The model of an expanding universe raises many unanswered questions that can be explained via an alternate physical model, presented herein. The proposed steady state model explains redshifts of signals, Olbers’ Paradox, the "horizon problem", and why distant galaxies appear smaller while distant Type Ia supernovae are fainter than expected. Also, the nature and origin of cosmic background radiation are explained, as well as why the presently observable universe appears 13 to 15 billion years old. The proposed model posits that the distance to a glowing object can be calculated from its redshift, which can also determine the reduction in a signal’s radiation intensity in space due to attenuation and spherical expansion. The theory was applied to calculate maximum magnitudes of distant type Ia supernovae; results were in better agreement with experimental data than those predicted by the expanding universe model, without invoking the dark energy concept. The theory also concurs that the peak of the observed radiation intensity for the galactic density of our universe should occur somewhere near a wavelength of about 1 mm and estimates the level of average radiation intensity in our steady state universe.

Subject headings: steady state universe – plasma cosmology – Big Bang – redshift and distances in space – galaxies – supernovae Type Ia – dark energy – cosmic background radiation (CBR) – cosmic microwave background (CMB) 

Editorial assistance by: Alex Anderson

Revised 5/21/2010 

As we observe nature, we try to define its behavior by the laws of physics, but our theory is only as good as the model we have selected to describe it. In the model for an expanding universe (the Big Bang theory), many questions about the state of our universe were explained. However, a few puzzling questions remain unanswered, with some of these questions leading to fundamental comprehension difficulties. Even the exact nature of the initial “explosion”, which initiated the expansion of matter or space shortly after the Big Bang is subject to some difficulties of interpretation (Filippenko 1998 and Weinberg 1976).

As we explore our homogeneous, isotropic and at the same time expanding universe, it grows exceedingly complex at greater distances, and new difficulties appear in explaining the behavior of matter in the very early universe (Peebles 2002 and Perlmutter 2003.) Introduction of the “cosmological antigravity” concept (Krauss 2002) together with the “quintessence” concept (Ostriker & Steinhardt 2002), “inflation” (Guth 1997), “reionization” (Villard, et al. 2004) and other concepts being investigated (Peebles 2002), are attempts to explain some of these observational difficulties. There are “horizon”, “flatness” and other problems (Filippenko 1998). The list of puzzling aspects of the expanding universe is long (Lerner 1990, and  Lerner 2005).

In spite of these difficulties, the Big Bang theory (or as it became known: “the standard model”) is currently well established. It is based on the following three observational facts: the abundance of the lightest elements in space, the expansion of universe (redshifting of signals), and the existence of cosmic background radiation (CBR) (Filippenko 1998). However, we have seen throughout history that widely accepted theories in astronomy have not always been right. This paper presents an alternate choice for the physical model of our universe, which also satisfies these three requirements, and explains previously unanswered questions, revealing the universe to be in a dynamic steady state. This paper is a comprehensive analysis of the radically new concept for the state of our universe.

Before proceeding with the explanation of the mechanism for the redshifting of signals in space, let us take a brief look at the presence of “lightest elements” in space. There are huge amounts of electromagnetic (EM) energy produced in space and glowing bodies of matter produce the bulk of the radiation energy. For example, energy from our sun, a very tiny portion of which we feel on Earth as heat, has been radiating into space for some 4.6 billion years (Gyr). Radiation power (luminosity) of other individual stars could be many times greater. One giant star in our galaxy, LBV 1806-20, is some 150 times larger and 5 to 40 million times brighter than our sun. “Next to LBV 1806-20, the Sun would appear just as miniscule as Mercury does next to the Sun” (Chang 2004).

Any star in our galaxy or in any distant galaxy is a prolific generator of EM energy, with the greatest amount of it (for quantum-mechanical principles) produced near the visible spectrum (Wolfson 1998). This narrow frequency range of radiated EM energy is of special interest to us, because it is the one that is responsible for the microwave radiation we observe on Earth. The peak intensity of most starlight spectra occurs at a wavelength slightly smaller than 0.0001 cm and is a function of the surface temperature of the star.

In addition to the observable radiation, billions of stars in billions of galaxies are filling space primarily with a huge number of protons and electrons, the two basic ingredients of the    

hydrogen atom (the most abundant element in the universe). In this mix, there are also a lesser number of particles and ions with heavier mass. The ejected particles are propelled through space in all directions from their source of origin at extremely high velocities, allowing them to escape into intergalactic space. Auroras confirm their existence in our solar system. With the help of the ionization process, taking place in space, all of these ejected charged and electrically neutral particles ultimately add to an existing very low-density plasma field of some finite particle density (a function of our galactic density) in a dynamic equilibrium in space.

The amount of mass ejected by a single star, when multiplied by the number of stars in one galaxy and then by the number of galaxies in some unit volume of space over billions of years, would represent a significant amount of mass being recycled in space just by glowing stars, particularly if the 15 Gyr time interval for the age of our universe was allowed to be extended. With solar eruptions and other emissions of particles from binary stars, pulsars, quasars, many nova and occasional supernova explosions, our universe is continuously being re-supplied with primarily the lightest elements of mass (but also gold and uranium). All of these processes are maintaining an “abundance of the lightest elements” of matter in space over billions of years.

It is believed that elements heavier than iron, but also lighter elements, are created during a supernova explosion (Moore 2002). The issue of lightest elements in space was extensively examined by Lerner (2008). In any case, no matter what the mechanism for the creation of space charge might be, low density plasma field does exist in the extremely cold intergalactic space (Thompson 1962). It is not the result of an event that just happened spontaneously some15 Gyr ago.

2.2 Proposal for a dynamic universe in steady state

The apparent brightness of a star, the luminosity of a galaxy, the maximum magnitude of a supernova (SN), the redshift value of signals from a glowing object in space, and the shape of the cosmic background radiation (CBR) curve are all real and exact facts. All of these entities that we can observe and measure on Earth are independent of the physical model we have chosen to represent our universe. But the choice of the model we have selected to describe our universe is based on the scientific perception of our mind. What we actually end up representing out there in space will depend very much on the correct choice of our model, which must ultimately be capable of explaining all “established experimental results” (A&A Journal).

It is natural that all of the assembled matter in space would be in a dynamic state, subject to initial conditions. The theory of relativity dictates that. But there are many small, volumes of space containing matter in a dynamic state, as part of a larger universe of an indeterminate size subject to the same conditions. Matter in any of these smaller areas of space anywhere in the universe may not stay put in one place over time, but would have to either expand or contract or even oscillate independently - and it does. Matter in these adjoining areas of space could interact and exchange matter with their neighboring volumes of space and even beyond, over a period of billions of years, since their boundaries are not uniquely defined. All of these events would take place in various, individual sections of our steady state universe, but within the restrictions imposed on each one of them by the general theory of relativity. However, our universe as a whole could be in a dynamic steady state.

Albert Einstein originally introduced a cosmological constant into his general relativity equations to “preserve a picture of a stable universe.” After learning that the universe appeared to be expanding, he discarded this constant, referring to it as “the biggest blunder” (Perlmutter 2003). Recently another constant was reintroduced into the general relativity equations to account for the mysterious dark energy in space. It appears as if general relativity equations would require a constant when the steady state universe is viewed on a macroscopic scale, however no constant would be needed for a microscopic view of space. This could not be the case.

The steady state universe is inherently unstable throughout all of space. The instability of matter in space is clearly visible in the near field of our universe on the microscopic scale. However, the bigger picture, which would have shown the instability in the larger space of the far field of the universe, is obscured by various thermonuclear processes. These processes continuously regulate the build up of total mass in all areas of the universe, and including in areas of space with excessive accumulations of mass. Redistribution of mass from these areas of space occurs automatically as soon as these accumulations of matter manifest themselves and long before they become uncontrollable.

This is a natural, self-regulating mass conversion process, which provides stability to all matter throughout all of space. Such a dynamic steady state universe could exist and at the same time be homogeneous and isotropic on a macroscopic scale. In this model of the steady state universe there is no preferential point in space into which all of the matter in the universe could ultimately collapse.

