A Plasma Universe With The Zero Point Energy
originally published in the Journal of Vectorial Relativity, September, 2008
Barry Setterfield– 15th April 2008
KEYWORDS: Plasma physics, filaments, ions, electric currents, magnetic fields, Marklund convection, Zero Point Energy, ZPE, vacuum properties, variable constants, quantized redshift, cosmology, galaxy formation.
I. EXPLORING PLASMA BEHAVIOR
A. Introducing plasma
Plasma is the major constituent of the universe with 99% of the cosmos being in this state. Astronomers use an instrument called a spectroscope which can readily discern ionized gases. As it turns out, the Sun and stars are gravitationally bound plasmas. Many of the beautiful photographs from the Hubble Space Telescope reveal formations of gas clouds out in space which are also a plasma. The electric current in fluorescent lights generates plasma by ionizing the gas in there. Neon signs glow because an electric current excites plasma in the tube. However, when very weak electric currents flow in plasma, it normally does not glow. This is called the dark current mode for plasma. It is only when the current is stronger that the plasma begins to emit light and is in glow mode, just like the neon signs. For extremely strong currents, the plasma goes into arc mode in the same way it does in a welder’s torch, or a lightning bolt. In a terrestrial lightning bolt, the lightning streamers are atoms in the atmosphere that are about 20% ionized and act as channels of plasma for the electric current that may reach 200,000 Amperes and expend an energy of 6 x 108 Joules. In contrast, lightning bolts on Jupiter release about 4,000 times as much energy [Peratt, op. cit., p.3].
Plasma can also be seen with the aurora borealis. In 1908, Birkeland found that if a current was sent through a near vacuum to a magnetized metal globe, luminous rings and streamers were produced around the magnetic poles of the globe. He concluded from this classic experiment with his "terrella" that auroras are the result of plasma in our upper atmosphere being excited by electrical currents from the Sun . The Triad satellite confirmed this in 1973 and 1974 [2, 3]. In fact, it was found that the earth is encased in a protective shell of plasma, called the earth's plasma-sphere, with which the ionosphere and magnetosphere are involved. These shield life on earth from high energy radiation that comes from space. Most recently, data from the Themis mission, a quintet of satellites that NASA launched in late 2006, has confirmed Birkeland's proposed cause for the auroras and added more detail. They have found that "a stream of charged particles from the sun flowing like a current through twisted bundles of magnetic fields connecting Earth's upper atmosphere to the sun" abruptly released the energy to produce the auroras. The comment was made that "Although researchers have suspected the existence of wound-up bundles of magnetic fields that provide energy for the auroras, the phenomenon was not confirmed until May, when the satellites became the first to map their structure some 40,000 miles above the earth's surface." Scientists Find Energy Source of Northern Lights gives a detailed comment about this.
B. Plasma & controversy
Because of the controversy, the term "Birkeland current" was not used until 1969, when Birkeland's prediction of the existence of these currents in auroras was being experimentally verified . The middle years of the 20th century also involved Hannes Alfvén in the controversy. In 1942 he calculated that if a plasma cloud passed through a cloud of neutral gas with sufficient relative velocity, the neutral gas wouldbe ionized and thus become plasma. This "critical ionization velocity" was predicted to be in the range of 5 to 50 kilometers per second. In 1961 this prediction was verified in a plasma laboratory, and this cloud velocity is now often called the Alfvén velocity. We see this happening in space, and it is one reason why gas clouds in space are usually ionized.
Alfvén built on Birkeland's approach, using both experiment and theory, just as Birkeland had. In 1970 Alfvén was awarded the Nobel Prize in Physics for his work in applying plasma physics to space phenomena. Nevertheless, Chapman continued to vigorously oppose Alfvén's explanations, even though they were experimentally based. One of Alfven's explanations included a prediction in 1963 that the large scale structure of the cosmos was filamentary . This was proved to be correct in 1991, to the amazement of many astronomers.
Earlier, in 1961, Alfvén also explained the Sun's visible features in terms of plasma currents, filaments and sheets . This explanation is currently being verified as a result of photographs obtained in July 2004 from the Swedish one-meter Solar Telescope (SST) at La Palma in the Canary Islands, and from the most recent Japanese space telescope, the Hinode, in March 2007. As the NASA quote above indicates, the tide is gradually turning in favor of the new plasma physics which is slowly divesting itself of Chapman's incorrect approach. Many astrophysicists are now becoming more conscious of the role played by electric currents and magnetic fields in astronomy generally.
C. The origin of magnetic fields
Electric currents always produce magnetic fields. If that current is traveling in a loop, such as the electron in its orbit or perhaps in the wire of a cylindrically wound solenoid, it will also produce a magnetic field. The polarity of that field depends on whether the electric charge is positive or negative. The convention established in the19th century states that if one looks at the current loop, and the current is anticlockwise, that side is a magnetic north pole, while a clockwise loop is the south polarity. Note that this convention defined the direction of the current as the direction of motion of a positive charge. But, in the case of bar magnets, we are dealing with the motion of negative charges (electrons) in atoms. Experiments have shown that an electron current is simply the reverse of a current of positive ions. Thus, for electron currents, or a current of negative charges the polarity of the magnetic field is the reverse of the usual current of positive charges or ions.
The same is true for the motions of positive ions or negative electrons in plasma out in space. Their motion will produce an electric current, and this current will, in turn, produce a magnetic field even if the current direction is linear rather than circular. It should be noted that plasma is the only state of matter in space where atoms are ionized and can form electric currents that give rise to magnetic fields. Thus, the existence of either an electric current or a magnetic field in space necessarily implies that plasma is present with the ions and electrons in motion. In astronomy magnetic fields are often noticed which appear to be far larger than the visible objects being observed. For this reason, many have concludedthat magnetic fields are intrinsic to space. But now, plasma research says we should look for currents on a much larger scale that are in turn producing these magnetic fields.
