NEWTON'S GRAVITATION AND COSMIC EXPANSION

Part 4 of 4 Parts
James Constant
grav@coolissues.com

Introduction

        The present theory in four parts is based on classical and relativistic mechanics, special relativity, and quantum mechanics. Each part of the work is presented as a separate web page. The first part of the work describes the Galactic Universe, the non relativistic part we are most familiar with. It discusses the cosmic force of gravitation, in terms of classical gravistatics, analogous to electrostatics, describes the action at a distance and retarded action types of universes, respectively, as likely and unlikely, Hubble's Linear Law, and non relativistic forces of expansion and Newtonian gravitation within the span of Hubble's Linear Law. It also provides values for the cosmic mass density, cosmic rest mass and radius. The theory disproves Mach's Principle and considers the Big Bang Theory unlikely.www.coolissues.com/gravitation/Nonrelativistic/ncosm1.htm. The second part, based on the doppler formula, describes the Extra Galactic Universe, the relativistic part which extends beyond the Galactic Universe. It discusses the cosmic forces of expansion and slowdown as they apply to the observed receding galaxies, develops a speed distance law from observations, gives a detailed relativistic description of the cosmic forces of expansion and gravitation, emphasizes the effect of mass shielding by the negative field of galactic and cosmic mass. The theory predicts that velocity speedup occurs at lower speeds (nearest distances) and velocity slowdown occurs at the higher speeds (farthest distances). Brillouin's theory of self shielding of mass by the negative mass of its field may well account for what astronomers call dark energy, energy not seen but which is assumed from its gravitational effects, in the distant cosmos. Based on the instantaneous action of Newton's theory of gravitation, the present theory adopts the idea that what we observe in the universe by redshift measurements also exists today. The theory finds unlikely the indirect observation and detection of black holes and leaves open the question of their nature. www.coolissues.com/gravitation/Relativistic/ncosm2.htm. The third part looks at the observations of redshifts of galaxies and the microwave background. I examine observations which lead to two models, the non linearly and linearly expanding universes. I discuss the sources of the redshift and microwave background, the forces acting on cosmic photons, cosmic redshift, and space expansion and the Big Bang. I find that receding galaxies are sources for the observed red shifts and extra galactic radiation is the source for the microwave background. I discount the Big Bang and characterize the Extra Galactic Radiation Universe at the farthest distances as having a Planck blackbody spectrum. www.coolissues.com/gravitation/Observations/ncosm3.htm. Finally, in this fourth part I compare the mainline and Einstein's theories, instantaneous and retarded action theories, Brillouin's field mass theory, and the present non linear and linear expansion theories. The present nonlinear expansion theory, based on the doppler formula or on a non linear departure from Hubble's linear law, is an infinite size eternal existence steady state. The present linear expansion theory, based on Hubble's linear law valid at all distances, is a finite size eternal existence steady state. The present theories introduce ideas of quantized space.

THEORIES COMPARED

Mainline Theories

        The Big Bang theory makes the case for a universe that began billions of years ago as an explosion from an infinitely small and dense amount of energy. Another prominent theory, the steady state theory, postulates that the universe has no beginning and no end and that matter is continuously generated between the galaxies. Both theories explain the observed cosmic expansion but both have weaknesses. For example, the Big Bang theory successfully accounts for the known abundances of hydrogen in the universe, explains the microwave background, but cannot explain its beginning. While the steady state theory avoids the beginning problem it cannot explain the observed microwave background. Today, the Big Bang theory dominates over its steady state competitor.1 The present theory studies two possibilities: a linear or non linear expansion of the universe each of which explains the observed redshift and the microwave background. The linear and non linear theories posit a finite or infinite universe, respectively. Present observations confirm neither theory. 