Because of the unopposed, mutual gravitational attraction between bodies in space, there is an inherent tendency for the matter in space to converge and to clump together. In most cases, these individual groupings of objects are widely separated from each other by space that is essentially devoid of all visible matter. One would expect all the attracted matter (visible and dark) in any galaxy or in any other of these clusters of galaxies to continue this merging process into some smaller volume of space with no quick end to this motion in sight. It seems that this converging matter in space, once subjected to a mutual gravitational attraction, is destined eventually to combine into one, or one of several individual black holes that are usually found close to the center of some of these areas of converging mass. It is a reasonable assumption based on the observed behavior of matter in these areas of space.

However, it appears that the bulk of all the mass of assembled glowing bodies anywhere in space is being recycled over time, while in the process of trying to merge into one single entity. This continuous mass conversion process is independent of any observed violent activity, which might be taking place in isolated areas of space, including black holes. Nearly all bodies of matter in various areas of space appear to have been assembled naturally, as if by “purely a material process of self organization”, a terminology used by Stenger(1992) to describe a similar event in nature.

These bodies in space were assembled near each other by gravity and set into some form of orderly, rotational motion around some fuzzy, common centers of gravity (centers of mass), such that they are all in a state of a complete dynamic equilibrium relative to each other. In each case, because of the acquired angular momentum, individual bodies of matter are free to move laterally, but they are restrained in their radial motion towards the center of their rotational system. Gravitational forces keep each system together in a dynamic equilibrium.

Observe the behavior of stars in the case of a simulated collision of two colliding galaxies forming one single, larger galaxy. Suspension of stars in spiral and even elliptical galaxies would be good examples of entrapment of mass in very close proximity to each other essentially in a timeless fashion. This behavior of matter in space greatly contributes to a state of relative tranquility of all the accumulated celestial bodies in various areas, even in areas of excessive accumulations of matter. Even the Pinwheel Galaxy, an unusual-looking structure in space, is a stable rotational star system. An example of suspension of bodies of dark matter close to each other would be the motion of our planets and the incessant revolutions of our moon for some 4.6 Gyr. 

All stars in various bodies of matter in space are individually in a dynamic equilibrium. During all this time they continue to convert a significant amount of their mass to smaller particles of mass and radiation energy, propelling them from a point source to faraway places, until the very end of their glowing lives. Originally, each star was assembled by gravity over a very long period of time by accumulation of small particles of matter, only to be disassembled by the thermonuclear processes in the same fashion.

There are many other more violent thermonuclear mass conversion processes in place for stars, leading ultimately to the same result -- a complete destruction of the star. For example, a type Ia supernova (SN Ia) is a thermonuclear explosion of a white dwarf star 1.4 times the mass of our Sun (Riess2003). In this explosion, probably all of the contents of the dwarf are ejected at velocities of some 10,000 km/sec into the deep space far beyond the area of gravitational influence of its parent galaxy, with no residue left behind. Thus, in one flash of light, a galaxy loses an entire medium-size star from its gravitational control, and continues to do so at a rate of about two or three times every millenium (Perlmutter 2003) for billions of years.

With other types of supernovae, novae and planetary nebulae, that “cast off their outer layers of material into space” (Hubble Site 2007) would be examples of instantaneous removal of large amounts of mass from stars in our universe. As new matter from other, similar events in space is accumulated in each dynamic system, feeding existing stars or forming new ones, all of the arriving mass is ultimately reconverted, thereby maintaining uniform mass density anywhere in space and thus preventing all matter from merging or simply collapsing into one.

Direct collisions of stars in our universe would most likely be similar in intensity as “mini” novae explosions, but probably are occurring only rarely, simply because we are dealing here with relatively small bodies of mass in motion and such inordinately large areas of space. If such a collision between two glowing stars were to occur, it might look like the photograph of the “Butterfly” nebula (Harrington et al. 2009). Even colliding galaxies with hundreds of billions of stars appear to produce no actual collisions. Supernovae, typically not very homogeneous and isotropic “Mini Bangs” from a point source (mini versions of the Big Bang) are not caused by direct collisions of stars.

Only in the galactic centers where planes of rotation of stars typically become less organized, and where older stars and remnants of their burned out cousins slowly converge and approach each other with time, a violent activity between stars is beginning to escalate. As individual stars approach the virtual center of a galaxy populated with many other stars and not a single large body of matter, their angular velocity slows down because of the constantly decreasing total number of stars near the center. It is not like the motion of planets in our solar system. 

Depending on the relative density of the remaining number of stars near the center of the galaxy, the speed of rotation of the whole system is maintained at about the same rate. The Pinwheel Galaxy would be a good example describing this behavior, where the speed of rotation throughout the galaxy appears to be essentially the same. The increasing density of stars due to the reduction of their angular velocity near the core of a galaxy brings individual stars in closer proximity. Thus, in various areas of the galactic center, two or more stars will find themselves close enough to begin interacting with each other (like binary stars), with even more stars joining them later (as in a triple star system.)

This process escalates and continues until the number of interacting stars is individually reduced, probably initiated by accretion of matter from a glowing companion star, a process similar to the type Ia supernova but without ever reaching conditions suitable for a supernova type explosion. Over the years, new stars would be joining these groups of stars as part of a complex and very violent process with no end in sight. Observe the photograph of the central region of our galaxy showing a very active core (Weaver et al. 2009).

No matter how complex or strange individual mass conversion processes might appear, one way or the other all of the accumulated matter is slowly converted to smaller particles and radiation, and is ultimately ejected from the core of the galaxy. But new matter is continuously streaming into the same area of space. It does not matter that a good portion of the ejected mass might never escape the gravitational pull of the parent galaxy. This process continues for the life of the galaxy, extending over billions of years, independent of the life span of individual stars.

Note that in the process of converting matter to smaller particles and radiation, only a relatively small amount of recycled mass would be needed at any one time to maintain the process of gradual redistribution of mass throughout all space. The much larger amount of residual mass is left behind, but in a state of enhanced balance in the same general area of space, as this process continues with no end in sight. And the larger the accumulation of unbalanced mass in any one area of space, the greater would be the resulting mass conversion process to restore a dynamic balance of matter, extending over billions of years. But eventually all matter in all areas of the universe will be recycled.

This is a very slow but efficient mechanism of keeping the inherent large-scale instability of mass in our steady state universe under perpetual control, maintaining all matter in the whole universe in a dynamic equilibrium. And all it takes, is time, which in this case is a readily available commodity. This mass conversion process in space is another marvel of nature.

A large amount of radiation is produced near the center of our galaxy. The bulk of this radiation is in the visible frequency spectrum, however emission of X-rays and radio frequency energy in these same areas was also observed. The Chandra X-ray observatory detects almost daily flair-ups of X-rays in the center of our galaxy, indicating some occasional, very violent behavior of matter. Because of this behavior of stars, galactic centers would also serve as generators of copious amounts of small particles of mass. The above described mass conversion processes serve as an "eternal source of material for new stars and galaxies" and become a "provision for the disposal of the debris" (Peebles 1993). These processes are thereby satisfying the more difficult requirement for the existence of a steady state universe, that of “continuous creation and disposal” of matter in space.

Thus, on one hand, gravitational force assembles individual particles of mass consisting of gas, dust and other dark matter from the far reaches of space to form new stars and feeding existing ones. It also forms galaxies and clusters of galaxies. The same force constantly controls the motion of each individual star in our universe until the very end of the star’s existence. It may take billions of years to accomplish some of these events. On the other hand, complex thermonuclear processes deep inside of each star keep them active until all the nuclear fuel is exhausted. Radiation from the surface of our sun provides us with light and thus sustains life on Earth. However, the same thermonuclear processes are responsible for the loss of mass from individual stars as soon as they begin to glow.

The process of systematic “disposal of the debris” continues throughout the long lifespan of each individual star, culminating in some spectacular fashion. There is probably no better example of the removal of the “debris” from the areas of excessive accumulation of matter than the one provided by the SN Ia explosion. During the life of a star, from the very beginning to the very end, the loss of mass is always violent and at or near relativistic velocities, to allow matter to escape gravitational influence of the star and probably to a large extent of the parent galaxy. It typically takes a very long time to complete the destruction of each individual star. The recycling of mass serves as a limiting factor on the accumulation of matter in any one galaxy or in any one area in space, thus maintaining the average mass density in space at a constant level.