D. Plasma & magnetic constriction
These phenomena were not generally understood in the early 20th century, even though the first clue was perceived by Pollock and Barraclough in 1905. They investigated a copper rod that had been struck by lightning near Sydney, Australia. The rod had been compressed and distorted by the strike. Their analysis established that the interaction between the large current flow in the lightning bolt and its own magnetic field had produced compressive forces that caused the distortion . It was not until 1934 that an analysis was performed by Bennett of the radial pressure exerted in such instances . This characteristic constrictive action, which is the product of the circumferential (or azimuthal) magnetic field, pinches the plasma into filaments and has now been called the Bennett pinch or Z-pinch . This pinching or bunching is usually accompanied by the accumulation of matter. This explains why interstellar matter displays such a variety of filamentary structures. The standard Bennett pinch due to the gradient of magnetic pressure pm is given by
where B is the magnetic flux density or magnetic induction, and μ is the magnetic permeability of the vacuum. Bennett also noted that the compression always occurred whether or not the material was fully ionized. Since then other pinch effects have been discovered that differ in their geometry and/or operating forces. All such pinched-current filaments are given the name 'Birkeland currents.'
By 1985, Birkeland currents had become well-known and discussion of their role in an astronomical context was opening up. In that year, Fälthammer made an important comment. He wrote, "A reason why Birkeland currents are particularly interesting is that, in the plasma forced to carry them, they cause a number of plasma physical processes to occur (waves, instabilities, fine structure formation). These in turn lead to consequences such as acceleration of charged particles, both positive and negative, and element separation (such as preferential ejection of oxygen ions). Both of these classes of phenomena should have a general astrophysical interest far beyond that of understanding the space environment of our own earth" .
Photographs of the Sun by the Swedish Solar Telescope revealed Birkeland currents called "spicule jets [that measure] about 300 miles in diameter, and a length of 2000 to 5000 miles" . During March 2007, the Hinode Space Telescope sent back solar images that also confirm Alfvén's analysis and reveal Birkeland currents 8000 kilometers long. At a NASA Press Conference, Leon Golub from the Harvard-Smithsonian Center for Astrophysics (CfA) said, "We've seen many new and unexpected things. Everything we thought we knew about X-ray images of the Sun is now out of date" . Additional images emphasizing the role of Birkeland currents on the Sun are in .
As far as plasma filaments and the rest of our solar system is concerned, Peratt mentions that space probes have found "flux ropes" in the ionosphere of Venus whose filamentary diameters are of the order of 20 kilometers [14, 15]. On a larger scale he lists examples of plasma filaments in the Veil, Orion, and Crab nebulas. Indeed, at the 1999 International Conference on Plasma Science in Monterey, California, the radio astronomer Gerrit Verschuur made an important announcement. After high resolution processing of the data from about 2000 clouds of so-called 'neutral hydrogen' in our galaxy, he found they were actually made up of plasma filaments which twisted and wound like helices over enormous distances. It was estimated that the interstellar filaments conducted electricity with currents as high as ten-thousand-billion amperes . Fifteen years earlier, Yusef-Zudeh et al. had pointed out that twisting filaments, held by a magnetic field, extend for nearly 500 light years in the center of our galaxy and were characteristically 3 light years wide . About the same time Perley et al. demonstrated that filaments may exceed a length of 65,000 light years within the radio bright lobes of double radio galaxies . Thus the magnetic pinch of a Birkeland current can maintain filaments of glowing matter over distances of thousands of light years.
However, some more recent examples are also appropriate. Space probes have shown that Jupiter's rings and moons exist within an intense region of ions and electrons trapped in the planet's magnetic field. These particles and fields comprise the Jovian magnetosphere and plasmasphere which extends 3 to 7 million kilometers towards the Sun and stretches in a windsock shape behind Jupiter, past Saturn's orbit, and Saturn sometimes passes through it. If this plasmasphere were in glow mode, it would appear larger than the full moon to us. Indeed, the Sun itself would fit within its limits [see a complete discussion at "A Look at Jupiter's Magnetosphere"]. NASA's Spitzer space telescope gives us an entirely different example. One of the first images it returned after launch was of the spiral galaxy M81. The Spitzer space telescope detects faint infra-red or heat radiation through clouds of obscuring material. It gave an excellent view of the filaments that form the entire galactic structure of the galaxy M81, with another picture here. Galaxies like this can extend to 150,000 light years in diameter. With these examples in mind, it can be seen that plasma filaments and Birkeland currents behave in a consistent way from the scale of laboratory experiments up to at least the size of galaxies. That is consistent behavior on a scale factor of 1020.
F. Plasma sheets and double layers
A related phenomenon is the formation of a Double Layer in plasma (usually abbreviated as DL). Irving Langmuir discovered that current-carrying plasmas isolate themselves electrically. Wherever there is a significant voltage difference between sections of plasma, it will be largely confined by the formation of two parallel layers with opposite charge. One layer will have an excess of positive ions while the other layer will consist of an excess of negative charges. Because this protective double layer formed so readily and spontaneously in ionized gases, it appeared as if it almost had a life of its own. As a result, Langmuir was moved to call this ionized gas "plasma" as it was reminiscent of blood plasma. He then invented his ingenious probe that measures DL voltage differences.
Since most of the voltage drop within a given section of plasma will be contained in the DL, it follows that this is where the strongest electric field will be found. It also means that these double layers can accelerate charged particles to very high energies. Thus, with the DL in earth's magnetosphere, kilovolt energies are common for charged particles [24 – 27]. In space, the energies are even higher. It is also of importance to note that Birkeland currents are usually sheathed in a double layer. Therefore such currents can be associated with very high particle energies and velocities.
Several mechanisms exist whereby a DL can be formed. One such mechanism occurs if plasma is divided into two regions with, for example, temperature or density differences, and a surface, plane or interface separating them. If we take the example with temperature differences, we find that electrons from the hot plasma will travel at a higher velocity than the cooler plasma. Now electrons may stream freely in either direction. But the flux of electrons from the hot plasma to the cooler plasma will be greater than the flux of the electrons from the cooler plasma to the hot plasma. This occurs because the electrons from the hot side have a greater average speed. Since more electrons enter the cool plasma than exit it, part of the cool region becomes negatively charged as the number of electrons there increases. The hot plasma, conversely, becomes positively charged. This results in a potential difference between the two regions. Therefore, an electric field builds up, which starts to accelerate electrons towards the hot plasma, reducing the net flux. In the end, the electric field increases until the fluxes of electrons in either direction are equal, and further charge build up in the two plasmas is prevented. The DL which has formed has a drop in electric potential that is exactly balanced by the difference in thermal potential between the two plasma regions. In general, the oppositely charged DL are usually maintained because their electric potential difference is balanced by a compensating pressure which may have a variety of origins.
