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Free from; http://www.reciprocalsystem.com/rs/cwkvk/index.htm GLIMPSES NEW PARADIGM OF A K.V.K NEHRU Reflections and Comments Glimpses of a New Paradigm How We Meet the New Age Ushered in by the Reciprocal System? Subversive Reflections on the Practice of Physics Dialogue with D B Larson: Part I Dialogue with D B Larson: Part II Scientific Correspondence Particle Physics Lifetimes of C-Atom Decays Lifetime of C-Argon, the Muon Internal Ionization and Secondary Mass The Lifetime of the Neutron Relative Abundance of the Elements The Inter-regional Ratio The Nature of Scalar Motion Electric Ionization The Law of Conservation of Direction Is Ferromagnetism a Co-magnetic Phenomenon? Theoretical Evaluation of Planck‘s Constant Superconductivity: A Time Region Phenomenon On the Nature of Rotation and Birotation The Photon as Birotation Birotation and the Doubts of Thomas Wave Mechanics in the Light of the Reciprocal System ―Quantum Mechanics‖ as the Mechanics of the Time Region ‗Non-Locality‘ in the Reciprocal System Some Thoughts on Spin High Energy Physics and the Reciprocal System Astrophysics Gravitational Deflection of Light Beam in the Reciprocal System New Light on the Gravitational Deflection of Radiation Path Gravitational Redshift according to the Reciprocal System The Gravitational Limit and the Hubble‘s Law Precession of the Planetary Perihelia due to Co-ordinate Time Glimpses into the Structure of the Sun, Part I Glimpses into the Structure of the Sun, Part II Distribution of the Masses of Protostars in Globular Clusters Intrinsic Variables, Supernovae and the Thermal Limit The Quasar Paradox? Radio Component Separation in Quasars Another Look at the Pulsar Phenomemon The Cosmic Background Radiation: Origin and Temperature The Large-scale Structure of the Physical Universe GLIMPSES OF A NEW PARADIGM For centuries 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 Dewey B 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 Introduction The objective of this article is to introduce 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 being a general theory As it is impossible to outline the whole theory in the short space of an article, an attempt has been made to present only those salient features that 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 Larson[1-7] The Conceptual Roadblock 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 an 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 based 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 what conceptual reforms these thinkers introduced into physical theory they all alike continued to subscribe to the container view of space and time and as a result blocked themselves from true progress Space, Time and Progression 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.‖ 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, 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 Corollary (1) 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 Corollary (2) At the unit level, not only is one unit of space like all other units of space, but 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, like space, is three-dimensional, and that space, like time, progresses 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 habitual 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 constantly accomplish 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 may exist, they have nothing to with directions in space The idea that space progresses in the same manner as time 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 once again the culprit that is barring 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 is derivable 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 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 Emergence of Physical Phenomena By virtue of the fact that either the space unit or the time unit could progress inward, rather than outward as they 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 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 thus 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 While such motion cannot be truly represented in the conventional, spatial reference frame, it 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 itself as a cloud expanding in space On the other hand, the greater-than-unit speed component manifests itself 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 itself to us as contraction in space and we observe this component as a superdense 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 superdense 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 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 superdense 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 unit speed and that a ‗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 While the photon gets detached from the background space-time progression in the dimension of its 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) Larson identifies such units of compound motion with the 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 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 nonexistence 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 through 117 can all exist in young matter In old matter, however, elements with the higher atomic numbers become subject to radioactive decay, by a process identified by Larson The Regions of the Physical Universe 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-thanunit-speed type In either case gravitation acts inward (in opposition to the outward progression of space-time) But in the case of the former type of atoms, since less-thanunit 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 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 not last for more than one natural unit of time (about oneseventh 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 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 In the Reciprocal System, we find no necessity to reconcile the absolute isotropy of this background radiation with the clumpiness of the spatial distribution of the material aggregates The Grand Cycle of the Universe 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 threedimensional 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-thanunit-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‘ nor to breaking of any conservation laws as in ‗continual creation.