*PRELIMINARY NOTE*

This document is intended to give an overview of the main conclusions reached from recent developments in light-speed research. In order to do this effectively, it has been necessary to include background information which, for a few, will already be well-known. However, for the sake of the majority who are not conversant with these areas of physics, it was felt important to include this information. While this overview is comprehensive, the actual derivation of many conclusions is beyond its scope. These derivations have, nevertheless, been fully performed in a major scientific paper using standard maths and physics coupled with observational data. Full justification of the conclusions mentioned here can be found in that thesis. Currently, that paper in which the new model is presented, is being finalised for peer review and will be made available once this whole process is complete.

*THE VACUUM*

During the 20^{th} century,
our knowledge regarding space and the properties of the vacuum
has taken a considerable leap forward. The vacuum is more unusual
than many people realise. It is popularly considered to be a void,
an emptiness, or just 'nothingness.' This is the definition of
a ** bare vacuum** [1]. However, as science has learned
more about the properties of space, a new and contrasting description
has arisen, which physicists call the

To understand the difference between
these two definitions, imagine you have a perfectly sealed container.
First remove all solids and liquids from it, and then pump out
all gases so no atoms or molecules remain. There is now a vacuum
in the container. It was this concept in the 17^{th} century
that gave rise to the definition of a** vacuum** as
a totally empty volume of space. It was later discovered that,
although this vacuum would not transmit sound, it would transmit
light and all other wavelengths of the electromagnetic spectrum.
Starting from the high energy side, these wavelengths range from
very short wavelength gamma rays, X-rays, and ultra-violet light,
through the rainbow spectrum of visible light, to low energy longer
wavelengths including infra-red light, microwaves and radio waves.

*THE ENERGY IN THE VACUUM*

Then, late in the 19^{th}
century, it was realised that the vacuum could still contain heat
or thermal radiation. If our container with the vacuum is now
perfectly insulated so no heat can get in or out, and if it is
then cooled to absolute zero, all thermal radiation will have
been removed. Does a complete vacuum now exist within the container?
Surprisingly, this is not the case. Both theory and experiment
show that this vacuum still contains measurable energy. This energy
is called the ** zero-point energy **(ZPE) because it
exists even at absolute zero.

The ZPE was discovered to be a
universal phenomenon, uniform and all-pervasive on a large scale.
Therefore, its existence was not suspected until the early 20^{th}
century. In 1911, while working with a series of equations describing
the behaviour of radiant energy from a hot body, Max Planck found
that the observations required a term in his equations that did
not depend on temperature. Other physicists, including Einstein,
found similar terms appearing in their own equations. The implication
was that, even at absolute zero, each body will have some residual
energy. Experimental evidence soon built up hinting at the existence
of the ZPE, although its fluctuations do not become significant
enough to be observed until the atomic level is attained. For
example [2], the ZPE can explain why cooling alone will never
freeze liquid helium. Unless pressure is applied, these ZPE fluctuations
prevent helium's atoms from getting close enough to permit solidification.
In electronic circuits another problem surfaces because ZPE fluctuations
cause a random "noise" that places limits on the level
to which signals can be amplified.

The magnitude of the ZPE is truly
large. It is usually quoted in terms of energy per unit of volume
which is referred to as ** energy density**. Well-known
physicist Richard Feynman and others [3] have pointed out that
the amount of ZPE in one cubic centimetre of the vacuum

Estimates of the energy density
of the ZPE therefore range from at least 10^{}44
ergs per cubic centimetre up to infinity. For example, Jon Noring
made the statement that *"Quantum Mechanics predicts the
energy density [of the ZPE] is on the order of an incomprehensible
10 ^{}*

In order to appreciate the magnitude
of the ZPE in each cubic centimetre of space, consider a conservative
estimate of 10^{}52 ergs/cc. Most people are familiar with
the light bulbs with which we illuminate our houses. The one in
my office is labelled as 150 watts. (A ** watt** is defined
as 10

*THE "GRANULAR STRUCTURE"
OF SPACE*

In addition to the ZPE, there
is another aspect of the physical vacuum that needs to be presented.
When dealing with the vacuum, size considerations are all-important.
On a large scale the physical vacuum has properties that are uniform
throughout the cosmos, and seemingly smooth and featureless. However,
on an atomic scale, the vacuum has been described as a *"seething
sea of activity" *[2], or *"the seething vacuum"*
[5]. It is in this realm of the very small that our understanding
of the vacuum has increased. The size of the atom is about 10^{}-8
centimetres. The size of an atomic particle, such as an electron,
is about 10^{}-13 centimetres. As the scale becomes smaller,
there is a major change at the ** Planck length** (1.616
x 10

This *"granular structure"
*of space, to use Pipkin and Ritter's phrase, is considered
to be made up of Planck particles whose diameter is equal to L*,
and whose mass is equal to a fundamental unit called the ** Planck
mass**, M*, (2.177 x 10

The physical vacuum of space therefore
appears to be made up of an all-pervasive sea of Planck particles
whose density is an unbelievable 3.6 x 10^{}93
grams per cubic centimetre. It might be wondered how anything
can move through such a medium. It is because deBroglie wavelengths
of elementary particles are so long compared with the Planck length,
L*, that the vacuum is 'transparent' to these elementary particles.
It is for the same reason that long wavelength infra-red light
can travel through a dense cloud in space and reveal what is within
instead of being absorbed, and why light can pass through dense
glass. Therefore, motion of elementary particles through the vacuum
will be effortless, as long as these particles do not have energies
of the magnitude of what is referred to as ** Planck energy**,
or M*c

*TWO THEORIES DESCRIBING THE VACUUM*

Currently, there are two theories
that describe the behaviour and characteristics of the physical
vacuum and the ZPE at the atomic or sub-atomic level: the ** quantum
electro-dynamic **(QED) model [8], and the somewhat more
recent