G. Cosmological plasma filaments and sheets
The Particle Physics and Astronomy Research Council (PPARC) website states that large-scale surveys of the cosmos "reveal the hierarchical structure of galaxies, galaxy clusters and superclusters linked by filaments and sheets surrounding huge voids.". These structures trace out the behavior of plasma filaments and sheets on a cosmological scale. This was just what Alfvén had predicted, yet it caught many astrophysicists unprepared. Some still try to account for these structures using gravity, but they require the very finely tuned action of "dark matter" to produce the desired result. Nevertheless, if these structures are compared with typical plasma behavior, one cannot avoid the conclusion that the inception of the cosmos involved plasma sheets, filaments and Birkeland currents. They also show consistent plasma behavior from the laboratory to cosmos-wide scales.
H. Sorting of elements by plasma currents
The order of elements going from the center of the filament outwards using the approximate first ionization potential in electron volts (eV) is then as follows: the radioactive elements Rubidium, Potassium, Radium, Uranium, Plutonium and Thorium (4.5 to 6 eV); Nickel, Iron and metals (7.7 eV); Silicon (8.2 eV); Sulfur and Carbon (10.5 to 11.3 eV); Hydrogen and Oxygen (13.6 eV); Nitrogen (14.5 eV); Helium (24.5 eV). As Peratt points out, this mechanism provides an efficient means to accumulate matter within a plasma . This property of plasma filaments, which causes different chemical elements to distribute themselves radially according to their ionization potentials, was initially studied in detail by Marklund, and is now called Marklund convection .
Marklund states "In my paper in Nature the plasma convects radially inwards, with the normal [predicted] velocity, towards the center of a cylindrical flux tube. During this convection inwards, the different chemical constituents of the plasma, each having its specific ionization potential, enter into a progressively cooler region. The plasma constituents will recombine and become neutral, and thus no longer be under the influence of the electromagnetic forcing. The ionization potentials will thus determine where the different species will be deposited, or stopped in their motion." Ionization potential charts show where, in a layered filament, the highest concentration of any element will probably be found. The velocity, v, with which the various ions will drift towards the center is given by 
Here, E is the electric field strength, B is the magnetic flux density or magnetic induction, and the electromagnetic force on ions causing them to drift is given by (E x B). It is generally true that the ion drift velocity in a system is given by the ratio of the electric field to the magnetic field, that is:
For electromagnetic waves, v = c, where c is the velocity of light. In plasma out in space, the typical drift velocity of ions can often approach the speed of light, or at least a significant fraction of it. The formula for the rate of accumulation of ions in a filament is given by dM/dt which is defined as :
where r is the radius of the filament, E is the electric field strength, I is the electric current, μ is the magnetic permeability of the vacuum and ρ is the number density of ions.
I. Interactions between plasma currents
In equation (5) the quantity μ is again the magnetic permeability of the vacuum. For a comment on this, please refer to the discussion following equation (14) and the preamble to equation (51).
J. Dusty plasmas
A discovery about the rings of Saturn by Voyager 2 in the early 1980's gave the impetus needed to open up discussion on dusty plasmas in the scientific literature. The images of Saturn revealed a pattern of nearly radial "spokes" rotating around the outer portion of the dense B ring. This was something that observers on earth had glimpsed for decades when conditions were favorable, but the spokes were often dismissed as illusory. In fact, as the spacecraft approached Saturn, the spokes appeared dark against the bright background of the rings, but as the craft pulled away the effect was reversed. This meant that the material making up the spokes scatters sunlight preferentially in the forward direction, a property of fine dust. Furthermore, the spokes were not stationary structures, but could form in as little as five minutes. Gravitational effects alone could never achieve this whereas electric and magnetic fields could. Goertz and Morfill demonstrated in 1983 that these spokes were a dusty plasma of micron sized particles that appeared to be about 80 km above the plane of the rings . It was later noted that their formation and disappearance coincided with powerful bursts of radio waves originating with Saturn's magnetic field called the Saturn Kilometric Radiation. This radiation is associated with lightning which caused dust particles to gain electrons and become electrostatically suspended above the plane of the rings .
At an altitude of 85 km above the earth are noctilucent or 'night-shining' clouds which are also examples of naturally occurring dusty plasma. These clouds, typically seen at high latitudes during early summer, are formed of ice crystals in the polar mesosphere at temperatures around 100 K. Because these crystals are near the ionospheric plasma, free electrons from there attach to the crystals to form a dusty plasma of charged ice crystals about 5 x 10-8 meters across . In general, if it is assumed that the capacitance of a dust grain of radius, a, is that of a spherical charged conductor of the same size, then the charge, Q, acquired by the grain is given by 
Here, V is the electrical potential difference between the grain and the plasma and ε is the electrical permittivity of the vacuum. In the case of a particle or grain at rest in a dilute plasma, the electron and ion currents will result in a potential difference for the grain or particle of
Here T is the temperature of the ions or electrons, k is Boltzmann's constant and e is the electronic charge. When this is applied to hydrogen plasma with kT equal to 3 eV (electron Volts), equations (6) and (7) suggest that a particle of radius of 10-6 meters will carry a charge equivalent to 5000 electrons . As a consequence, electrostatic forces on dust grains can be seen to be significant.
