears to our view as a featureless uniformity in which nothing is happening and constitutes the null background. Thus unit speed, and not zero speed, turns out to be nature’s starting point. Larson refers to this background space-time progression as the ‘natural reference frame,’ and identifies the unit speed with the speed of light, c.
By virtue of the fact that either the space unit or the time unit could progress inward, rather than outward as it does in the case of the space-time progression, speeds other than unity become possible. Larson points out that it is these deviations (or ‘displacements’) from the unit speed that constitute observable phenomena, namely, radiation, gravitation, electricity, magnetism and all the rest. These are autonomous, independent motions in contra-distinction to the ever-present background progression.
This gives rise to two possibilities. Suppose k number of reversals occur in the space component, and suppose the unit speed of space-time progression contains n space units per n time units (n/n = 1). Such a situation produces less than unit speeds, (n-k)/n. Since such a motion detaches itself from the space-time progression in its spatial aspect, we find it to be a motion in space. The second possibility is that the reversals occur in the time component of the motion. This results in greater than unit speeds, n/(n-k). In this second case it is the time component which gets detached from the background progression and we note that it constitutes what might be termed a motion in time (not ‘time travel’). This is the reason why unit speed (c, the speed of light) is the upper limit for motion in space. It does not mean, as concluded in Relativity, that speeds greater than c are impossible in the physical universe: it only means that such speeds do not manifest in our conventional, stationary reference frame of three-dimensional space as displacements in space. These greater than unit speeds (namely, the motion in time) can be represented truly only in a ‘stationary’ reference frame of three-dimensional time.
Our state of knowledge so far has disposed us to assume tacitly that motion means motion in space; the possibility of motion in time has never been imagined, much less investigated. Such motion, though cannot be truly represented in the conventional, spatial reference frame, has nevertheless some observable features by virtue of the inverse relationship between space and time. For example, in a supernova explosion, if sufficient energy is available, Larson points out that some of the constituent matter of the star gets propelled to greater than unit speeds. The less than unit speed component manifests as a cloud expanding in space. On the other hand, the greater than unit speed component manifests as a cloud expanding in time (since it is a motion in time). In view of the reciprocal relation between space and time referred to above, this expansion in time manifests to us as contraction in space and we observe this component as a super-dense and compact star. Thus we have the red giant/white dwarf combination so frequently found as supernova product.
Larson’s theoretical investigations show that the same concept of motion in time can explain every other type of super-dense astronomical phenomena, not just the white dwarfs. He shows that as age advances, the central regions of massive galaxies keep on accumulating motion in time (since greater than unit speeds do not involve movement in space, this matter does not leak out). When enough energy accumulates, it results in a stupendous explosion in which the central part(s) of a galaxy gets ejected and is found as a super-dense star system, which, of course, is observed as a quasar. All the strange and unconventional characteristics of quasars—like their high density, large redshift, stupendous luminosity, jet-structure, peculiar radiation structure, evolution—can be deduced from the theory.
We have seen that the null condition of the Universe of motion is the unit speed and that the ‘displacement’ from this condition takes the form of either less than unit speed (s/t) or greater than unit speed (the latter being equivalent to less than unit inverse speed, t/s). Larson identifies this displaced speed with radiation, and the speed displacement with its frequency. (SD, ii, pages 303-304)
While the photon gets detached from the background space-time progression in the dimension of the oscillation, it does not have any independent motion in the dimension of space perpendicular to the dimension in which the vibratory motion occurs. Thus the photon is permanently situated in the space unit of the space-time progression in which it is created. But from the context of the stationary spatial reference frame any location of the space-time progression appears to progress outward (away) at unit speed. Thus, while actually the photon is stationary in the natural reference frame, ostensibly it appears to move away at unit speed. Incidentally we might note that, when in a single process a photon pair happens to be created, while the individual photons seemingly appear to fly off in space in opposite directions, they continue to be connected in time. This results in a correlation between them that is not representable in three-dimensional space (the EPR paradox).
Once photons are available, the possibility of a compound motion appears wherein the photon could be subjected to a rotational displacement in two dimensions (covering all the three dimensions of space). (SD, ii, page 348) Larson identifies such units of compound motion with atoms of matter. Because of the two facts that the maximum possible speed is unity and that the background space-time progression is already taking place at that speed in the outward (away from each other) direction, all autonomous (independent) motions (speeds) have to take place in the inward (toward each other) direction only. Thus the units of rotational displacement start moving in the inward direction, reversing the pattern of space-time progression. Larson identifies this inward motion with gravitation. (ML, page 136, 156, 163; SD ii, page 236-7, 241, 328)
We now see that there is no propagation involved in gravitation, nor it can be screened off: it is the inherent motion of each atom toward every other atom—in fact, toward every other location of the space-time progression, whether or not occupied by an atom. The non-existence of propagation time and the seeming action-at-a-distance, both owe their origin to the above fact. Theoretical analysis reveals that elements with atomic numbers 1 through 117 can all exist in young matter. In old matter, however, elements with the higher atomic numbers start turning radioactive, by a process identified by Larson.