*THE QED MODEL OF THE VACUUM*

At the atomic level, the QED model
proposes that, because of the high inherent energy density within
the vacuum, some of this energy can be temporarily converted to
mass. This is possible since energy and mass can be converted
from one to the other according to Einstein's famous equation
[E = mc^{}2], where 'E' is energy, 'm' is mass, and
'c' is the speed of light. On this basis, the QED model proposes
that the ZPE permits short-lived particle/antiparticle pairs (such
as a positive and negative pion, or perhaps an electron and positron)
to form and almost immediately annihilate each other [2,11]. These
particle/antiparticle pairs are called ** virtual particles.
**Virtual particles are distinct from Planck particles which
make up the structure of the vacuum. While virtual particles are,
perhaps, about 10

The Heisenberg uncertainty principle
states that the uncertainty of time multiplied by the uncertainty
of the energy is closely approximated to ** Planck's constant
'**h' divided by 2p. This quantum uncertainty, or indeterminacy,
governed by the value of 'h', imposes fundamental limitations
on the precision with which a number of physical quantities associated
with atomic processes can be measured. In the case under consideration
here, the uncertainty principle permits these virtual particle
events to occur as long as they are completed within an extraordinarily
brief period of time, which is of the order of 10

Consequently, a proton or electron
is considered to be the centre of constant activity; it is surrounded
by a cloud of virtual particles with which it is interacting [12].
In the case of the electron, physicists have been able to penetrate
a considerable way into this virtual particle cloud. They have
found that the further into the cloud they go, the smaller, more
compact and point-like the electron becomes. At the same time
they have discovered there is a more pronounced negative charge
associated with the electron the further they penetrated into
this cloud [13]. These virtual particles act in such a way as
to screen the full electronic charge. There is a further important
effect verified by observation and experiment: the absorption
and emission of these virtual particles also causes the electron's
"jitter motion" in a vacuum at absolute zero. As such,
this jittering, or ** Zitterbewegung**, as it is officially
called [14], constitutes evidence for the existence of virtual
particles and the ZPE of the vacuum.

*THE SED MODEL OF THE VACUUM*

In the SED approach, the vacuum
at the atomic or sub-atomic level may be considered to be inherently
comprised of a turbulent sea of randomly fluctuating electro-magnetic
fields or waves. These waves exist at all wavelengths longer than
the Planck length L*. At the macroscopic level, these all-pervasive
** zero-point fields **(ZPF) are homogeneous and isotropic,
which means they have the same properties uniformly in every direction
throughout the whole cosmos. Furthermore, observation shows that
this

Importantly, with the SED approach,
** Planck's quantum constant**, 'h', becomes a measure
of the strength of the ZPF. This situation arises because the
fluctuations of the ZPF provide an irreducible random noise at
the atomic level that is interpreted as the innate uncertainty
described by Heisenberg's uncertainly principle [4,16]. Therefore,
the zero-point fields are the ultimate source of this fundamental
limitation with which we can measure some atomic phenomena and,
as such, give rise to the indeterminacy or uncertainty of quantum
theory mentioned above. In fact, Nelson pointed out in 1966 that
if the ZPR had been discovered at the beginning of the 20

In the SED explanation, the ** Zitterbewegung**
is accounted for by the random fluctuations of the ZPF, or waves,
as they impact upon the electron and jiggle it around. There is
also evidence for the existence of the zero-point energy in this
model by something called the surface

The Casimir effect is directly
proportional to the area of the plates. However, unlike other
possible forces with which it may be confused, the Casimir force
is inversely proportional to the fourth power of the plates' distance
apart [18]. For plates with an area of one square centimetre separated
by 0.5 thousandths of a millimetre, this force is equivalent to
a weight of 0.2 milligrams. In January of 1997, Steven Lamoreaux
reported verification of these details by an experiment reported
in ** Physical Review Letters** (vol.78, p5).

The surface Casimir effect therefore
demonstrates the existence of the ZPE in the form of electromagnetic
waves. Interestingly, Haisch, Rueda, Puthoff and others point
out that there is a microscopic version of the same phenomenon.
In the case of closely spaced atoms or molecules the all-pervasive
ZPF result in short-range attractive forces that are known as
** van der Waals forces** [4, 16]. It is these attractive
forces that permit

The common objections to the actual existence of the zero-point energy centre around the idea that it is simply a theoretical construct. However the presence of both the Casimir effect and the Zitterbewegung, among other observational evidences, prove the reality of the ZPE.

*LIGHT AND THE PROPERTIES OF SPACE*

This intrinsic energy, the ZPE,
which is inherent in the vacuum, gives free space its various
properties. For example, the magnetic property of free space is
called the ** permeability** while the corresponding
electric property is called the

Because light waves are an electro-magnetic
phenomenon, their motion through space is affected by the electric
and magnetic properties of the vacuum, namely the permittivity
and permeability. To examine this in more detail we closely follow
a statement by Lehrman and Swartz [22]. They pointed out that
light waves consist of changing electric fields that generate
changing magnetic fields. This then regenerates the electric field,
and so on. The wave travels by transferring energy from the electric
field to the magnetic field and back again. The magnetic field
resulting from the change in the electric field must be such as
to oppose the change in the electric field, according to ** Lenz's
Law**. This means that the magnetic property of space has
a kind of inertial property inhibiting the rapid change of the
fields. The magnitude of this property is the

The electric constant, or permittivity,
of free space is also important, and is related to electric charges.
A charge represents a kind of electrical distortion of space,
which produces a force on neighbouring charges. The constant of
proportionality between the interacting charges is 1/Q, which
describes a kind of electric elastic property of space. The quantity
Q is usually called the ** electric permittivity** of
the vacuum. It is established physics that the velocity of a wave
motion squared is proportional to the ratio of the elasticity
over the inertia of the medium in which it is travelling. In the
case of the vacuum and the speed of light, c, this standard equation
becomes

As noted above, both U and Q are directly proportional to the energy density of the ZPE. It therefore follows that any increase in the energy density of the ZPF will not only result in a proportional increase in U and Q, but will also cause a decrease in the speed of light, c.