The depletion of electrons by absorption on dust particles affects plasma waves. For example, sound waves in plasma, also known as ion-acoustic waves, propagate at higher velocities and with significantly less damping in plasmas that contain negatively charged dust particles. The first physics experiment done in the weightlessness of the International Space Station in February of 2001 was with dusty-plasmas to see how they behaved in the depths of space. It was known as the Nefedov Plasma Crystal Experiment . A typical structure formed in this dusty plasma was a sharply defined void surrounded by a dusty plasma region constrained by fluid vortices along the outer edges of the container and along its central horizontal axis . The result was similar to the honeycomb or bubble and filament structure typical of macroscopic galaxy cluster distribution.
K. Plasma instabilities and vortex formation
First, there is sausage mode in which plasma filaments contract at regular intervals. The filament radius thereby varies along the axis of the filament. There can be standard sausaging by this process or, alternatively, sausaging with either axial hollowing or axial bunching. As in the case of the Z-pinch, this process also accumulates and concentrates matter. Second is the sinuous, hose or kink mode in which the filament bends sideways without any change in the form of the filament other than the position of its center of mass. Third, the filamentation mode can occur in which the main filament breaks up into a number of smaller filaments. These smaller filaments may have an elliptical cross-section or a pear-shaped (pyriform) cross-section. Fourth is a ripple mode where the filament is distorted by small-scale ripples on the surface. Sometimes these macroscopic instabilities are labeled as magnetohydrodynamic, hydrodynamic, or low frequency instabilities.
In contrast, microscopic instabilities usually excite local fluctuations of density and electro-magnetic fields in plasma. These microinstabilities can sometimes grow and be directly linked with a macroscopic counterpart. For example, the filamentation mode can be the macroscopic stage of a growing transverse electrostatic microinstability known as the Weibel instability .
When ions or electrons propagate along an axial magnetic field in a filament, a threshold can be passed with the resultant plasma current that causes the break-up of the beam into discrete vortex-like current bundles. This is called a "slipping stream" or diocotron instability. This type of instability may also arise if charge neutrality is not locally maintained such as when electrons and ions separate. There then arises a shear velocity which azimuthally results in vortex phenomena which axially form current bundles or filaments. On earth, this azimuthal vortex can be seen as auroral curtains . The instability can occur in solid or annular filaments as well as in sheet beams. The axial vorticity component is given by W which is mathematically described as 
Here e is the electronic charge and ε is the permittivity of free space while Ne and Ni are the numbers of electrons and ions respectively. These instabilities result in profound cosmological effects when coupled with other plasma phenomena and the behavior of the Zero Point Energy.
II. EXPLORING THE ZERO POINT ENERGY
A. What is a vacuum?
B. Planck, Einstein, Stern, Nernst and the ZPE
Here, f is frequency, c is light-speed, and k is Boltzmann's constant. In (9), the last term is independent of temperature as it remains when T goes to zero. Thus h is only a scale factor to align theory with data and no quantum interpretation is needed. The ZPE strength is then given by h.
In 1913, Einstein and Stern published a classical physics analysis of interactions between matter and radiation with dipole oscillators representing charged point particles . They remarked that if, for some reason, these oscillators were immersed in a ZPE, Planck's radiation formula would result without the need to invoke quantization at all. This has proven correct, as many have made these derivations which show that, immersed in a ZPE, the irreducible energy of each oscillator is (½)hf . In 1916, Nernst noted that this required an intrinsic cosmological origin for the ZPE .
C. Proofs for the ZPE and a choice for Physics
In 1925, physics had a choice. Planck's 1901 theoretical concept of h gave the right results mathematically, but lacked any physical cause for observed phenomena. It was purely theoretical. On the other hand, Planck's second theory could be adopted, supported by Einstein and Stern's, as well as Nernst's papers, and verified by Mulliken's experiments showing that the ZPE was a physical reality. Classical physics plus an intrinsic ZPE could then account for all the observational data. This approach of using classical physics with an added ZPE received wide attention up until 1925. But then four major papers were published in four years using Planck's first theory without the intrinsic ZPE. These four papers swung the balance and set physics on a course that led to Quantum Electro-Dynamics or QED. Then, in 1962, de Broglie pointed out that the choice made almost forty years before ignored both the earlier discussions and the evidence. He indicated that the option of using classical physics and an intrinsic ZPE definitely needed further examination .
After de Broglie's book, many papers were published discussing the theory which had been abandoned. This new approach came to be called Stochastic Electro-Dynamics, or SED physics. A number of seminal papers based on an all-pervading ZPE, derived and interpreted classically the black-body spectrum, Heisenberg's uncertainty principle, the Schroedinger equation, and explained the wave-nature of matter . These were the factors that, interpreted without the ZPE, gave rise to QED concepts. In listing some of SED's successes, it was stated that "The most optimistic outcome of the SED approach would be to demonstrate that classical physics plus a classical electromagnetic ZPE could successfully replicate all quantum phenomena" . As a result, many phenomena have both SED and QED explanations. In SED physics the uncertainty in a subatomic particle's position is due to intense random battering by the waves of the ZPE. Since h is a measure of ZPE strength, this uncertainty is also proportional to h.
D. ZPE characteristics
E. The Casimir effect and virtual particles
These electromagnetic waves are of all wave-lengths and in all directions. Thus, the ZPE is like a restless sub-atomic sea, with peaks and troughs in the energy density of its waves. And, like the ocean, its waves collide, peak, and form 'white caps'. In the case of the ZPE, these 'white caps' manifest as tiny virtual particles which briefly appear as positive and negative pairs and then annihilate. Their positive and negative charges maintain the electrical neutrality of the vacuum. By 1955, experimental evidence had shown that such particle/anti-particle pairs will collide and release a pulse of energy upon annihilation. A wide variety of these particles wink in and out of existence so it is often called a virtual particle zoo. There are enormous numbers of them in any given volume. For example, at any instant, the human body has over 1020 virtual particles flashing into and out of existence.
III. THE ORIGIN AND BEHAVIOR OF THE ZPE
A. Preliminary matters
B. The fabric of space and Planck particle pairs
Gibson notes expansion generates separation and vorticity with PPP . Charge separation gives electric fields and a tension. Vorticity caused PPP spin, which generated magnetic fields, and added further tension. Gibson points out that this vorticity also fed energy into the system, which allowed more PPP production. This inelastic system would have strong vortices and long persistence times [59, 60]. PPP numbers would thus increase along with ZPE strength until all vorticity died away. As PPP numbers increased, so did the tension in the fabric of space until it balanced the expansion force. The expansion then ceased and oscillation began. As the ZPE built up by this process, it would be maintained by the feedback mechanism described in [51, 61].
