Reciprocity XX #2, Summer, 1991
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.
In the 1980’s, astronomers have surveyed billions of light years 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 light years 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 3×1016 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  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 light years, 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 2,000 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 2,000 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.
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 light-years. …Astronomers have now identified a score of galaxies more than 10 billion light-years 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.
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:
We thus find that there is a constant inflow of widely dispersed matter into the material sector from the cosmic sector.
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 three-dimensional 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 do indeed fall within the observed range.
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 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.
Larson 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 do 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.”16 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.
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 three-dimensional space but in the region of three-dimensional time.
Continue to Part II…