Observations Gravitation Part III

NEWTON'S GRAVITATION AND COSMIC EXPANSION

Part 3 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 cosmic 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 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.This 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 theory and characterize the Extra Galactic Radiation Universe at the farthest distances as having a Planck blackbody spectrum. In Part 4 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 linear and non linear theories introduce ideas of quantized space. www.coolissues.com/gravitation/Relativistic/ncosm4.htm

RED SHIFT AND MICROWAVE BACKGROUND

Sources of Red Shift and Microwave Background

There are a number of theories available to explain the sources of the observed red shift and microwave background. The cosmological redshift theory assumes that the underlying universe expands and that galaxies ride the expansion like points in an expanding balloon. Redshift occurs because of the relativistic doppler motion. However, there is no evidence or even a logical reason for this assumption of universe expansion. Next, the gravitational redshift theory assumes a static universe in which galaxies are stationary in or move in a stationary underlying universe. The static universe is the universe of our local experience and observation of nearby galaxies. It is the universe discussed in Part I of the present theory, which I call the non-relativistic universe, which extends to the upper limit of Hubble's linear law. Here, galactic masses do not change relativistically speaking. In a purely static universe, redshift occurs because the more distant galactic photons must travel through more mass between them and the observer. Next, the doppler redshift theory assumes a dynamic universe in which the galaxies expand away from the observer in a manner suggesting an explosion. It is the universe discussed in Part II of the present theory, which I call the relativistic universe. The pros and cons of each theory lead to endless speculations and may never succeed in identifying the true source of the observed redshift. All theories are best guesses and the best man can do is keep on observing the heavens. Since logic and reason are imperfect guides and since experiments at the cosmic level are impossible, the science of cosmology will always be incomplete and speculative.

Cosmologists generally agree that the source of the observed microwave background is the Extra Galactic Radiation Universe, but they disagree about its nature, whether a Big Bang or steady state eternal existence.¹ Most cosmologists believe that the observed red shift and microwave background are due, respectively, to doppler speeds and to an expanding universe of leftover radiation from an initial Big Bang.² In the present theory, receding galaxies due to an expanding universe are sources of the observed doppler redshifts. There are two possibilities to be resolved by observation, a linear or non linear expansion of the universe. If linear, the universe is a cavity whose radius is about 21.1 bly. If non linear, the universe is infinite size. Each type universe predicts a different distance to be proven by observation. Distance 21.1 bly is computed from Hubble's linear law. Distances beyond 21.1 bly reflect a non linear universe computed from equation (2.1) and the relativistic doppler formula equation (2.3).

The Galactic Universe stretches out to about 93.9 bly (z=12), the distance of the farthest galaxy yet detected.³ Galaxies in this region are shielded gravitationally by the negative field mass of cosmic mass. Beyond the Galactic Universe, and into the Extra Galactic Radiation Universe which is almost closed to us, we do not see many galactic spectra. Here galactic mass has converted to radiation⁴ which travels to us through the Galactic Universe. The microwave background is due to photons which originate in the Extra Galactic Radiation Universe.

Suppose that all stars are treated as approximate black body radiators. Then for each star the surface temperature will determine the frequency and color at which most of its energy is radiated. The temperature and emitted frequency of a blue star is higher than the temperature and emitted frequency of a red star. The thermal frequency spectrum of a galaxy is uniform but, as temperature increases with speed and distance free atoms build up, and lines appear in the spectrum for each type atom. The black body approximation is a good one for all but the very cool stars. Hot stars are nearest being ideal black body radiators. Very cool stars are non-ideal because their black body character is not preserved. I consider the hot Extra Galactic Universe as an ideal black body source for the microwave background.