        In 1665 Newton published his theory of gravitation and laws of motion all abundantly confirmed on the local, terrestrial and planetary scales and reaching to the farthest galaxies. Galactic clusters, spanning distances of about 10 mly, are the largest gravitationally bound bodies in the universe.2 They are located within the span of Hubble's linear law.3 Clusters have radii of about 5 mly which is about the distance to the low end of Hubble's linear law. Our galaxy is not part of a cluster because while the observed distance to the low end of Hubble's linear law is about r1~4.32 mly, the approximate radius of a cluster, not many other galaxies are within that distance to qualify it as a cluster.4

        Within its ambit, Newton's law of gravitation is action at a distance, i.e., gravitation acts instantaneously. As shown in Part I, a gravistatic has developed along lines of Maxwell's electrostatics. In 1905 Einstein developed his special theory of relativity, abundantly confirmed by measurements and experiments. His theory has been successfully incorporated into classical mechanicsinto which it merges at the lowest speeds. It predicts that no mass, but only electromagnetic radiation, can travel at the speed of light. In 1917 Einstein published his theory of gravitation based on Riemann's geometry of curved space claiming that it superceded Newton's theory. As proof, Einstein offered predictions for three classical tests almost identically predicted by Newton's theory, namely, redshift, bending of light, precession of perihelia. Later, a fourth test, the radar echo delay, was added. Those claiming proof of Einstein's theory do so by reducing Einstein's equation to a so called Newtonian approximation.  Einstein's theory is retarded action and claims that gravitation travels at the speed of light.

        In 1929 Hubble observed a linear relationship between the redshift and distance of galaxies. If we assume that the redshift is due to doppler speed, we conclude that the galaxies are receding from us and the more distant ones are receding faster than the nearby ones. This is the current consensus and, today, Hubble's linear law is known to extend between its low end at a distance of about r1~4.32 mly (v~0) and high end of about r2~3.96 bly (v/c=0.203). Within this span, velocities are low enough so the motions of galaxies are essentially nonrelativistic. Below distance r1~4.32 mly (v~0) the galaxies approach rather than recede. I compute distances using equation (2.1).

        Within Hubble's linear span, the cosmic expansion suggests an expansion force based on Newton's 2nd law of motion, which counteracts Newton's law of attraction. The two forces equate at distance r1~4.32 mly (v~0) which allows the present theory to obtain values for the cosmic rest mass ratio lo/r1~4.1825x10-8, the cosmic rest mass radius lo~GMo/c2=1.71x1017 cm, cosmic rest mass Mo~2.3x1045 g and galactic density q~8x10-30 g/cm3. There is no comparable result available from Einstein's theory.

Einstein's Theory

        Two fundamental questions of cosmology ask: What are the causes of the observed cosmic expansion and slowdown? Einstein's theory answers these questions in metaphysical terms. It claims the expansion is that of space itself and the slowdown is due to adeus ex machina cosmological constant.

        Hubble's discovery of the expanding universe obviated the need for Einstein's theory of gravitation. Einstein's theory was based on the need for a cosmological constant, a fudge factor invented by Einstein in 1917 to counteract cosmic expansion. Nevertheless, many cosmologists continue to search for ways to explain the cosmic expansion through Einstein's General Relativity Theory. Einstein's proponents ask the question whether gravity is strong enough to eventually stop the expansion and cause the universe to collapse or will the cosmos expand forever. They hold that the answer is in the average density of matter: a high density universe will collapse, whereas a low density universe will expand eternally. The dividing point is the critical density universe, which expands forever at an ever decreasing rate. Because, in Einstein's theory, the average curvature of the universe is tied to its average density, geometry and density are linked. Thus, determining geometry determines density and vice versa. A new incarnation of Einstein's old cosmological constant shifts away from density. We are now told that the presence of the new cosmological constant in Einstein's equations seems to be inevitable since it arises not from relativity ad hoc but from quantum mechanics. It makes gravity repulsive not attractive. However, all calculations and estimates based on the new cosmological constant are absurdly large values. If density were that high, all matter in the universe would instantly fly apart. Theorists have been trying to figure why their calculations don't work.5