C. ZPE strength should increase with time then oscillate
In (10), U is the ZPE energy density. Orbital time, T, is a ratio with T = 1 at the cosmos origin and T = 0 near the present. The symbol (~) means "is proportional to" in this paper. The behavior of the ZPE thereby follows basic physics which indicates the ZPE built up rapidly, but its rate of increase slowed with time. Once the cosmos had expanded to its maximum size, this now static cosmos will oscillate about its final position. This will increase the ZPE energy per unit volume when the cosmos was at its minimum position, and decrease its strength at the maximum position. If the cosmos has several modes of oscillation, a graph of the ZPE strength is expected to contain flat points in a manner similar to reference . So even after the ZPE built up to its maximum value, it is expected that there will be cosmological oscillations in its strength. This will be echoed in the experimental values of ZPE-dependent quantities.
IV. ZPE AND ATOMIC CONSTANTS BEHAVIOR
A. ZPE and Planck's constant
where U is uniquely the energy density of the ZPE. This relationship may also be expressed as:
In (12), and in this paper, h1 is the present value, while h2 is at some distant galaxy at an earlier time. The experimental data indicate h has varied, along with synchronous variations in atomic quantities related by the ZPE. The officially declared value of h has increased systematically until 1970. After this, the data show a flat point, or a small decline (Fig.1). In 1965, Sanders noted that the increasing value of h was only partly due to improvements in instrumental resolution, which was an inadequate explanation . This follows since quantities like e/h, where e is electronic charge, or h/2e the magnetic flux quantum, and Josephson's constant, 2e/h all show synchronous trends centered on 1970 even though measured by different methods. The officially declared h values are all listed in detail in Atomic Constants, Light and Time.
B. ZPE and the speed of light
Changes in ZPE strength also mean changes in the electrical permittivity, ε, and magnetic permeability, μ, of space. But space is a non-dispersive medium, so the ratio of electric energy to magnetic energy in a wave must remain constant. This requires the intrinsic impedance of space, Ω, to be invariant, so that:
From (13) it follows that c must vary inversely to both the vacuum permittivity and permeability, so that
Thus, at any given instant, c would be the same in all frames of reference throughout the cosmos. Note that (14) can be derived without any assumptions about the behavior of c, ε, or μ, just as Maxwell did. His equations support large cosmic variations in c with time provided both the permittivity and permeability of free space varied as in (13) and (14), . Maxwell used CGS units where this variation is allowed, but SI units consider μ to be invariant. This situation arose because c was assumed to be invariant when the SI units were formulated. As a result, μ was also designated as having a constant value.
If the energy density of an electromagnetic field is given by U, with E and H being the electric and magnetic intensities of the waves, proportional to their amplitudes, then the standard equation reads:
Applying (15) exclusively to the intrinsic properties of the vacuum means the energy density, U, refers to the vacuum Zero-Point Fields with E and H specifically the electric and magnetic intensities of the ZPF. If the ZPE wave intensities, or their proportional amplitudes, remain unchanged, both E and H will also remain unchanged as the ZPE strength varies. Then, as U varies, so does ε and μ such that from (14)
This has implications for both radiation intensities and radioactive heating since radiant energy densities are dependent upon the permittivity and permeability of space. So, when ZPE strengths were lower, the energy density of electromagnetic radiation was proportionally lower . But this is offset for stellar and radioactive sources as photon production rates are proportional to c leaving intensities constant . We can then write:
Experimental evidence indicated c was declining, so ongoing discussions occurred in many journals up to the mid 1940's. Thus, in 1886, Newcomb reluctantly concluded that the values of c obtained around 1740 were in agreement with each other, but were about 1% higher (over 2000 km/s faster) than in his own time . In 1941, Birge made a parallel statement while writing about the c values obtained by Newcomb and others around 1880. Birge conceded that: "these older results are entirely consistent among themselves, but their average is nearly 100 km/s greater than that given by the eight more recent results" . Since both scientists held to a constant c, their admission is significant. The c values recommended by Birge in 1941 are plotted in Fig. 2. In all, 163 determinations of c with thousands of experiments using 16 methods over 330 years comprise the data for declining c published in August 1987 . In 1993, Montgomery and Dolphin did rigorous statistical analyses confirming the declining trend was significant, but it had flattened out around 1970 . Changes in c raise queries about E = mc2 , but before examining that, another matter must be dealt with.
C. The electronic charge
Data out to the frontiers of the cosmos support this to parts per million, including the fine structure constant, designated as α = [e2/ε][1/(2hc)] with e the electric charge . But data show α is constant too, which means
However, (16) has ε proportional to U. This means equation (19) requires the following proportionality:
The difficulty is that many experiments measure e in the context of the permittivity of its environment. Thus changes in e alone often have to be deduced from other quantities such as the ratio h/e. This ratio should be proportional to the square root of U, while h is directly proportional to U. When the h/e data for Fig. 3 are examined as in , the proportionality in (20) is supported. We now return to atomic masses.
D. The ZPE origin of mass
Here, ω is the Zitterbewegung oscillation frequency of the parton, with Γ the Abraham-Lorentz damping constant given by e2/(6πεmc3). Substituting for Γ in (21) and collecting mass terms, m, then gives us
From (19) we note e2/ε is constant . Now Dirac stated the jitter occurs near c and Puthoff shows the jitter frequency is ω= kc, with k inversely dependent on parton size and independent of c. So we have:
All frequencies follow (23), as shown later. When (23) is linked with equations (18), (19), (20) we have
Since atomic masses m are proportional to 1/c2, then in E = mc2, energy, E, will be conserved as c varies. Equation (24) is supported by declared values of electron/proton masses which increase until 1970. After that, a flat point or slight decline occurred (Fig. 4). Data are in reference . The Rydberg constant for an infinite nucleus, R∞, is a check on trends as it has five varying quantities. They are combined in such away that the result, R∞ = [e2 / ε]2 [2 π2 m / (ch3)], should be constant. The official values of R∞ in Figure 5 confirm this.