Finally, it is said that the Newtonian gravitational force of an infinite number of stars in an infinite universe would be so great that it would tear our solar system apart. The fact is, however, that the same gravitational force of billions upon billions of galaxies in our presently observable “enormous” universe (Filippenko 1998) already 30 billion light years (Glyr) in diameter 15 Gyr ago and still rapidly expanding in size, has failed to strip our solar system of any of its simple gravitational attachments like planets, moons, asteroids, or even distant comets. Our Sun appears to be in full control of its satellites with no obvious, observable gravitational deviations over a period of about 4.6 Gyr.

We know that under certain controlled conditions EM fields can parametrically increase or decrease the velocity of charged particles, thereby allowing a bi-directional exchange of energy levels between the two interacting media. These exchanges of energy are well known and have bee extensively utilized. Amplitude attenuation of signals in propagating waves certainly takes place in space, but it is not universally recognized. The process of frequency perturbation in EM waves with time or distance is not as obvious, but it also does take place in signals as they are propagating through an imperfect vacuum of space containing a large quantity of randomly scattered and widely separated charged particles. A continuous frequency perturbation ultimately leads to gradual frequency reduction, representing additional loss of energy in the propagating wave, along with attenuation due to scattering of the signal. Long periods of interaction time between the two media would be required to produce observable results.

There are no laws of physics stating conservation of frequency in space, only energy. Thus, under certain conditions, the frequency of any propagating EM wave could "slow down" gradually, but continuously, as the signal travels through an imperfect vacuum of space for billions of years. The frequency of a radiated EM wave is not crystal-controlled, and when there is a change in frequency, it is only natural that there must be a frequency reduction, representing a loss of energy.

When a propagating signal encounters a charged particle, it recognizes the particle as a discontinuity or an obstacle to its uniform motion in space. The particle causes a momentary perturbation in the EM field of the wave. Although most of the energy in the signal is transmitted through the area where the charged particle is located, a minute portion of the wave is reflected or scattered in all directions (primarily at the signal’s frequency) as EM noise. The size of the point charge encountered by the EM wave is minute compared to the signal's wavelength. It offers no preferred direction to the wave because it is spherically symmetric. Therefore, it has an identical three-dimensional effect on all the signals of any frequency incident on the point charge, regardless of the direction of propagation of the wave and the orientation or polarization of its electric field.

Physical interpretation of the collision process can be stated as follows: the oscillating electric field of the wave momentarily subjects the charged particle to an alternating force attempting to move the particle by accelerating it along the lines of its electric field. This field is perpendicular to the direction of propagation of the wave. The amplitude of the force is proportional to the signal’s electric field and to the number of charges on the particle of mass. This force is extremely small and it exists for an infinitesimally minute, but finite interval of time. Because the force on the charged particle changes its direction with each half cycle of the signal's electric field, the particle's position or its motion in space is basically not affected.

By applying a minute force to the particle, the wave is performing work, and it is expending a small amount of its energy in the process. In turn, the particle exerts an equal and opposite force on the alternating electric field. This force produces a loading effect on the electric field of the wave as it momentarily deforms the wave front, causing the phase of the wave to slip ever-so-slightly in the vicinity of the charged particle. Changes in phase, in turn produce a small, initially-local stretching or lengthening of the interval of each half cycle of the wave, resulting in a minute delay or retardation in the signal’s wavefront at the point of discontinuity. The small delay in propagation time of the wavefront near the singularity point will ultimately cause local frequency retardation.

At first, the bulk of the energy in the signal’s wavefront around the collision point is transmitted without being affected. But after transitioning the singularity point, the phase of the wavefront with an initially small local distortion near the collision point will begin to expand in an attempt to re-adjust itself to one common value, thereby ultimately decreasing the original frequency of the whole wavefront by a minute amount. Any changes in each individual wavefront are independent of the essentially identical changes taking place in the preceding and following wavefronts of the same signal.

These changes in individual wave fronts occur independent of the frequency periodicity between the wave fronts, which continuously readjust themselves to the reduced frequency of the signal’s wavefronts, producing infinitesimally small frequency reductions throughout the whole propagating signal. These frequency reductions are merely a result of minute but continuously occurring perturbations in the wavefronts experienced by the essentially uniform EM waves of the signal propagating through the imperfect vacuum of space. Long periods of time would be required to observe these changes in the signal.

As Filippenko (1998) pointed out, “photons easily scatter off of free electrons.” The collision of the signal with each charged particle is a complex process involving higher-order space harmonics of the fundamental frequency of the signal to satisfy boundary conditions at the area of discontinuity caused by the point-charge singularity. The charged particle has a catalytic effect on the energy transfer from the propagating to the scattered wave of any frequency, and this process continues for as long as the charged particle is present, affecting all signals of all frequencies simultaneously. This is a microscopic view of the interaction process between an EM wave and a single point-charge in space.

The action of one single charged particle on the propagating wave is identical to the interaction process that causes a signal to experience a propagation delay (and attenuation) in a homogenous low-density plasma field (Goldston et Rutherford 1995). In this particular case, the wavefront, colliding with a uniformly distributed space charge field, remains essentially intact over the lateral surface of the wavefront causing an uniform reflection of the signal with time.

In our case of randomly scattered and widely separated charges, granular distribution of particles causes a significant lateral non-uniformity in the wave front at the point of collision. One single isolated distortion created in the wavefront, when added to many other similar distortions in the same wave front at other locations with time, ultimately leads to frequency reduction in the signal with time or distance.

If we were to tag along a particular signal's wave front, traveling through this unusual space charge field with randomly distributed and widely separated point charges, we would observe interactions taking place over the wave front similar in appearance to the ones created by a very light rain continuously falling on the placid surface of a pond. Perturbations created by individual charges in the wave front would expand laterally over the front's surface with time and ultimately with slightly variable frequency components along the way. These minute, lateral variations in the wave front would average out or blend in with other similar disturbances produced in the same wave front at other locations with time.

With time, after each collision, the uniformity of the signal’s wavefront with infinitesimally small frequency and amplitude changes will attempt to re-establish itself without distortion, like a body of water returning to its placid state. The uniformity of the wavefront is a requirement of EM theory, for a uniform propagation of a signal in space without any obstruction in its path. But with time each wavefront will continue to collide with other particles in its path as this process continues. Except for these periodic, minute energy reductions in the wavefront, there would be no loss of information carried by each individual signal.

Propagation delay in signals through areas of high local concentrations of space charge, like those near the surface of a star or in the proximity to a galaxy or cluster of galaxies would produce some focusing of the signal. The change in the direction of propagation of the signal’s wave front in this environment would be similar to the focusing effect produced by a gravitational lens.

An alternate view of the collision process could be stated as follows: We know that a propagating signal can behave like a wave, but it can also exhibit particle-like behavior (duality principle). The quantum interpretation of light states “If you don’t detect it, light behaves like a wave and exhibits interference effects.” … “light behaves as a particle, delivering its energy in discrete particle-like bundles” … “waves and particles are related, but only statistically” (Wolfson 1998). A collision of an electron with a signal cannot always be classified as an interference and we would expect some particle-like transfer of energy to take place during each collision.

In 1923, Arthur Compton demonstrated that a propagating wave in a collision with an electron not only transfers energy to the particle by reducing its frequency, but that at very high frequencies each individual transfer of energy could be in quantized amounts of energy sufficiently large to be observable in a laboratory environment (Wolfson 1998). One would typically expect that during each individual collision of a signal with a charged particle, particularly at higher levels of frequency and signal intensity, a few photons would be ejected from the wave and scattered, ultimately causing a reduction in the signal’s amplitude. But, as a result of the collision, a small number of photons from the collision area would continue their motion through space as parts of the original wavefront with slightly reduced frequency components.

Subsequent collisions of this particular wavefront with other charged particles at other locations with time would increase the number of photons with slightly reduced frequency components in the wavefront. These few photons will merge later with the signal’s wavefront, ultimately causing a slight frequency reduction in the wavefront, as previously stated.