The observed high temperature red shift and low temperature microwave background both preserve black body characters from which I conclude that their sources are near ideal black body radiators. In fact, the microwave background radiation is the most perfect blackbody radiation in nature. The spectrum of the 5 cm microwave background is a perfect black body spectrum of a single temperature of 2.726^o degrees. Most cosmologists believe that this constitutes the strongest support for the Big Bang model. They say it tells us that the universe was once so dense and compact that it was a single body, a body that could be characterized by a single temperature.⁵ Earlier, in connection with equation (1.7), I questioned the Big Bang theory on grounds its decreasing density is not likely to describe an action at distance universe. Later, I discount the Big Bang theory on grounds it cannot explain its beginning.

Stars are visible at different frequencies and at different distances and, with more accuracy at nearest galaxies, their distances can be estimated. Since we cannot obtain distances of the sources for the microwave background, and since the microwave background is at a single frequency, I initially consider whether the sources for the microwave background are invisible stars located in a spherical shell at a single undetermined distance. The shell thickness must be finite, otherwise the distance separations of invisible sources outside the shell would produce a microwave background with different temperatures at different microwave frequencies. However, the farthest stars need not be in a single spherical shell because their speeds, and therefore their redshift frequencies, are substantially identical at all distances. Certainly, the sources for the microwave background might be invisible stars located in the Extra Galactic Radiation Universe. For reasons discussed next, invisible stars must be least likely and radiation in the Extra Galactic Universe must be the most likely source for the microwave background.

Emitted frequencies reaching the Earth from visible stars are red shifted under action of doppler motions of galaxies. Observations tell us that the sources of the visible stars are located in spherical shells at all distances and corresponding doppler frequencies. Special relativity tells us that at distances invisible stars are presumed to exist their speeds, and therefore their redshift frequencies, are substantially identical at all distances v~c. Thus, assuming invisible stars preserve their blackbody character, one possible source for the observed microwave background is invisible stars located in the Extra Galactic Radiation Universe beyond the visible Galactic Universe. However, since few galaxies are seen in the Extra Galactic Universe and since stars convert their masses to radiation, it is not likely that invisible stars exist beyond that region. Moreover, there is a 5 order magnitude difference between the redshifted optical frequencies received from galaxies and the microwave frequency of the microwave background. Assuming that converted radiation preserves a blackbody character, another possible source of the observed microwave background at constant temperature is converted radiation located at remotest distances in the Extra Galactic Radiation Universe.

Since it is unlikely that invisible stars exist and are ideal blackbodies located in the Extra Galactic Radiation Universe, I finally conclude that the sources for the microwave background cannot be invisible stars but must be radiation located in the Extra Galactic Radiation Universe which extends beyond the visible Galactic Universe. Radiation from the Extra Galactic Radiation Universe is perfect blackbody radiation at a single frequency. Unlike visible galactic photons, extra galactic radiation is not determined by the doppler association between frequency and mass velocity. In this view the cosmos is an eternally expanding sphere, a ball of radiation, which has evolved to its present cooled down galactic state at the center of the sphere.

Galactic And Radiation Photons

Beyond the Galactic Universe, at speeds approaching the speed of light, all mass has likely been converted to radiation energy. As distance increases, the fundamental weak, electromagnetic and strong forces are overcome. Assuming mass can be converted to radiation, one can say that electrons, nuclei, protons and then, quarks are stripped from disintegrating and disappearing atoms releasing high energy photons. Since all matter has presumably been converted to energy in the form of high energy photons, the line spectrum is no longer available as indicator of galactic doppler frequencies and speeds. Our association of recession speed with special relativistic formulas no longer work. We are left only with Hubble's law which suggests linearity beyond its high end and Planck's and Einstein's Quantum theories which hold that energy E is frequency v, E=hv in which h is Planck's constant.⁶ The Extra Galactic Radiation Universe, in which particles and photons travel at the speed of light, is characterized as having a continuous thermal spectrum. In the present theory, the visible Galactic Universe is at the center of the Extra Galactic Radiation Universe, an immense ideal blackbody radiator, characterized by an immense single temperature and immense frequency.

