**ENERGY COMPRESSIBILITY**

**Astrophysics and Variable
Speed of Light (VSL) Theories**

**Part 1: Compressible Flow and
Relativity**

·
**Introduction**

·
**The Nature of Energy**

·
**Compressible Energy
Flow: A Fundamental Variable Speed of Light (VSL) Theory**

·
**Longitudinal
Compressive Waves and Transverse Electromagnetic Waves**

·
**Compressible Energy Flow and Relativity**

**1.
****A New Problem with Addition of Velocities**

**2.
****The Fitzgerald/Lorentz Solution to Relativity**

**3.
****Einstein’s Special Relativity Solution**

**4.
****Historical Comment on Special Relativity**

**5.
****The Compressible Energy Flow Solution**

**6.
****Unsteady Flow and Acceleration: Effects of Spatial
Directionality on Michelson-Morley Fringe Shifts**

**7.
****Results of Recent Laser/Maser/Oscillator Tests on
Variability of Speed of Light**

**8.
****Revision to Lorentz Transformations and Form Invariance**

**9.
****Summary of Review of Relativity **

·
**Equation of State for Compressible Systems**

·
**Wave Speed Ratio c/c _{o} and the Isentropic Ratios**

·
**The Energy Equation
Has Two Forms: World A → World B Transformations; A Binary
Universe**

·
**The Hidden Mass or Dark Matter of the Universe: A New Solution**

·
**The Dark Energy of the Universe: A New Solution**

·
**The Equation of State in Compressible Flow Also Has Two Forms**

·
**Transformations from World A Matter to World B Matter**

·
**Summary**

__APPENDIX
A Compressible
Photon Flow and the Results of
Michelson-Morley Type Experiments__

** **

**INTRODUCTION **

** **

This Website presents a new, physically
based, variable speed of light (VSL) theory which is an application of standard compressible fluid flow theory.

**The
theory treats energy flows and associated transformations of matter as being compressible. **

Several recent approaches towards solving
major problems in cosmology and astrophysics connected with comic inflation,
dark matter and dark energy have involved
abandoning the currently accepted
fixed value for the speed of light **c**
in space ( 3 x 10^{8} m/s). Such
theories are called **Variable Speed of
Light Theories (VSL)**. ** **Currently,
most of these proposals are still in the stage of *ad hoc* speculation.

However**, compressible **energy flow theory**,** is an application of well established, standard gas dynamics and
aerodynamic theory [1,2] and is
therefore based on a century of
scientific and engineering results.
**It introduces the necessary VSL
condition as a physically-based
formulation**, instead of a tentative, ad hoc VSL proposal.

First, we outline the basic concept of
energy compressibility and show its relationship to the variable speed of
light, and to relativity.

Then, because the compressible energy flow
equation contains a parameter (**n)** which
represents the number of ways the energy of the system is divided, and which
can have either positive or negative integral values, the theory introduces the
possibility of a **binary universe** [ A B] in which
transformations of matter can take place involving release of radiant energy.

**THE
NATURE OF ENERGY**

The name energy is derived from a Greek root
relating to work or relating to activity
[Gk. *energeia; * e*nerges * from *en-*on* +* *ergon*-* *work].* *

The precise scientific concept of energy
in science emerged only quite late in the 19^{th} century. Previously,
the idea was implicit in Galileo’s
concept of mechanics, and later it was called by Huygens *vis
viva* or living force.* *Energy is still today a somewhat subtle
concept [3]. This is probably due to the fact that it emerges from the
mechanics of motion, not as a directly observable entity, but only as a
calculated quantity ½ mV^{2} which is conserved or unchanged in
magnitude during physical motions (V).
This conserved or unchanging quantity which is involved in the mechanical
motions of a material body of mass **m**
is named **kinetic energy **usually
denoted by T: ** [ K.E. = T = ½ mV ^{2}].**

A second kind or category of energy is
stored energy or **potential energy. **The
sum of these two kinds of energy, kinetic and potential, is the total
mechanical energy E of the system, and this is the quantity that is conserved.
Of course, in a complete treatment of the subject other kinds of energy such as
electrostatic and electromagnetic energies, gravitational energy, chemical
energy, surface free energy, and so on must be included, but in our present
thermodynamic approach the mechanical energy will suffice.

Since energy is always conserved in any
physical change, it is obviously a powerful
and fundamental scientific concept. As so it is a curious fact that the
science of mechanics can actually be formulated ( in terms of force and
momentum) without ever bringing in the concept
of energy at all. However,
alternatively, it is also possible to formulate mechanics entirely from the
concept of energy, and this approach, the Hamiltonian formulation, results in
the most general and powerful formulation of the science of mechanics. It is
little wonder that energy appears as a fundamental but still subtle concept.

It should also be pointed out that the
concept of compressibility is applied here only to energy flows between
material particles, or to energy flows within the various physical *fields, *such as the electromagnetic
field, the gravitational field, the quantum field and so on. There is no question of postulating the
separate physical existence of an energy field *per se.*

__COMPRESSIBLE__** ENERGY FLOW: A Fundamental, Variable Speed
of Light (VSL) Theory**

The
standard, kinematical, steady flow, compressible energy equation is [1,2]:

** c ^{2}
= c_{o}^{2} - V^{2}/n
(1)**

where **c**
is the__ variable__

[In engineering and thermodynamics, the ratio of the specific heats **k** = c_{p}/c_{p} is
often used instead of n. The relationships between n and k are: n = 2/(k -
1) and k = (n + 2) /n].

Next, we extend the compressible energy
flow concept from a material fluid to the flow of light i.e. to a flow of
photons. The question of whether this is justified will be dealt with later,
where it will be shown that compressibility at the critical or Mach 1 flow
speed (where V = c = c*; V/c* = 1 = M) brings about physical changes that
convert longitudinal, compressive wave motions ( e.g. acoustic type,
compressible waves) into the
necessary transverse wave motion, such
as must apply to a flow of photons of light in a compressible electromagnetic
field, and which will justify the
extension of the compressible energy theory to the case of light and other
electromagnetic phenomena. It is also perhaps worth pointing out that an
incompressible medium would have an infinite wave speed; consequently any
finite wave speed, such as the speed of light in space, suggests that
compressibility may be involved.

For **isothermal
flow**, that is for flow with constant temperature, n is equal to infinity.
This makes the term V^{2}/n in Eqn.1 equal to zero and so c always just
equals c_{o}. This means that for isothermal flow, relative motion (V)
has no effect on the wave speed c.

For one-dimensional energy or particle
flows, such as in a linear accelerator, **n**
equals 1. For uniform motions such as in the Michelson-Morley experiment which
will be discussed in detail below, **n **appears
to be equal to 9. For accelerated flows n appears to have values between 1 and
8.

The **critical
wave speed** c* occurs when the flow speed V equals the wave speed. This is
called the **Mach 1 speed**; V = c =c*
and V/c = V*/c* = M = 1. Speeds less than the critical speed are **subcritical
**(in gases they are called subsonic ). Speeds greater than the
critical speed c* or V* are called **supercritical
** (in gases, supersonic). At the
critical speed the physical behaviour of the medium alters, becoming stiff or
quasi-solid so to speak. In
supercritical flow the wave equations alter to resemble those governing
vibrating strings or membranes.

The **maximum
flow speed** is the escape to a vacuum V_{max}, which is given
by **V _{mav}
=n c_{o . }**Therefore, for any value of n
greater than unity the escape flow speed V

We see that, once compressibility occurs
in a flow, then the wave speed c is no longer a constant but varies with the
relative flow velocity V. When V is zero the wave speed has its maximum or
static value c_{o}. As V increases, the wave speed c diminishes from the maximum
wave speed c_{o }in an amount given by Equation 1, and vice versa._{
}. When the flow speed V equals the maximum or escape speed V_{max}
, the wave speed c has decreased to zero.

For unsteady energy flow, such as in a wave
pulse, we have an additional term added to Equation 1:

**c ^{2} = c_{o}^{2}
- V^{2}/n - 2cV/n
(2)**

The extra energy term, interaction energy,
or 2cV term in Eqn. 2 may indicate the physical basis for the ** wave/particle duality** of quantum
physics..

__The plot
of the energy equation c ^{2} = c_{o}^{2}
- V^{2}/n ( ±n) is as follows:__

(Note that in
World B there is no upper limit to
either V or c ).

The first physically based, variable speed of light
theory appeared in 1979, and work has continued since then **[Power, 4, 5, 6, 7, 8, 9, 10, 11].
O**ther VSL theories have been advanced, mostly *ad hoc *proposals designed to
solve various cosmological problems that have arisen with general relativity ** [Moffatt, Magueijo, Barrow,Youm [
12,13,14,15]. **

**LONGITUDINAL
COMPRESSIVE WAVES AND TRANSVERSE
ELECTROMAGNETIC WAVES**

There are innumerable, striking,
insightful analogies between compressible flow and nearly all parts of physics.
However, if these are to be more than interesting similarities, we must
establish that the compressible wave speed c in Eqn. 1 corresponds
physically to the speed of a **transverse,** electromagnetic wave, for
example light waves at speed c. This transverse wave nature of electromagnetic
disturbances was a fatal problem for the validity of the old ‘ether medium’
theory in the early 20^{th} century.

With **compressible**
flow, however, we can now invoke the physical transformation that takes place
at the critical or Mach 1 speed (c = V =
V*; V*/c = M = 1), where the flow physically transforms to a shock
discontinuity whose longitudinal
compression physically restricts all vibration to the transverse direction only. Essentially, the uniformly
moving electron emits no electromagnetic waves; once acceleration or vibration
of the electron sets in, electromagnetic waves (photons) are emitted. These, on
the present compressibility theory, are now compression wave/particles with
only lateral or transverse wave motions physically permitted. The photons then
travel at the compressive local wave speed c. In space, with no relative flow
V, c becomes the static wave speed c_{o} equal to 3 x 10^{8}
m/s. In the presence of matter and when there is relative motion we have two
different possibilities:

a) Steady relative motion: c = c_{o} [
1- (1/n) (V/c_{o})^{2}]^{1/2;}; ^{}

b) Unsteady, pulsed, or accelerated
relative flow: c = c_{o }[1 ±
(1/n) (V/c_{o}) ]

Steady motions, since they involve a
second order term in the ratio V/c_{o, } affect the speed of light appreciably only for
large velocities. Even the orbital speed of the earth at 30 km/s affects the
speed of light by not more than one part
in a billion or so.