In the case of weak signals (which are of interest to us), the removal of energy from the wave is also in minute, measured, frequency-dependent increments per each half cycle of the wave. The increments of energy removed from the wave would probably be confined to wave and particle interaction, which would require very long periods of time to produce observable results. This parametric process of frequency decay with distance is sometimes referred to as “tired light.” Observations of distant signals typically occur at very low signal levels. For example, the Hubble Ultra Deep Field (HUDF) photograph was obtained by recording signals from distant objects at a rate of one photon per minute by the Hubble telescope (Wilson 2004).

We have stated that our universe is filled with many randomly distributed and widely separated (compared to wavelength) point charges. These charges present a local, three-dimensional non-uniformity to all propagating wavefronts simultaneously. Each individual point charge momentarily (but continuously) disrupts the local uniformity of each individual front. A gradual perterbation of frequency in these wave fronts over a very long interval of time ultimately causes a significant frequency reduction and attenuation in the propagating signal. It also introduces additional propagation delay in all signals.

Thus, when there is a change in any signal’s frequency taking place in our homogeneous and isotropic universe, it is logical that it would be as a simple exponential decay and the rate of change of frequency with time or distance has to be proportional to its frequency. The equation for frequency variation in space of our universe is then given by:

f / fo = e ^ ( - d / D ) = lo / l = 1 / ( z + 1 ) , (1)

where f / fo is the frequency reduction factor which stands for the ratio of the observed frequency of the signal to its original value. It is the inverse of the ratio of the two wavelengths, ( lo / l). Its relationship to the redshift “z” (by definition) is shown above. In the exponential equation,“d” denotes the distance to any glowing object in space and "D" is a distance parameter inversely proportional to the equilibrium space charge density of our universe. At small values of z, D is given by the ratio of the distance to a glowing object to its redshift. The numeric value of D could be obtained from any reliable redshift and position information of any glowing object in space, which is located somewhat close to Earth.

A collection of data showing variation of redshift with distance for an expanding universe with the Hubble constant value of 70 km/s/Mpc was made by Powell (2002). From these data, for objects up to a distance of roughly 0.8 Glyr (or a redshift of about 0.06), the value of our constant D remains essentially the same and comes out to be about 13.96 Glyr. In terms of redshift (z), the distance to any glowing object, for all values of redshift, is then given by:

d = 13.96 ln ( z + 1 ) = 13.96 ln ( l / l o ) in Glyr. (2)

Equation 1 shows that during each interval of 32.144 Glyr the wavelength of ANY propagating EM wave in our universe increases by one order of magnitude over its previous value. To demonstrate our point, let us assume that all radiation from any star in our universe is monochromatic and all of it is produced at a wavelength of 0.000053 cm (the wavelength of our Sun’s peak radiation intensity). It is a good estimate of wavelength for the bulk of radiation produced by our Sun. A signal with an initial wavelength of 0.000053 cm would first increase its wavelength to 0.00053 cm after travelling 32.144 Glyr. The wavelength would then increase to 0.0053 cm and after a "mere" 128.6 Glyr (Eq. 2) the wavelength of the original signal in the visible spectrum would increase to 0.53 cm and fall into the high band of microwave frequencies. Thus the mechanism of frequency reduction in signals of our universe becomes evident.

The microwave radiation we measure on Earth is due to frequency decay of signals originating near the visible frequency spectrum, produced by billions of stars in billions of galaxies in the vast spaces of our universe, which is in steady state. In this instance, redshifting of signals is NOT frequency reduction produced by the recession of glowing bodies from the observer. That is, it is not caused by the differential in their relative positions produced by an expansion of matter or space.

The distance to any glowing object in space of our steady state universe, given by Equation 2, is valid for all values of z. Unlike relativistic velocity constraints in an expanding universe, the steady state model of the universe has no restriction on distance. As previously stated, Equation 2 shows that at small values of z, the distance to a glowing object in space is directly proportional to its redshift, with 13.96 Glyr being the proportionality constant. At small values of redshift, this constant should be equivalent to the product of the velocity of light and the Hubble time constant in an expanding universe (Filippenko 1998).

An attempt to check the value for the Hubble constant, based on “observational data” used to determine our constant “D” resulted in an essentially identical value for the constant. This finding implies that even at very small values of redshift, the Hubble constant was probably used by Powell(2002) to obtain distance information. Therefore the value of our constant “D” could have been obtained directly from the Hubble time constant.

The recession velocity of a glowing object in space, in an expanding universe, is proportional to its distance and redshift (constant expansion), but only for smaller values of redshift (Filippenko 1998). At larger values of redshift, the velocity of the object is related to its redshift by the relativistic formula (Silk 1989). The distance to the object is then equal to the product of its recession velocity and the Hubble time constant (Filippenko 1998).

Radial separation between objects in space in a steady state universe can easily be obtained from Equation 2. For example, a galaxy with a redshift of 5.34 would be 25.78 Glyr from Earth. Its line-of-sight separation from its potential neighboring galaxy with a redshift of 5.340534 would be 1.2 Mlyr.

The wavelength of any signal of interest to us is much greater than the diameter of a point charge. Even near the visible frequency spectrum the wavelength of the signal is billions of times larger than the diameter of the point charge. However, each point charge controls a significantly larger area of the signal’s electric field in its vicinity than merely its physical size. We can refer to this coupling area near the point charge as the “effective coupling cross-section” for the signal’s electric field, with this coupling being relatively more effective at shorter wavelengths.

The strength of any propagating signal is defined by its amplitude, which is directly proportional to the signal’s electric field of any frequency, anywhere in space. With the signal frequency’s exponential variation with time or distance, the rate of change of the signal’s amplitude due to scattering with time or distance in a homogeneous and isotropic universe containing plasma, as well as the signal’s amplitude itself, would have to have an exponential dependence with time or distance. Indeed, both of these amplitude variables must vary proportionately with frequency (Eq. 1). These are all products of the same signal scattering process taking place in the imperfect vacuum of space.

Since the amplitude of the signal varies proportionally with its frequency, the square of the signal's amplitude, defined here as the signal's "amplitude intensity" (AI), must also vary proportionally with the square of its frequency. This statement implies that for each interval of distance of 32.144 Glyr, or for every order of magnitude of frequency reduction, scattering of the signal causes the AI of the propagating wave to decrease by two orders of magnitude. For signals far away from their source of origin (with decreasing effect of spherical expansion), a continuous scattering of a small amount of energy in the wave becomes the major mechanism for the reduction in their AI. It would be independent of and in addition to the reduction in the signal’s intensity due to spherical expansion

In defining a signal’s AI, which is proportional to the observed signal’s radiation intensity (the amount of light) of any frequency at any one single point in space, we have not taken into account the second mechanism for the loss of signal intensity. This additional loss, also caused by scattering of the signal, is due to frequency reduction in the signal from its actual original value in space.

We have shown that attenuation decreases the amplitude intensity of a signal (AI) from any glowing object in space as the square of its frequency. That is, the signal intensity from any galaxy or a type Ia supernova (SN Ia) or any other glowing object in a steady state universe decreases proportionately as the square of ( z + 1 ). This reduction in the signal intensity is independent of and in addition to the reduction in magnitude of the signal produced by spherical expansion.

Application of this concept to observational data leads to interesting results. For example, a few SNe Ia were observed at a redshift of 0.4. Equation 2 places them about 4.7 Glyr from Earth. When we consider only the effect of amplitude attenuation, which provides us with the largest error correction, then the observed “relative intensity of light” for these SNe Ia should be about one half of their expected value. This adjustment in the maximum magnitude of the observed SNe Ia appears to agree with published observational data (Hogan et al. 2002).

This argument could explain why “High-Z type SNe Ia are fainter than expected” (Filippenko 1998), which is currently attributed to an accelerated expansion of our universe. It is said that with a non-zero cosmological constant, “dark energy adds gravity that is repulsive and can drive the universe apart at ever increasing speeds” (Hogan et al. 2002). It was originally thought that we were a part of a “flat” universe with no cosmological constant and that the universe would ultimately experience a rapid deceleration.