This discussion on mass suggests we should also look at the Newtonian gravitational constant, G, which is related to m. On SED physics, the ZPE battering of charged particles produces mass. Additionally, charged particles in motion produce secondary electromagnetic radiation which attracts all charged particles in the vicinity, the sign of the charge only altering the phase of the interaction. Analysis shows this attraction is identical to gravity [49, 74]. The SED approach therefore presents the force of gravity as already unified with the other forces in physics. G has units of [meters3/(kilogram-seconds2)]. Since mass is in the denominator of G it cancels out changes in the product Gm. Thus Gm is constant for a varying ZPE as shown in .
E. Varying frequencies, atomic clocks, and the ZPE
Consider a photon going through space with dropping speed. Equations (18) and (26) require its wave-length, λ, to be fixed, and its frequency, f, dropping with c. It's like a slowing train hauling box cars. The car length (wavelength) is fixed, but the number of cars passing per second (frequency) gets less. Thus we can write
The data forced Birge to the same conclusion. He said "if the value of c is actually changing with time, but the value of λ in terms of the standard metre shows no corresponding change, then it necessarily follows that the value of every atomic frequency ... must be changing" . The frequency of light emitted from atoms depends on the frequency that electrons orbit nuclei, which depends on their velocity . Electron velocity, v, in the first orbit in Allen's Astrophysical Quantities, page 9 (Springer Verlag 2000) is given as
Thus, atomic orbital frequencies, F, obey the same proportionality as light frequencies do. So when c is higher, F is higher and all atomic time intervals, t, are shorter, so t is proportional to 1/c. This is discussed in detail in reference . Some atomic time is based on electron revolution times in the first Bohr orbit. So the time, t, an electron takes for 1/(2π) revolutions in that orbit is given as [Allen's op.cit.]
Proportionalities are from (11), (16), (18), (19), (24). Ref. [66, 69] show radiometric time follows (29). Data comparisons between orbital and atomic clocks have been done by several observatories. One analysis stated: "Recently, several independent investigators have reported discrepancies between the optical observations and the planetary ephemerides… [They] indicate that [atomic clocks had] a negative linear drift [slowing] before 1960, and an equivalent positive drift [speeding up] after that date… This study uses data from many observatories around the world, and all observations independently detect the planetary drifts … [which] are based on accurate modern optical observations and they use atomic time." . The data turnaround again occurred near 1970 (Fig. 6). Comparing radiometric dates with orbital dates for historical artefacts shows the effects of cosmos oscillation recorded from 1650 BC to 1950 AD . It is graphed in Fig. 8. This means the main part of the ZPE curve associated with the redshift data began before about 2600 BC when the Fig.6 curve was again at its current value. A full discussion on this is reserved for a separate paper.
F. ZPE, atomic orbits and the quantized redshift
Therefore atomic stability only exists because of the ZPE. Puthoff demonstrated that the power radiated and absorbed by the electron governed the orbit angular momentum, which is proportional to h. Thus, as the ZPE strength increased with time (and h increased), all orbit angular momenta increased and light emitted from atomic transitions would be more energetic or bluer. As we look back into the past, the light emitted would be redder at earlier epochs. In a static universe, this is why progressively more distant galaxies have their spectral lines shifted to the red end of the spectrum . This redshift, usually designated (1 + z), is thus proportional to 1/h and is given by
In (30A), x is distance such that (x = 0) near our galaxy while (x = 1) at the origin of the cosmos. This overcomes problems with finding an absolute distance scale. Astronomers often substitute the quantity v/c for x where v is the inferred velocity of expansion. Note atomic orbits based on angular momenta [mvr = nh/(2π)] go in quantized jumps so redshift quantizations are not surprising . Now electrons form a standing wave so the length of their orbit (2π r) divided by wavelength (h/mv) is a whole number n. Therefore 2π mvr = nh. If n is held constant so r is also a constant, then the angular momentum can only change when h changes by a factor of 2π. Atomic orbit angular momenta then go in jumps of n(2π) with n an integer. Therefore we write
giving us the quantized redshift. Thus Guthrie and Napier's 37.6 km/s becomes [c / (2538 π)] with n = 1269.
The relationship between (1 + z) and Planck's constant is confirmed by the physics in . That demonstrated the build-up of ZPE strength due to turbulence and recombination actually followed equation (10). Yet (10) is the inverse form of (30A) except in (10) we have orbital time T while in (30A) we have distance x. As looking back in time is the same as looking out further into the cosmos, this is to be expected. Two different approaches thereby show the redshift and ZPE are inversely related so that we can write:
Redshift data then confirm ZPE behavior back to the origin of the cosmos as in Fig. 7. The behaviour over time of ZPE dependent atomic quantities has thus been elucidated. That behavior has the form:
Note that even after T = 0, which it did earlier in our history when z = 0, the data still show an oscillation which changed direction in 1970. Finally, the years elapsed, te, on the atomic clock, or its equivalent, namely the distance in light years that light has travelled, is then given by substituting for T in the integral of (32) which is:
When T = 1, the terms in square brackets in (33) total 2.5708. Now the cosmos is 14 billion atomic years old, and light has traveled 14 billion light years. The numerical value of K must accord with that.