‘ The Solid State 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 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 The inside of unit space is therefore referred to as the time region by Larson 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) 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 accurately calculate the various solid state properties of hundreds of elements and compounds New Light on Quantum Phenomena 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 threedimensional 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 to be localized in the conventional reference frame This is the origin of the nonlocality 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 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 Conclusion We have endeavoured 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, such as multi-dimensional motion, the scalar region of the universe, etc., have had to be omitted entirely 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 a 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 Surely one might question the rationale of omitting some of these important contributions of the theory when at the same time emphasizing its all out nature The real reason is—as has been hinted at the outset—no matter how simple and logical the new conclusions are from the viewpoint of the new paradigm, since one is habituated to the old paradigm, some of them might look unimaginable or utterly unscientific Having invested one‘s entire professional career in the existing paradigm, one‘s mind does not take kindly to the prospect of a basic paradigm change The first few contacts are the most difficult ones as Kuhn points out One would not be inclined even to pay attention to the new conclusions, much less evaluate them on their own merit References Larson, D.B., The Case Against the Nuclear Atom, (North Pacific Publishers, Portland, OR, USA, 1963) THE LARGE-SCALE STRUCTURE OF THE PHYSICAL UNIVERSE Extensive astronomical observations carried out during the decade that passed have for the first time revealed a most unexpected picture of the universe on a cosmic scale The picture that emerged is defying all the present cosmological theories In the present Paper, therefore, an attempt has been made to apply the principles developed in the Reciprocal System of theory with a view to show that the conclusions reached are in consonance with these recent observational findings In order to demonstrate the power of the Reciprocal System as a truly general physical theory, in Part II of the Paper, a mathematical treatment of the concepts developed herein will be undertaken and the results compared with facts The Bubbles in Space In the 1980‗s, astronomers have surveyed billions of lightyears into space and millions of galaxies and analyzed their redshifts These studies show that the galaxies are not distributed evenly in space but tend to occur in clusters and then these clusters themselves occur in large groups (the superclusters) The most unexpected discovery, however, is the occurrence of immense voids in space, empty of galaxies, between the superclusters.1,2 Three-dimensional maps of the universe prepared from the redshift surveys indicate that ― the universe is made up of gigantic bubbles: spherical or slightly elliptical regions of space apparently void of matter, whose outer surfaces are defined by galaxies All the galaxies lie on the surfaces of bubbles that measure from about 60 to 150 million lightyears across.‖³ The investigations of Geller and Huchra4 have brought to light large-scale clustering of galaxies stretching in the form of ―gigantic filaments and sheets‖ 170 Mpc (megaparsecs) by about 15 Mpc The group led by Faber5 finds the `Great Attractor,‗ a stupendous concentration of galaxies with ― a diameter of about 80 Mpc and a mass of 3x1016 Suns That would be the mass of tens of thousands of typical galaxies, including the dark matter one infers from the dynamics of galaxies.‖6 Reference [2] gives a graphic description: ―Three-dimensional maps of the distribution of galaxies show features quite unlike those of most other astronomical objects: the galaxies are concentrated in enormous sheets and filamentary structures whose greatest dimension, roughly 100 million lightyears, is an order of magnitude larger than its lesser dimensions .Moreover, within each structure the galaxies are not evenly distributed: one can distinguish more densely populated clumps and strings Finally, interspersed among the largest structures are huge voids, virtually free of galaxies, that are between 100 and 400 million light years across.