Unsteady motions or accelerations, since they involve a first order
term in the ratio V/c_{o}, can detectibly affect the speed of light for
relative flow speeds which are a factor
of 10^{4 } smaller than steady
motions, i/e down to a meter per second and less..

The complete evaluation of the concept of
compressibility against all the experimental facts on the nature and speed of
light is obviously a very considerable task. A full theoretical treatment of development of transverse wave motion in critical, compressible flow requires
advanced gas dynamics and electromagnetic theory. It will be of interest to see how many of the varied
electromagnetic phenomena can be encompassed by compressibility considerations,
and what unexpected new insights may emerge.
Many close analogies between electromagnetic and hydrodynamic phenomena
have, of course, long been known [16].

**COMPRESSIBLE
ENERGY FLOW AND RELATIVITY**

The concept of relativity in physics can have several
meanings. We have (a) *physical* relativity and (b) *reference coordinate * relativity. Physical relativity can be illustrated
in the case of the of air flow past the
wing of an airplane. Here only the relative speed of the air past the wing is
physically relevant. It does not matter to the physical pressure forces whether the air is blowing past the airplane wing on
the ground, or if the wing is moving through the air in flight. Only the
relative air flow V past the wing determines the physical pressure effects of lift and drag on the wing. This is
the meaning of relative motion V in the theory of compressible fluid flow.

When we come to the flow of light we must also
distinguish physical from coordinate relativity, and in each case we must avoid
uncritical assumptions about the physically relevant speed.

The compressible flow velocity V in
Equation 1 is a physically relative
flow. One might suspect therefore
that compressibility of flow has something to say about the theory of
relativity, and this is indeed so. If we
put the mass m into Eqn. 1 explicitly, we have

(m)c^{2}
= (m)c_{o}^{2} - (m) V^{2}/n = E

which has the form of the familiar special
relativity mass/energy relationship E =
mc^{2}, but now with a variable
wave speed c and a kinetic energy term V^{2}/n^{.}.

In compressible flow, the physical
behavior of the flow in terms of pressure, density, temperature, wave speed, and so on does not depend on whether the flow
is moving past a material body or whether the body is moving through the
compressible field. Both are relative motions and will have the same physical
effects.

When we turn to measurements of the speed of light in
space, we shall find, if we assume that light is a compressibility effect, that
we will have to adjust our light speed for any motion or speed of our measuring
apparatus through space, since by Equation 1 any relative motion V will alter
the speed of light c.

This problem with light arose very soon after the
nature of light as an electromagnetic wave was discovered in the late
nineteenth century. The addition of the speed of light **c** to the velocity **V **of a
light measuring instrument, for example, an interferometer mounted on the earth
which is moving through space at V = 30 km/s around the sun, was soon found to
be a big problem. Compressible flow was then not at all well understood, and so
the addition of velocities was made using only the classical or so-called
Galilean method. How this attempt failed, and how the solution embodied in Einstein’s special relativity theory came to
gradually be adopted, will now be discussed.

**1. The New
Problem with Addition of Velocities**

The classical or “Galilean” addition of velocities is
algebraically straightforward. To take a nineteenth century example , of the
kind used by Einstein to demonstrate the classical addition of velocities, if a
train is moving through a railroad station at V_{t} = 20 mph and a
passenger on the train is walking through the railroad car toward the engine at
V_{p}= 3 mph, then his speed over- the- ground as seen by the
stationmaster is simply the sum of the velocities, 20 _{ }+ 3 = 23 mph or [ V_{t} + V_{p} = 23]. The
Galilean transformations between one inertial coordinate frame and another
moving relative to it at velocity V are expressed as follows:

x = x′ +
vt

y = y′

z = z′

t = t′

u_{x } = u_{x}′ + V (Classical direct addition of velocities)

Turning to the case where light waves are involved
with the motion of material bodies, researchers at first reasoned that, since
light was now thought to be a wave, then the light wave must be moving in some sort of universal wave
medium or ‘electromagnetic ether’, just
as sound waves move in the material medium, air. Measurements of the speed of
light in an apparatus such as an interferometer on the earth’s surface should
then show an addition of light velocity **c**
to the velocity of the earth through space V_{o} of 30 km/s ( c + V_{o}) along that direction, but, at right angles
to the motion the speed of light, would remain
unaltered at c. The effect on
the speed of light of this difference (
c + V_{o}) versus c, although very small- it being only about one part
in a billion - could be measured in a sensitive interferometer designed by the
American physicist **Michelson.** The effect of the difference in velocities
along the orbital motion and at right angles to it should show up in the
interferometer as a tiny displacement or ‘shift’ in the position of the light interference
fringes as the instrument was rotated through a 90 degree angle. The equation
for the expected fringe shift calculated on direct
addition of velocities is:

= [2(V/c)^{2}]
*l* /

where *l* is
the optical path length ( in Miller’s instrument *l* was 32 m and the wavelength of the
light used was 5.7 x 10^{7} m) , V
is the relative motion of the earth in orbit
30 km/s, and c is 3 x 10^{8} m/s, the speed of light in
space.

For the dimensions of the instrument used by Miller,
for example, the expected fringe shift should have been 1.12 fringes. The
tests, however, showed that only about 1/9 th of the expected shift predicted
by the classical addition of velocities actually occurred. Expressed in terms
of velocity through space, this small observed shift corresponded to about 1/3
of the expected orbital velocity of the earth i.e. to only about 10 km/sec
versus 30 km/sec. What was wrong?

Several decades of great debate and repetition of the
Michelson experiment followed. The result was always the same. The expected,
classically calculated fringe shifts were never observed. Either the much
smaller than expected fringe shifts that were observed had to be explained, or
they had to be discarded as experimental error and some other theory of light
propagation through space devised.

**2. The
Fitzgerald/Lorentz Solution to the
Problem of Addition of Velocities**

**Fitzgerald** and **Lorentz** independently ( on the
assumption that the small observed fringe shifts were actually just
experimental noise and should be taken as a zero shift) proposed that the
orbital motion of the earth through space somehow compressed or contracted the electrons of the interferometer itself
along the direction of the motion in just the right amount to mask the
predicted fringe shift completely. This
purely *ad hoc *solution to the
problem produced the Fitzgerald/Lorentz contraction factor , which can be
expressed as .

l′/ l =
[1 - (V/c)^{2}]^{1/2} , or

l/ l′ =
[ 1 - (V/c)^{2}]^{-1/2 } =

where l is the length of the instrument at rest, and l′
is the (contracted) length when moving at velocity V. c is the speed of light through space ( 3 x
10^{8} m/s). In terms of the Michelson interferometer, l would be the
length of the optical arm at right angles to the earth’s motion and **l′** would be the length of the
contracted arm along the direction of the orbital motion through space around
the sun. When the instrument is rotated through 90 degrees the lengths would
become interchanged. By applying this correction factor to the velocity
additions in the two different directions the fringe shift predictions became
zero.

Of course, this meant discarding the small observed
fringe shifts and treating them as being zero. However, they were certainly
very small, and could be considered as being within the experimental error of
most of the instruments of the day. Lorentz
expanded his theory and derived corresponding corrections to length and time
measurements in relatively moving systems which would be in accord with a nil
effect of the Michelson/Morley experiments.

It is important to note that the Fitzgerald/Lorentz explanation,
although somewhat odd, is still a physical one. They proposed this physical
contraction of as body’s length in order to nullify or exactly cancel out the classical addition of velocities which
was giving a far too large fringe shift prediction. Still, the solution somehow
seemed artificial, since when one tried to measure the orbital motion of the
earth through the electromagnetic ether or through space, the proposed physical contraction effect intervened to
just exactly cancel the effect of the motion and made it impossible to observe.
Was motion real and precisely calculable, or was it just apparent and
relative? On another view, the new
contraction factor was just a sort of
fudge factor which served to reconcile a bad prediction with observation.

**3.
Einstein’s Special Relativity Solution**

In 1905 **Einstein** proposed a radical solution that succeeded in
deriving the Fitzgerald /Lorentz
contraction factor, not from the
proposed physical contraction, but from two apparently contradictory
physical propositions. This theoretical derivation, although seemingly
irrational, gave the same contraction factor that Fitzgerald/Lorentz had
proposed, and so it quieted the intellectual uneasiness of many physicists with
the unexpected results of the Michelson/Morley type experiments.

What Einstein essentially did was this. He argued
that, since we cannot detect motion through space ( i.e. if we take the Michelson-Morley type attempts at motion detection as showing no
motion at all) therefore all motions are
relative. Thus two uniformly moving systems have the same laws of motion. Both are equally valid, and the same laws of
nature, such as simple addition of velocity, should apply in each. Next, he
assumed that all measurements are made with light signals or by other
electromagnetic observations. Thus the
constant and finite speed of light comes into the matter, and the second of his
two propositions emerges, namely the __constancy of the speed of light for all
observers even those moving relatively to each other__.

When his two postulates are combined, the Fitzgerald
/Lorentz contraction factor automatically emerges from his theory. In addition to producing the desired
contraction factor Einstein’s derivation also gave reconciling equations for
length and time which were identical to the Lorentz transformations, and so
this added to their credibility as revealing a fundamental discovery of some
mysterious complexity in nature itself.

To take a simple, but still accurate, illustration
using the addition of velocities and his constant light speed assumption, we
have in one system the speed of light as c (and so its squared value is c^{2}).^{ }In another system moving uniformly
with respect to the first system at the velocity V, we have the speed of light
as seen from the stationary system to be [ c^{2} - V^{2 }]^{1/2} Now, according to Einstein’s relativity
assumption there is no preferred reference measurement frame and one value is
as good as the other. Moreover the speed of light must actually be the same for
all observers, and so we are obliged to set the values for each of them as
equal

c^{2}
= [ c^{2} -V^{2} ]^{ }

This is an obvious algebraic impossibility ,and so to
reconcile the numerical incompatibility, Einstein then introduced a factor which would automatically
make them equal, so that there would be no algebraic contradiction and
calculations adding the speed of light to the full speed of material bodies
could still be made between moving
systems with no arithmetic error, as follows

c^{2 } = ^{2} [c^{2}
- V^{2}]

And, dividing by c^{2}, we get the value of
his adjustment or ‘transformation’ factor

= [1 - (V/c)^{2}
]^{-1/2}

We see that this is the Fitzgerald/ Lorentz contraction factor which has now emerged
automatically from Einstein’s two assumptions. He then went on to apply this
correction factor to length, time, and
to all of the subsidiary or related
physical quantities of velocity mass,
work, energy and so on:

1/ = [1 - (V/c)^{2} ]^{1/2} = l′ / l = dt′ / dt = W/W_{o} = E_{o }/ E = m_{o
}/ m etc.