The doppler formula for redshift frequency received on Earth from galactic photons is given by

z[12 (3.1)

in which v_o is the frequency of radiation sent by a galaxy, e.g. the H and K lines of Calcium for which v_o~7.6x10¹⁴/s, an optical frequency, and v is speed. Redshift is given by the formula Dv=v_o-v. Accordingly, v decreases and Dv increases as z and v/c increase.

Cosmic ray particles at 10²²/s are the highest energies observed in nature. They exceed gamma rays by several orders. They travel almost at the speed of light and some at least appear to originate likely as products of enormous explosions.⁷ Excluding these extremely rare cosmic ray particles, gamma rays with frequencies about 10²⁰/s are the highest photon frequencies observed.⁸ Doppler redshift frequencies at about v=10¹⁵/s fall within the optical part of the electromagnetic spectrum. Accordingly, the frequency sent by a galaxy cannot exceed v_o[10²⁰/s. Since microwave background frequencies at about v=10¹⁰/s received on Earth fall within the microwave part of the electromagnetic spectrum, number z~v_o/v=10⁵-10¹⁰ which far exceed the farthest detected object at a distance 93.9 bly (z=12), a distance beyond which matter converts to radiation, and for which one cannot assume that galaxies exist beyond that distance as sources for the microwave background.

Since mass presumably converts to radiation beyond the visible Galactic Universe, in the Extra Galactic Radiation Universe which begins at about 3.96 bly (z=0.228), the high end of Hubble's linear law, and goes beyond 93.9 bly (z=12), and since the microwave background requires substantially larger number z~v_o/v=10⁵-10¹⁰, I conclude that the source for the microwave background cannot originate in the receding motion of galaxies. It is reasonable, therefore, to assume that the source for the microwave background is the Extra Galactic Universe.

When applied to photons which originate from receding galactic motion, equation (3.1) is valid only for z[12. Later, in view of Hubble's linear law, I will assume that the formula which applies to photons which originate in the Extra Galactic Universe is provided by

r[21.1 bly (3.2)

in which number z, which ranges from 0 to º, is obtained from Hubble's linear law at all distances r.

Forces Acting on Cosmic Photons

Cosmic force F_c, equation (2.11), expressed for galaxies, is not valid for making predictions for photons. Forces on galaxies are not the same as forces on photons. For photons, I start by replacing m_Av by hv/c in equation (2.5), m_A by hv/c² in equation (2.7), where h is a constant and v is the photon's frequency at distance r. See the related discussion in connection with equations (2.5)-(2.10) for galactic mass. Thus, for photons

F_c=F_e+F_i= (3.3)

in which h is a constant, v_o,v=frequency, G=gravitational constant, q=density, H= Hubble's constant, c=speed of light, and r is distance. Equation (3.3) says that an incoming photon is repulsed (redshifted) by a constant expansion force F_e and is attracted (blueshifted) by a decreasing Newtonian type gravitation, inside force F_i. Since the photon received on Earth is redshifted, F_e>>F_i. As shown later, the same conclusion is obtained by noting that that the first term in parenthesis is much greater than the second term.

The density in the Galactic Universe (r<r₂) is obtained from equation (2.10) by setting = . Thus,

r<r₂ (3.4)

which relates density q_g to distance r. At distances r[3.96 bly, the high end of Hubble's linear law, q_g=0.8x10^-29g/cm³.

For galactic photons, in view of equation (3.1), frequency v in equation (3.3) is always finite because z never becomes infinite. Thus, if equation (3.4) is used in equation (3.3), the gravitational term tends to zero as r decreases.

Equations (3.3) and (3.4) are valid for galactic photons. Equation (3.4) says that density in the Galactic Universe is constant but falls off at the farthest distances. However, I assume the total density q remains constant

q=q_g+q_r=0.8x10^-29g/cm³ (3.5)

where q_r= radiation density. Accordingly, q_r=q-q_g=0.8x10^-29(1-e^-2Hr/c)g/cm³, i.e, q_r is constant at the farthest distances.