*WHY ATOMS DON'T SELF-DESTRUCT*

But it is not only light that
is affected by these properties of the vacuum. It has also been
shown that the atomic building blocks of matter are dependent
upon the ZPE for their very existence. This was clearly demonstrated
by Dr. Hal Puthoff of the Institute for Advanced Studies in Austin,
Texas. In ** Physical Review D**, vol. 35:10, and later
in

Instead of ignoring the known laws of physics, Puthoff approached this problem with the assumption that the classical laws of electro-magnetics were valid, and that the electron is therefore losing energy as it speeds in its orbit around the nucleus. He also accepted the experimental evidence for the existence of the ZPE in the form of randomly fluctuating electro-magnetic fields or waves. He calculated the power the electron lost as it moved in its orbit, and then calculated the power that the electron gained from the ZPF. The two turned out to be identical; the loss was exactly made up for by the gain. It was like a child on a swing: just as the swing started to slow, it was given another push to keep it going. Puthoff then concluded that without the ZPF inherent within the vacuum, every atom in the universe would undergo instantaneous collapse [4, 23]. In other words, the ZPE is maintaining all atomic structures throughout the entire cosmos.

*THE RAINBOW SPECTRUM*

Knowing that light itself is affected by the zero-point energy, phenomena associated with light need to be examined. When light from the sun is passed through a prism, it is split up into a spectrum of seven colours. Falling rain acts the same way, and the resulting spectrum is called a rainbow. Just like the sun and other stars making up our own galaxy, distant galaxies each have a rainbow spectrum. From 1912 to 1922, Vesto Slipher at the Lowell Observatory in Arizona recorded accurate spectrographic measurements of light from 42 galaxies [24, 25]. When an electron drops from an outer atomic orbit to an inner orbit, it gives up its excess energy as a flash of light of a very specific wavelength. This causes a bright emission line in the colour spectrum.

However when an electron jumps to a higher orbit, energy is absorbed and instead of a bright emission line, the reverse happens -- a dark absorption line appears in the spectrum. Each element has a very specific set of spectral lines associated with it. Within the spectra of the sun, stars or distant galaxies these same spectral lines appear.

*THE REDSHIFT OF LIGHT FROM GALAXIES*

Slipher noted that in distant
galaxies this familiar pattern of lines was shifted systematically
towards the red end of the spectrum. He concluded that this redshift
of light from these galaxies was a ** Doppler effect**
caused by these galaxies moving away from us. The Doppler effect
can be explained by what happens to the pitch of a siren on a
police car as it moves away from you. The tone drops. Slipher
concluded that the redshift of the spectral lines to longer wavelengths
was similarly due to the galaxies receding from us. For that reason,
this redshift is usually expressed as a velocity, even though
as late as 1960 some astronomers were seeking other explanations
[25]. In 1929, Edwin Hubble plotted the most recent distance measurements
of these galaxies on one axis, with their redshift recession velocity
on the other. He noted that the further away the galaxies were,
the higher were their redshifts [24].

It was concluded that if the redshift represented receding galaxies, and the redshift increased in direct proportion to the galaxies distances from us, then the entire universe must be expanding [24]. The situation is likened to dots on the surface of a balloon being inflated. As the balloon expands, each dot appears to recede from every other dot. A slightly more complete picture was given by relativity theory. Here space itself is considered to be expanding, carrying the galaxies with it. According this interpretation, light from distant objects has its wavelength stretched or reddened in transit because the space in which it is travelling is expanding.

*THE REDSHIFT GOES IN JUMPS*

This interpretation of the redshift
is held by a majority of astronomers. However, in 1976, William
Tifft of the Steward Observatory in Tucson, Arizona, published
the first of a number of papers analyzing redshift measurements.
He observed that the redshift measurements did not change smoothly
as distance increased, but went in jumps: in other words they
were ** quantised** [26]. Between successive jumps, the
redshift remained fixed at the value it attained at the last jump.
This first study was by no means exhaustive, so Tifft investigated
further. As he did so, he discovered that the original observations
that suggested a quantised redshift were strongly supported wherever
he looked [27 - 34]. In 1981 the extensive Fisher-Tully redshift
survey was completed. Because redshift values in this survey were
not clustered in the way Tifft had noted earlier, it looked as
if redshift quantisation could be ruled out. However, in 1984
Tifft and Cocke pointed out that the motion of the sun and its
solar system through space produces a genuine Doppler effect of
its own, which adds or subtracts a little to every redshift measurement.
When this true Doppler effect was subtracted from all the observed
redshifts, it produced strong evidence for the quantisation of
redshifts across the entire sky [35, 36].

The initial quantisation value that Tifft discovered was a redshift of 72.46 kilometres per second in the Coma cluster of galaxies. Subsequently it was discovered that quantisation figures of up to 13 multiples of 72.46 km/s existed. Later work established a smaller quantisation figure just half of this, namely 36.2 km/s. This was subsequently supported by Guthrie and Napier who concluded that 37.6 km/s was a more basic figure, with an error of 2 km/s [37-39]. After further observations, Tifft announced in 1991 that these and other redshift quantisations recorded earlier were simply higher multiples of a basic quantisation figure [40]. That figure turned out to be 8.05 km/s, which when multiplied by 9 gave the original 72.46 km/s value. Alternatively, when 8.05 km/s is multiplied by 9/2 the 36.2 km/s result is obtained. However, Tifft noted that this 8.05 km/s was not in itself the most basic result as observations revealed a 8.05/3 km/s, or 2.68 km/s, quantisation, which was even more fundamental [40]. Accepting this result at face value suggests that the redshift is quantised in fundamental steps of 2.68 km/s across the cosmos.