‖ Broadhurst and his collaborators7 have investigated the galaxy redshifts out to a distance of 2000 Mpc in two narrow regions in the direction of the Galactic north and south poles where the obscuration by dust is the least Their measurements reveal periodic oscillation of the density of galaxies with distance, all the way out to 2000 Mpc The Fourier spectrum of these oscillations peaks sharply at a spacing of 128 Mpc (about 417 million lightyears), as though dense globs of galaxies are alternating with regularly spaced voids Trouble for the Conventional Theories There are two diametrically opposite views of galaxy formation Some astronomers hold that the galactic structures form as ascending cascades According to their `bottom-up‗ theory galaxies form out of a soup of gas and dust and subsequently coalesce to form clusters and superclusters Other theorists advocate the ‗top-down‘ theory which proposes that the matter in the universe first collapses into vast pancake-like sheets, which then fragment, giving rise to superclusters, clusters and galaxies (the descending cascades) But neither model predicts the formation of bubbles which have the sharply-defined surfaces of galaxies that are now observationally revealed John Horgan8 commenting in Vigyan (Scientific American, Indian edition) states: ―The cold dark matter model predicts that most galaxies take at least several billion years to form, so few should be found at distances greater than 10 billion lightyears Astronomers have now identified a score of galaxies more than 10 billion lightyears away.‖ Since astronomers currently assume that the universe began in a big bang about 13 billion years ago, Horgan remarks that: ―Theorists have a hard time explaining how galaxies formed so soon after the big bang.― While models positing cold dark matter thus have difficulty producing such large structures as now discovered, Powell9 remarks that: ‖ models that assume fast-moving dark particles–―hot dark matter‖–do not accurately mimic the smaller-scale details seen in the universe Cosmologists agree, at the very least, that current theories are far from complete.‖ Among other things, the universality and the immensity of the spherical voids have caught the theorists utterly unawares ―Valérie de Lapparent and Margaret J Geller note that the immense size of the bubbles suggests that powerful stellar explosions–and not the force of gravity, as is widely thought–had the primary role in the formation of the universe.‖³ Some astronomers suggest that supernova explosions drove matter into spherical shells, but the predicted shell sizes are orders of magnitude smaller than those of the observed bubbles Another severe problem that now plagues the astronomers is concerning the recent findings by the Cosmic Background Explorer (COBE) satellite which show the temperature of the microwave sky to be uniform to within one part in 10,000 At much finer angular resolution than that of COBE, recent measurements of selected patches of microwave background by Readhead10 find no fluctuations down to two parts in 100,000 Since astronomers conventionally regard the microwave background radiation as the relic from the primordial (hypothetical) big bang, its absolute isotropy implies that the early universe was extremely uniform The current theories of cosmology–including the ‗inflationary theory‘–are unable to account how the large-scale structure of the distribution of galaxies now evident emanates from the prevenient absolute uniformity The `Cycle' of the Universe We will now try to examine what the Reciprocal System of theory has to offer in this regard The most important factor that is relevant to our present discussion is the finding of the Reciprocal System that the vista of the physical universe is not limited to the familiar three-dimensional space of the conventional reference system but that, by virtue of the reciprocal relation between space and time, there exists another half, the cosmic sector, the region of motion in three-dimensional time For a complete description of the logical development of the Reciprocal System that leads to the discovery of the various ‗regions‘of the universe Larson‗s original works11,12,13 must be consulted We will give here a brief outline of the evolutionary process of the dual sector universe to serve our present purposes Quoting from Larson14: ―1 Because of the reciprocal relation between space and time in scalar motion, there is an inverse sector of the universe in which motion takes place in time rather than in space All scalar motion phenomena in three-dimensional space are thus duplicated in the cosmic sector ―2 There is a limiting size for galaxies, and some of those that reach this limit explode, ejecting fragments, known as quasars, at speeds in the ultra high range, between two and three times the speed of light ―3 When the retarding effect of gravitation is reduced enough by distance to bring the net speed of a quasar above two units (twice the speed of light) the gravitational effect inverts, and the constituents of the quasar are dispersed into three-dimensional time (the cosmic sector of the universe) ―4 The effect of the explosion and its aftermath is to transform a quantity of matter from a state in which it is highly concentrated in space to a state in which it is widely dispersed in time ―5 By reason of the reciprocal relation between space and time in scalar phenomena, it follows that the inverse of the foregoing processes likewise take place, the net effect of which is to transform a quantity of matter from a state in which it is highly concentrated in time to a state in which it is widely dispersed in three-dimensional space ―We thus find that there is a constant inflow of widely dispersed matter into the material sector from the cosmic sector.