Galaxies begin converting to radiation beyond beyond 3.96 bly, the high end of Hubble's linear law, and certainly have done so beyond r₄=93.9 bly (z=12), the distance of the farthest galaxy yet detected. In the Extra Galactic Universe which, I presume all galactic mass at the farthest distances is converted to radiation characterized as an ideal blackbody. I assume the constant density of radiation q_r is Planck's blackbody spectrum,

r>r₂ (3.6)

in which v=frequency, c=speed of light, e=total energy, k=Boltzman's constant and T= temperature. Equation (3.6) relates density q_r to frequency v.

For extra galactic photons, since frequency v and temperature T are constant, if equation (3.6) is used in equation (3.3), the gravitational term increases as r increases beyond r>r₂.

Equations (3.3) and (3.6) are valid for extra galactic photons in the Extra Galactic Radiation Universe. Equation (3.6) says that density in the Extra Galactic Universe is constant because frequency and temperature are constant at any farthest distance.

Since the extra galactic blackbody radiation is characterized by a single maximum frequency v_m, according to Wien's law it must also have single temperature T

hv_m=4.965kT (3.7)

Equations (3.6) and (3.7) are valid for extra galactic photons, the source for the microwave background. They discount the idea for a Big Bang Universe, since they assume a blackbody source characterized by a single maximum frequency v_m and maximum temperature T, with spectral frequencies distributed similarly at all distances of the Extra Galactic Universe, from about 3.96 bly to infinity, and thus supporting the idea of infinite size and eternal existence.

Cosmic Redshift

The two basic phenomena of cosmology are the observed redshift of galaxies and the microwave background. Two theories seek separate explanations, namely, the Big Bang (explosion creating matter from infinitely small space; decreasing density) and steady state theories (matter continually created; constant density).⁹ Both theories assume space expansion and explain redshift (as doppler motion) but only the Big Bang theory explains the microwave background (as a relic of an explosion). The present theory also assumes that space expands, or so appears to expand, that galaxies produce the observed optical redshift and the Extra Galactic Radiation Universe produces the observed microwave background.

A photon which originates in a receding galaxy in the Galactic Universe is different from one that originates in the Extra Galactic Universe. Photons have total work done due to cosmic force F_cequation (3.3) in which q=q_g+q_r equation (3.5). Galactic photons have total work done in the Galactic Universe. Extra galactic photons, on the other hand, have work done in the Extra Galactic Universe and have additional work done after entering the Galactic Universe.

The work done by cosmic force F_c on an incoming photon of frequency v at distance r from a source of frequency v_o at distance r_o is

(3.8)

Using equation (3.3) in equation (3.8), gives the redshift of the photon due to cosmic force F_c in the Galactic and Extra Galactic Universes

(3.9)

in which q is given in equation (3.5). From equation (3.9), I obtain the cosmic redshift in terms of space expansion and gravitation parts

(3.10)

which says that cosmic redshift has terms due to expansion force F_e and gravitation inside force F_i. Equation (3.10) provides two contributing causes for redshift, namely, due to space expansion and due to a gravitation term represented by the integral. Its virtue is that it was obtained from equation (3.8), a basic definition of work done on a photon and confirmed by the classical redshift experiment. As shown next, D_em>>jr_o²v.

Equation (3.10) provides a frequency distance association different from Hubble's linear law observation. Assuming Hubble's linear law is valid at all distances r[21.1 bly

(3.11)

and, since the integral in equation (3.10) [ jr_o²v

(3.12)

in which j=3.76x10^-57/cm²is a constant, r[2x10²⁸ cm (21.1 bly) from equation (3.11) when v=0, and note that v_o>>v. Using these numbers, I find that D_em>>jr_o²v which indicates that D_cm~D_em. I conclude that it is space expansion force F_e and not the internal gravitation force F_i that produces redshift at all distances. Thus, if space expands linearly, the integral in equation (3.10) is insignificant compared to the redshift due to expansion term D_ev at all distances.