*RE-EXAMINING THE REDSHIFT*

If redshifts were truly a result of an expanding universe, the measurements would be smoothly distributed, showing all values within the range measured. This is the sort of thing we see on a highway, with cars going many different speeds within the normal range of driving speeds. However the redshift, being quantised, is more like the idea of those cars each going in multiples of, say, 5 kilometres an hour. Cars don't do that, but the redshift does. This would seem to indicate that something other than the expansion of the universe is responsible for these results.

We need to undertake a re-examination of what is actually being observed in order to find a solution to the problem. It is this solution to the redshift problem that introduces a new cosmological model. In this model, atomic behaviour and light-speed throughout the cosmos are linked with the ZPE and properties of the vacuum.

The prime definition of the redshift, 'z', involves two measured quantities. They comprise the observed change in wavelength 'D' of a given spectral line when compared with the laboratory standard 'W'. The ratio of these quantities [D/W = z] is a dimensionless number that measures the redshift [41]. However, it is customarily converted to a velocity by multiplying it by the current speed of light, 'c' [41]. The redshift so defined is then 'cz', and it is this cz which is changing in steps of 2.68 km/s. Since the laboratory standard wavelength 'W' is unaltered, it then follows that as [z = D/W] is systematically increasing in discrete jumps with distance, then D must be increasing in discrete jumps also. Now D is the difference between the observed wavelength of a given spectral line and the laboratory standard [41]. This suggests that emitted wavelengths are becoming longer in quantum jumps with increasing distance (or with look-back time). During the time between jumps, the emitted wavelengths remain unchanged from the value attained at the last jump.

The basic observations therefore indicate that the wavelengths of all atomic spectral lines have changed in discrete jumps throughout the cosmos with time. This could imply that all atomic emitters within each galaxy may be responsible for the quantised redshift, rather than the recession of those galaxies or universal expansion. Importantly, the wavelengths of light emitted from atoms are entirely dependent upon the energy of each atomic orbit. According to this new way of interpreting the data, the redshift observations might indicate that the energy of every atomic orbit in the cosmos simultaneously undergoes a series of discrete jumps with time. How could this be possible?

*ATOMIC ORBITS AND THE REDSHIFT*

The explanation may well be found in the work of Hal Puthoff. Since the ZPE is sustaining every atom and maintaining the electrons in their orbits, it would then also be directly responsible for the energy of each atomic orbit. In view of this, it can be postulated that if the ZPE were lower in the past, then these orbital energies would probably be less as well. Therefore emitted wavelengths would be longer, and hence redder. Because the energy of atomic orbits is quantised or goes in steps [42], it may well be that any increase in atomic orbital energy can similarly only go in discrete steps. Between these steps atomic orbit energies would remain fixed at the value attained at the last step. In fact, this is the precise effect that Tifft's redshift data reveals.

The outcome of this is that atomic orbits would be unable to access energy from the smoothly increasing ZPF until a complete unit of additional energy became available. Thus, between quantum jumps all atomic processes proceed on the basis of energy conservation, operating within the framework of energy provided at the last quantum jump. Increasing energy from the ZPE will not affect the atom until a particular threshold is reached, at which time all the atoms in the universe react simultaneously.

*THE SIZE OF THE ELECTRON*

This new approach can be analysed further. Mathematically it is known that the strength of the electronic charge is one of several factors governing the orbital energies within the atom [42]. Therefore, for the orbital energy to change, a simultaneous change in the value of the charge of both the electron and the proton would be expected. Although we will only consider the electron here, the same argument holds for the proton as well.

Theoretically, the size of the spherical electron, and hence
its area, should appear to increase at each quantum jump, becoming
"larger" with time. The so-called ** Compton radius**
of the electron is 3.86151 x 10

*THE ELECTRONIC CHARGE*

With this in mind, it might be
anticipated, on the SED approach, that if the energy density of
the ZPF increased, the *"point-like entity"* of
the electron would be *"smeared out"* even more,
thus appearing larger. This would follow since the ** Zitterbewegung**
would be more energetic, and vacuum polarization around charges
would be more extensive. In other words, the spherical electron’s
apparent radius and hence its area would increase at the quantum
jump. Also important here is the

The QED model can explain this
formula another way. There is a cloud of virtual particles around
the "bare" electron interacting with it. When a full
quantum increase in the vacuum energy density occurs, the strength
of the charge increases. With a higher charge for the *'point-like
entity'* of the electron, it would be expected that the size
of the particle cloud would increase because of stronger vacuum
polarisation and a more energetic ** Zitterbewegung**.
(Note that

*THE BOHR ATOM*

Let us now be more specific about
this new approach to orbit energies and their association with
the redshift. The** Bohr model** of the atom has electrons
going around the atomic nucleus in miniature orbits, like planets
around the sun. Although more sophisticated models of the atom
now exist, it has been acknowledged in the past that the Bohr
theory

where ‘n' is a whole number
such as 1, 2, 3, etc., and is called the ** quantum number.**
As mentioned above, 'h' is

*BOHR'S SECOND EQUATION*

Bohr's second equation describes
the kinetic energy of the electron in an orbit of radius 'r'.
** Kinetic energy** is defined as mv

where 'e' is the charge on the electron, and 'Q' is the permittivity of the vacuum. This kinetic energy is equal in magnitude to the total energy of that closest orbit. When an electron falls from immediately outside the atom into that orbit, this energy is released as a photon of light. The energy 'E' of this photon has a wavelength 'W' and both the energy and the wavelength are linked by the standard equation

As shown later, observational evidence reveals the 'hc' component in this equation is an absolute constant at all times. The kinetic energy and the photon energy are thus equal. This much is standard physics [42]. Accordingly, we can write the following equality for the ground state orbit from Bohr's second equation:

However, as A. P. French points out in his derivation of the relevant equations [42], the energy 'E' of the ground state orbit, can also be written as

where 'R' is the ** Rydberg constant** and is equal
to 109737.3 cm

where 'K' is the ** Rydberg wavelength** such that

*A NEW QUANTUM CONDITION*

If we now follow the lead of Bohr,
and quantise his second equation, a solution to several difficulties
is found. Observationally, the incremental increase of redshift
with distance indicates that the wavelengths of light emitted
from galaxies undergo a fractional increase. Therefore, for the
ground state orbit of the Bohr atom, the wavelength 'K' must increment
in steps of some set fraction of 'K', say K/__R__ = R*. This
means that K = __R__R*. Furthermore, the wavelength increment
D can be defined as

Here, the term '__n__' is the
** new quantum integer** which fulfils the same function
as Bohr's quantum number 'n'. Furthermore, Planck's quantum constant
'h' finds its parallel in 'R*'. As a consequence, 'R*' could be
called the

Under these circumstances, the Rydberg quantum wavelength 'R*' is defined as

It therefore follows that wavelengths increment in steps of

This new quantisation procedure means that the energy (E) of the first Bohr orbit will increment in steps of D E such that

This holds because of two factors.
First, if '__n__' decreases with time, it will mimic the behaviour
of the redshift which also decreases with time. High redshift
values from distant objects necessarily mean high values for '__n__'
as well. Second, all atomic orbit radii 'r' can be shown to remain
unchanged throughout any quantum changes. If they were not, the
abrupt change of size of every atom at the quantum jump would
cause obvious flaws in crystals, which would be especially noticeable
in ancient rocks. This new quantisation procedure effectively
allows every atom in the cosmos to simultaneously acquire a new
higher energy state for each of its orbits in proportion as the
ZPE increases with time. In so doing, it opens the way for a solution
to the redshift problem.

*A QUANTUM REDSHIFT*

In the Bohr atom, all orbit energies
are scaled according to the energy of the orbit closest to the
nucleus, the ground state orbit. Therefore, if the ground state
orbit has an energy change, all other orbits will scale their
energy proportionally. This also means that wavelengths of emitted
light will be scaled in proportion to the energy of the ground
state orbit of the atom. Accordingly, if W_{ 0} is any arbitrary
emitted wavelength and W_{1} is the wavelength of the ground state
orbit, then the wavelength change at the quantum jump is given
by

Now the redshift is defined as
the change in wavelength, given by 'D', divided by the reference
wavelength 'W'. For the purposes of illustration, let us take
the reference wavelength to be equal to that emitted when an electron
falls into the ground state orbit for hydrogen. This wavelength
is close to 9.12 x 10^{}-6 centimetres. For this orbit, the value
of 'D' from the above equation is given by 7.91197 ´ 10^{}-11
centimetres since (__n__ = 1) in this case. Therefore, the
redshift

and so the velocity change

This compares favourably with
Tifft's basic value of 2.68 km/sec for the quantum jumps in the
redshift velocity. Furthermore, when the new quantum number takes
the value (__n__ = 28), the redshift velocity becomes cz =
72.8 km/sec compared with the 72.46 km/s that Tifft originally
noticed. It may also be significant that for (__n__ = 14),
the redshift velocity is 36.4 km/s compared with the 36.2 km/s
that was subsequently established by Tifft.

Imposing a quantum condition on the second Bohr equation for the atom therefore produces quantum changes in orbit energies and emitted wavelengths that accord with the observational evidence. This result also implies the quantised redshift may not be an indicator of universal expansion. Rather, this new model suggests it may be evidence that the ZPE has increased with time allowing atomic orbits to take up successively higher energy states.

*AN INCREASING VACUUM ENERGY?*

The key question then becomes,
why should the ZPE increase with time? One basic tenet of the
Big Bang and some other cosmologies is an initial rapid expansion
of the universe. That initial rapid expansion is accepted here.
However, the redshift can no longer be used as evidence that this
initial expansion has continued until the present. Indeed, if
space were continuing its uniform expansion, the precise quantisation
of spectral line shifts that Tifft has noted would be smeared
out and lost. The same argument applies to cosmological contraction.
This suggests that the initial expansion halted before redshifted
spectral lines were emitted by the most distant galaxies, and
that since then the universe has been static. In 1993, Jayant
Narliker and Halton Arp published a paper in ** Astrophysical
Journal** (vol. 405, p. 51) which revealed that a static
cosmos which contained matter was indeed stable against collapse.

However, the initial expansion was very important. As Paul S. Wesson [48], Martin Harwit [49] and others have shown, the physical vacuum initially acquired a potential energy in the form of an elasticity, tension, or stress as a result of the inflationary expansion of the cosmos. This might be considered to be akin to the tension, stress, or elasticity in the fabric of a balloon that has been inflated. Over time, this tensional energy changes its form. In exactly the same way that energy is liberated when liquid water changes to ice, so also the tensional energy of the vacuum is liberated in the form of radiation [50]. As Harwit points out, the energy residing in the elasticity of the vacuum (a form of potential energy) becomes converted into radiation (a form of kinetic energy) [49]. In the new model under consideration here, it is maintained that this potential energy becomes converted specifically into the zero-point radiation (ZPR) as the initial tension of the inflated cosmos 'relaxes' over time.

What is being proposed on this new model is that the ZPR content of the vacuum was low initially, but has built up with time as the potential energy of the elastic tension changed its form into the ZPE of the vacuum electro-magnetic fields. The redshift data indicate that this conversion of the vacuum elasticity into the ZPE essentially followed an exponential decay.