‘ Origin of the Bubbles The two principal forces deciding the course of events in the universe are gravitation and outward progression of space-time The ultimate ejection of quasars into the cosmic sector takes place when the net speed reaches two units Then gravitation ceases to operate in space This leaves the outward progression of the natural reference system unopposed, and that progression carries the constituent units of the spatial aggregates outward in all directions at unit speed (the speed of light) Thus, centered around the physical location of the erstwhile quasar, a spherical void starts growing All the matter that constituted the quasar now gets either uniformly dispersed over the expanding spherical surface or ejected out of the material sector altogether This leaves the inside of the void genuinely empty Meanwhile there is a continual inflow of matter, which has been similarly ejected from the cosmic sector Since it comes from sources that are not localized in the threedimensional space it emerges in the conventional reference frame spread absolutely uniformly throughout its extent In addition, the rate of inflow of this matter is constant, since the Reciprocal System posits a steady state on the large scale Therefore the density of matter in the expanding bubble rises steadily, starting from zero This diffuse matter in the bubble, however, is not observable until such time that it condenses into stars and becomes self-luminous In the meantime the bubble appears as a void (The reason why we prefer to call it bubble rather than void must now be apparent.) Since the phenomena that give rise to these bubbles, namely, the ejection of quasars and their ultimate exit into the cosmic sector of the universe, are the necessary end results of the evolutionary process in the material sector, one must see the whole of space strewn with these bubbles Their diameters, of course, reflect their lifetimes We will show in Part II that the sizes of these bubbles predicted from the Reciprocal System indeed fall within the observed range Growth and Decline of the Bubbles Consider a large sphere of diffuse (unconsolidated) matter of uniform density We note that while the inward speed due to gravitation, being proportional to the total mass, increases with radius and density, the outward speed due to the progression of the natural reference system is constant Therefore, at the center of the sphere there is a net outward speed, and as we move away from the center this net outward speed decreases and eventually reaches zero at some radius Let us call this radius the ‗zero-point radius.‘Beyond this point gravitation predominates and the net speed becomes inward The zero-point radius varies inversely as the density of matter in the sphere In the early stages of the bubble the density is extremely low and the zero-point radius far outspans the actual radius Thus the net speed everywhere in the bubble is outward Since the bubble is already expanding at unit speed, which is the maximum that is possible in the dimension of the conventional reference system, the net positive (outward) coordinate speed has no further effect on the rate of expansion It must be seen that the expansion of the bubble is a scaling expansion, that is, corresponding locations in the bubble at two different stages are related by the same geometrical relationship The matter density in the bubble always remains uniform, although this uniform density steadily increases due to the ever-present inflow As the density increases, the zero-point radius decreases Meanwhile the actual radius is increasing Therefore, at some point of time these two radii become equal That is, the net scalar speed at the bubble periphery becomes zero We will call this the ‗point of criticality,‘ the corresponding radius the ‗critical radius‘ and the time when it happens (measured from the instant of creation of the bubble) the ‗critical time‘ of the bubble Beyond this point, with further accumulation of matter, the zero-point radius becomes smaller than the actual radius and the scalar direction of the net coordinate speed of the spherical shell of matter between these two radii becomes inward This net inward speed can now act to oppose the outward progression and slow down the expansion of this portion of the bubble, while the portion inside of the zero-point radius continues expanding unabated at unit speed The speed differential occurring across this shell at the bubble periphery raises the density there relatively rapidly This rise in density acts as a positive feedback to augment the inward speed of gravitation in this shell further, and makes possible the collapsing and condensing of the matter in the peripheral regions of the bubble In due time, it can be shown, this collapsing matter forms into the Globular Star Clusters and becomes observable The ostensible effect is the seeming cessation of the expansion of the bubble or its retardation As the density of matter in the bubble continues to rise, more Globular Clusters start precipitating, in successive spherical layers towards the bubble center, and we see that the observable radius of the ‗void‘ (zero-point radius) decreases If conditions are unaltered it takes infinite time for the matter at the center to reach the stage of star formation But long before that, the concentration of the consolidated and aggregated matter, in the form of the Globular Clusters and groups of these clusters in the outer stretches of the bubble, rises high enough for the central mass to be brought into the ambit of their gravitational limits (See Reference [15] for gravitational limits.) This finally terminates the existence of the bubble as its diffuse material is swallowed up by the surrounding stellar aggregates The Uniformity of the Microwave Background The problem of reconciling the high degree of uniformity of the cosmic microwave background radiation with the observed large-scale non-uniformity of the galaxy distribution does not arise in the Reciprocal System for the simple reason