If, under the theory of space expansion, Hubble's linear law is not valid at all distances, then equations (3.11) and (3.12) apply only within Hubble's linear span between 4.32 mly and 3.96 bly beyond which, under the theory of doppler motion, relativistic equation (3.1) would apply.

Do cosmic forces produce cosmic redshift? Equations (3.1) and (3.11) support the non linear and linear space expansion theories, respectively. However, neither theory results from cosmic force F_cacting on photons and producing redshift equation (3.10). Equation (3.1) is obtained from doppler theory and equation (3.11) is obtained from Hubble's observation of a linear association between redshift and distance. While the present theory supports the assumption that space expands, elsewhere, I speculate that this assumption is an apparent illusion. http://www.coolissues.com/gravitation/SpaceExpansion/spexp.htm

Space Expansion And The Big Bang

Relativistic doppler frequency equation (3.1) and speed distance equation (2.1), applicable to galactic photons, are set forth again

(3.13)

in which v_o=frequency of radiation sent by a galaxy, v=frequency of radiation received on Earth. The corresponding doppler redshift is given by the formula

(3.14)

Equations (3.13)-(3.14) reflect doppler frequency and doppler redshift as a function of velocity or indirectly as a function of distance. At small relativistic speeds, equation (3.14) reduces to Hubble's linear law zc=v=Hr (velocity proportional to distance). As long as receding mass exists, equations (3.13)-(3.14) are universal laws for receding matter valid in the Galactic and Extra Galactic Universes. Observationally, equations (3.13)-(3.14) are confirmed reliably only through about 3.96 bly, the high end of Hubble's linear law, which is but a fraction of the detectable Galactic Universe which extends to about 93.9 bly (z=12), the distance of the farthest galaxy yet detected. While the linear part of equation (3.14), Hubble's linear law, is confirmed by observation, its non-linear part has not yet been confirmed.

The linear part of doppler redshift equation (3.14) associates doppler speed with observationally confirmed Hubble's linear law. However, beyond about 3.96 bly, the high end of Hubble's linear law, equation (3.14) doppler velocities begin to diverge from linearity. Because equation (3.14) is valid for all types of relative motions, its only requirement is that the galactic motion be nonlinear at the farthest distances. Whatever equation (3.14) suggests, if non linearity beyond 3.96 bly is confirmed, it only disproves linear space expansion but leaves open the question of non linear space expansion.

The relativistic doppler redshift equation (3.14) and the linear space expansion redshift suggested by Hubble's linear law are distinct formulas. The first comes from special relativity, which does not assume the expansion of space or an explosion, and the second comes from the assumed linear cosmic expansion of space. Both are confirmed within the span of Hubble's linear law. The formula for the assumed linear cosmic expansion at all distances is

r[21.1 bly (3.15)

in which r[2x10²⁸ cm (21.1 bly) from equation (3.11) when v=0. This is a remarkable result because it says if one assumes that Hubble's linear law equation (3.15) applies at all distances beyond 3.96 bly (z=0.228), the high end of Hubble's linear law, then one must necessarily conclude that the universe is a finite one with a radius of R_c=21.1 bly.

Beyond 3.96 bly (z=0.228), for Galactic photons the linear doppler frequency association with distance must be replaced by its relativistic form, equation (3.14), in which galactic redshift is no longer a linear function but is now a non-linear function of r. Equation (3.14) says that the universe is an infinite one.