However much Einstein succeeded in reconciling an
assumed zero result of the Michelson-Morley experiment with retaining the classical
addition of velocities, his procedure of equating things that are clearly
unequal seemed to most scientists to be somehow unreasonable, and therefore
only to be accepted because it was required**
by the nature of physical reality itself**, that is to say, that it was
imposed or **required by the experimental
facts**.

**However, in
actual fact, the Michelson-Morley experiments never produced a zero observed
fringe shift**; there was always a
small shift of about 1/10 of the classically expected value, but it was never
zero. So now today, if the small
residual fringe shifts of all Michelson/Morley experiments can be explained by
a sound physical theory, then the abandonment of strict rationality would no longer be an experimentally based
requirement, and would now be scientifically unjustified.

For the review of the Michelson-Morley experiments see
__ ____APPENDIX
A Compressible
Photon Flow and The Results of Michelson-Morley Type Experiments__

It may be well
to point out here that, from the point of view of compressibility theory and
its Equation 1, the correct procedure is not the addition of **velocities** but, instead, it is the ** addition of energies. **This is perhaps why Einstein, in effect,
in order to derive his special relativity contraction factor γ, had to
equate not two unequal velocities c and
( c - V) but the __squares__
of the velocities, i.e. two **energies ( **assuming
unit mass**)** c^{2} and (c^{2} - V^{2})
to get his c^{2 } =^{ } ^{2 }(c^{2}
- V^{2}).

__4.
Historical scientific quotations on the relativity problem__

At this point, to properly set the historical
background, we shall turn to some comments by scientists over the years on
this theory of relativity.

1. *Special
Relativity*, **A.P. French**, Norton,
New York, 1968

**“In the first encounter with Einstein’s
relativity, one may get impressions like these:**

**There is a lot of algebraic wizardry - much
of it bewildering. One can learn to do some of the tricks, but it doesn’t make
much physical sense. Such feelings are
very natural. No matter how long one has lived with the results of special
relativity, there is something very non-intuitive about it… But relativity does
make good sense and is not in a separate compartment from Galileo-Newton”.**

2. *Space, Time
and Matter.* **Hermann Weyl.** Dover,
New York, 1952

**“Although conditions were such that,
numerically, even only 1 per cent of the displacement of the fringes expected
by Michelson could not have escaped detection, no trace of it was to be found
when the experiments was performed.**

**In fact, not only the Michelson-Morley
experiment but a whole series of further experiments designed to demonstrate
that the motion of the earth through
space around the sun has an influence on
combined mechanical and electromagnetic phenomena, have led to a nul result..**

**We
are to abandon our belief in the objective meaning of simultaneity; it
was the great achievement of Einstein in the field of the theory of knowledge
that he banished the dogma from our minds and this is what leads us to rank his
name with that of Copernicus.”**

3. *The Emperor’s
New Mind.* **Roger Penrose.** Vintage
1990.

**“It may seem outrageous to introduce such a
strange concept of time-measure, at variance with our intuitive notions.
However, there is now an enormous amount of experimental evidence in favor of
it.”**

4. *A Brief
History of Time*. **Stephen Hawking**.
Bantam Books, 1988.

**“The special theory of relativity was very
successful in explaining that the speed of light appears the same to all
observers ( as shown by the Michelson-Morley experiment) and in describing what
happens when things move a speeds close to the speed of light.”**

5. *Introduction
to the Theory of Relativity.* **Peter
Gabriel Bergmann. Dover, 1942.**

**“ The Lorentz transformation equations do
away with the classical notions of space and time. The experiment of Michelson
and Morley has been repeated many times under varying conditions. All these new experiments have confirmed the
original results, with the exception of those which were carried out by D.C.
Miller. It is very difficult to decide
why Miller’s experiments show an effect which appears to indicate an ‘ether
drift’ of about 10 km/sec. However, since all the evidence of other experiments
points to the accuracy of the Lorentz transformation equations, it is
reasonable to assume that Miller’s results were caused by systematic
experimental error which has not yet been discovered. “**

6. *Theory of
Relativity.* **Wolfgang Pauli**.
Preface 18 Nov. 1956 Inn Dover . 1981.

**“There
is a point of view according to which relativity theory is the endpoint
of classical physics , which means physics in the style of
Newton-Faraday-Maxwell, governed by the ‘deterministic” form of causality in space
and time.**

**By its epistemological analysis of the
consequence of the finiteness of the velocity of light ( and with it all signal
velocities) the theory of special relativity was the first step away from naïve
visualization. The concept of the state of motion of the luminiferous ether, as
the hypothetical medium was called earlier, had to be given up , not only
because it turned out to be unobservable, but because itt became superfluous as
an element in mathematical formalism, the group-theoretical properties of which
would only be disturbed by it.”**

**7. ***Special
Relativity *. **Albert Shadowitz**. Dover. 1968

**“ ..the correctness of the Michelson-Morley
experiment. This experiment, however, had been performed very carefully. It duplicated,
with much greater accuracy, the results of an earlier experiment carried out by
Michelson alone in 1881. Also, when the experiment was repeated by others the
same results were obtained. The velocity was always the same, for all
observers, in all directions. There was
no way out: the Michelson-Morley experiment was correct. It violated common
sense by stating that the velocity of light in a vacuum, c, was the same for
all observers. But it was true.**

**(Einstein’s ) second axiom was that c, the
velocity of electromagnetic waves in a vacuum, was indeed a constant for all
observers. At the time it was made, his was a very bold step, for the
experimental evidence in favor of this was not then overwhelming, as it is
today. Then as now, it was contrary to common sense. This axiom accepted the
experimental evidence as fact.”**

8. * Space
and Time.* **Hermann Minkowski**.
108. In the Principle of Relativity, a
collection by Dover, New York 1952.

**“The views of space and time which I wish
to lay before you have sprung from the soil of experimental physics, and
therein lies their strength. They are radical. Henceforth space itself and
time itself, are doomed to fade away
into mere shadows, and only a kind of union of the two will preserve an
independent reality.”**

9. As usual, **R.
Bruce** **Lindsay and Henry Margenau**
are factual, comprehensive and balanced. In their * Foundatuons of Physical Reality*,
Dover 1957 they write:

**“Michelson’s interferometer method was
sensitive enough to detect a chan”ge by the shift in the interference fringes
brought about by a rotation of the apparatus. When the experiment was first
performed in 1881 the values … obtained
were of the order of one-tenth to one-fourth of the expected value.**

**The strange results were attributed to
experimental error, and it was concluded that the experiment was inconsistent
with the assumption of a stationary ether with respect to which the earth
moves. Alternatively, one could say that even if the earth does move through
the ether the experiment might, for some reason, be incompetent to detect this
motion. When the experiment was repeated more carefully and with more elaborate
apparatus by Michelson and Morley in 1887 the result was that the indicated
relative velocity of the earth and ether did not exceed one-fourth of the
earth’s orbital velocity. , As D.C Miller has pointed out, this was not
strictly speaking a null result. Nevertheless, it has been so interpreted for
many years.**

**The experiment has been repeated with
various modifications and refinements a
great many times/. The work of Miller has been the most extensive and appears
to indicate a genuine positive result with a time difference corresponding to a
maximum velocity of about 10 km/sec, which however has a slight seasonal
variation. (Other observers ( mentioned in Miller’s paper, to which reference
should be made for details) have
reported results corresponding to velocities as low as 1 km/sec. and have
interpreted them as indicative of a nul
effect. It seems clear that the whole
question is still an open one and further work should be carried out. The
situation is interesting, for a great deal of theorizing during the last years
of the nineteenth century and the first part of the twentieth were based
definitely on the existence of a nul result of the experiment.”**

[Just how pivotal the Michelson-Morley results are can
be seen from the following additional comments by Lindsay and Margenau in the
same book]:

**“It must be confessed that the theory of
relativity is by no means complete, its greatest shortcomings being its failure
to take account of electromagnetic properties and of the quantum theory in the
quantum domain… It may be appropriate to
raise again the question discussed in connection with the experimental findings
of D.C. Miller and their bearing on the special theory; if the predicted
observations of an eventually modified general relativity theory do not agree
with the precise experimental results , what attitude should one take towards
the theory? Its real realm of
usefulness in the future will in all probability be in the field of
cosmological speculation.”**

10 .**D.C. Miller**
himself put it this way ( *Reviews of Modern Physics*. July 1933):

**“Since the Theory of Relativity postulates
an exact nul effect from the ether-drift-experiment which had never been
obtained in fact, the writer ( Miller)
felt impelled to repeat the experiment. “**

Both Lorentz and Einstein took an intense interest in
the D.C. Miller extensive work, meeting with him, discussing his results and
encouraging him to continue the tests.

11. **Einstein**
himself is characteristically both restrained and straightforward in his
assertions:

*(a )
Relativity*. Hartsdale House, New York. 1947: “If the principle of relativity were not
valid we would therefore expect that the direction of motion of the earth at
any moment would enter into the laws of nature.
However, the most careful observations have never revealed any such
anisotropic properties in terrestrial physical space.”