        From the point of Einstein's theory, Hubble's linear law arises from the expansion of space itself which should slowdown in time because of gravitational attraction. The slowing should lead to a departure from Hubble's linear law. The most distant galaxies should be receding faster than Hubble's law would predict. However, recent observations show that the expansion has been speeding up, not slowing down. The evidence for a cosmic speedup has gotten much stronger and has revealed not only an accelerating phase but an earlier epoch of deceleration.6 Today, confusion about cosmic acceleration is driving theorists to explore every avenue possible to understand the nature of the energy that is driving the speedup. 7

        What shall we make of this picture? As stated, Einstein's cosmological constant, intended to counter gravity by geometry, was obviated by Hubble's discovery of cosmic expansion but then resuscitated to counter gravity by energy density. To date, the new theory has produced absurd results. But if the observed cosmic expansion obviates countering gravity by ad-hoc geometry why would it not counter gravity by unknown energy density based geometry? Physically, Riemann's geometry is not tied to energy density and there is no connection between immaterial geometry and density and the expansion discovered by Hubble. In Einstein's theory, space expands or contracts depending on density without an expanding or contracting force. A yet to be discovered type of matter density, deduced from quantum theory without experiment, intends to make gravity repulsive not attractive. Einstein's theory of gravitation is a grand intellectual mathematical edifice which now seeks an experimental base in quantum theory.

        In Newton's theory, the observed expansion of space is due to an expansion force that counteracts gravity. In Einstein's theory, there is no talk of an expansion force but of an ad hoc cosmological constant which ties Riemann's geometry to an unknown matter density which, along with the hope of connecting quanta and gravitation, can be deduced from quantum mechanics without experiment. Einstein's proponents say that space expands or contracts based on this unknown type of matter density. Einstein's theory countering gravity by an ad hoc cosmological constant does not explain the observed cosmic expansion.

        Cosmologists have preferred Einstein's theory to Newton's laws to describe the Universe. Einstein's theory, however, is very complex and does not yield exact mathematical solutions. So rather than using Einstein's theory, cosmologists have made some simplifying assumptions, first, the Cosmological Principle (homogeneous and isotropic universe) and, second, the Weyl Postulate (predictable motion of galaxies)8  These assumptions claim to describe the universe as a whole even though we only have access to local observations. They exclude non conforming theories and validate Einstein's theory of General Relativity.

        The Cosmological Principle assumes that the universe is homogeneous and isotropic, i.e., averaged over large enough distances, one part of the universe looks approximately like any other part. In accordance with observations of distant galaxies, a universe must be non-static if it follows the cosmological principle. That is, the principle requires that the universe be either expanding or contracting. A non-static universe is also implied, independent of these observations of distant galaxies, as the result of applying the cosmological principle to General Relativity. When applied, the principle severely restricts the large variety of possible cosmological theories. Weyl's Postulate assumes that there is a predictable geometric motion of galaxies, i.e., like particles in a substratum (fluid) which lie on geodesics diverging from a common point. The postulate can be understood as the assumption that we should consider only cosmological models in which there are such geodesics, orthogonal to the world lines of the fluid particles.

        Einstein's theory claims its foundational base upon the Cosmological Principle and Weyl's Postulate, neither of which decrease its mathematical complexity. It obtains mathematical solutions by reducing its equations to a form called the Newtonian approximation in order to explain classical tests almost identically predicted by Newton's theory. There is no problem saying that Einstein's theory in its weak field approximation reduces to Newton's theory. However, relying on Newton's theory to prove Einstein's theory is corrupt science. 

           The Cosmological Principle and Weyl's Postulate are suspect for a number of reasons, first, their assumptions are just that, second, to the extent that they are based on observed galactic expansion, they are not unique to Einstein's theory and, third, they do not incorporate ideas of quantum mechanics. Observed evolution tells us that, at each epoch, the universe is far from homogeneous and isotropic. If we look at the observed universe at any time in the past, in the Galactic and Extra Galactic Universes, it looks different, with different scenes. The Galactic Universe is different from the Extra Galactic Radiation Universe. Through time, the universe has undergone an evolutionary metamorphosis with different forces acting upon different forms of matter at different times. Evolution trumps the Cosmological Principle and any theory that depends upon it.9 The Cosmological Principle, which assumes a homogeneous and isotropic universe, would exclude the Big Bang theory, which assumes decreasing density. While tentatively sustainable in the Galactic Universe, the assumptions by the Cosmological Principle and Weyl's Postulate, that there are predictable motions of galaxies in a homogeneous and isotropic universe, are unsustainable in the Extra Galactic Universe, which presents ideas from quantum mechanics. I see no reasons for which a theory, whose exact mathematical predictions are confirmed by observations, need rely on the Cosmplogical Principle and Weyl's Postulate. 