that the source of the background radiation is not set in the conventional three-dimensional space at all Both its absolute isotropy and lack of connection with the spatial distribution and evolution of the material aggregates result from the fact that the background radiation originates from ‗aggregates‘ in the three-dimensional temporal reference frame of the cosmic sector Larson16 explains :― electromagnetic radiation is being emitted from an assortment of sources in the cosmic sector, just as it is here in the material sector Radiation moves at unit speed relative to both types fixed reference systems, and can therefore be detected in both sectors regardless of where it originates Thus we receive radiation from cosmic stars and other cosmic objects just as we from the corresponding material aggregates But these cosmic objects are not aggregates in space They are randomly distributed in the spatial reference system Their radiation is therefore received in space at a low intensity and in an isotropic distribution.‖ Of its low intensity we have had occasion to elaborate elsewhere.17 There is another point of significance that emerges from the nature of the origin of the background radiation and is noteworthy It is not the case that this radiation starts its journey entirely at the edges of the universe and reaches us after traversing long stretches of space Insofar as the locations in three-dimensional space through which the atoms of the cosmic aggregates happen to pass are randomly distributed, the background radiation originates ubiquitously So long as large enough volumes of space are considered (in view of the low energy density of this radiation) the existence of absorbing media does not have any effects on its overall isotropy and uniformity The possible attenuation by intervening dust and gas–whose occurrence is an almost certainty–is not alluded to in the astronomical literature for the simple reason that the large-scale anisotropy it introduces is patently contrary to the observed fact, and thus it poses an additional problem for the current theories Summary of Part I Recent astronomical observations reveal the occurrence of large-scale voids/bubbles in space Galaxies and their clusters appear distributed in sheet-like and stream-like structures at the peripheries of these cosmic bubbles None of the current cosmological theories is able to accommodate these facts, leave alone predict them It is shown that, in contradistinction, the Reciprocal System of theory not only explains their occurrence but also predicts their existence Recent observations of the cosmic microwave background radiation reveal its absolute uniformity to an accuracy that leaves no room for the current theories to reconcile this uniformity with the observed large-scale non-uniformity of the distribution of galaxies In the case of the Reciprocal System, however, this difficulty does not arise since it shows that the cosmic background radiation originates not in the region of threedimensional space but in the region of three-dimensional time Part II: Mathematical Aspects of the Cosmic Bubbles In Part I of this Paper (Reciprocity, XX (2), Summer 1991, pp 5-8), we have highlighted the recent observational findings in the field of astronomy leading to the discovery of large-scale voids in space coupled with the distribution of galaxies as clumps at the peripheries of these voids We called these voids bubbles We have demonstrated there how the new facts could be readily explained in a natural way by the Reciprocal System of theory In the present Part we attempt to develop the mathematical consequences of those concepts delineated in Part I Since we cannot afford to repeat, Part I must be read in order to be able to follow the present treatment For ease of referring, section numbers and reference numbers are continued from Part I Analysis of the Motion in the Bubble With the knowledge of the origin and nature of the bubbles we can now attempt to evaluate some of their properties Let c = the speed of light = 2.99793 x 1010 cm/s G = the universal constant of gravitation = 6.673 x 10-8 cm³/g.s² r = radius of the bubble, cm t = time since creation of the bubble, s [sigma] = rate of mass inflow into the material sector, g/cm.³s [rho] = [sigma].t = mass density in the bubble at time t, g/cm³ M = total mass of a material aggregate, g M0 = mass of the Sun = 1.99 x 1033 g d0 = gravitational limit of a consolidated material aggregate, cm k0 = a constant = 3.5664 x 1018 cm P = the universal constant of progression = 1.044 x 10-11 cm/s² v = speed, cm/s a = acceleration = v (dv/dr), cm/s² We note from Reference [15] the following: d0 = k0 (M/M0)½ P = G.M/d0² = G.M0/k02 We will first evaluate the expressions for the speed due to progression and the speed due to gravitation in the bubble In the beginning stages, (see Section 5), the net speed in the entire mass is outward and we have to consider the expressions relevant to motion in equivalent space Only when gravitation balances (or predominates) progression does the motion come back into the space of the conventional three-dimensional reference frame 8.1 Speed due to Progression In the conventional reference system ap = vp (dvp/dr) = P, or vp = (2.P.r) ½ On the basis of the explanation given in Reference [15] the corresponding speed in equivalent space is given by vp,e/v0 = (vp/v0)²/2 where v0, the zero-point speed, is given by v0 = (2.G.M/d0) ½ = (2.P.d0) ½ Therefore we get vp,e = [alpha] (r/[rho])¼ where [alpha] = (P/2.k0) ẵ (0.75 M0/[pi])ẳ = 1.7861 x 10-7 cgs unit 8.2 Speed due to Gravitation In the conventional reference system, considering a location at the periphery of the bubble ag = vg (dvg/dr) = 4.[pi].G.[rho].r/3, or vg = (4.