**(b) In his original paper entitled On the Electrodynamics of Moving Bodies
. Annalen der Physik, 1905 ( The
Principle of Relativity . Dover , New York, 1952), he wrote: “the unsuccessful attempt to discover any
motion of the earth relative to the
light medium suggests that the
phenomena of electrodynamics as well as mechanics posses no properties
corresponding to the idea of absolute rest”.**

**(c) (Scientific American , March 1930
quotes Einstein as saying : “ If Professor
Miller’s research is confirmed, my theory falls, that’s all.” **

__5. The New
Compressible Energy Flow Solution to the Velocity Addition Problem:__

In 1979 it was first realized that the theory of
compressible energy flow had something fundamental in common with the Einstein
theory of relativity. The work began with a study *Shock Waves in a Photon Gas* (4)] on the Fizeau Effect related to
the speed of light in moving water. A
proposal was requested by NASA and a number of papers followed **Power [4,5,6,7,8,9,10,11]. ** The connection to relativity arose because the
fundamental Fitzgerald/Lorentz/Einstein contraction factor (1- (V/c)^{2)})^{-1/2} has
exactly the same (inverted) form as
in the compressible energy flow equation
for the special case where n, the energy division parameter is unity. We have
the steady flow energy equation

c^{2}= c_{o}^{2} - V^{2}/n,

and, dividing through by c_{o} to get the
compressibility ratio of wave speeds c/c_{o,} we have

c/c_{o}
= [ 1 - 1/n(V/c_{o})^{2}
]^{1/2},

which is identical to the inverse of the
Fitzgerald/Lorentz/Einstein factor = [ 1 - (V/c_{o})^{2}]^{-1/2} with n set to unity.

In compressible flow, the Lorentz contraction factor becomes a physical
speed of light ratio c_{o}/c.

At first, this remarkable result was simply
interpreted as showing that special relativity was basically a physical compressibility effect, since all the
transformations for length, time, mass, work, velocity etc. could now be
derived by simply computing the wave speed compression ratio c/c_{o, } for the case where n = 1:

c/c_{o}
=1/ = [ 1 - 1/n(V/c_{o})^{2} ]^{1/2}
= l′/l = dt′/ dt = W/W_{o}
= E_{o }/ E = m_{o }/ m = ν/ν_{o} etc.

Later, however, the analysis led to a critical review
of the numerous Michelson-Morley type experiments over the past century. It was
then realized that the discarded, small, residual, observed fringe shifts
effects in that experiment, which
Lindsay and Margenau emphasized were real, **could
all now be interpreted as a detection of
the (local) motion of the earth ( and the attached Michelson
interferometer) through space at the orbital speed of 30 km/s.**

This is because, when the Michelson-Morley type
results were reanalyzed using various values for the energy partition parameter
n, it was found that n = 9 gave a very
good fit to the experimental data from a
dozen or so separate experiments,
and that the fit improved as the sophistication of the instruments improved,
with the deviation being less
than 1% for some highly stable laser
interferometers where the experimental errors are minimal.

The Miller interferometer had an optical path length l
of 32 m, and the wave length of light * *was 5.7 x 10^{-7} m. The classical
fringe shift expected with the orbital speed of the earth V taken as 30 km/s
was = [2(V/c)^{2}]
*l* / which gives shift of 1.12 fringes. The observed value
was 0.122. When the compressible formula
[2(V/c)^{2}] *l* / n with n = 9 is used,
the expected fringe shift becomes. 0.124, in good agreement with the observed
value.

Further tests by Michelson et.al., Kennedy and
Thorndike, Illingworth, Joos, Picard and
others followed. These all give results with n = 9 which agree with the
compressibility predictions. See __APPENDIX
A Compressible
Photon Flow and The Results of Michelson-MorleyType Experiments__

We can see more clearly the changed situation with
compressible flow if we restate the fringe shift equation to include the energy
partition parameter n. We then have for the fringe shift

= [(V/c)^{2}]
2*l* / n
(3)

and for the ‘contraction’ factor , we have

c/c_{o}
= 1/ = [ 1 – 1/n(V/c_{o})^{2} ]^{1/2} ; or γ = [ 1 – (V/c_{o})^{2}
] ^{-1/2 } = c_{o}/c (4)

Let us now examine three different physical cases.

First we take **isothermal
flow where n is equal to infinity **( n **=
)**. In this case
the expected fringe shift becomes zero from Eqn. 3 and the wave speed c becomes
always c_{o} for all observers. These two conditions match the Einstein
assumptions of a zero detectible fringe shift in Michelson-Morley-Miller
optical experiments, and also yield his constant value for c for all observers on internally consistent
physical flow grounds. However,__
his Lorentz contraction factor then simply becomes unity!__ Special relativity, when physically based, becomes internally inconsistent. Furthermore, if the system is isothermal,
then the speed of light is constant and all the related dynamic and
thermodynamic variables ( V, p. v. T, , etc.) must also be
constant; therefore there can be no forces, and no global
cosmic expansion or contraction without
violating the first law of thermodynamics. The constant speed of light
proposition therefore appears to be inconsistent with the observations of
mechanics, of gravitation and of an expanding universe.

Second, if we **take
n equal to 1,** we get the
Lorentz/Fitzgerald contraction factor
from Eqn. 4 in the same form
as Einstein did, but now the predicted
fringe shift of Eqn. 3 becomes the maximum value predicted by the classical addition of velocity which is never experimentally observed. Moreover, the speed of light must now be a variable and dependant on the
flow speed V, thereby contradicting his constant speed of light assumption.

So if we take the Einstein constant speed of light
assumption we inevitably we get the wrong fringe shift, and if we take his
Lorentz transformation factor we must get a
variable speed of light.

However, when we **take
n = 9**, we get the predicted fringe shift values for the Michelson-Morley-Miller experiments which are
actually observed. Therefore, compressible flow equations yield fringe shift
values which agree with the observations, and are physically and internally consistent; in contrast, special relativity is internally
contradictory, is not physically based, and its fringe shift predictions do not
agree with experiment __APPENDIX
A Compressible
Photon Flow and The Results of Michelson-MorleyType Experiments__

Thus, while compressibility can physically explain, simply and directly, a positive shift from Equation 3, special relativity cannot. For special relativity, Eqn. 3 is to be
discarded, and, instead, a rather involved argument must be advanced for the
existence of an (unobserved) length
contraction. This hypothetical contraction
in a specific direction is designed to exactly cancel a predicted fringe
shift and to justify an essentially arbitrary decision to claim that all fringe
shifts observed under uniform motion must actually be zero. In compressible
flow fringe shifts continually occur as the fractional speed of light c/c_{o} changes due to observable relative
motion V, or due to the equally
observable fractional changes in frequency _{o} ].

**An so we are
back to the possibility envisioned by Lindsay and Margenau in the excerpt
above, namely that: (a) the Michelson
Morley experimental results are real, (b) they fit a self-consistent,
experimentally verified physical theory, (c) the earth’s orbital, and axial
motions through ( local) space are
detectible by optical or electromagnetic observations.** What are the
consequences?

__6. Unsteady Flow and Acceleration:
Effect on Spatial Directionality of
Michelson-Morley Fringe Shifts__

There were two problems with Miller’s
results. First, his observed fringe shifts while undoubtedly real, were only
about one third (and the corresponding ‘ether drift’ velocities only about one
ninth ) of the classically expected values. Second, everyone agreed that his maximum fringe shifts should
occur when one of the interferometer arms is aligned with the orbital speed ( V_{o} = 3 x
10^{8} m/s) at noon and midnight, and would therefore be
periodic at 6 hourly intervals. Instead, they
occurred almost randomly at other times during the sidereal day as the
earth turned on its axis in space. Both of Miller’s problems must be addressed.

We have shown above ( and in Appendix A)
that the first problem of the magnitude
of the fringe shifts is resolved when the compressible flow parameter n = 9 is
introduced. The second problem, the directionality of the fringe shift maxima,
requires taking into account the hitherto neglected accelerated motions that
are associated with the rotation of the interferometer itself on its own axis
as the reading are made.

These rotational motions are very small in
comparison with the orbital speed of 30,000 meters per second. But, the steady flow of the earth’s orbital
motion is a second order effect in the ratio of V and c_{o } i.e. _{.}[( V_{o}/c_{o})^{2}
], with the fringe shift given by

= (2*l* / ) [(V^{2}/c_{o}^{2})] /n (3)

whereas, in the case of unsteady flow,
that is for accelerated motions and pulse flow, we have instead a first order
equation in (V/c_{o}) and a first order fringe shift:

= ( 2l/) ( V/c_{o})/n

And so, even very small motions, if they
are unsteady or involve accelerations, can
produce fringe shifts which are
comparable to those produced by the much
larger uniform orbital speed. We also
must not uncritically assume that the value for n is always the same for
accelerated motions as for uniform or steady flow motions.

Let us, for example , consider the
tangential rotational speed V_{T }of Miller’s interferometer. The
instrument was 4 m in diameter and rotated
once in 50 seconds. The tangential rotation velocity V_{T} was therefore about 0.25 m/s.

Inserting Miller’s value of 32 m for the
optical path length l and 5.7 x 10^{-7} m for the wave length of light, the fringe shift to be expected is = (2l /)(0.25/c_{o})/n. For n = 9
we get 0.094. For n = 2 the shift is
0.047, and for n = 9 it is 0.01. This
additional rotational fringe shift is
also periodic in a half-turn of the instrument, just as is the case for the orbital
fringe shift. Therefore it will interact with the latter effect to obscure the
expected dependence of maximum orbital fringe shift on the noon and midnight
orientations. This interaction or interference could therefore account for
Miller’s second problem of lack of an expected six hourly **directionality i**n his orbital fringe shifts.

For the radial component of rotational
motion, (V_{r} = 0.16 m/s), the associated fringe shift is 0.06 for n =
1, for n equal to 2 it is 0.03 and for n = 9 it is 0.007, the effect being periodic in a full 360 degree turn of the
instrument. This radial
acceleration may possibly account for the so-called full turn effect which Miller always observed, and which had
about the same magnitude as the orbital half-turn fringe shift. Morley, Miller
and Lorentz were all quite concerned
with the full turn effect. Miller in his
data analysis simply filtered out the large
first harmonic shift and retained
only the second harmonic or half turn periodic effect as pertinent to the orbital
speed or ‘ether drift’ test. Lorentz considered that the full turn effect
challenged the validity of special relativity
and that the existence such an effect would be forbidden by it [21].

The introduction of accelerations into the
fringe shift calculation clearly complicates the matter. However, it also -
together with the introduction of a variable energy partition parameter n -
allows us to explain the observations of the various classical Michelson-Morley
type experiments in a satisfactory manner. The matter of accelerations and the
possible variability of n in such cases will be discussed in more detail in the
next section.