Instantaneous and Retarded Action Theories

        There are two types of universes, the instantaneous and retarded action universes. In either case, consider a spherical shell at distance r. Energy dE within the shell of constant thickness dr is

        dE=2or2drq                                                                                                    (4.1)

in which q=energy density.

        In the instantaneous action universe, dE is a fraction of the total energy E=4oR3q/3 in the universe, where R is the size of the universe. Since observations show that q is approximately constant, certainly in the Galactic Universe, see Fig 1.1, and is assumed constant in the Extra Galactic Universe by the present theory, total energy E and size of the universe R are finite or infinite.

        In the retarded action universe dE is the total energy and dr is the epoch in the universe in which neither past or future exists. The retarded action theory, which proceeds like a frame to frame viewing of a film, does not explain what holds the frames together as does a film. Past and future frames do not exist. And it does not explain how Mach's principle can influence the present, lacking a past universe. The retarded action universe requires that gravitational effects transmit at finite speed which has never been observed. Thus, observations rule out the retarded action universe, Einstein's theory and, therefore, is least likely.

        While the action at a distance universe is based on instantaneous action of Newton's law of gravitation, the retarded action universe is based on retarded action along lines of Maxwell's electrodynamics. I note some indicators that reinforce choice of instantaneous action. Thus, it is unlikely that cosmic force Fc is a retarded force because a retarded action Fc violates Newton's third law of motion which holds that for every action there is an equal and opposite reaction. Our experience is that Newton's outside force Fg is an instantaneous force and no evidence exists that cosmic force Fc, obtained from classical gravistatics, is a retarded force. No evidence exists of a gravidynamic system, analogous to Maxwell's electromagnetic system; or for retarded action by gravitational energy; or that gravitational energy waves exist and can flow between masses. Indeed, action at a distance precludes gravitational energy waves. Einstein's assumption of the existence of gravitational waves which travel at the speed of light imply an unlikely retarded action universe.

Brillouin's Field Mass Theory

        Another complication is mass shielding which weakens the gravitational effect of a massive or relativistic mass when that mass is observed at large distances. This effect was described by Brillouin who insists that the negative field mass of any mass must be taken into account.10 Thus, in addition to rest mass, relativistic mass, actual mass (massive or relativistic), we now have the concepts of apparent mass and negative field mass. Such mass may well account for what astronomers call dark energy, mass or energy not seen but is assumed from gravitational effects observed in the cosmos. The effect of mass shielding by the negative mass of fields modifies the expansion and gravitational forces and introduces more uncertainty at distances beyond 93.9 bly (v/c=0.9882, z=12), the distance of the farthest galaxy yet detected. On a cosmic scale, positive actual mass and negative field mass is distributed in a ratio that varies from about 100% positive 0% negative in the near parts of the Galactic Universe to about 50% positive 50% negative in the farthest parts of the Galactic Universe. There is no talk of the effect of negative mass of fields in Einstein's theory.

        In effect, lA=l+lf=2a equation (2.15), is a statement of the conservation of cosmic mass in the "full field effect" region of the universe. Elsewhere, in the "no field effect" and "some field effect" regions, equation (2.14), the fraction of cosmic mass within distance r is

        mu         mu                                                                     (4.2)

which, in view of the speed distance law, equation (2.1), is an indirect function of distance. Thus, in the "no field effect" region, when r~a v~0, lA=lo=1.71x1017 cm (0.18 ly), a distance small compared to observed cosmic distances. In the "full field effect" region r>>a, v~c and lA=l+lf=2a represents all the mass in the universe. Since l>>2a there is a 50%-50% distribution between relativistic actual mass and field mass l~lf in the "full field effect". In the "no field effect" region of our everyday experience integrating negative field mass which surrounds actual mass leads to our familiar potential energy.11 Since cosmic mass is assumed conserved, then

        mu                                                                                             (4.3)

which states that the size of cosmic diameter 2a equals cosmic rest mass equivalent distance lo, a surprisingly low distance 0.18 ly. And, since mass is energy, the conservation of mass implies a finite universe equation (4.1). Einstein's theory does not speak to the conservation of cosmic mass.