*RECONSIDERING LIGHT-SPEED*

It is at this point in the discussion
that a consideration of light-speed becomes important. It has
already been mentioned that an increase in vacuum energy density
will result in an increase in the electrical permittivity and
the magnetic permeability of space, since they are energy related.
Since light-speed is inversely linked to both these properties,
if the energy density of the vacuum increases, light-speed will
decrease uniformly throughout the cosmos. Indeed, in 1990 Scharnhorst
[51] and Barton [20] demonstrated that a lessening of the energy
density of a vacuum would produce a higher velocity for light.
This is explicable in terms of the QED approach. The virtual particles
that make up the *'seething vacuum'* can absorb a photon
of light and then re-emit it when they annihilate. This process,
while fast, takes a finite time. The lower the energy density
of the vacuum, the fewer virtual particles will be in the path
of light photons in transit. As a consequence, the fewer absorptions
and re-emissions which take place over a given distance, the faster
light travels over that distance [52, 53].

However, the converse is also
true. The higher the energy density of the vacuum, the more virtual
particles will interact with the light photons in a given distance,
and so the slower light will travel. Similarly, when light enters
a transparent medium such as glass, similar absorptions and re-emissions
occur, but this time it is the atoms in the glass which absorb
and re-emit the light photons. This is why light slows as it travels
through a denser medium. Indeed, the more closely packed the atoms,
the slower light will travel as a greater number of interactions
occur in a given distance. In a recent illustration of this light-speed
was reduced to 17 metres/second as it passed through extremely
closely packed sodium atoms near absolute zero [54]. All this
is now known from experimental physics. This agrees with Barnett's
comments in **Nature** [11] that *'The vacuum is certainly
a most mysterious and elusive object…The suggestion that
the value of the speed of light is determined by its structure
is worthy of serious investigation by theoretical physicists.'*

On the new model,the redshift measurements imply that light-speed, c,
is dropping exponentially. For each redshift quantum change, the speed of light has
apparently changed by a significant amount. The precise quantity
is dependent upon the value adopted for the ** Hubble constant**
which links a galaxy's redshift with its distance.

*AN OBSERVED DECLINE IN LIGHT-SPEED*

The question then arises as to
whether or not any other observational evidence exists that the
speed of light has diminished with time. Surprisingly, some 40
articles about this very matter appeared in the scientific literature
from 1926 to 1944 [56]. Some important points emerge from this
literature. In 1944, despite a strong preference for the constancy
of atomic quantities, N. E. Dorsey [57] was reluctantly forced
to admit: *'As is well known to those acquainted with the several
determinations of the velocity of light, the definitive values
successively reported … have, in general, decreased monotonously
from Cornu's 300.4 megametres per second in 1874 to Anderson's*
*299.776 in 1940 …'* Even Dorsey's own re-working of
the data could not avoid that conclusion.

However, the decline in the measured
value of 'c' was noticed much earlier. In 1886, Simon Newcomb
reluctantly concluded that the older results obtained around 1740
were in agreement with each other, but they indicated 'c' was
about 1% higher than in his own time [58], the early 1880's. In
1941 history repeated itself when Birge made a parallel statement
while writing about the 'c' values obtained by Newcomb, Michelson,
and others around 1880. Birge was forced to concede 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' *[59]. Each of these three eminent
scientists held to a belief in the absolute constancy of 'c'.
This makes their careful admissions about the experimentally declining
values of measured light speed more significant.

*EXAMINING THE DATA*

The data obtained over the last 320 years at least imply a decay in 'c' [56]. Over this period, all 163 measurements of light-speed by 16 methods reveal a non-linear decay trend. Evidence for this decay trend exists within each measurement technique as well as overall. Furthermore, an initial analysis of the behaviour of a number of other atomic constants was made in 1981 to see how they related to 'c' decay. On the basis of the measured value of these 'constants', it became apparent that energy was being conserved throughout the process of 'c' variation. In all, confirmatory trends appear in 475 measurements of 11 other atomic quantities by 25 methods. Analysis of the most accurate atomic data reveals that the trend has a consistent magnitude in all the other atomic quantities that vary synchronously with light-speed [56].

All these measurements have been
made during a period when there have been no quantum increases
in the energy of atomic orbits. These observations reinforce the
conclusion that, between any proposed quantum jumps, energy is
conserved in all relevant atomic processes, as no extra energy
is accessible to the atom from the ZPF. Because energy is conserved,
the c-associated atomic constants vary synchronously with c, and
the existing order in the cosmos is not disrupted or intruded
upon. Historically, it was this very behaviour of the various
constants, indicating that energy was being conserved, which was
a key factor in the development of the 1987 Norman-Setterfield
report, ** The Atomic Constants, Light And Time** [56].

The mass of data supporting these conclusions comprises some 638 values measured by 43 methods. Montgomery and Dolphin did a further extensive statistical analysis on the data in 1993 and concluded that the results supported the 'c' decay proposition if energy was conserved [60]. The analysis was developed further and formally presented in August 1994 by Montgomery [61]. These papers answered questions related to the statistics involved and have not yet been refuted.

*ATOMIC QUANTITIES AND ENERGY CONSERVATION*

Planck's constant and mass are two of the quantities which vary synchronously with 'c'. Over the period when 'c' has been measured as declining, Planck's constant 'h' has been measured as increasing as documented in the 1987 Report. The most stringent data from astronomy reveal 'hc' must be a true constant [62 - 65]. Consequently, 'h' must be proportional to '1/c' exactly. This is explicable in terms of the SED approach since, as mentioned above, 'h' is essentially a measure of the strength of the zero-point fields (ZPF). If the ZPE is increasing, so, in direct proportion, must 'h'. As noted above, an increasing ZPE also means 'c' must drop. In other words, as the energy density of the ZPF increases, 'c' decreases in such a way that 'hc' is invariant. A similar analysis could be made for other time-varying 'constants' that change synchronously with 'c'.

This analysis reveals some important
consequences resulting from Einstein's famous
equation [E = mc^{}2], where 'E' is energy, and 'm' is mass.
Data listed in the Norman/Setterfield Report
confirm the analysis that 'm' is proportional to 1/c^{}2
within a quantum interval, so that energy (E) is unaffected as
'c' varies. Haisch, Rueda and Puthoff independently verify that
when the energy density of the ZPF decreases, mass also decreases.
They confirm that 'E' in Einstein's equation remains unaffected
by these synchronous changes involving 'c' [16].