__7. Results of Laser/Maser/Oscillator Tests on the Variability of
the Speed of Light in Space __

Following
the optical Michelson-Morley type
experiments described above, there were
a number of tests carried out using
masers and lasers and crystal oscillators in various configurations and combinations.. These include:

22. Ives, H.E., and Stillwell, G. R. An Experimental Study
of the Rate of a Moving Atomic Clock *J. Opt. Soc. Amer*. 28, 7, 215-226,
(1938) .

23. J. P. Cedarholm and C.H. Townes,
A New Experimental Test of Special Relativity. *Nature*, **184**, 1350-51
(1959).

24. T.S. Jaseja,
Javan, J. Murray, and C.H. Townes*, *Test of Special Relativity or of the
Isotropy of Space by the Use of Infrared Masers. * Phys. Rev.*** 133**, A1221 (1964).

25. Brillet, A and Hall, J.L. Improved Laser Test of the Isotropy of Space*.
Phys. Rev. Letters* 42,9, 49 ( 1979).

26. Wolf, P., et al.
Test of Lorentz Invariance using
a Microwave Resonator. *Phys. Rev. Lett*. 90, 6, 060402 ( 2003).

27. Muller H, et al.,
Modern Michelson- Morley Experiment using Cryogenic Optical
Resonators. *Phys. Rev. Lett*. 91, 2, 020401, (2003).

All of these tests involved measuring a
frequency change against the expected Lorentz frequency relationship for
uniform flows. One group of tests
involves a (V/c_{o})^{2}
or second order term

=_{o} [ 1 -
(V/c_{o})^{2} ]^{1/2}

None of these researchers suspected,
however, that the compressibility
parameter **n** might be involved and that the proper test,
instead, might be

= =_{o} [ 1 -
(1/n) (V/c_{o})^{2} ]^{1/2} ; _{o} = 1- [ 1-
(1/n) (V/c_{o})^{2}]^{1/2}

In addition, we have seen above that
acceleration terms can be about the same order of magnitude as the steady flow
effects usually sought. For this second
group, which comprises the unsteady flows, and starting from rest conditions
with c_{o} as the rest wave
speed, we have a first order equation in
(V/c_{o})

_{o} =1 ±
(1/n) (V/c_{o}), or

_{o}= (1/n) (V/c_{o})

Since all of the published
laser/maser/oscillator tests ignore both the energy partition parameter **n** and acceleration effects, their
conclusions are now more or less invalid.

A complete analysis of all the recent
tests listed is outside the scope of the present study. In some instances not
enough information on the precise dimensions of the instrumentation and the
operational procedures is given in the original papers to reassess the results
arising from unsteady flow effects. More seriously, in most cases, large
frequency shifts arising from rotation are simply discarded completely as
presumably due to magnetic or other effects, or to systematic frequency drift,
and only the residual changes in the shifts at different times of the day are
examined.

(1) **Stillwell and Ives** [22] (1938) used the rays from a canal ray tube to test for a Doppler shift caused by the rays
moving at about 1/5 x 10^{6} m/s or 0.005 of the speed of light. They
established that within experimental error the emitted frequency was altered by
the factor [ 1- (V/c_{o})^{2}
]^{1/2}. Thus was a positive
demonstration of the effect of motion of a light source on the speed of the
emitted light. [It therefore differs completely from the Michelson Morley experiment
where special relativity requires that there be no observable effect whatever
from the motion of the source on the optical transmission of light i.e. it requires a zero fringe shift.

Compressibility, on the other hand
requires and accepts a positive effect in both experiments: a positive fringe
shift in Michelson-Morley and a positive frequency shift in Stilwell and Ives,
as observed.

(2) **Cedarholm and Townes** [23] (1959) used an ammonia maser to look for
an ether drift effect in the Doppler shift.
They compared the frequencies of two such masers with their opposing
beams run in parallel, and when the apparatus was rotated through 180°. Their
tests were run at intervals over a year.
The expected beat shift f, based on an ether drift effect, was f =
[4uV/c_{o}^{2}] where V = 30 km/s, u
the speed of the ammonia molecules is 600 m/s, and the frequency of the
excited molecules is 2.387 x 10^{10} /s. The expected beat shift was
19.8 cps, so that the actual expected frequency shift was half this or about 10
cps. The observed shift was only 1.08 ± 0.02 cps. Their conclusion was, since
the observed shift of 1.08 was far less than the predicted 10 cps, that the
speed of light was thereby shown to be unaffected by the orbital motion of the
earth in space of 30 km/s.

Cedarholm et al., in effect, simply
discarded the small 1.08 cps frequency shift they observed at each revolution,
considering it as due mostly to magnetic effects, and instead, considering only
the variability of the observations from turn to turn which was about 1/50 cps
they concluded that there was no orbital speed effect.

However, if compressible flow with n = 9
is included, then the predicted
frequency shift becomes f = 10/9 = 1.11 cps , which agrees well with the
observed value of 1.08.

(3) **Jaseja, Javan, Murray and Townes** [24] (1964), using two rotating
masers positioned at right angles to one another, tested for the ether drift
second order effect in (V/c)^{2}. They reported on a short six hour test in
January. Upon rotation through 90° they
got a basic, repeating frequency shift
of 275 kc/s plus a variation of not more than 3 kc/s. They discarded the
observed repeatable frequency shift on rotation of 275 kc/s as presumably due
to magnetostriction, and concluded that there was no evidence of any frequency
shift effect arising from the from the earth’s orbital motion of 30 km/s

Their expected frequency shift equation
was (V/c_{o})^{2} , which for V = 30 km/s gives
3000 kcs expected frequency shift on rotation. Only about 275kcs shift was
observed and was discarded. However,
when the compressibility parameter n is included, we get (V/c_{o})^{2}
/9_{ }which gives 3000/9 = 333 kcs predicted versus 275 observed. Put
another way 275 kcs ( 275kHz) gives a velocity of 27.2 km/s which is within 10% of the earth’s
orbital speed of 30 km/s.

If the unsteady effects of rotation are
included, using estimates of the effective radius of rotation of their
apparatus of about 1 meter or less, we get about 20 kcs with n = 9, 100 kcs
with n = 2, and 200 kcs shift with n = 1. These additional unsteady shifts will
add or subtract from the basic rotational shift of 275 kcs depending on their
respective periodicities with respect to that of the basic shift.

The conclusion now is that Jaseja et al. did
detect the effect of the steady orbital motion of the earth plus unsteady or
accelerated motions of rotation, and that the observations generally agree with
compressibility predictions.

(4) **Brillet and
Hall** [25] in 1979 used a helium- neon stabilized laser beam coupled to a
Fabry -Perot resonator and mounted on a
rotating table. .They tested for frequency shifts related to the earth’s
rotation and orbital motion looking for a zero effect as required by the
Lorentz contraction formula 1- [(1/n)
(V/c_{o})^{2} ]^{1/2} where n is equal to one. They observed
a large frequency shift on rotation of the apparatus on its axis which they labeled spurious and caused by
what they termed centrifugal stretching of the Fabry-Perot interferometer due
to rotation. They state only that : The centrifugal stretching due to
rotation is - 10 kHz at f = ( 1 turn)/13 sec) and implies a compliance -10
times that of the bulk spacer material. This frequency shift cannot , however, be due to
centrifugal stretching since their Fabry-Perot interferometer which is their
length etalon is mounted __tangentially__ on the rotating table and not
radially where any centrifugal effect would have eto act if it were to alter the
length of an instrumental component. It seems most probable that their
frequency shift observed upon rotation is the same one as found by Jaseja et
al. where it amounted to 275 kHz. Brillet and Hall do not give the observed
frequency shift for a full turn of their instrument. If their 10 kHz is a
frequency shift rate per second ( and
their inclusion of the rotation rate seems to support that) then the frequency
shift due to rotation would be 10 x 10 kHz = 100 kHz ,since their operational
rotation rate is given as a table rotation frequency , f, of 1 per -10
sec.

If their observed and discarded frequency shift is 100
kHz, then with n = 9 we get a motion in space of V = [(_{o})9 c_{o}]^{1/2} = 30.25
km/sec, using their basic laser frequency of equal _{ }to 8.85 x 10^{13} cps.. Thus,
Lorentz violations have been observed in
this test as well as in the others cited above, and the alternative conclusion from
compressibility considerations now is that (a) the variability of light
speed c/c_{o}, (b) frequency shift and (c) the
motion of the earth through space of V ≈ 30 km/s may in fact all be
verified.

Brillet and Hall, having screened out any rotational
effects and drift ( including cosmic drift) effects, went on to test the tiny residual frequency fluctuations for
correlation with the earth’s motions, and quite naturally finding none of
statistical significance after their efficient screening of the real effects,
concluded instead that Lorentz violation was now ruled out to a new and higher
degree of precision.

(5) **Wolf et al.
[**26**] and Muller et al.** [27] in
2003 have taken up experimental work again since the last major test by Brillet
and Hall. They no longer rotate their instrumentation, operating it in a fixed
laboratory orientation in the manner of Kennedy and Thorndike . This procedure
relies on the rotation of the earth on its axis and the earth’s orbital motion
around the sun for the relative motion test. This means that the effects shows
up only as an accumulated systematic frequency drift over the lapsed time for
the motion ( namely 86,400 sec. diurnally , and
1.58 x 10^{7} sec. semiannually). Given that any systematic
drift of the instrumentation is once again routinely eliminated from the data
as being spurious, these new tests for space motions using only [ 1 - (1/n) (Vc_{o})^{2}
]^{-1/2} where n is always taken
as unity and there is no distinction made between steady and accelerated
motions , are nearly meaningless, although the instrumental precision is
impressive indeed.

The great precision now possible with use of lasers
and masers in optical experiments on the effect of motion on the speed of light
is potentially a great advance. However, the theoretical or expected outcome of
the test must also be correctly formulated
if the proper conclusions are to be drawn from the increasingly more
precise observations. The addition and subtraction of relative
speeds to the speed of light cannot be arbitrary or uncritical, but must be in
accord with the physical nature of the interaction of light with the
instrumentation. Otherwise, only greater and greater precision in
establishing that an inapplicable theory
will result. All the above experiments test
the observations against Lorentz violation [28], that is to say against
[ 1 - (1/n)(V/c_{o})^{2}]^{-1/2} where n is always
taken as unity whereas compressibility
requires a test for steady motions against [ 1 - **1/9**(V/c_{o)}^{2} ]^{ -1/2} which in general means that fringe shifts or
frequency oscillations as little one ninth of the Lorentz permitted values are
the real physical effects to test against. Small effects presently discarded
completely are actually the very
evidence for detection of relative
motion which is the object of the experiments in the first place.