        Basically, Brillouin's field mass theory assumes a galaxy of actual rest mass lo, or the universe, when seen from a long distance, is a large finite sphere of radius r with a core of actual mass of diameter 2a<<r at its center surrounded by positive relativistic mass l and negative field mass lf. While this model makes the observation of galaxies difficult, its suggestion for the conservation of mass, and thus a finite cosmic sphere, puts a serious question on a theory of non linear expansion of the universe which predict an eternal existence infinite universe. What is the role of negative field mass in cosmology?

The Present Theory

        The present theory considers two types of universes, linear and non linear expanding universes. The linear universe is based on Hubble's observation of a linear law that relates galactic redshift linearly to distance; the non linear universe is based on the relativistic doppler formula or as a modification of Hubble's linear law. The issue between the two types of universes depends on future observations showing the absence of linearity or non linearity. A linear universe is a finite size sphere in which space expansion is an illusion in existing space; a non linear universe is an eternal infinite sphere in which space expands or in which an explosion in existing space has occurred. Based on present observations, all we can say is that non linearity has not been confirmed and, therefore, the most likely universe is a linear universe. In what follows, I explain what the observations show for each theory keeping in mind that assumptions and conclusions in one theory may not apply to the other theory.

Non Linear Theory

        The observations show that the nearest galaxies, the ones that fall into Hubble's linear law, imply non relativistic speeds, the farthest ones imply relativistic speeds. These facts suggest a speed distance law, equation (2.1), which permits knowing distance to compute speed and vice versa. The results can then be compared with actual observations. Thus, beyond r2~3.96 bly (v/c=0.203,z= 0.228), the high end of Hubble's linear law, galaxies extend to about 93.9 bly (v/c=0.9882,z=12), the distance of the farthest galaxy yet detected. The derivative of the speed distance law, equation (2.2), shows that a speedup occurs at distances within 10.55 bly (v/c=0.5) and slowdown occurs beyond that distance which, when compared to observations[8] is off by a factor of 2 which I attribute either to a lack of refinement, inaccuracy of measurements, or due to the effect of negative field mass. The present theory, based on the doppler formula, having developed a speed distance law is a great convenience for expressing the cosmic expansion and gravitational forces and understanding cosmology, conceptually and qualitatively if not accurately, within a factor 2. There is no comparable result available from Einstein's theory.

        In the Galactic Universe it is necessary to account for the effect of relativistic speeds of both galaxies and the cosmos. Indeed, Einstein's special relativity, along with the speed distance law, equation (2.1), permits the classical statement and development of presumed forces of expansion and gravitation following Newton's laws. Newton's gravitational force predominates at the nearest distances below r1~4.32 mly (v~0), the low end of Hubble's linear law, and if galaxies still exist beyond about 93.9 bly (v/c=0.9882,z=12), the distance of the farthest galaxy yet detected. However, beyond 3.96 bly, the high end of Hubble's linear law, it becomes increasingly likely that galaxies have converted to radiation energy and the expansion and gravitational forces, developed for galactic masses, must be recast in terms of radiation photons.