[pi].G.[rho]/3) ½ r The corresponding speed in equivalent space is given by vg,e/v0 = (vg/v0)²/2 Adopting v0 from Eq we get vg,e = ò [rho]ắ r5/4 where ò = [pi] (2.G.k0/9) ẵ (0.75/M0 [pi])ẳ = 2.391 x 10-3 cgs unit 8.3 Net Speed In the conventional reference system, the net speed is (using Eqs and ) = vp - vg = (2.P.r) ½ - (4.[pi].G.[rho]/3) ½ r and in equivalent space (using Eqs and ) vn,e = vp,e - vg,e = ([alpha] - ò.[rho].r) (r/[rho]) ẳ 8.4 Zero-Point Radius We have called the radius of a uniform spherical mass at whose periphery the net speed becomes zero the zero-point radius, rz Equating Eq to zero and using Eqs and , we obtain [rho].rz = [alpha]/ß = (3.P)/(2.[pi].G) = 7.47 x 10-5 g/cm2 This relationship gives, for any given value of mass density, the corresponding radius where the net speed becomes zero 8.5 Advent of Criticality In Section we have set forth that the mass of the expanding bubble reaches a critical state when its actual radius equals the zero-point radius We have called this radius the critical radius rcr and the corresponding age of the bubble the critical time tcr Substituting in Eq [rho] = [sigma].tcr and rz = rcr , and noting that rcr = c.tcr we get tcr = ([alpha]/(ò.c.[sigma]))ẵ seconds Now if the rate of mass inflow, [sigma], could be evaluated, one obtains the time it requires for the bubble to reach criticality and the corresponding size of the bubble We, therefore, proceed as follows 8.6 The Universal Constant of Materialization We may call [sigma] the universal constant of materialization, like we call G and P respectively the corresponding universal constants Noting that r = c.t and [rho] = [sigma].t we rewrite Eq vn,e = ([alpha] - ò.[sigma].c.t)(c/[sigma])ẳ At the moment of the quasar exit (that is, the start of the bubble expansion), we take t = Therefore, at this moment, vn,e reduces to vn,e,0 = [alpha] (c/[sigma])¼ This is an outward speed and can be equated to the speed that is coming in, vi, with the inflowing matter from the cosmic sector, wherein gravitation acts inward in time (equivalent to outward in space) It is not yet attenuated by gravitation in space (as could be seen from ß.[sigma].c.t² = 0) The inter-sector transition of matter takes place on individual mass unit basis Normally, the speed effective on unit mass basis is the unit speed c However, as elaborated in Reference [15], the scalar rotation of atoms that is the origin of gravitation is distributed over 156.444 directions (degrees of freedom) in the time region (the region inside unit space) and directions in the time-space region (the region of motion in three-dimensional space) In the corresponding situation of the cosmic atom, the cosmic gravitation gets distributed over 156.444 directions in the space region (the region inside unit time) and directions in the space-time region (the region of motion in three-dimensional time) Consequently, the incoming speed, vi , is given by vi = c/(156.444 * 8) remembering that the contact between motion in space and motion in time is onedimensional Equating Eqs and we arrive at the important value [sigma] = 9.2679 x 10-47 g/cm³ s The Bubble Parameters We can calculate the critical time by Eq , the corresponding critical density by [rho]cr = [sigma].tcr , and the total mass of the bubble at criticality: tcr = 1.643 x 108 years rcr = 1.643 x 108 lightyears [rho]cr = 4.8055 x 10-31 g/cm³ Mcr = 3.7994 x 1015 Solarmasses We will examine these results one by one to see if they tally with the observations 9.1 Matter Density All the above values can be seen to be within the range of corresponding actual observed values Current estimates of the density (in g/cm³) of matter are as follows18: Interstellar space 10-24 Space near edge of galaxy 10-28 Intergalactic space 10-31 The calculated critical density is slightly higher than the estimated density in intergalactic space but very near it 9.2 Globular Clusters As the net speed at the bubble periphery changes its scalar direction from outward to inward (on reaching criticality), it initiates the collapse of a large number of individual masses of diffuse matter all around the spherical boundary of the bubble Each of these masses, as it collapses, further splits into a number of aggregates of stellar size, eventually resulting in a Globular Cluster We will not here enter into detailed discussion of the mechanics of the formation of the Globular Clusters for want of space The interested reader may refer to Larson.13 At this juncture we would merely want to make an estimation of the collapse time of these Globular Clusters Let us consider the condition at the bubble periphery There the net speed is given by Eq Letting [rho] = [sigma].t, r = c.t (strictly r < c.t since gravitation now predominates: but its effect is negligible in the initial stages of the post-critical phase), and x the radius of a proto-Globular Cluster of mass Mg, we have dx/dt = = (2.P.c.t)½ - (4.[pi].G.[sigma].c².t³/3) ½ The equation can now be integrated between the limits x = xg to and t = tcr to tg, where xg = [Mg/(4.[pi].