Because of their ideal properties, SNe Ia have been used as standard candles since the early 1980’s. They all have the same intrinsic brightness (Perlmutter 2003). Observational data reported by Perlmutter et al. (1998) show individual deviations in the effective or the observed magnitude of the High-Z SNe Ia in logarithmic values of magnitude from the “ideal magnitude” (IM), which we can define here as:

IM = 24.2 + 5 log (z) . (3)

Figure 2 Ideal and the observed CBR curves. The observed CBR curve shown here is based on the CBR curve by P.J.E. Peebles (1993).

Up to this point we have dealt only with the energy loss in the propagating wave due to the reduction in the signal's intensity caused by the amplitude attenuation of the wave. At higher values of redshift, however, the energy loss in the transmitted wave due to frequency reduction from its original value is substantial and must be taken into account. It is a similar issue as the K-correction used for maximum magnitude adjustment when observing distant SNe Ia in an expanding universe (Perlmutter 2003).

With the amplitude and frequency of all signals varying exponentially in space with time or distance, the frequency dependent component of each signal’s intensity would also be reduced proportionately with frequency and must have the same exponential relationship as its amplitude and its frequency. That is, for each order of magnitude reduction in the signal's frequency, the transmitted wave incurs an additional order of magnitude loss in its radiation intensity due to frequency reduction, proportional to the energy loss experienced by one photon of its frequency. This definition of energy loss in the signal radiation intensity due to frequency reduction from its original value, together with spherical expansion, definitions of distance (Eq. 2) and “amplitude intensity” (AI) provide a complete description of the behavior of signals in a steady state universe.

Putting aside the effect of spherical expansion, if we were to combine energy losses due to amplitude attenuation and frequency reduction incurred in space by a propagating wave, then for each order of magnitude reduction in the observed frequency (or 32.144 Glyr of distance), our signal’s “radiation intensity” (defined here as RI), previously consisting only of the “amplitude intensity” (AI), due to amplitude attenuation of the signal, will be reduced by an additional order of magnitude for all values of frequency. With this three order of magnitude reduction in the signal’s intensity due to scattering, the RI of any signal from any area of our universe would be reduced by a total of three orders of magnitude and would vary similarly to the left side of the observed cosmic background radiation (CBR) curve in Figure 2. This three order of magnitude variation in the RI with frequency can easily be seen for signals originating in the far field of space, observed on Earth at wavelengths greater than one cm. Thus, two orders of magnitude reduction in RI are due to amplitude attenuation of the signal and one order of magnitude is due to frequency reduction over and above the reduction in radiation intensity due to spherical expansion.

At long wavelengths, with decreasing effectiveness of AM on radiation intensity (Fig. 1), the reduction in the RI with increasing wavelength is controlled entirely by amplitude attenuation and frequency reduction due to interaction of the signal with space charge. Note that we handled the loss of the signal's energy due to amplitude attenuation completely independently from the energy loss in the signal due to frequency reduction. But these two energy loss mechanisms, which are caused by continuous scattering of a small portion of the propagating wave in an IMPERFECT vacuum of space, are intimately connected. They are interdependent.

Individual values of RI from signals of the same original frequency, when observed at any one given frequency, may have originated in different areas of our universe that are equidistant from Earth. By the same token, the lower the observed signal’s frequency, the farther in space would be its source of origin if both signals were of the same original frequency. In general, the bulk of the radiation energy received on Earth is from various glowing bodies in space that emit energy near the visible frequency spectrum. The distance to their location would be given by Equation 2. However, sources of infrared and ultraviolet radiation, contributing to radiation measurement at the same frequency on Earth, would be located closer to or farther away, respectively.

If we were to measure RI of signals from a small group of radiation sources originating in the far field of our universe (as observed on Earth at any one single frequency), then the total RI of this energy group would have a definite value, corresponding uniquely to that frequency. It also means that if we were to measure radiation energy from another similar group of signals in our view but originating farther in space, and reaching Earth at one order of magnitude lower frequency, then the RI of these signals at the reduced frequency would be only one tenth of one percent of the value recorded earlier at the higher frequency.

Specifically, if we were to measure RIs on Earth from similar groups of signals at wavelengths of 0.1, 1, 10 and 100 cm (corresponding to radiation energy originating 105, 137, 170 and 202 Glyr in space at a wavelength of 0.000053 cm), the shape of the curve connecting these points would look similar to the left side of the observed CBR curve in Figure 2.

As the signal's frequency and its radiated energy density change slowly with time or distance in space, all signals (including high frequency signals) are slowly attenuated and redshifted at the same time and no visible light emanating from the far away galaxies would ever reach Earth at observable levels. Depending on the galaxy's position in our homogeneous and isotropic universe, almost all of its radiated energy received here would be redshifted toward infrared, microwave, and ultimately, radio frequency, with an attenuated amplitude. Herein lies the explanation for Olbers’ Paradox.

Also, since the change in the signal's amplitude is proportional to its frequency, lower frequency radio signals should appear as if they are more prevalent at larger distances, biut from the same areas of space (Filippenko 1998), as compared to radiation produced in the visible frequency spectrum.

We derived several magnitudes for SNe Ia defining their behavior in space based only on the variation of the amplitude intensity (AI) due to amplitude attenuation of the signal from any point in space of a steady state universe. However, the effect of frequency reduction on the loss in radiation intensity (RI) of transmitted signals at higher values of redshift becomes significant and must be considered, prompting us to modify some of our previous results.

We stated that the variation in RI of signals in space, due only to the reduction in the signal’s frequency from its original value with time or distance, was proportional to its frequency. That is, it is inversely proportional to ( z + 1 ) (Eq. 1). Its logarithmic value is given by the product of five times the log of the square root of (z + 1). For example, a SN Ia with a redshift of 1.5 will incur an additional loss in its magnitude equal to 0.995 due to the signal’s frequency reduction from its original value. This redshift related frequency reduction issue is similar to the K-correction used for the adjustment of maximum magnitudes of SNe Ia in an expanding universe Perlmutter 2003.)

If we introduce this additional energy loss in the signal intensity due to frequency reduction into our equations, the logarithmic magnitude correction MCAI in Equation 4 becomes:

MC = 7.5 log ( z + 1 ) = 7.5 log ( l / l o ). (7)

In Equation 7, MC takes into account all RI losses caused by scattering of a small amount of energy in propagating signals; that is, losses due to amplitude attenuation of the signal and losses due to the signal’s frequency reduction with time or distance in a steady state universe. Equation 7 is valid for all values of redshift. At larger values of redshift, MC is attenuating as the inverse cube of its redshift, or a 7.5 reduction in magnitude for each order of magnitude change in redshift or wavelength.

Likewise, when we take into account both RI changes in signals due to amplitude attenuation and frequency reduction, the variation in the maximum magnitude (MM) for a SN Ia in a steady state universe becomes: 

MM = 24.2 + 5 log {[ ( z + 1 ) ^ 1.5 ] ln ( z + 1 )} = 18.48 + 5 log {[ ( l / l o ) ^ 1.5] d }. (8)

The MM in Figure 1 always has a higher attenuation value than MMAI, following the IM curve from z = 0 to a z of about 0.2. However, at higher values of redshift, MM attenuates in space as the inverse cube of its redshift. Both of these variables are radiation intensities, except that MM takes radiation intensity reduction in the signal due to frequency reduction from its original value into account, while MMAI does not. The total attenuation of RI in the far field of our universe is controlled primarily by amplitude attenuation and frequency reduction of signals as embodied in the MC curve (Eq. 7). Spherical expansion plays only a minor role.

If we were to measure the apparent maximum magnitude of SN Ia in space, without correction of the observed value for frequency reduction from its original value, we should compare experimental data to the logarithmic magnitude MM in Figure 1. This would give us the greatest attenuation a SN Ia can have at this value of redshift in a steady state universe. However, if we were to measure the maximum magnitude of a distant SN Ia while correcting its RI for the signal’s frequency reduction in space from its original value, the maximum magnitude should be compared to the value given by MMAI in Figure 1. These two curves in Figure 1 define a range of maximum magnitude of SNe Ia from the least attenuation value (given by MMAI) to the highest possible observable attenuation value (given by MM) that could be obtained in a steady state universe at a given value of redshift. The two curves depend only on how the effect of frequency correction in the measurement of the RI value of a type SN Ia was implemented.