        The Radiation Universe begins at about 3.96 bly, the high end of Hubble's linear law. It is a region made uncertain by the difficulty or lack of direct observation and the infirmity of theories. Here, we must speculate. It is widely believed that the main evidence for the Radiation Universe is the observed microwave background. However, there is no agreement about how the Radiation Universe connects to the microwave background. Proponents of the Big Bang theory say that the universe started out, from an infinitely small energy, as a big explosion whose leftover is the microwave background. The present theory, based on the doppler formula, makes several assumptions, first, that the Radiation Universe has a black body character, second, that expansion and Newtonian type forces operate on the radiation, third, that energy in the universe is infinite and, fourth, that the radiation travels at the speed of light as suggested by galactic mass converting to radiation as speeds approaching the constant speed of light. With these assumptions, I conclude that the observed microwave background, with its uniform black body temperature and frequency, can be explained as radiation whose sources are in the Radiation Universe at different distances each emitting the same radiation frequency.

        The universe I have described, based on the doppler formula, is an infinite size eternal existence steady state, one in which a cosmic force Fc=Fe+Fi must exist to explain the motion of galaxies and photons. An action at a distance universe is most likely because retarded gravitational action has never been observed and for other reasons discussed previously in the Section entitled Instantaneous and Retarded Action Theories. In such a universe, while Newton's outside force Fg works with greatest effect in the nearest local regions of the universe, a Newtonian inside force Fi works cosmically and Mach's principle is disproved because inside gravitational force Fi=0 when r=0 equation (2.16). At farther regions of the universe an expansion force Fe takes over. In the Galactic Universe, the receding galaxies are observed as doppler redshifts. Because of mass shielding, the effect of negative mass of the cosmic field is that the actual mass of the universe is much greater than its apparent mass. Slowdown of the galaxies occurs because relativistic speed v/ct1 as distance increases. Observations indicate that the density of galactic matter drops off at the farthest cosmic distances Fig 1.1. Assuming galaxies still exist at the farthest regions, Newton's inside force Fi and negative field mass work against expansion force Fe resulting in a zero cosmic force Fc=0. In the Radiation Universe, galactic matter breaks down into radiation, which is observed as the microwave background.

        The present non linear theory, based on a modification of Hubble's linear law equation (3.15), assumes that 

        4.4                                                                                                     (4.4)

or some similar equation established empirically by future observations of departure from Hubble's linear law. Equation (4.4) is justified because, in a non linear expansion, Dv/vot1 necessarily as  rtoo.  A virtue of equation (4.4) is that it competes with the doppler formula equation (3.14). Thus, if future observations show a departure from linearity one cannot necessarily conclude the cause being either equation (4.4) or equation (3.14).

Linear Theory

        There must be a cause(s) for an expanding universe. An explosion without cause is a defect of the Big Bang theory. That space expands by geometry without cause, Einstein's space, is unscientific imagination. That space warps in the presence of mass is another way of saying that gravitational forces exist, notions which cannot explain the observed cosmic radial expansion. Moreover, an explosion alone does not say that space expands by itself. An explosion can happen in existing space and, while it may account for a non linear expansion, certainly, cannot account for a linear expansion at all distances. No theory gives a satisfactory explanation for the expansion of space which is now taken for granted. In the present theory, based on Hubble's linear law, I consider the expansion of space is apparent. Consider a spherical cavity in which radiation energy flows radially both ways, from rim to center decreasing frequency (redshift) and from center to rim increasing frequency (blueshift). A person at the center views incoming redshift but cannot see outgoing blueshift. That person would say that what he sees looks like an explosion but cannot explain its model or beginning. In the present theory, based on Hubble's linear law, the cavity paradigm is a finite size eternally existing sphere steady state universe.

        In a retarded action theory the universe is seen initially as a ball of radiation, which has evolved to its present cooled down galactic state. Galactic rest mass has evolved from initial radiation energy reminding us of the 2nd Law of Thermodynamics and Arrow of Time, from past to present. The arrow of time appears irreversible and no oscillating models of the universe appear possible. The Galactic Universe is cooling down and will eventually evolve into a Freeze Universe. Billions of years from now, the stars will have exhausted their nuclear fuel and the sky will be littered with galactic cinders. Life as we know it will have adapted, morphed and then died. Initially, mankind will seek to migrate to more hospitable planetary and galactic systems as our own planet and galaxy spend their fuel. Or, life may find ways to live in cooler climes. At least for some time, as cosmic cooling proceeds, it is likely that intelligent life will find a way to survive in the new freeze environment but likely in different form. But, the iron laws of physics say that all things die, including Universes. New universes and new life in new forms cannot be born again unless the 2nd Law of Thermodynamics and arrow of time are reversible. It amuses me that cosmologists talk about metaphysical wormholes connecting us to parallel universes to which we can all go when our earthly paradise fades.