[rho]cr/3)]1/3 The following Table gives the calculated collapse time as a function of the protoGlobular Cluster mass Mg (Solarmasses) Collapse Time (years) 10³ 0.41 x 108 104 0.59 x 108 105 0.85 x 108 106 1.22 x 108 The relationship between the collapse time and Mg obtained by regression is Collapse Time = 0.138 x 108 (Mg)0.158 and indicates that a star of, say, one Solarmass would condense in 0.138 x 10 years Thus the individual stars form well before the Globular Cluster as a whole arrives at its final stage of equilibrium In passing, we would like to remark that while it is possible for the Globular Cluster to form from a matter density of about x 10-31 g/cm³ under the gravitational assistance of the bubble as a whole, simple calculation from Eq shows that, left to itself, it requires a density of nearly 10-26 g/cm³ to accomplish the same result 9.3 The Bubble Size The above calculations indicate that it takes nearly 0.4 to 0.6 x 108 years for the Globular Clusters to form and become observable after the bubble attains criticality During this period the original bubble continues to expand, though not at the speed of light, at a slightly slower rate Adding, therefore, a distance of 0.4 x 108 lightyears to the radius at criticality we find that the bubble diameter at this juncture works out to be (1.643 x 108 + 0.4 x 108) = 4.1 x 108 lightyears It must be noted that this result gives the maximum possible size Beyond this stage the observed size actually decreases because (i) gravitation retards/nullifies the expansion and (ii) continued formation of Globular Clusters and dwarf galaxies shifts the spherical boundary between the visible and the dark matter ever inward, toward the bubble centre From Eq we can see that the apparent void radius (equal to the zero-point radius) varies with time as r = rcr tcr/t Since the number of clusters grows as time passes, their combined gravitational effect draws up the matter at the bubble core and simultaneously they close in on it A preliminary calculation on the basis of the gravitational limit of the surrounding group of clusters indicates that the last stage of the bubble, before it rapidly dissipates, will occur at a bubble diameter of about 84 million lightyears The observed bubble sizes reported in the literature range from 60 to 400 million lightyears Broadhurst's survey,7 though covering only two narrow regions but extending to depths of 2000 Mpc, puts it at 417 million lihgtyears (see Section 1) Thus the results of calculations made on the basis of the Reciprocal System of theory are entirely in agreement with the facts 9.4 Total Mass The bubble mass at criticality has been calculated to be 3.8 x 1015 Solarmasses But as the formation of the Globular Clusters and other galaxies continues in the post-critical stage, the incessant inflow of matter from the cosmic sector adds to the total mass When the bubble eventually reaches the supercluster stage its mass–that is, the mass of that portion of the original bubble that condenses into groups of clusters and clusters of stars–would be well within the 1016 Solarmass range of the current estimates 10 Computer Simulations B.B Mandelbrot,19 investigating fractal shapes in nature, has studied the distribution of galaxies and clusters of galaxies in three-dimensional space By postulating the existence of intergalactic voids he tried to evolve models of clustering His findings are very interesting and pertinent He starts with a completely filled space and keeps on removing spherical volumes of matter Both the size of the spherical hole and the location of its centre are chosen randomly The size of the hole is treated as a Poisson random variable with a distribution N (>v) [proportional] 1/v which reads as the number of holes with volume greater than v is inversely proportional to v The model is simulated on computer His results–both the covariance between two points in space and the covariance between two directions in the sky–indicate a very good fit of data The graphics output shows the views of the material remained after removing the spherical chunks and bear an amazing resemblance to the actual sky maps 10.1 Unforced Clusters A rather significant and unforeseen result of Mandelbrot‗s model above is that the distribution of the remaining points shows an apparent hierarchical structure Mandelbrot exclaims: "Each point stands for a whole minicluster In addition the miniclusters are themselves clustered They exhibit such clear-cut hierarchical levels that it is hard to believe that the model involves no explicit hierarchy, only a built-in self-similarity."20 Or again, "Increasing clustering is not provoked by the concentration of all points around a few of them but by the disappearance of most points, leading to an increasing number of apparent hierarchical levels."21 Hence he refers to them as ‗unforced clusters.‘ His finding is directly in line with the conclusions which Larson obtains from the Reciprocal System ― the largest units in which gravitation is effective toward consolidation of its components are the groups of galaxies These groups begin separating immediately, but until the outward movement produces a clear-cut separation, their identity as distinct individuals is not apparent to observation Here, then, is the explanation of the large ―clusters‖ and ―superclusters‖ of galaxies These are not structural units in the same sense as stars or galaxies, or the groups of galaxies that we have been discussing.‖22 (Emphasis added.) These are default clusters with apparent hierarchical structure brought into relief by the randomly generated bubbles 10.2 Difficulties with Mandelbrot‘s Model The above model suffers from two shortcomings, and Mandelbrot has to introduce two ad hoc assumptions to make it successful These concern the hole size distribution assumed by him (Eq ) Firstly, while the model shows reasonable verisimilitude when limited portions of sky are considered, the overall sky maps are completely wrong in that they include voids as immense as one-tenth of the sky or more This defect could be traced to the unrealistically large hole sizes allowed by the hyperbolic distribution function N (>v) [proportional] 1/v and could be eliminated by imposing an ‗upper cutoff,‘ vmax , on the hole size Secondly, the unrealistically large number of small-sized holes allowed by this hyperbolic distribution leaves no portion of