One final note should be added on the
choice of the energy partition parameter **n**
in the case of unsteady motions. A possible difference from the value n = 9 for
steady motions is not really so unexpected in unsteady compressible flow when
we consider that when unsteady flows and
accelerations occur ** forces and inertia **also
immediately arise. However, at the moment
the value for n that is appropriate in each case of accelerated motion
appears to be a matter for experimental determination in this relatively
unexplored area of optics and photonics.

In the case of material gases, it is well
established that the accelerations in boundary layer, for example, bring about
many unexpected complications including changes in specific heat which require
a change in the value of n.

In conclusion, the data from Stilwell and
Ives, Cedarholm and Townes, Jaseja et al., and from Brillet and Hall fit the predictions of compressible flow
theory. The oscillator tests of Wolf et al. and Muller et al. apparently discard the essential relative motion data as
due to systematic drift or other spurious effects, and so these tests can not
yet be fully evaluated.

**8.
Revision to Lorentz Transformations and Lorentz Form Invariance**

The standard Lorentz transformations of special
relativity are:

x = ( x′
- vt)/

y = y′

z = z′

t = (t′ + vx′/c^{2})/

where = [ 1- (V/c)^{2}]^{-1/2}

These highly useful formulae for high-speed ( i.e. relativistic) mechanics
will obviously be changed somewhat by the proposed new revision of special
relativity.

1. The principal change necessary will be
to replace _{n=1} = [1 - (V/c)^{2} ]^{-1/2} by a **generalized correction factor** with
other values of the energy partition factor n included namely _{n} = [1 - 1/n(V/c)^{2} ]^{-1/2} n being always a positive number whose value is to be determined by experiment
for each class of physical applications.
[For example, for terrestrial optical interactions of the
Michelson-Morley type the proper value for n appears from the experiments to be
9].

a). For n = 1, that is for 1-dimensional flow, and
probably also for highly accelerated flows,: the value of is the current Lorentz
transformation value _{n=1}
= [1- V/c)^{2} ]^{-1/2} ;
c < c_{o} for any velocity V; V_{max} = n c_{o} = c_{o} . Length corrections due to relative motion are
a maximum and are given by the Lorentz/Fitzgerald/Einstein contraction factor.

b)
For n = ∞, that is for isothermal flow, the value for _{n} is unity;
c = c_{o} = constant; V_{max
}=c_{o} n = ∞. Relative
motion has no effect on physical parameters such as length at all.

c) For 1 < n < ∞ , that is for
n-dimensional flow , the value for _{n}is [1 - 1/n(V/c)^{2}
]^{-1/2} ; c < c_{o}
for any value of V greater than zero; V_{max} = √n c_{o}.
Corrections for relative motion to length, etc, are less than the Lorentz
maximum and depend on the value of 1/n.

2. In the **Minkowski** space-time representation of special relativity where the
variables are x and ct, the angular contraction or *squeezing* of the transformation axes given by tan = v/c is to be
replaced by tan = (1/ n )V/c_{o. }.The magnitude of the angular contraction
or squeezing together of the transformation axes then ranges from a maximum for
n = 1 to zero for n = ∞

3. In the **Minkowski **representation** **by rotation of rectangular axes in
imaginary space-time where the variables are x and ict, the angular rotation
given by tan = iv/c is to be
replaced by tan = (1/ n) iV/c_{o} .

It is worth pointing out here that the
concept of **space-time **introduced by
Minkowski as a new discovery in physical reality is a commonplace graphical representation
of the effect of motion in compressible flow theory, where x-t diagrams are designated as the ** physical
plane** and the ratios V/c

4. In place of the usual **metric interval ds** of special
relativity where ds^{2} = dx^{2} + dy^{2 } + dz^{2} – c^{2}t^{2}
= (V^{2} - c^{2})dt^{2} and c always stands for the
maximum static speed of light in space, we must instead now write

**ds ^{2} = [ V^{2}/n - c_{o}^{2}]
dt^{2 } = -c^{2}dt^{2}**

where the distinction now made between c
and c_{o} is crucial if the proper physical relationships of
compressible flow are to be respected. [It is worth noting, however, that the
special relativity custom of writing (V^{2}
- c_{o}^{2}) for reasons of mathematical symmetry for example,
is unphysical and gives rise to negative
ds^{2 } and imaginary values
of ds itself. The proper and physically correct
expression is

c^{2}t^{2}
= c_{o}^{2}t^{2} - (V^{2}/n)t^{2}

This would make ds = c dt where c is now
the **variable speed of light**
calculated from Equation 1.

The above changes mean that Lorentz
invariance as presently employed is not **in
general** correct and applies only if the
compressibility and attendant change in c with change in V is neglected, that is if c
is arbitrarily held constant. Alternatively we could perhaps say that Lorentz
invariance applies only to accelerated motions where n = 1.

It is worth noting here that the metric **ds **in special relativity theory
deriving from Minkowski is essentially different from compressible flow theory.
In the Minkowski formulation of special relativity, ds can be either positive
or negative at will or convenience. That is, it can be arbitrarily ether

ds^{2}
= (dx^{2} + dy^{2} + dz^{2} ) –c^{2} t^{2}
, or
ds^{2} = c^{2}t^{2} - ( dx^{2} + dy^{2}
+ dz^{2} ).

But in compressible flow theory any arbitrary change
in sign is forbidden since it represents two completely different physical
fields.

For World A systems with n a positive integer and
where only compressive shocks occur, the proper form would be

ds^{2} = c_{o}^{2} t^{2} - (dx^{2} + dy^{2} + dz^{2}
)/n, corresponding to c^{2 } = c_{o}^{2} - V^{2}/c.
This of course makes ds = c dt, where c is now the variable speed of light from
Equation 1.

The Minkowski formulation and its sign discrepancies
is especially important since it is the basis for generalized metric tensor in **general relativity** theory. In addition, the value for n never explicitly appears in general
relativity, and this therefore restricts any
validity to the n = +1 case only. Therefore, whether the general relativity
theory properly applies to gravitation
is at present in question, since it has been necessary to introduce the
compressible Chaplygin gas with n = -1 to try and solve the cosmological dark
energy problem.

5. In summary and contrast, in the case where n = 1 .
with [ 1 - (V/c_{o})^{2}
]^{-1/2}, compressibility predicts
the maximum decrease in the speed of light c with relative motion, together
with maximum fringe shift and/or maximum
frequency shift. Special relativity for the same case requires a zero change in c , and predicts a
zero fringe shift and a maximum ( unobservable) length contraction.

For n = 9 which predicts fringe shifts and frequency
oscillations which are one-ninth of the
classical predicted values, the data match the
known orbital and axial motions of the earth in space. Special
relativity rejects the possibility of detecting such motion and must therefore
discard the observations of experiment
and treat them as being zero.

Because this matter of Lorentz transformations and
Lorentz invariance is so important, it
may benefit from a further restatement as follows:

__Case: n =1 __ When n is equal to unity all the
increased energy of motion (V^{2})
acts to reduce the wave speed c (Equation 1). If one still insists on
using the classical addition of velocities (c ± V) in the ‘rest” coordinate system
as special relativity theory does, then all the corresponding physical
quantities in any relatively moving system will have to be adjusted by a so
called ‘contraction factor’ because the
possibility of a compression of the wave speed c has been ignored in the
classical addition assumption. The correction factor in this case is [1 - V^{2}/c_{o}^{2}]-^{1/2}.

__Case: n greater then 1__: In these cases, only a fraction (1/n) of the increased energy of any motion
(V) acts to reduce the wave speed The correct
addition of velocity would then be c ± V/n) , so that if the classical addition of velocities (c ± V)
is still used in the ‘rest’ system, than all the corresponding physical
quantities in any relatively moving system will have to be corrected by a
correction factor with the appropriate value of 1/n, which now is [1 - 1/n (V/c_{o})^{2} ]^{1/2}.
For the application of this to the Michelson-Morley type experiments see ( See __APPENDIX
A Compressible
Photon Flow and The Results of Michelson-Morley Type Experiments)__

It should also be noted that most oscillator/resonator
experiments now test for general Lorentz invariance under a model
where both rotations and boosts or linear motions may be present.
However, Lorentz invariance tests employ only the second order [ 1 – (V/c_{o})^{2}] ^{-1/2}
as a criterion, whereas, as we have seen, compressibility not only requires
discrimination between first and second order effects in V/c_{o} but
requires the assignment of the proper integral value for n, from 1 to 9. If these basic physical modes and differences are not recognized, then actual observed
speed of light variations may
unknowingly be discarded or lost in an inappropriate test which misses the real physical effects.

Although
special relativity is restricted to uniform motions it still is
routinely used in **accelerator **calculations where the accelerations are enormous because
it gives close answers to the observed increase of momentum of elementary particles of matter with
increasing velocity. In these cases the
Fitzgerald/Lorentz /Einstein transformation and correction factor with n equal
to 1 gives good results. This now appears to mean that in accelerators the
additional energy of motion V^{2} is not partitioned and all change in
motion directly adds to or subtracts from the wave speed c. When the correction
factor with n equal to 1 is plotted, it is seen that for very large values of V
( near the maximum speed of light c_{o}), the change in wave speed c progressively
diminishes; and so, to reach zero wave speed would require infinite
velocity (i.e. infinite mass or infinite
momentum). This would explain the underlying
reason why it has always been
assumed that there is agreement between special (uniform velocity) relativity
and accelerator ( non-uniform velocity )
experiments. The special relativity corrections in fact do not **exactly** apply even to uniform motion
experiments, but they are invoked to
explain the observations involving
accelerated motions where they are supposed not to apply! Physically
based compressible flow corrections, in contrast, apply without contradiction
to both motions.