        But, is the Arrow of Time irreversible? To further speculate, as the Galactic Universe cools down, the cosmos gives off heat (thermal radiation) energy. Heat photons released during the cooling down process are directed radially away from rest and actual mass at the speed of light and are, therefore, blueshifted outward becoming more energetic and more electromagnetic. This heat energy is feedback which eventually rejoins the eternal Radiation Universe. In this sense, time is eternal and the 2nd Law of Thermodynamics and Arrow of Time, from hot to cold as presently observed, are countered by a reverse 2nd Law of Thermodynamics and Arrow of Time, from cold to hot as assumed in the present theory, with both the direct and reverse versions operating simultaneously and eternally. While the 2nd Law of Thermodynamics and Arrow of Time are well established local laws of physics, what evidence do we have that a reverse 2nd Law of Thermodynamics and arrow of time exist? The evidence is obvious. Outgoing photons, as do incoming photons, follow Hubble's linear law equation (3.15) at all distances. Cosmically, there is no reason why outgoing photons do not blueshift.

        In the present instantaneous action theory, based on Hubble's linear law, the cosmos is seen as a finite size eternally existing steady state cosmic sphere which contains the Local, Galactic, and Extra Galactic Radiation Universes. Since observations show that galactic mass density qg is approximately constant throughout the Galactic Universe equation (3.4) and Fig 1.1, I assume that energy density q=qg+qr equation (3.5) is constant at all distances. Since cosmic mass is preserved equation (4.3), I conclude that cosmic energy and cosmic radius Rc are finite

           R= Ec=constant=Mcc2                                                                         (4.5)

in which Mc is the cosmic mass equivalent of cosmic energy Ec. Hubble's linear law, when solved for frequency equation (3.2) further supports my contentions that cosmic radius is finite Rc=21.1 bly and that energy Ec is constant.

        As computed from equation (4.5), the cosmic mass equivalent of distance Rc=21.1 bly is Mc=2.68x1056g which is some 11 orders above the computed from observations cosmic rest mass Mo=2.3x1045g equation (1.9). Such wide difference between the cosmic mass equivalent Mc of distance Rc and cosmic rest mass Mo is explained by the fact that the energy dE in a shell dr at distance r increases as distance increases. The instantaneous action linear universe predicts 11 orders unseen equivalent mass above missing mass predicted by present observations.

        In its relativistic form Newton's second law of motion is written as F=dp/dt in which p=momentum. We usually think of force F and momentum p in terms of mechanics. However, the law is equally valid when written in terms of work W and energy E as Fdr=dE. In the cosmic cavity, energy is quantized at spherical levels »hvm in which »=1,2,3 . . . increases with distance r. Quantized energy levels, therefore, represent changes in energy dE, decreasing the energy of incoming redshift photons and increasing the energy of outgoing blueshift photons. The source of cosmic expansion force Fc is the quantized energy in the cosmic cavity.

        The cavity paradigm differs from ideal Planck cavities in that its rim lacks a well defined boundary value and its interior does not have a single temperature. Instead it has a maximum frequency and temperature quantization at each energy level. Recall that Wien's law equation (3.7) relates maximum frequency vm to a single temperature T in a Planck cavity. In the cosmic cavity paradigm, Wien's law applies only to a single quantized energy level dE. For the cosmic cavity paradigm, read Wien's law as follows

        »hdvm=4.965»kdT         »=1,2, . . . .                                                               (4.6)

in which »dvm is the maximum frequency and »dT is the single temperature of a single quantized energy level dE. This does not change Wien's law but it tells us that each energy level in the cosmic cavity paradigm, with well defined boundary, is a Planck blackbody spectrum equation (3.6).