The MM curve in Figure 1 appears to be an extension of the curve reported by Perlmutter et al. (1998) for WM = 0 and  WL = 1 (dark energy equal to one) in a flat, expanding universe. Note that in an imperfect vacuum of space with low density plasma (and no dust) the MM curve represents the absolute maximum attenuation a SN Ia can have for a given value of redshift. In theory, this value cannot be exceeded.

In our discussion we have assumed the Hubble constant to have a vlue of 70 km/s/Mpc (Powell 2002). A smaller value of the Hubble constant, for example, of 65 km/s/Mpc as suggested by Filippenko (1998) would not affect the graphical results shown in Figures 1 and 2, because all the derived magnitude variables are functions of the redshift only. The actual magnitude of the Hubble constant appears only in the definition of distance in Equation 2. A smaller Hubble constant affects only the physical distribution of matter in space, resulting in a universe, which is more conpact. The relative distances to objects in space are directly proportional to the Hubble time constant.

3.5 Comparison of theory with observed results obtained on type Ia supernovae

Calculated values of MMAI (Eq. 6) and MM (Eq. 8) at redshifts of 0.4, 0.5, 0.6 and 0.83 are in agreement with observational data reported by Perlmutter et al. (1998). In fact, the location of the bulk of SNe Ia reported by the Supernova Cosmology Project (Perlmutter, et al. 1998) appears to be centered along the MMAI curve, with a few High-Z SNe Ia approaching the MM curve. These results appear to explain the “unusual” behavior of signals from high redshifted glowing objects in space, claimed to be due to an accelerated rate of expansion of matter without the help of dark energy, which is said to “pervade all of the empty space” of our universe.

The agreement between theory and experimental results extends to other SNe Ia with higher values of redshift. New data on distant SNe Ia was reported by Riess, et al. (2006). These data were obtained with the rmhomrrt Hubble telescope. The results provide many detailed measurements made on SNe Ia at redshifts extending all the way to z = 1.551 (SN2003ak). Revealing photographs of five of these SNe Ia and of their host galaxies were shown on the internet (Hupp/Brown et al. 2006). Over 12 SNe Ia had redshifts greater than 1.2. 

The maximum magnitude of SN2003ak was 25.8, or only 1.13% under the value given by MMAI. SN2002fx, with a redshift of 1.40, had a maximum magnitude of 25.5 or 1.22% lower than the value of MMAI at this redshift. For simplicity, these maximum magnitude values were taken from Asiago SN Catalogue (2005), bypassing published data by Riess, et al.(2006). The locations of these two new SNe Ia are shown in Figure 1, appearing to be located along the MMAI curve. Data obtained by Riess, et al. (2006) appears to be an expansion of Perlmutter et al. (1998) data to higher values of redshift.

The most distant supernova observed thus far (SN 1997ff) exploded 10 Gyr ago, 10 Glyr away from Earth (Riess et al. 2001). It had a redshift of about 1.7, later corrected to be 1.755 (Riess et al. 2006). In a steady state universe, a redshift of 1.755 would place SN 1997ff at a distance of 14.15 Glyr (Eq. 2), indicating that this event actually took place 14.15 Gyr ago. The reported maximum magnitude for SN 1997ff was 26.77 (Barbon, et al.1999). The calculated maximum magnitude for this SN Ia should be 24.23 (Eq. 5), as a result of spherical expansion only. The correction in the maximum magnitude of the SN due only to amplitude attenuation should be 2.20 (Eq. 4), resulting in the total magnitude value of 26.43 (Eq. 6). The calculated value of MMAI for this SN Ia is 1.01 percent under its observed magnitude of 26.77 (Bian, et al. 2005), after correction of its magnitude value for frequency reduction.

Figure 1 shows that the location of the three maximum magnitudes of the most distant SNe Ia observed thus far happened to lie very close to their corresponding theoretical values as predicted by the MMAI curve. Thus by applying relatively simple math to a logical concept, we obtained results, which are in an amazingly good agreement with observational data on distant SNe Ia. 

Finally, the SN 1997ff occurred some 10 Gyr ago. This SN Ia was most likely an explosion of a white dwarf (Riess 2003). Before becoming a dwarf however, this star, initially similar in size to our sun, was probably glowing for a period of some 10 Gyr. Its life span as a white dwarf is unknown, but it might have been many additional Gyr (Saharian 2010). Thus, by observing the SN 1997ff explosion, which occurred 10 Gyr ago, we have witnessed a spectacular death of a star that probably first began to glow some 20+ Gyr ago. The total increment of time encompassed by this event exceeds the total life span allowed by the theory for an expanding universe. This was not the only event we have observed. Many more distant SNe Ia were observed at distances extending to 10 Glyr (Riess et al. 2006). Discovery of a few SNe Ia at the fringes of our presently observable universe, some 13 Glyr in space, would truly challenge the validity of the time limit imposed on the age of our universe by the theory of the expanding universe. It would be ideal to observe some distant SNe Ia at redshift values approaching 12 (Wilson 2004) not just to prove their existence, but also to measure their maximum magnitude.

We have shown that at very High-Z values, scattering of signals reduces the observed magnitude of SNe Ia rapidly with redshift (or distance). The overall reduction in RI of signals due to space charge interaction is inversely proportional to the cube of (z + 1) and is in addition to the reduction in RI due to spherical expansion. This observation applies for all individual glowing objects in space. For example, the galaxy 0140+326RD1 has a redshift of 5.34 and is 12.22 Glyr from Earth (Dey et al. 1998). But in a steady state universe it would be 25.78 Glyr from our planet (Eq. 2). That is, it would be 2.11 times farther in space and 2.11 times larger than we presently think. The luminosity of this galaxy in the steady state universe would be reduced from its original value by a factor of 255 due to interaction of its signals with space charge.

From the total value of brightness for the Galaxy 0140+326RD1, a 6.02 magnitude reduction in brightness would be due to space charge interaction (Eq. 7) and the balance would be due to the spherical expansion of signals from the galaxy 25.78 Glyr away. A potential SN Ia in this galaxy would have a MM of 31.55 (Eq. 8). From this total, 6.02 magnitudes would be from attenuation due to space charge interaction and the bulk of it (25.53) would be from spherical expansion (Eq. 5), a ratio of intensity reduction of about one to 64 million at this value of redshift.

The observed brightness of this SN Ia would be 3.71 magnitudes lower, or only 3.3 percent of its value, given by IM. By correcting for the energy loss in RI of this SN Ia due to frequency reduction from its original value, it would be 1.7 magnitudes lower, or only 21 percent of its value given by IM.

By itself, the additional signal attenuation due to space charge interaction, at modest values of redshift represents only a very small additional loss when compared to the loss in the signal’s intensity due to spherical expansion. However, because of attenuation due to space charge interaction, and because of the increased distance to a glowing object in space of a steady state universe, very distant galaxies of normal size would appear smaller and not as bright than they actually are when observed in an expanding universe

Observational results of the deep space confirm this conclusion. It is said that these smaller, “younger” galaxies of the early universe are the building blocks for the larger present-day galaxies, like those closer to Earth. In a steady state universe, there should be no variation in the average size of galaxies with distance. Their average size is determined only by the galactic density in space, which is at equilibrium.

Recent observations of HUDF found some galaxies stated to range in redshift from 7 to 12, and reported to be approximately 0.8 to 0.4 Gyr old at the time of radiation emission (Savage, et al. 2004). Roger Thompson believes that they have spotted some galaxies in the near-infrared spectrum at a redshift of 12, dating to approximately 0.4 Gyr after the big bang, or when the universe was 2 to 5 percent of its present age (Savage, et al. 2004). To paraphrase Massimo Stiavelli, the HUDF project head, “Hubble takes us to within a stone’s throw of the big bang itself.” (Wilson 2004). We may not fully agree with this statement, but the picture of the very distant space is truly fascinating and it is factual. It is a great scientific accomplishment.