For Extra Galactic photons the linear redshift-distance association equation (3.15) remains linear beyond 3.96 bly. The frequency distance association is given by equation (3.11) in which there are two unknowns v_o and r, since v=microwave background frequency and H/c=Hubble's constant are known. The frequency distance equation (3.11) is rewritten as

r[21.1 bly (3.16)

from which I estimate the distances to and frequency of the Extra Galactic Universe. The Extra Galactic Universe stretches from 3.96 bly, the high end of Hubble's linear law, to 21.1 bly, obtained from equation (3.16) when v=0. Next, since v/v_o<<1, r at the farthest distances, and since v_o>>10¹⁵/s, the frequency of the H&K lines of Calcium, and v_o[10²¹/s, the frequency of the highest photons known in nature, namely, gamma rays, I conclude that v_o~10¹⁸-10²¹/s. I speculate, therefore, that converted radiation has a constant maximum frequency which falls in the X ray and gamma ray portions of the electromagnetic spectrum.

While equation (3.14), based on doppler redshift of receding mass, is a non linear function of distance, equation (3.15) is a linear function of distance, because it follows Hubble's linear law at all distances. Doppler redshift equation (3.14), implies a different cause for redshift (non linear space expansion or Big Bang explosion) than does linear redshift equation (3.15). Confirmation of the non linearity of galactic doppler speeds, beyond the high end of Hubble's linear law, leads to the conclusion that the universe is a non linear space expansion in an infinite eternal universe or an explosion in an existing static universe. Cosmologists say that the Big Bang explosion was not in existing space but in the expansion of created Space. ¹⁰ I discount the idea of an explosion creating space on grounds it is a metaphysical idea. It does not explain its beginning and, as bishop Berkeley said, space cannot be understood without matter. In logic, or by observation, one cannot explain an explosion that creates space and matter that did not exist previously.

Fig 3.1 grossly depicts what theories of equations (3.14) and (3.15) predict for galactic and extra galactic photons. Fig 3.1

Observationally, going from left to right in Fig 3.1, for all photons there is a linear redshift increase in Hubble's linear span, between 4.32 mly and 3.96 bly, above which there is a linear redshift increase for extra galactic photons equation (3.15) which ends at 21.1 bly and a leveling off to infinity for extra galactic photons equation (3.2), and for galactic photons equation (3.14) which extends to about 93.9 bly (z=12), the farthest distance of an observed object and, assuming galaxies still exist, beyond that to infinity. While Galactic photons produce the observed redshift, Extra Galactic photons produce the observed microwave background.

Beyond 3.96 bly, the high end of Hubble's linear law, observations are few and show no significant departures from linearity that would associate galactic redshift to their recession speed. The issue between linear or non linear expansion of the universe is a major open question of cosmology.

¹ Prabhakar Gondhalekar, The Grip of Gravity, Cambridge University Press 2001, pages 273-275

² Prabhakar Gondhalekar, above, page 270; http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation

³ See endnote 3 in Part II . For z=12 I compute v/c=0.988 and r=93.9 bly; http://www.coolissues.com/gravitation/Appendix/app2.htm

⁴ Notwithstanding atomic and nuclear explosions, there is no proof that mass can be permanently converted to radiation. While temporary annihilation is known, namely, electrons and positrons converting temporarily to photon(s) which then convert back to electrons and positrons, permanent annihilation of mass has never been seen and, therefore, is unlikely. What has been seen is permanent photon production from quantized mass along with production of other particles. In the present work, when I say mass is converted to radiation or photon energy E=mc² I mean that some quantized mass is converted to radiation or photon energy DE=Dmc² and the balance of mass changes its quantized energy state. Before and after conditions must conserve energy and momentum.

⁵ Prabhakar Gondhalekar, above, pages 273

⁶ Robert Eisberg and Robert Resnick, Quantum Physics, John Wiley & Sons 1974, pages 34-38.

⁷ Http://www.ast.leeds.ac.uk/haverah/high.shtml

⁸ Robert Eisberg and Robert Resnick, above at pages 38. Here I discount the vastly more powerful cosmic ray photons (about 1% of all cosmic rays) because of their infrequent occurrence.

⁹ Jayant Narlikar, The Structure of the Universe, Oxford University Press 1977 Chapter 4

¹⁰ Jayant Narlikar,above page 267

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By the same author http://www.coolissues.com/gravitation/sameauthor.htm