        The linear universe just described is a finite radius Rc spherical cavity with constant energy, which continually exchanges energy between its Radiation and Galactic parts. Internally, hot radiation flows radially from its rim towards its center and transforms to galactic matter which cools off and gives off heat which travels back radially towards its rim and transforms to hot electromagnetic radiation. The process is eternal. Planck's blackbody spectrum equation (3.6) requires that temperature »T decreases with increasing redshift of incoming photons and increases with increasing blueshift of outgoing photons. This leaves the center of the cavity, the Galactic Universe, cooler than its rim, the Extra Galactic Universe.

        Redshift equation (3.15) was discovered by Hubble who prematurely reasoned it was due to the doppler effect. Without waiting to have doppler equation (3.14) confirmed by observation, and putting the horse behind the carriage, cosmologists later reasoned equation (3.15) was due either to an explosion or expansion of space. The idea of an explosion does not explain its beginning. And, some cosmologists say that immaterial space can expand by itself because it alone explains the cosmic redshift.12 The idea that immaterial space expands by itself is a metaphysical idea that cannot be deduced from material observations for, otherwise, space would be material. It is in the same metaphysical category as Kant's immaterial space and geometric flat and curved spaces. The present theory, based on Hubble's linear law, says there was no explosion producing a doppler effect and no expansion of immaterial space by itself. Instead, the present linear theory offers a finite size eternal existence steady state quantized spherical cavity in which energy flows simultaneously inwards from hot to cold and outwards from cold to hot, in which man has only observed the incoming redshift part.

        In science we have metaphysical ideas like Newton's Absolute Space and Einstein's Relative Space; in mathematics we have Euclid's flat space and Riemann's curved space. In philosophy Kant held that immaterial space is an a priori understanding but Berkely said that space without matter cannot be understood. In my view, distance and time are forms of energy. Since energy is quantized, from equation (4.1)

        dr         dE=»hdvm     »=1,2, . . .                                                         (4.7)

which, according with Planck's postulate of energy quantization, looks like an atomic energy level diagram. Equation (4.7) predicts an infinite number of energy levels, each number » corresponding to a distance r. i.e., »~r. Thus, for each energy decrease/increase dE at distance r there is a corresponding distance increase/decrease dr, i.e., incoming photons are redshifted and outgoing photons are blueshifted. Distance and time are forms of energy because they interact with photons. The idea that distance and time are immaterial is a metaphysical idea which must be discarded because material photons do not interact with immaterial things but only interact with matter.

1 Simon Singh, Big Bang, The Origin of the Universe, Harper Collins Publishers 2005

2 Wallace Tucker, Harvey Tanenbaum, Andrew Fabian, Black Hole Blowback, Scientific American, March 2007 p 43-49. Galaxies line up in filaments that crisscross intergalactic space like freeways. In between the roads are regions of relatively low density and at the crossroads, where multiple filaments converge, are clusters of galaxies.

3 Fred Hoyle, Astronomy and Cosmology, W.H. Freeman and Co., San Fransisco 1975 page 81 Table 3.2 Some rich clusters of galaxies.

4 Id page 76 Fig 3.9 and page 77 Table 3.1 The local group.

5 Lawrence Krauss and Michael Turner, A Cosmic Conundrum, pages 71-77, Scientific American, September, 2004; Steven Weinberg, Gravitation and Cosmology, John Wiley & Sons, 1972 page 614. 

6 Adam Riess and Michael Turner, From Slowdown to Speedup, Scientific American February 2004 pages 62-67

7 Lawrence Krauss and Michael Turner above page 77

8 Jayant Narlikar, The Structure of the Universe, Oxford University Press, 1977 pages 118-121.

9 Id, page 109 (Milne and Macrea's Cosmology based on Newton's theory) and page 121 (Friedman's Cosmology based on Einstein's theory)

10 Leon Brillouin, Relativity Re-examined, Academic Press 1970 pages 93-95 2[9],1[7]

11 Id, pages 17-20

12 Charles Lineweaver and Tamara Davis, Misconceptions About the Big Bang, Scientific American March 2005 page 36. 2[5]

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Copyright © 2004 by James Constant

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