Previously, ground-based telescopes observed distant objects that existed about 0.5 Gyr after the Big Bang at a redshift value of 10, but with the help of a gravitational lens (Savage, et al. 2004). Other releases of photographs made public and available on the Internet showed that these somewhat distorted, “ultra young” galaxies of the expanding universe looked similar to those of Hubble Deep Field-North (HDF-N) or HDF-S (Gribbin 2001). They had a similar distribution pattern. In a steady state universe, some of them, at a red shift of 12, would be 35.81 Glyr from Earth. Their light, which we observe on Earth today, would have departed from there 35.81 Gyr ago. An estimated 10,000 galaxies were found in an area of space equal to about one tenth of our moon’s diameter (Beckwith, et al. 2004). This small area of our universe showed just a few galaxies in the earlier photographs, including those made by HDF (Wilson 2004).

Subsequent HUDF data released in September 2004 show that as we manage to look deeper into space, we find nothing very unusual but more of the smaller galaxies exhibiting very high redshift values. These photographs show a few tiny, compact red dots, randomly scattered and widely separated in space. Approximately 100 of these slightly distorted distant galaxies were observed in deeper space. Each distant galaxy was circled for ease of identification (Windhorst & Yan 2004). Some of these galaxies might date back to approximately 0.4 to 0.8 Gyr, or nearly the beginning of time (Savage, et al. 2004). It is reasonable to expect that we would find even more distant High-Z galaxies in deeper space. If we were to look the same distance in the opposite direction, we probably would obtain an identical picture of space as was the case for HDF-N and HDF-S (Gribbin 2001).

Recent observations of the deep space with the new and upgraded instruments on the Hubble telescope provided a new photograph of the HUDF. In this new photograph, referred to as HUDF09, some galaxies were found to be approximatley 0.6 Gyr old (Villard et al. 2009). Otherwise, the two photographs of the very deep space looked essentially the same. It appears that new cameras on the Hubble telesccope were more sensitive, requiring much less abservational time to record the same picture of space. At about the same time, a new photograph of a portion of the Southern Field, known as Great Observatores Origins Deep Survey (GOODS) showed a few new and not previously observed galasies dating back to 0.65 Gyr after the Big Bang (Villard, et al.2010). The views of the very distant space in the GOODS field and that shown in the HUDF a view of an expanding universe, but it could equally be that of a stationary or static universe. In this particular case, the difference between the two models lies only in our explanation of the observed redshifts from distant galaxies. The question is: Are the observed redshifts 

In a steady state universe, the luminosity of these galaxies with a redshift of 12 would be reduced by a factor of 2197 (8.35 magnitudes) due to signal and space charge interaction over and above its value from spherical expansion. It would be a 5.0 magnitude reduction in intensity (99%) from the one given by IM in Equation 3. This would make them appear significantly fainter than expected. Their actual size would be three times larger than what would be apparent in an expanding universe model at this value of redshift because of their greater distance. 

As one considers the observation that galaxies in the expanding universe appear reduced in size the greater their distance from Earth, one can make this additional observation: If we were able to determine the value of redshift differential from the opposite sides of a distant galaxy when it is viewed on edge, one should be able to determine its rate of rotation. In an expanding universe, a reduction of the size of a distant galaxy beyond what would have been normally expected, would make the galaxy appear to rotate at a faster pace. Recent observations of distant galaxies made by van Dokkum et al. (2008) appear to confirm this observation. In a steady state universe, the galaxy would be actually farther away and larger than we think, and therefore it would be rotating at a lower speed.

The depicted area of distant space as shown in the HUDF photograph is equivalent to an area of space as seen through an eight-foot-long soda straw (Thompson, et al. 2004). Actually, it is a very tiny view of space 12.7 Glyr away as if seen through a stirrer-straw with the size of the HUDF field shown in the photograph being 3.6 Mlyr on the side (Windhurst 2008). At a redshift value of 12 in the steady state model of the universe, the HUDF photograph would measure 10.2 Mlyr across, 35.81 Glyr away.

Based on this information, the HUDF volume of space in a steady state universe is about 22 times larger than its equivalent of the expanding universe. Its average galactic density calculates to be about one galaxy per each 124 cubic Mlyr up to a distance of 35.81 Glyr in space. This value of galactic density is about equal to the one estimated by Powell (2002) for a two Glyr deep universe, with the dwarf galaxies included. The HUDF data indicates that we are probably surrounded by some 1.6 x 10 Ù 12 galaxies to a distance of 35.81 Glyr, encompassing a spherical space of about 72 Glyr in diameter. It appears that no matter where we look, we find more galaxies with a reasonably constant, large-scale galactic density, confirming that on the large scale the steady state universe is homogeneous and isotropic.

Finding just a few widely separated galaxies formed so very early from the beginning of time, or shortly after the very rapid expansion of space has presumably ended and with the universe still expanding, raises some interesting questions. Earlier, we tried to demonstrate in our Andromeda example that it would take an appreciable amount of time to form stars and even more so for galaxies, in that sequential order. It takes time to form stars initially, and only then can they be assembled into galaxies, but in each case from an initially homogeneous and isotropic distribution of matter. If so, how could galaxies form at the fringes of our presently observable universe by the time the universe was only about 0.4 to 0.8 Gyr old? However, the more troublesome questions arising from these observations are why only a few galaxies, separated laterally by such large distances from each other, were formed in this same period of time in such a vast space? 

Actually, the separation between galaxies in deep space, where some of these 100 galaxies were located, is even greater than it appears, because the photograph of the deep space by Windhorst & Yan (2004) shows only a very small view of a three-dimensional space projected onto a two-dimensional plane. That is, in the HUDF photograph, the tiny viewing diameter of the Hubble telescope capured only a few widely separated galaxies of the deep space, inlcuding some 100 very distant galaxies. Their images were then projected onto a small area as shown in the photograph. In most cases, even the galaxies which appear to be next to each other as if they were in the process of merging, would be merely in the same line of sight but yet with a significant depth of separation between them. For this reason the separation between galaxies would have to be greater when the redshift differential between individual galaxies is taken into account.

Most likely the redshifts of 100 individual galaxies in the very deep space are not identical, but in the deep field of a steady state universe, even a minor difference in redshift between two galaxies that appear to be very close to each other in the photograph would produce a significant separation in depth between them. For example, a one tenth of one percent differential in redshift between two galaxies at a redshift value of 12 would correspond to a separation of about 12 Mlyr of depth.  A one-half percent difference would correspond to a distance in space of 60 Mlyr. A 7 to 12 range of redshift would encompass a depth of space of about 6.8 Glyr. The bulk of the 10,000 galaxies in the HUDF field are probably located in this large area of space.

In an expanding universe it would have been more reasonable had we found many more than just 100 of the smaller galaxies in the deepest portion of the HUDF space formed very early from an initially homogeneous and isotropic plasma field. This space should have been filled with small galaxies. So then what happened to all of this homogenous and isotropic matter that was originally located in this huge area of space where these few galaxies were observed? Did all this matter merge in less than 0.4 to 0.8 Gyr into the few very widely separated galaxies visible today, or were there other galaxies too small to be observed with present-day equipment located in this area of space? If so, why the difference in the size of these galaxies supposedly formed from a uniform distribution of matter that was initally very small and basically invisible?

Clearly, the observed distribution of matter in space of a 0.4 to 0.8 Gyr old universe which has just gone through an incomprehensible period of inflation, soon after “the matter and radiation decoupled from each other” when the early universe was just 0.3 Myr old (Filippenko 1998), and shortly before, during or after the “reionization epoch” of the universe said to have ended 0.5 to one Gyr after the big bang (Villard et al. 2004) is contratry to what one would have expected to find at this moment in the early life of an expanding universe. But what lies beyond those few distant galaxies in space, which this picture of the young 0.4 to 0.8 Gyr universe was able to convey, becomes the crucial question. We will need to wait for future photographs of even deeper space to resolve this issue. However, it is beginning to look more and more as if we are a part of a very large galactic universe.