If we continue this analysis,
the behaviour of mass 'm' is found to be very closely related
to the behaviour of the ** Gravitational constant** 'G'
and gravitational phenomena. In fact 'G' can be shown to vary
in such a way that 'Gm' remains invariant at all times. This relationship
between 'G' and 'm' is similar to the relationship between Planck's
constant and the speed of light that leaves the quantity 'hc'
unchanged. The quantity 'Gm' always occurs as a united entity
in the relevant gravitational or orbital equations [66]. Therefore,
gravitational and orbital phenomena will be unchanged by varying
light speed as will planetary periods and distances [67]. In other
words, acceleration due to gravity, weight, and planetary orbital
years, remain independent of any variation of 'c'. As a result,
astronomical orbital periods of the earth, moon, and planets form
an independent time-piece, a dynamical clock, with which it is
possible to compare atomic processes.

*THE BEHAVIOUR OF ATOMIC CLOCKS*

This comparison between dynamical
and atomic clocks leads to another aspect of this discussion.
Observations reveal that a higher speed of light implies that
some atomic processes are proportionally faster. This includes
atomic frequencies and the rate of ticking of atomic clocks. In
1934 'c' was experimentally determined to be varying, but measured
wavelengths of light were experimentally shown to be unchanged.
Professor Raymond T. Birge, who did not personally accept the
idea that the speed of light could vary, nevertheless stated that
the observational data left only one conclusion. He stated that
if 'c' was actually varying and wavelengths remained unchanged,
this could only mean *'the value of every atomic frequency...must
be changing'* [68].

Birge was able to make this statement because of an equation linking the wavelength 'W' of light, with frequency 'F', and light-speed 'c'. The equation reads 'c = FW.' If 'W' is constant and 'c' is varying, then 'F' must vary in proportion to 'c'. Furthermore, Birge knew that the frequency of light emitted from atoms is directly proportional to the frequency of the revolution of atomic particles in their orbits [42]. All atomic frequencies are therefore directly proportional to 'F', and so also directly proportional to 'c', just as Birge indicated.

The run-rate of atomic clocks
is governed by atomic frequencies. It therefore follows that these
clocks, in all their various forms, run at a rate proportional
to c. The atomic clock is thereby c-dependent, while the orbital
or dynamical clock ticks independently at a constant rate. In
1965, Kovalevsky pointed out the converse of this. He stated that
if the two clock rates were different, *'then Planck's constant
as well as atomic frequencies would drift' *[69]. This is precisely
what the observations reveal.

This has practical consequences in the measurements of 'c'. In 1949 the frequency-dependent ammonia-quartz clock was introduced and became standard in many scientific laboratories [70]. But by 1967, atomic clocks had become uniformly adopted as timekeepers around the world. Methods that use atomic clocks to measure 'c' will always fail to detect any changes in light-speed, since their run-rate varies directly as 'c' varies. This is evidenced by the change in character of the 'c' data following the introduction of these clocks. This is why the General Conference on Weights and Measures meeting in Paris in October of 1983 declared 'c' an absolute constant [71]. Since then, any change in the speed of light would have to be inferred from measurements other than those involving atomic clocks.

*COMPARING ATOMIC AND DYNAMIC CLOCKS*

However, this problem with frequencies
and atomic clocks can actually supply additional data to work
with. It is possible in principle to obtain evidence for speed
of light variation by comparing the run-rate of atomic clocks
with that of dynamical clocks. When this is done, a difference
in run-rate is noted. Over a number of years up to 1980, Dr. Thomas
Van Flandern of the US Naval Observatory in Washington examined
data from lunar laser ranging using atomic clocks, and compared
their data with data from dynamical, or orbital, clocks. From
this comparison of data, he concluded that *'the number of atomic
seconds in a dynamical interval is becoming fewer. Presumably,
if the result has any generality to it, this means that atomic
phenomena are slowing down with respect to dynamical phenomena'*
[72]. Van Flandern has more recently been involved in setting
the parameters running the clocks in the Global Positioning System
of satellites used for navigation around the world. His clock
comparisons indicated that atomic phenomena were slowing against
the dynamical standard until about 1980. This implies that 'c'
was continuing to slow, regardless of the results obtained using
the frequency-dependent measurements of recent atomic clocks.

*AN OSCILLATION IS INVOLVED*

These clock comparisons are useful in another way. The atomic dates of historical artifacts can be approximated via radiometric dating. These dates can then be compared with actual historical, or orbital, dates. This comparison of clocks allows us to examine the situation prior to 1678 when the Danish astronomer Roemer made the first measurement of the speed of light. When this comparison is done, light-speed behaviour is seen to include an oscillation on top of the exponential decay pattern revealed by the redshift. This evidence seems to suggest that the oscillation peaked somewhere around 500 AD. Furthermore, it is of interest to note that measurements of several atomic constants associated with 'c' also seem to indicate that the 'c' decay curve may have bottomed out around 1980 and has started to increase again. More data are needed before a positive statement can be made.

Because the oscillation is small, it only becomes apparent as the exponential curve tapers off. As both Close [73] and D'azzo & Houpis [74] pointed out in 1966, this is typical of many physical systems. The complete response of a system to an input of energy comprises two parts: the forced response and the free or natural response. This can be illustrated by a number of mechanical or electrical systems. The forced response comes from the injection of energy into the system. The free response is the system's own natural period of oscillation. The two together describe the complete behaviour of the system. In this new model, the exponential curve represents the energy injection into the system as the initial elastic tension changed its form into the ZPE, while the oscillation comes from the free response of the cosmos to this energy injection. This dual process has affected atomic behaviour and light-speed throughout the cosmos.