An **experimental
test** of the applicability of compressible theory and the correctness of n =
1 for accelerations appears available as follows: When flow speed v equals the
wave speed c, (i.e. V = c = c*) we have the
** critical flow** condition,
and the ratio of this critical wave speed c* to the static or maximum
wave speed c

c*/c_{o }= [ n/(n + 1)]^{1/2}

For n equal to unity, this ratio becomes equal to
0.707, which means that c* will occur at
a wave speed equal to 0.707 of the
maximum speed of light 3 x 10 ^{8} m/s. Now at the critical speed V* =
c* there is always the possibility that a **shock**
wave will form, so that instead of a smooth curve between two variables, such
as velocity squared (V^{2}) and
mass m, there will instead be an abrupt discontinuity in the curve at
the critical speed. Therefore, an inspection of accelerometer data should show
such a change in the curves. It is also
possible in compressible flow for the transition through the critical speed to
occur shock free. This, however, can occur only under certain definite
restricted physical conditions which are well established, and therefore these
cases are also available for testing. The existence of a value of n other than
unity in an acceleration could obviously also be established.

__9. Summary of Review of Relativity__

A). Special relativity is: (a) based on
arbitrary postulates, (b) derives the specialized Lorentz contraction factor [ 1- (V/c)]^{-1/2}
by inserting it as an arbitrary mathematical correction (c) maintains the non-detectiblity of uniform
motion (invoking the reality of the unobservable contraction factor) only by
rejecting the observed fringe shifts of Michelson-Morley type experiments and
insisting that the results must always be equivalent to a zero shift, (d) accepts
observed doppler frequency shifts to establish the reality of time dilation
caused by uniform motion, but at the
same time rejects the large frequency
shifts of rotational experiments to maintain its nul Michelson-Morley interpretation, (f) is restricted to uniform motions,
while at the same time appeals to the
observations of enormously accelerated motions to establish the mass/energy
relationship of the theory.

B). Compressible flow theory is (a) physically-based on long established
theory, (b) is internally consistent involving no arbitrary corrections (c)
derives a universal , physically based compressibility factor c/c_{o} = [ 1 - (1/n) (V/c_{o}^{2}]^{1/2}
, (d) accepts all observed data for both
uniform and non-uniform, accelerated motions ( including rotations), (e)
predicts length contraction effect for uniform motions from the observed fringe shifts of Michelson-Morley
experiments, as c/c_{o} = 1 - [ 1- (1/n)(V/c_{o})^{2}
]^{1/2} , (f) predict time dilation from the observed frequency shifts
of oscillator experiments such as Ives and Stilwell where _{o} = c/c_{o} = 1 -
[ 1- (1/n)(V/c_{o})^{2} ]^{1/2} for uniform motions and
then _{o} = c/c_{o} = 1/n(V/c_{o}) for accelerated motions,
both linear and rotational verifies the
mass-energy relationship involving n = 1, while predicting experimentally
testable deviations in mass/energy curves at
critical c* = V* speeds.

C). Energy compressibility on the analysis
to date establishes **a physically-based,
self consistent, universal relativity** for all types of motions, steady and
accelerated, which is verified by, and accepts the data of, all the available
observations.

D). In the early decade of the 20^{th}
century when physicists were struggling with the effects of relative motion on observations of
electromagnetic propagation, compressible flow theory was only developing. Lorentz himself at a conference in 1928 [21] speculated that compressibility might
possibly help with the problems raised by the Michelson-Morley experiment. He apparently did not pursue the matter.

However, it was only after World War II
that compressible flow theory matured in aeronautics, gas dynamics and
the physics of compressible atmospheres, so that its explanatory power became
widely known. In hindsight it might
appear that the possibility of the contraction factors of relativity theory
actually being a physical compression effect should have been followed up earlier,
but at the beginning of the relativity era the full scope of compressible flow
theory was simply not available. Later on, relativity had become so entangled
with the mistaken notion that the result of the Michelson-Morley experiment was
actually zero, that it was then overlooked. Today, with the problems in
cosmology so pressing that variable speed of light (VSL) theories are
abounding, the applicability of compressible flow theory to the problem seems
much more obvious.

**WAVE
SPEED RATIO c/c _{o} AND THE
ISENTROPIC RATIOS**

**c/c _{o} = [1 -1/n(V/c_{o})^{2}]^{1/2
} = (p/p_{o})^{1/(n+2)}
= (ρ/ρ_{o)}^{1/n} = (T/T_{o})^{1/2 }(5)**

All the basic state parameter ratios of a compressible isentropic flow are
therefore specified by the wave speed ratio c/c_{o}.

We point out that in engineering and thermodynamic
practice the ratio of the specific heats k is often used instead of n. The
relationships between n and k are: n = 2/(k-1)
and k = (n + 2) /n

The isentropic
ratios then become

**c/c _{o} = [1 - ((k-1)/2)(V/c_{o})^{2}]^{1/2
} = (p/p_{o})^{(k-1)/2k}
= (ρ/ρ_{o)}^{(k-1)/2} = (T/T_{o})^{1/2 }(5a)**

In the present report only n is used, as it is appears
more transparent to the underlying physics by
representing the number of ways the energy of the system is divided, and
in particular for relativity applications because it represents the portion of the flow
velocity energy V^{2} that affects the wave speed energy c^{2 } in Equation 1.

**THE
ENERGY EQUATION HAS TWO FORMS: WORLD A →WORLD
B **

In the basic energy equation c^{2} = c_{o}^{2} - V^{2}/n, the parameter **n** can be either positive or negative. In all ordinary material gases it is positive. It is
negative, to take one example , in a theoretical state called a Chaplygin gas or ‘tangent gas’ , where n =
-1. This duality in the sign of **n**
gives us the possibility of transformations of matter as follows:

A). If n is
positive, energy Equation 1 plots as an ellipse in velocity variables c and V,
and the isentrope then is a concave
downward curve. The plot in variables c^{2}
and V^{2} is a series left-sloping straight lines in the energy
variables c^{2 } and V^{2}. (Fig. 1). The maximum wave speed is then c_{o}
and the maximum flow speed is V_{max}.

B). If n is negative , energy equation becomes an hyperbola in the velocity variables c and V, and a series of right-sloping straight lines in the energy variables.

__c ^{2}
= c_{o}^{2} - V^{2}/n
( ±n)__

__Fig. 1.
The Compressible Flow Energy Equation__

**EQUATION OF STATE FOR COMPRESSIBLE SYSTEMS**

**pv
= RT ; p/**** = RT ;
c ^{2 } = k p/**

where k = c_{p}/c_{v} = (n+2)/n; p = pressure; v = volume; 1/v = the density; R = gas
constant; T = temperature.

** **

** **

Since **n** in
the energy equation can theoretically be either positive or negative, **the equation of state also** has not just
one, but two possible forms:

**World A ( positive n) and World B (
negative n) Compressible Fluid **

** Equations of State**

__In World A:__ (d^{2}p/dv^{2})_{s}
> 0. Compression waves (condensed
energy waves) steepen with time to form compression shocks, and these in turn
produce the condensed energy elementary particles of matter ( protons, neutrons,
electrons, etc.) Rarefaction waves, on
the other hand, die out.

__In World B: __ (d^{2}p/dv^{2})_{s}
< 0). Rarefaction waves ( rarefied energy waves) steepen to form rarefaction
shocks. Compression waves and compression shocks would die out.

In the tangent gas case, plane waves of finite amplitude can propagate without change of form, that is without steepening or flattening.

**THE
HIDDEN MASS, OR ‘DARK MATTER’ OF THE UNIVERSE: A NEW SOLUTION**

Currently, the observed astronomical motions of
certain structures of the universe, such as spiral galaxies, can be explained
by Newton’s laws of motion only with the assumption that there is present in
and around the structures additional hidden or
optically and electromagnetically unobservable dark matter which greatly exceeds the quantity of optically and
electromagnetically observed mass The
existence and nature of this dark matter is a central problem of cosmology
today.

c^{2}
= c_{o}^{2} - V^{2}/n - 2cV/n.

In all known material gases n is a
positive integer, but the possibility of it being alternatively a negative
number, either integral or fractional,
raises the possibility of a binary, evolving universe encompassing both
our ordinary, condensed energy matter and the astronomical ‘dark matter’.

The adiabatic equation of state in compressible flow is

**pv ^{k} = const. **

Where **n**
= 2/(k-1) ; k = (n+2)/n = = c_{p}/c_{v}
,the ratio of specific heats of the fluid.
As in the energy equation, n and k
can be either positive or negative. Positive n values correspond to all know
material gases where compression waves are the rule and wave speeds are equal
to or less than the static wave speed c_{o}** (World A). **Negative values
of n (**World B**) yield hypothetical
exotic fluids where k can be variously positive or negative. Rarefaction waves
are the rule. Here, wave speeds are
always superluminal , that is c is greater than the static wave speed c_{o}.

**THE
DARK ENERGY OF THE UNIVERSE**

Within the last five years, observations on the Hubble
red shift have indicated that the expansion of the universe, instead of slowing
down, may actually be accelerating. To explain this, a hypothetical dark energy has been postulated in the amount
of around two-thirds of the total mass/energy of the universe. (The combined
dark matter and dark energy make up
around 96% of the total matter of the universe). This postulated strange energy
is also supposed to have negative pressure and to exert gravitational __repulsion__
so as to account for an accelerating
expansion. The application of the theoretical Chaplygin gas ( World B, n = -1) to this problem is now under
intensive study.

** **In 1999 the discovery of anomalous red shifts in the cosmic microwave background CMB by **Bachall, Ostriker, Perlmutter and
Steinhardt **[17] was interpreted to mean an accelerating expansion of the
universe under the influence of an anomalous ‘negative pressure energy’, which
was called dark energy.

The proposals of **Kamenshchick, Moschella and Pasquier** [18,19,20] that the dark matter and dark energy can both be related to the so-called Chaplygin gas - also called the
tangent gas in aerodynamic theory [1,2] - has now opened the door to widespread
active investigation of the suggested involvement of **negative-n
states** with dark matter and dark
energy.

In the Chaplygin gas n and k are both
negative and equal to -1; its wave speed c,
interpreted as the speed of light, is always superluminal, since in (Eqn
1), with n negative, V^{2} always adds to the static wave energy c_{o}^{2}.