Conventional observations of deep space have shown that at very high redshifts, the unexpectedly rapid decay of galactic intensity with distance must be due only to amplitude attenuation and frequency reduction of signals, and also because these galaxies are actually farther away than prevoiusly thought. The galaxies in the far field of space soon become essentially unobservable by optical means. The very few galaxies, which we are still able to detect in this area of our universe with present equipment, at reasonable values of redshift, are probably the largest in size, or the brightest, or both. But, of the number of galaxies that should have appeared in our view at these larger distances, the majority are “lost in space” to our view as if we have reached “the edge” of the presently-observable, expanding universe with a radius of some 13 to 15 Glyr all around us. But there are many more galaxies in deeper space as enhanced observational techniques using the Hubble telescope to obtain the HUDF photograph have demonstrated (Wilson 2004). Finally it is interesting to point out that in the current HUDF photograph of space, as captured by the Hubble telescope’s camera, all pictures of different galaxies were taken as they appeared during the observation moment of each individual galaxy, but all of these images were recorded at different times extending over a time span of many Gyr.

Figure 1 shows that at modest values of redshift, the contribution of MC (Eq. 7) on signal attenuation is very small compared to that of AM (Eq. 5). Both of these variables contribute to the overall signal attenuation MM (Eq. 8). However, at larger distances, that is at redshifts greater than 100, the large value of the logarithmic magnitude of AM changes very little with redshift and remains essentially flat, keeping the rate of attenuation of signals due to spherical expansion in check. The magnitude of MC due to space charge interaction, on the other hand, increases as the cube of its redshift.

At this high rate of change, a point will soon be reached when MC will match attenuation levels comparable to those of the AM curve. For a short period of distance in space, both curves would produce nearly the same attenuation in the total RI. However, attenuation due to MC will continue to increase, rapidly becoming a dominant factor for attenuation of signals originating in the deep space of our universe. The crossover point in space for the two curves will take place when the AM is equal to the MC, about 28.9 magnitudes each, or at a value of z of about 7229. 

We stated that most of the radiation in our universe was produced by stars in a narrow band of frequencies and that signals of different frequencies (as measured later on Earth) originated in different areas of our “enormous” steady state universe. The lower the frequency of the observed signal, the farther away was the source of its origin. Predicated on these facts, the value of redshift of 7229 places the crossover point of the two curves at a distance of about 124 Glyr (Eq. 2) from the source of radiation, independent of the original signal’s frequency.

For example, a signal originating 124 Glyr in space at a wavelength of 0.000053 cm (corresponding to the peak wavelength of our sun’s RI) would have a crossover point at a wavelength of about 0.38 cm when observed on Earth. This crossover point appears to occur slightly to the left, but near the very top of the observed cosmic background radiation (CBR) curve in Figure 2. If the peak wavelength for the bulk of radiation intensity from all the stars in space were shorter, a characteristic of radiation, which is typically produced by stars with higher surface temperatures, our crossover point would move slightly to the right. It will then approach the peak of the observed CBR curve in Figure 2.

We stated that luminosities of many stars in our universe could exceed that of our sun by several orders of magnitude. A few giant blue stars could easily outshine many older yellow stars like our sun. If we were to assume that a good portion of radiation in our universe was produced by the higher temperature stars, then the wavelength of the bulk of radiation at the crossover point received on Earth would have to approach the 0.1 cm peak wavelength of the observed CBR frequency spectrum in Figure 2.

With some of this radiation emitted at a wavelength of 0.0000138 cm, the crossover point for this frequency would occur at the very peak of the observed CBR curve in Figure 2. However, some of the radiation emitted at the wavelength of 0.000053 cm would also contribute to the total radiation intensity observed at 0.1 cm. This radiation would be originating 105 Glyr in space (Eq. 2).

In fact, radiation intensity measured on Earth at the wavelength of 0.1 cm consists of radiation produced by billions of stars at wavelengths of approximately 0.000053 to 0.0000138 cm, extending over an interval of space from about 105 to 124 Glyr.

The crossover point between the AM and the MC curves is just a distance indicator in space. It shows us where signal attenuation due to spherical expansion of radiation from any glowing object in space is equal to that produced by space charge interaction. The distance to the crossover point is independent of the original frequency of the signal, but crossover points for signals of different frequencies occur at different wavelengths. They do not have to be exactly at the peak wavelength of the observed CBR frequency spectrum in Figure 2. The two values have only to be in the proximity of each other.

Keep in mind that recombining of signals of lower frequencies (longer wavelengths) from individual sources into common wavefronts will occur before those of higher frequency signals originating in the same area of space, after having traveled an equal distance. A longer wavelength allows for a more sustained interaction period between phases of individual wavefronts.

For example, radiation originating at longer wavelengths of 0.000053 cm, 124 Glyr in space has passed the 0.1 cm mark and has just reached the left side of the CBR curve, as observed on Earth, at a wavelength of 0.38 cm. At distances greater than 124 Glyr, this radiation will continue its never-ending journey through space as a fully formed wavefront, attenuating as the cube of its continuously decreasing frequency, now caused primarily by scattering of the signal.

Radiation originating at even longer wavelengths will attain fully formed wavefronts before reaching the 124 Glyr point in space. Likewise, the wavelength of 0.38 cm will be reached before the interval of time of 124 Gyr. By the time these signals have traveled 124 Glyr, this radiation would have been continuously attenuating as a cube of its frequency, with its magnitude eventually following the left side of the observed CBR curve in Figure 2. Its observed wavelength would have exceeded the 0.38 cm value.

On the other hand, radiation energy originating at shorter wavelengths of about 0.0000138 cm, 124 Glyr in space has just reached the peak wavelength of the CBR curve in Figure 2 and would have to travel an additional distance of about 19 Glyr before becoming a fully formed wavefront, finally reaching the left side of the CBR curve. It will then be observed on Earth at a wavelength of about 0.38 cm. Beyond this point in space, it will follow the same attenuation path as that of the signals originating at longer wavelengths.

The behavior of radiation energy originating in space in the range of wavelengths from 0.0000138 to 0.000053 cm (124 Glyr away) and observed on Earth at wavelengths of 0.1 to 0.38 cm, is very different from those originating anywhere else in space. This is the transition area for radiation energy. In this area of space, essentially all signals from individual radiation sources (but of the same frequency) are finally beginning to propagate through space as unified wave fronts. The significance of the 0.1 cm wavelength point, corresponding to the peak wavelength of the observed radiation on Earth, will become clearer when we consider the nature of background radiation from the near field of our universe.

Furthermore, with the wavelength for the peak radiation intensity occurring at 0.1 cm, it appears that the bulk of radiation produced in our universe consists of signals originating at shorter wavelengths of the radiation spectrum than those from our Sun. It is dominating the behavior of energy of the whole spectrum, because radiation originating near shorter wavelengths 124 Glyr in space is still in the process of creating fully formed wavefronts as it passes the 0.1 cm wavelength point in space. It determines the shape of the observed CBR curve in Figure 2 at the wavelength of 0.1 cm.

The observed CBR spectrum in Figure 2 is a composite of all RIs from all radiation sources in our universe. Space charge interaction of signals transforms the frequency spectra of the huge number of stars down into the microwave range. We believe that radiation received on Earth from glowing objects in the near field of an inhomogeneous and unisotropic space is primarily from individual objects. Its behavior is governed by the AM curve (Eq. 5). It is caused by the inability of spherically expanding signals from these sources to form coherent isotropic radiation fronts in a relatively short period of time. This behavior of signals determines the shape of the cosmic background radiation curve in Figure 2 at wavelengths less than 1 mm.

The shape of the radiation curve at long wavelengths is determined by space charge interaction of signals from a continuous distribution of glowing matter in the far field of space. It produces radiation, which attenuates in space as the inverse cube of its wavelength and is controlled by MC (Eq. 7). In reference to Earth, the dividing line between these two areas of radiation sources in our universe is roughly 124 Glyr away from any observer anywhere in space. Spherical expansion and space charge interaction of signals from billions of galaxies in our universe appear to produce a radiation spectrum similar to that from a warm body of matter which is controlled by the quantum mechanical principle. However, mechanisms used to produce the two radiation spectra are not the same.

Up to now we were concerned only with the behavior of radiation emanating from “individual” glowing objects located in the near field of space. However, in order to obtain a complete picture of behavior of radiation in space, we must also analyze variation in radiation intensity from a continuous sea of glowing matter. We have to determine how this type of radiation, which usually originates in distant areas of our universe, would appear to an observer on Earth as a function of frequency.