A. The behavior of electric and magnetic quantities
But if E is the magnitude of the electric field strength, then the electrostatic force F is also given by
Therefore, from (20) and (35), it follows that the magnitude of the field strength, E, is given by
Field strengths can also be written as E = V/r in volts per meter. Since distance, r, is unchanged, then:
There is an alternative derivation, since the potential at a given point is defined in  as:
This means that the energy of a charged conductor, given by ½ eV, is constant from (20) and (37). Therefore, from the definition of capacitance, C = e/V, and from (38), it will behave as follows:
Since forces are constant in this scenario (see above), then from equation (5) it is required that we have
If the currents are of equal magnitude, and (16) is applied to (40), then I behaves as follows:
From (41) electric currents generally will be proportional to √c. Reference  equation (6) supports this. Further, as power, P, equals current, I, multiplied by voltage, V, then from (37), (38) and (41) we have
So power in watts is inversely proportional to ZPE strength. Also, the resistance, R, in ohms, is given by:
Resistances thus remain fixed as the ZPE varies. This is experimentally supported by Hall resistance values given by the Von Klitzing constant. Therefore, both resistivity and conductivity are also constant. It should be noted that magnetic field strengths have magnitudes defined as (H = I / r) in units of amperes/meter. Since r is unchanged, then from (41) it follows that H is proportional to I. We thus have:
This gives uniformity with the magnitude of the electric field strength, E, which bears the same proportionality with c and U, thereby maintaining symmetry between electric and magnetic phenomena. From these results, the magnetic flux density or magnetic induction, B, is given by 
It should be noted the attractive force in a plasma cosmology is the long range force between two current filaments. This is proportional to 1/r, while the short-range repulsive force between them is proportional to 1/r4. The forces remain unchanged with ZPE variation, but other behavior does not.
B. Examining plasma equations
Equation (3), the drift velocity of ions linked with Marklund convection, is given by the relationship
The proportionality follows from (36) and (45). Thus drift velocities were higher when ZPE strengths were lower in the early universe. Consequently, matter could accumulate in plasma filaments much more readily than they do now, and this mechanism, even now, is much more efficient than gravity. Equation (4) reinforces that contention as the rate of accumulation of material in filaments becomes:
This result comes from (18), (36), (41) and confirms that such processes were more efficient in the early days of our cosmos. The voltage build-up by dust collecting electrons in plasma is given by:
Here, the last step is from (20). Voltages were thus greater when the ZPE strength was lower. Equation (8) is the axial component of the vorticity, W, that forms current bundles or filaments when an instability occurs. This has the following proportionality:
This component was more effective in forming filaments when the ZPE was lower and c was higher.
Electric and magnetic field strengths are greater when the ZPE is lower from (36) and (44). When two filaments interact, long-range attractive forces result in an approach velocity given by 
In (51), the current is I, while L is the length of the filamental region involved in the attraction and M is the mass of electrons and ions in length L. Peratt showed galaxy sized filaments typically approach each other today at about 1000 km/s . This interaction will be more rapid when the ZPE strength is less.
One final quantity remains to be discussed; the speed of sound in plasma. Sound moves slowly in low pressure, dense gas, while it moves quickly in high pressure, light-weight plasma. At the inception of the cosmos, the initial plasma was intrinsically linked with light photons which have low density but high pressure. This resulted in plasma that had a sound speed 57% of c [84, 85]. Thus sound waves in plasma traveled much faster when ZPE strength was lower and c was higher.
The conclusion is that, when the cosmos was younger, plasma processes formed filaments, accumulated material, pinched and formed astronomical objects much more quickly than is now possible because ZPE strengths were lower. In contrast, gravitational processes were much more leisurely.
VI. FORMING A PLASMA UNIVERSE
A. The original plasma and its composition
The composition of this plasma is also important. On the Big Bang modeling the universe was initially filled with a sea of protons, neutrons and electrons in a composition that finally resulted in the formation of about 77% hydrogen and 23% helium. Because a nucleus of mass 5 does not exist, but is needed for the nuclear cookery to continue, the Big Bang process stops there. The remaining elements are envisioned as forming inside stars which explode these elements into space when they become supernovae. These elements then become incorporated into later generations of stars and planets. But quasars from the earliest epochs with redshifts around z = 6.5 or greater, show the same iron abundance as pertains at present [see Nature 483 (3 November 2005), pp.45-50, and Astrophysical Journal 515 (1999) pp. 487-496]. This problem for the Big Bang model is enhanced since neither the equivalent spectral line width nor the Fe II/Mg II line ratio increase from then to now. Furthermore, Population I and II stars from these distant objects all show the same metal enrichment as is currently the case in our galaxy. Since a number of similar observations have noted these facts, the indications are that all the elements up to iron (and probably the rest of the Periodic Table) were in existence in their present abundances when the quasars and early stars were formed. This is a problem for all Big Bang models.
This problem does not exist in plasma physics since fusion occurs easily in z-pinched double layers, and particularly strongly in current filaments in arc-mode plasmas . But fusion is considered to occur only at ignition temperatures of millions of degrees Kelvin, so it may be wondered how this is possible. The reason is that the acceleration energy of a charged particle is given by the particle's charge number (one for an electron or proton) multiplied by the voltage it is accelerated through. This unit of energy is called the "electron-volt," (eV). To equate electron-volts to degrees Kelvin, one multiplies by 11,604.45 . As a result, a 50-million-degree ignition temperature is easily achieved with a mere 4308.7 eV with no restriction on which elements may be formed. Thus elements are formed rapidly enough to be in the first quasars and stars. So plasma physics eliminates the problem of element formation.
B. The Cosmic Microwave Background (CMB) radiation
The overall CMB pattern can be shown to be the precursor to the observed pattern of filaments and voids formed by clusters of galaxies. This same pattern is typical of those formed by plasma and was predicted by Alfvén, yet sound waves are implicated in the process. In plasma, it is found the "presence of sound wave[s] can cause quite large changes in the ionization balance depending on the magnitude and frequency of the waves as well as the atomic parameters" . Plasma sound waves (ion-acoustic waves) cause ions to move, creating currents which are then confined by their secondary magnetic fields and form filaments. Experimental observations show the sound's volume and wavelength were both important. Thus, the filamentary pattern, resulting from the action of sound waves, must have formed rapidly as sound velocity was 57% of c, and c was significantly higher with the low ZPE strength.