the sky not covered by the holes In fact, Mandelbrot imposes the constraint that P (>v) = 1, for v < (where P stands for probability) to save the model It would, therefore, be interesting to see what the Reciprocal System has to offer in this context 10.3 Distribution of the Hole Size According to the Reciprocal System According to the Reciprocal System the large-scale universe is in a steady state That is, both the rate of inflow of matter from the cosmic sector and the rate of final quasar transitions to the cosmic sector are uniform in time (as well as in space) and equal each other Therefore, for a given volume of space, the number of bubbles created per unit time, which is the number of quasars exiting per unit time, is given by dN/dt = b where b is a constant directly calculable from [sigma] and the average mass of a quasar Assuming an average quasar mass of 109 Solarmasses, b works out to be 1.37 x 10-15 per second per cubic megaparsec of space For = tcr : Beyond the critical point, we have seen that the bubble size decreases according to Eq We obtain on differentiating it dt/dr = - rcr tcr/r² = - rcr²/c.r² since rcr = c.tcr by Eq Finally dN/dr = (dN/dt)(dt/dr) = - b.rcr²/c.r2 On integrating N2 (>r) = b ((rcr²/r) - rcr)/c where, again, N2 is the number of bubbles of radii larger than r N2 is the contribution to the bubble population from the post-critical phase We have shown in Section 9.3 that in the post-critical phase there is lower cut-off to the bubble size due to its quick dissipation Let this lower cut-off radius be r0 On adding N1 and N2 from Eqs and respectively we get the following total distribution For 0) is not infinite but a finite constant (see Eq ) Similarly the difficulty of occurrence of unrealistically large-sized holes does not arise either This is because there is a maximum possible size, rcr ; and this comes out as a natural consequence of the development of the theory in the case of the Reciprocal System–not as an arbitrary constraint imposed on the model to make it conform to the reality 11 Summary The astronomical observations of the recent decade have brought to light the large-scale distribution of galaxies in the universe and the near perfect uniformity of the cosmic microwave background to an extent that has not been possible earlier An unexpected fact that has come to be established is the ubiquitous occurrence of spherical voids of gigantic proportions throughout space Current theories are nonplussed Larson has shown that galaxies, on reaching an age limit, explosively eject fragments of their cores, imparting to them ultra high speeds These fragments are quasars When gravitation is attenuated by distance (time) the net speed of quasars reaches two units, the limit of the material sector Then gravitation–which always acts inward–ceases to act in space and starts operating in time This leaves the outward progression of space unchecked and all the constituent matter of the quasar, which hitherto stayed put, is dispersed in all directions in space at the speed of the progression Thus, centred at the location of the original quasar, a spherical void starts growing Since the ejection of quasars and their exit are inevitable stages in the evolution of material aggregates these voids ought to be a universal phenomenon Preliminary calculations demonstrate that their observed sizes and other parameters are in consonance with the theoretical predictions All these latest observational findings that the current theories are at a loss to account for, are logically explained by the Reciprocal System starting from the foundation of its Fundamental Postulates This Paper, thus, demonstrates once again the cogency and power of the Reciprocal System as a general physical theory References Stephan A Gregory and Laird A Thompson, ―Superclusters and Voids in the Distribution of Galaxies,‖ Scientific American, 246 (3), March 1982, p 88 A S Szalay and Y B Zel‗dovitch, ―The Large-scale Structure of the Universe,‖ Scientific American, 249 (4), October 1983, p 56 Science and the Citizen section, ―Cosmic Cartography,‖ Scientific American, 254 (3), March 1986, p 49 Margaret J Geller and John P Huchra, Science, 246, 1989, p 897 A Dressler and S M Faber, Astrophysics J Letters, 354, 1990, L 45 Bertram Schwarzschild, ―Gigantic Structures Challenge Standard View of Cosmic Evolution,‖ Physics Today, 43 (6), June 1990, p 20 Thomas J Broadhurst et al., Nature, 343, 1990, p 726 John Horgan, ―Universal Truths,‖ Vigyan, October 1990, p 88 Corey S Powell, "Up Against the Wall," Scientific American, 262 (2), February 1990, p 12 10 Anthony Readhead et al., Astrophysics J., 346, 1989, p 566 11 Dewey B Larson, Nothing but Motion, North Pacific Pub., Portland, Oregon, U.S.A., 1979 12 Dewey B Larson, The Neglected Facts of Science, North Pacific Pub., Portland, Oregon, U.S.A., 1982 13 Dewey B Larson, The Universe of Motion, North Pacific Pub., Portland, Oregon, U.S.A., 1984 14 Dewey B Larson, The Neglected Facts of Science, op cit., pp 112-113 15 K V K Nehru, ―The Gravitational Limit and the Hubble‗s Law,‖ Reciprocity, XVI (2), Winter 1987-88, pp 11-16 16 Dewey B Larson, The Neglected Facts of Science, op cit., p.73 17 K V K Nehru, ―The Cosmic Background Radiation: Origin and Temperature,‖ Reciprocity, XIX (4), Winter 1990-91, p 20 and XX (1), Spring 1991, pp 1-4 18 William K Hartmann, Astronomy: the Cosmic Journey, Wadsworth Pub Co., U.S.A., 1978, p 309 19 Benoit B Mandelbrot, The Fractal Geometry of Nature, W.H.Freeman & Co., U.S.A., 1983 20 Ibid., p 294 21 Ibid., p 298 22 Dewey B Larson, The Universe of Motion, op cit., p Special Thanks to the folks who set up the web site that made this document possible! http://www.reciprocalsystem.com/rs/links.htm