An interesting fact that needs special mention is that the rotational displacement that constitutes the atoms could be either of the less than unit speed type or the greater than unit speed type. In either case gravitation acts inward only (in opposition to the outward progression of space-time). But in the case of the former type of atoms, since less than unit speeds produce motion in space, gravitation acts inward in space, resulting in the formation of aggregates in the three-dimensional spatial reference frame. Larson calls this portion of the universe the material sector. On the other hand, the atoms constituted of greater than unit speeds manifest motion in time. The resulting gravitation acts inward in time, and produces aggregates in the three-dimensional temporal reference frame. Larson refers to this matter as cosmic matter, their inward motion in time cosmic gravitation, and this portion of the physical universe the cosmic sector. We therefore discover another half of the physical universe where all the phenomena pertaining to our sector are duplicated, but with the roles of space and time interchanged. Even though cosmic matter occurs as ubiquitously and abundantly as ordinary matter we do not encounter it readily. Firstly, the atoms of the cosmic stars and galaxies are aggregated in three-dimensional time but are randomly distributed in space, so that we see a cosmic star not as a spatial aggregate but atom by atom. Secondly, while the cosmic gravitation moves the cosmic atoms inward in time, our own matter progresses outward in time. Thus, even the chance of encounters of atoms with cosmic atoms do not last for more than one natural unit of time (about one-seventh of a femtosecond).
Larson identifies all the exotic particles that abound in the high-energy environment of the particle accelerators with the ‘cosmic atoms,’ with some additional features acquired under the artificial environment.
A further fact of interest is that while the radiation emitted by the stars of our sector is at a high temperature, that which is emitted by the cosmic stars would be at a high inverse temperature, that is, at a low temperature. Since radiation moves at unit speed, unit speed being the border between both the sectors of the universe, it is observable from both the sectors, in whichever sector it originates. Therefore, the radiation emitted by the cosmic stars, as it comes from a region not localized in space, is received in the material sector (that is, the three-dimensional spatial reference frame) with an absolutely uniform and isotropic distribution. We observe this as the low-temperature, cosmic background radiation, of course. In the Reciprocal System, we find no necessity to reconcile the absolute isotropy of this background radiation with the lumpiness of the spatial distribution of the material aggregates.
We have already mentioned that quasars are the high (greater than unit) speed explosion products of aged galaxies. When gravitation in space is attenuated by distance (time) and becomes negligible, the quasar as a whole shifts from the region of less than unit speed (conventional spatial reference frame) to the region of greater than unit speed (the three-dimensional temporal reference frame). Gravitation ceases to act in space and starts acting in time. This leaves the outward progression of space-time without check (as there is no inward progression of gravitation in space) and the constituents of the quasar start flying out in space at unit speed. Eventually the quasar ceases to exist as a spatial aggregate and disappears altogether from the material sector. In other words, the atoms of the erstwhile quasar emerge into the three-dimensional temporal reference frame of the cosmic sector at totally random locations (in time).
The corollary is that similar set of events occurs in the cosmic sector—cosmic atoms aggregate in three-dimensional time forming cosmic stars and galaxies, parts of which explode on attaining a size limit and eject cosmic quasars, which eventually exit the cosmic sector and end up entering the material sector. Since they come from a region not localized in space, these incoming cosmic atoms would be uniformly and isotropically distributed throughout the three-dimensional space. Since the transfer occurs at the unit speed we ought to observe these particles at unit or near-unit speed. These, of course, are the observed cosmic ray primaries.
The Reciprocal System traces out in detail how these cosmic atoms, being greater than unit speed structures in a less than unit speed environment, promptly decay ejecting speed (energy) and ‘cosmic mass’ (that is, inverse mass), finally ending up as the most primitive atomic structures of the material sector, namely, hydrogen. Then the entire cycle of aggregation in space and eventual ejection begins. In the long run, as much matter comes from the cosmic sector as it leaves the material sector. Thus the dual sector universe as a whole is in equilibrium and steady state, while each sector continues to expand in space or in time as the case may be. There is no necessity to assume the singularity of a ‘big bang’ or to break any conservation laws as in ‘continual creation.’