*LIGHT-SPEED AND THE EARLY COSMOS*

The issue of light-speed in the
early cosmos is one which has received some attention recently
in several peer-reviewed journals. Starting in December 1987,
the Russian physicist V. S. Troitskii from the Radiophysical Research
Institute in Gorky published a twenty-two page analysis in ** Astrophysics
and Space Science** regarding the problems cosmologists
faced with the early universe. He looked at a possible solution
if it was accepted that light-speed continuously decreased over
the lifetime of the cosmos, and the associated atomic constants
varied synchronously. He suggested that, at the origin of the
cosmos, light may have travelled at 10

In 1993, J. W. Moffat of the University
of Toronto, Canada, had two articles published in the ** International
Journal of Modern Physics D **(see also [75]). He suggested
that there was a high value for 'c' during the earliest moments
of the formation of the cosmos, following which it rapidly dropped
to its present value. Then, in January 1999, a paper in

Like Moffat before them, Albrecht
and Magueijo isolated their high initial light-speed and its proposed
dramatic drop to the current speed to a very limited time during
the formation of the cosmos. However, in the same issue of ** Physical
Review D **there appeared a paper by John D. Barrow, Professor
of Mathematical Sciences at the University of Cambridge. He took
this concept one step further by proposing that the speed of light
has dropped from the value proposed by Albrecht and Magueijo down
to its current value over the lifetime of the universe.

An article in ** New Scientist**
for July 24, 1999, summarised these proposals in the first sentence.

*IMPLICATIONS OF THIS PROPOSED MODEL*

**(1). Energy output from distant astronomical
sources**

Distant quasars [76] and gamma ray bursts [77] have an intense stream of redshifted photons coming from them. However, similar objects which are known to be closer, do not have the same energy output. There is a phenomena that seems to be related to distance resulting in a dilemma regarding the energy source for both types of objects.

It is normally assumed that redshifted photons outside our galaxy were emitted with the same energy as un-shifted photons within our galaxy. However we know that redshifted photons have lower energy. This model accepts that these photons had a lower intrinsic energy at emission. It can be shown that the energy output by stars will remain approximately the same at all quantum jumps. Therefore stars must have emitted more lower energy photons per unit of volume in times past, thus preserving the approximate total energy output.

This explains why we see the much more intense streams of redshifted photons from distant astronomical objects as compared with similar nearby objects: in order to maintain the total energy output, more lower energy photons were emitted earlier.

**(2). Quantum 'shells'**

This model assumes each quantum change occurs instantaneously throughout the cosmos. Yet a finite time is taken for light emitted by atomic processes to reach the observer. Consequently, the observed redshift will appear to be quantised in spherical shells centred about any observer anywhere in the universe. The distance between shell boundaries will be constant because of the unique behaviour which is described by equations derived from the observational data. This distance between shell boundaries is about 138,000 light years and marks the distance between successive redshift jumps of 2.73 km/s. All objects that emit light within that shell will have the same redshift.

**(3). 'Missing mass' in galaxy clusters**

The relative velocities of individual galaxies within clusters of galaxies are measured by their redshift. From this redshift measurement, it has been concluded that the velocities of galaxies are too high for them to remain within the cluster for the assumed age of the universe. Therefore astronomers have been looking for the 'missing mass' needed to hold such clusters together by way of gravitational forces. However, if the redshift does not represent velocity, as is currently accepted, then the problem disappears. As actual relative velocities of galaxies will be small, no mass is 'missing.' (Note that this does not solve the problem of the 'missing mass' within spiral galaxies which is a separate issue.)

**(4). A uniform microwave background**

An initial very high value for light-speed means that the radiation in the very early moments of the cosmos would be rapidly homogenised by scattering processes. This means that the radiation we observe from that time will be both uniform and smooth. This is largely what is observed with the microwave background radiation coming from all parts of the sky [78]. This model therefore provides an answer to its smoothness without the necessity of secondary assumptions about matter distribution and galaxy formation that tend to be a problem for current theories.

**(5). Corrections to the atomic clock**

As a consequence of knowing how light-speed and atomic clocks have behaved from the redshift, atomic and radiometric clocks can now be corrected to read actual orbital time. As a result, geological eras can have a new orbital time-scale set beside them. This will necessitate a re-orientation in our current thinking on such matters.

**(6). Final note**

The effects of changing the vacuum energy density uniformly throughout the cosmos have been considered in this presentation. This in no way precludes the possibility that the vacuum energy density may vary on a local astronomical scale, perhaps due to energetic processes. In such cases, dramatically divergent redshifts may be expected when two neighbouring astronomical objects are compared. Arp has listed off a number of potential instances where this explanation may be valid [79, 80].

*SUMMARY*

This model proposes that an initial small, hot, dense, highly energetic universe underwent rapid expansion to its current size, and remained static thereafter. The vacuum potential energy in the form of an elasticity, tension, or stress, acquired from the initial expansion, became converted exponentially into the vacuum zero-point radiation. This had two results. First, there was a progressive decline in light-speed. Concurrently, atomic particle and orbital energies throughout the cosmos underwent a series of quantum increases, as more energy became available to them from the vacuum. Therefore, with increasing time, atoms emitted light that shifted in jumps towards the more energetic blue end of the spectrum. As a result, as we look back in time to progressively more distant astronomical objects, we see that process in reverse. That is to say the light of these galaxies is shifted in jumps towards the red end of the spectrum. The implications of this model solve some astronomical problems but, at the same time, challenge some current historical interpretations.

**ACKNOWLEDGMENTS:**

My heartfelt thanks goes to Helen Fryman for the many hours she spent in order to make this paper readable for a wide audience. A debt of gratitude is owed to Dr. Michael Webb, Dr. Bernard Brandstater, and Lambert Dolphin for their many helpful discussions and sound advice. Finally, I must also acknowledge the pungent remarks of 'Lucas,' which resulted in some significant improvements to this paper.

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