C. Galaxy formation
As two filaments approach, the plasma between them becomes concentrated and the result is a double radio galaxy, with the two current filaments producing the radio lobes. As the interaction continues, and filaments approach more closely, quasars and active galactic nuclei form, followed by the various types of elliptical galaxies. Finally, at the end of the sequence, a variety of spiral galaxy types form as arms develop and lengthen, then thin out as they wind around the elliptical core. This process can be timed in the laboratory and up-scaled to observed galactic dimensions. But galaxy formation rates will be much faster with higher c values and lower ZPE strengths, as the velocity of the approach and interaction of the filaments will then be correspondingly more rapid.
D. The formation of stars
For the formation of Population I stars in the spiral arms, experiments and simulations show that "star formation follows closely the morphology of the plasma in the spiral arms that are usually fragmented because of the diocotron instability. The well-known Baade description that stars in spiral arms appear 'like beads on a string' is also an equally apropos description for the simulated galaxies. … The vortex motion of the beads of stars in the arms provides the characteristic cot(ψ) motion on the rotational velocity curves of spiral galaxies" . In other words, flat rotation curves for spiral galaxies are a natural consequence of plasma physics, which avoids the need for dark matter or new gravitational physics.
In summary, Peratt states that the experiments and simulations "show first the formation of elliptical galaxies. Then, as the synchrotron-radiating Birkeland current-conducting outer plasma components move inward on the elliptical core, peculiar galaxies form and in sequence the spiral types Sd, Sc, Sb, and Sa (or their barred equivalents SBd, SBc, SBb, SBa). Stars form first in the densely compressed elliptical core (Population II stars) and then in the pinched plasma that make up the spiral arms (Population I stars)." Sorting of elements by Marklund convection in filaments, the Population I stars in the spiral arm filaments means they will have a higher metal content than the Population II stars in the core. The Population II stars formed rapidly before the spiral arm filaments developed. The plasma was thus more homogeneous and unsorted than when the Population I stars formed. Similarly, in the spiral arms of galaxies, the plasma pinch rapidly forms the Population I stars like strings of beads along the many lesser filaments there. The plasma spheres formed by the pinch would then undergo rapid collapse gravitationally to their final size ensuring both Population II and Population I stars lit up very quickly.
E. Planet formation
This two-fold sorting model of plasma physics for planets is borne out in actual practice. Thus planets near the center of the major filament will be composed of large quantities of nickel-iron and silicates. This is in fact the case. Mercury is predominantly a huge iron core, which occupies about 75% of the planet's diameter, overlaid by a small amount of silicates. The iron core of Earth is less in proportion to that of Mercury, occupying only 55% of the diameter, while that of Mars is lower again at 50% of the planet's diameter. At the same time, the silicate mantles increase in size as we go out from Mercury to Mars. It may therefore be conjectured that the parent(s) of the asteroids were composed of a small amount of nickel-iron, a large amount of silicates with a good percentage of water. The compositions of the various meteorites and asteroids support this as water content ranges up to 20% in some cases.
If we go further out in our solar system, Jupiter and Saturn only have a small quantity of nickel-iron in their cores which are largely composed of silicates surrounded by water ice. Their mantles are mainly liquid metallic hydrogen with atmospheres of hydrogen and some helium with small quantities of nitrogen compounds. Further out again, we have Uranus and Neptune whose basic structure is similar to Jupiter and Saturn with the significant difference that there is an extensive layer of highly compressed water in which is dissolved a large quantity of nitrogen in the form of ammonia. The main trend is clear. Each planet is layered in a way which follows the ionization sequence and the predominant composition of the planets follows the same sequence as we go out from the Sun. Equations (6) and (7) are also of interest. Depending on the initial strength of the ZPE, dust in plasma could grow to bodies 10-2 meters or more and be still be influenced by plasma dynamics instead of the 10-6 meters we have today. The small spherical chondrules in meteorites are of this size, yet their origin has usually been considered a mystery.
In overview, then, the planets of the solar system display the effects of this two-fold sorting process, with the major moons representing a third level of filamentation and sorting. This process is expected to operate rapidly compared with gravitational models because both sorting and interaction velocities are more efficient and rapid with lower ZPE strength. This also means that the associated electromagnetic compression on the confined plasma can be expected to rapidly initiate any final gravitational collapse needed to form a planet which would already be differentiated.
It may be thought that any gravitational collapse of a sphere sorted or layered by Marklund convection might result in a high temperature internally and on the surface. However, this does not take into consideration the fact that the properties of the vacuum were different. This difference resulted in the energy density of radiation, including heat radiation, being lower in proportion to the ZPE strength as suggested by (16) above. These facts, and the consequences, are discussed in more detail in reference . The outcome is that planets started off layered with cool interiors and surfaces. They then heated up by rapid radioactive decay deep in their interiors, particularly the short half-life elements. This heating resulted in a predictable series of events in the inner solar system. An explanation of this sequence of events can be found in "A Brief Stellar History."
Recent developments in plasma physics have given a strong indication of how galaxies and stars have formed out of plasma filaments using known processes. These processes depend on the physical properties of the vacuum, and, as such, are dependent upon the strength of the Zero Point Energy (ZPE). The data indicate that ZPE strength has increased with time, even in a static cosmos. This means that the physical properties of the vacuum have changed, and that this change also affected the behavior of plasmas. With a lower ZPE in the past come stronger electric currents, field strengths and voltages, while resistances and forces remain unchanged. It was shown that these changes result in faster interaction between filaments with faster velocities of approach, more rapid sorting of ions and faster accumulation of material. This makes galaxy and star formation a less time-consuming process. Planet-formation processes using pinch instabilities and a rapid sorting of ions in plasma filaments also results in each planet having a layered structure initially. The planets would start off relatively cool, but since radioactive elements would be concentrated near the centers of planets, the radioactive heating would result in a predictable series of events. This ZPE approach then allows many problems that confront Big Bang cosmologists to be avoided, including dark matter and dark energy, and at the same time emphasizes that plasma phenomena can account for the basic features of the universe.
Horizontal axis:Time T = 0 now, and T = 1 at origin of cosmos.
Graph of the inverse of ZPE behavior and h.
 K Birkeland, "The Norwegian Aurora Polaris Expedition 1902-1903", (1908).
Washington DC: American Geophysical Union, 1984.