Because of the fact that the minimum space that can occur in physical action is one natural unit of space (the quantum of space), if two atoms are made to approach each other they cannot come any nearer than one unit of space. However, by virtue of the reciprocal relation between space and time, these atoms can accomplish the equivalent of moving inward in space by actually moving outward in time. This they promptly do until a force (motion) equilibrium is achieved, giving rise to the solid state of matter. Since less than one unit of space does not exist, within the unit of space all motion could be in time only. Larson therefore refers to the inside of unit space as the time region. The space-time progression always acts away from unity. In the outside region away from unity is also away from zero (outward). But in the inside region away from unity is towards zero. Therefore the space-time progression is inward in the time region. Since gravitation always opposes space-time progression, it acts outward in the time region (repulsion). (ML, page 136, 156, 163; SD ii, page 236-7, 241, 328)
Further, while the space-time progression is constant at unit value, gravitation attenuates with distance. The two motions (forces) therefore reach a stable equilibrium at some distance in the time region and produce the configuration of solid state. Larson finds that a single theory of cohesion explains all kinds of bonds. Basing on purely theoretical computations he is able to calculate quantitatively the various solid state properties of hundreds of elements and compounds accurately.
Since in the time region only motion in time can truly exist, the appropriate reference frame that ought to be adopted for the description of the phenomena is the three-dimensional temporal reference frame, and not the conventional, spatial reference frame. The origin of the conventional reference frame is at zero speed, whereas the origin of the temporal reference frame is at zero inverse speed, which is tantamount to infinite speed in the context of the conventional spatial frame, and consequently a location pertaining to the temporal reference frame is found not localized in the conventional reference frame. This is the origin of the non-locality characteristic so perplexing in quantum theory. This reciprocal (inverse) relation between these two types of reference frames also explains why a localizable particle in the context of a temporal reference frame needs to be regarded as an endless repetition, namely, as a wave, in the context of the spatial reference frame. Thus the Reciprocal System throws new light on the concepts of quantum theory. As the time region is a region of motion in time, it requires the adoption of a temporal reference frame for the description of particle phenomena. But, being irrevocably wedded to the spatial reference frame of the material sector, we are unable to accomplish this. However, we are able to accomplish the equivalent of adopting the temporal reference frame by resorting to the expedient of adopting the wave picture in the place of the particle picture.
This insight resolves the problem of the wave-particle duality. It further clarifies that the question of adopting the wave picture arises only on entering the time region, the region inside the unit of space. To associate a wave with every gross object is unwarranted.
There are yet unforeseen insights brought to light by the Reciprocal System. In the outside region, that is, in the context of the three-dimensional spatial reference frame, speed (s/t) is directional (vectorial). However, in the time region, that is, in the context of three-dimensional temporal reference frame inverse speed (t/s) is the quantity that is ‘directional’ while speed appears scalar. But it must be cautioned that this ‘direction’ pertains to the realm of three-dimensional time and has nothing to do with direction in space. Thus inverse speed, though it could be ‘directional’ in time, is not a vector. In the universe of motion all physical quantities can be reduced to space-time terms. Larson, in a major overhaul of the dimensions of various physical quantities, arrives at the conclusion that the dimensions of energy are those of inverse speed, namely, t/s. Consequently, energy needs to be represented by complex numbers in the time region and negative energy states are as natural in the time region as negative speeds (velocities) are in the spatial reference frame.
We have endeavored to sketch out some of the important contributions of the Reciprocal System to the understanding of the physical universe starting from a new paradigm—the concept of a universe of motion, in place of the current one of a universe of matter embedded in a framework of space and time. The examples cited here are expected to convey the broad-enough scope of the theoretical system and establish that a prima facie case exists for a general theory. It is only fair to record that some of the more esoteric aspects of the Theory, like multi-dimensional motion, the scalar region of the universe, etc. have entirely to be omitted for pedagogical reasons and hence interesting questions concerning two large and important fields, namely, of electricity and magnetism, could not be considered in this article. Mention must also be made of the fact that Larson finds the basic constituent of the universe according to the new paradigm, namely, motion, to be scalar motion. Even though the existence of this kind of motion has been recognized, it has played a very minor and insignificant role in physical theory hitherto. So, Larson carries out a full-scale investigation of the properties and possibilities of scalar motion and discovers that this type of motion plays the central role in the drama of the physical phenomena. He finds, for example, that some of the unexplained physical facts are really the unfamiliar features of certain types of scalar motion. In this preliminary article we have refrained, for practical reasons, from dwelling on this important contribution of the Reciprocal System.