The Chaplygin gas has the following form:

**pv ^{-k} = const. ** where k = -1 and n = -1, that is

**pv ^{-1 } = p(1/v) = const. ** and
since 1/v = , the density, then we have

**p= A/**

**World A ( positive n) and World B (
negative n) Compressible Fluid **

** Equations of
State**

Since the Chaplygin gas curve has negative n (unlike the asymptotic World
A isentropes ( a) where n is positive)
it intersects the v axis.
Therefore, **negative pressures** can be experienced, and it is this property that
is used to explain the observed anomalous red-shift currently interpreted as
being an accelerated expansion of the
universe. At the present time extensive
investigation is continuing into this new possibility.

This problem of the dark energy of the universe will be explored in future Updates of the
Website.

**The
following are relevant excerpts from [11]**** ( Summary of a Universal Physics, **

**RAREFIED OR
‘CELESTON’ MATTER IN (WORLD B)**

Rarefaction shocks
in World B would form rarefied, elementary particles ( which we shall designate *celestons*). These are the counterparts to the baryons,
mesons and leptons of out World A of condensed energy forms . ( The
electron-neutrino , muon-neutrino _{ }and
tau-neutrino _{ }may possibly
be already known examples of World B particles).

**TRANSFORMATIONS
FROM WORLD-A MATTER TO WORLD-B MATTER**

We now propose a transformation from World A matter to World B matter. This transformation A B takes place at a critical pressure p* . Because of an entropy relationship

S_{A} = n/(+n);( entropy increases) and
S_{B} = n/(-n) (entropy
decreases)

the transformation A B once begun, would be irreversible.

At an Initial or Creation Event ( e.g. a Big Bang) in a compressible expanding universe we would have p >>>p*, and so only condensed elementary particles of World A matter could emerge.

World B (rarefied
or celeston matter) could only form when the critical pressure p* was
reached. This point, however, might be
reached *locally* **(for example, in the centre of a spiral galaxy vortex where the
pressure is lower**) before the expansion of the universe had reduced the
overall cosmic pressure to the critical value p*.

The Initial Event
would usher in a Unitary World A of condensed matter only ( p > p*) . Our
present era (p ≥ p* ) is that of a **Binary
Universe** ( A + B) where both compressed and rarefied energy forms of matter can exist.

A final cosmic state ( p < p*), which will begin when the overall cosmic pressure falls to the critical value, will again usher in a Unitary universe, but this time it will consist of World B, rarefied, or celeston matter only.

The gravitino
ν_{g} would be the simplest possible rarefaction wave form, or
celeston. How the graviton relates to the electron-neutrino, or to the
muon-neutrino is a matter for study by quantum specialists, as is also the
further theoretical investigation of the
various possible other types of celeston particles which might be
generated by a rarefaction shock process using negative values for the entropy
parameter n. The scientific grounding of
such a theory would necessarily rest on astronomical data.

The energy change E in the transformation A B is given from the energy equations

E = c_{B}^{2} - c_{A}^{2} = V^{2}[
1/n_{A-}- 1/n_{B}]

Since n_{A}
is positive and n_{B} is negative, energy must be __evolved__ in the
A B transformations.

It might, therefore, be possible to calculate the energy evolved in galactic transformations of the type A B from the above equation, that is to calculate the energy released by the production of the proposed celeston matter from our ordinary condensed World A matter in the vortex core of a galaxy. Thus might be another experimental test of the A B transformation.

**CONCLUSIONS**

Compressible energy flow provides a physically-based,
variable speed of light (VSL) theory.

Compressibility will require a revision to the theory
of special relativity. The experimental evidence requiring this lies (1) in the
results of the Michelson- Morley type experiments whose small interference
fringe shifts, previously discarded as zero,
can now be related by the modified fringe shift equation = [2 *l* (V/c_{o})^{2} ]/n ,with n = 9, to the
orbital and rotational motions of the earth through local space, and
(2) in the more recent maser/ maser/ resonators and oscillator
experiments where for steady flow _{o} = 1 - [ 1 - (1/n) (V/c_{o})^{2}]^{1/2}
and for accelerated flows _{o}= (1/n)
(V/c_{o}).

Compressible energy flow theory predicts a possible
binary universe and A B energy transformations.

The prediction of a binary material cosmos by
compressible energy flow theory may provide the first plausible scientific
explanation for the existence and nature of the all- pervasive ‘dark matter’
and ‘dark energy’ of the universe, which taken together are today thought to
comprise 96% of the cosmos.

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Special Theory of Relativity.* John Wiley and Sons, N.Y. , 4^{th}
ed. 1961

__FUTURE UPDATES__**:
Part 2: Compressibility and Quantum Physics**

** Part 3:
Compressibility and Cosmology **

**Copyright © 2004
Bernard A. Power, Consulting meteorologist (ret.)**

__APPENDIX A__

**Compressible Photon Flow and The Results of
Michelson-Morley Type Experiments**

Bernard A. Power^{1}

*Dorval, Quebec, Canada *

August 2002

The interference fringe shifts that are
always observed with experiments of the Michelson-Morley type have never been
completely explained. Special relativity
and isothermal compressible flow theory both predict that no fringe shift
should occur at all. However, with nine
degrees of energy partition, compressible theory applied to photon flows
predicts the fringe shifts that are observed and which appear to reflect the
earth’s basic motion in space.

PACS number(s): 03.30.+p., 01.55.+b., 47.40.Dc.

The
failure of a long series of classical experimental tests to detect any motion
between the earth moving in its solar orbit and some sort of theoretical
substratum or ether, using the Michelson interferometer to detect any
anisotropy in the speed of light in space, eventually led to the abandonment of
ether models and the universal adoption of the special theory of relativity.

With
encouragement from Lorentz and Einstein among others, however, a continuing
test of the Michelson-Morley [1] experiment by D. C. Miller [2] at Cleveland
and at Mt. Wilson was carried on until
the mid -nineteen twenties. All of these
observations refuted the ether drift hypothesis. But, equally, all of them yielded a definite
small fringe shift upon rotation of the interferometer. The tests of D.C. Miller were the most
extensive, spanning several years of time and covering most of the epochs or
seasons of the earth’s orbital year.
Instead of the full expected shift of = 1.12 fringe, he found a smaller average shift (= 0.122) which corresponded to a computed ether drift
velocity of about 10 km/s rather than the expected earth’s orbital speed of 30
km/s. The observations did show a very
small seasonal and azimuth oscillation which, however, could never be put into
any convincing relationship to physical effects.

Later
versions of this type of interferometer experiment [3-7] generally reported
considerably smaller average shifts, and, as these gradually came to be viewed
as being simply statistical or environmental effects, inquiry was eventually
dropped [10].

For
the classical Michelson-Morley experiments, the expected fringe shift,
calculated on the basis of Galilean addition of orbital velocity to the speed
of light, is given by

= 2 *l* (V_{o} /c_{o})^{2}
/
(1)

Here
*l* is the optical path length (32
meters in the Miller apparatus), c_{o} is the speed of light in space,
V_{o } is the mean orbital speed of the earth taken
as 30 km/s, and the wavelength of
light used by Michelson-Morley and by Miller is 5.7 x 10^{-7} m. The expected fringe shift from Eq.1 was
1.12. A zero fringe shift was to be
expected from special relativity, and eventually the smaller fringe shifts
(0.122 average) which were always observed were also taken as being effectively
zero. However, there is a third possibility, which is that of compressibility
in the energy flow. Lorentz [3]
speculated that compressibility might somehow be a factor in reconciling
Miller’s results with the apparently necessary properties of the hypothetical
ether then under discussion: He said* …in the case of Planck’s modification of
Stokes theory. A further possibility
would be a compressible ether. This
would remove even the necessity of having an irrotational ether*.

If,
however, we apply compressibility, not to an ether, but instead to an energetic field - for example a compressible fluid flow, a
compressible gravitational field, a compressible ‘vacuum’ field, or a
compressible photon flow - we have the basic steady state energy equation [11-12]^{}

c^{2}
= c_{o}^{2} - V^{2} /n
(2)

Here the mass m is taken as being
unity, as is usual in hydrodynamics; c_{o} for a photon flow is the
static compression wave speed equal to 3 x 10^{8} m/s (when V the
uniform relative motion is zero); c is the reduced wave speed under any uniform
relative flow V; n is the number of degrees of freedom of the field, that is
the number of ways the energy of the system is equally divided. For one-dimensional motions (n = 1) the right
hand side of Eq. 2 becomes (c_{0} + V)( c_{0} – V) which is
also the going-and-coming addition of velocities used in deriving the classical
fringe shift Eq. (1). Since these
predicted shifts are nine or ten times too large, attention historically then
turned to finding a theory that predicts
zero fringe shifts instead. In
the present theory we can rearrange Eq.
(2) with n = 1 to get

c/c_{0} = [1 -
(V/c_{o})^{2}]^{1/2 }(3)

and
the right hand side now becomes, when inverted, identical to the
Lorentz/Fitzgerald contraction factor, which, if it is arbitrarily applied to
shorten the length of the interferometer
arm in the direction of V, will then
exactly cancel the reduction in the speed of light caused by V and give a zero
fringe shift. A second way to employ
compressibility to get a zero shift
would be to take n = ∞ so that in Eq. (2) V^{2}/n becomes zero, and c is always
equal to c_{0};
thermodynamically this would
require isothermal flow.

There
is also, however, the possibility of having a compressible photon flow with
multiple degrees of energy partition. When this option is explored there is at
once an improvement in explaining the observed residual fringe shifts. However, there is still no really good fit
obtained until we take n = 9. For steady
flow the fringe shift Eq. (1) becomes

= 2 *l* (V_{o} /c_{o})^{2}
/9
(4)

Relationship
(4) greatly changes the prediction of fringe shifts since these now become only
one ninth of the classical expectations from Eq.(1), while classical ether
drift velocities associated with any observed shift become three times larger.
For example, Miller in his day expected a fringe shift of 1.12 from Eq. (1),
whereas now, with compressible flow and n = 9 assumed, we find that the
expected fringe shift becomes 0.125 which is close to what Miller observed (2), his average
for the four seasons being 0.122. The
flow velocity now becomes three times
larger, so that = 0.122 corresponds
not to Miller’s computed 10 km/s but to x 10 km/s or 30
km/s which is the expected orbital
speed.

The
small velocity changes associated with the earth’s cosmic motions are: (a) the change in the earth’s orbital
velocity V_{o} from perihelion on January 3 to aphelion on
July 3 of approximately 498 m/s over the
half solar year; (b) changes in the
expansion and contraction velocity V_{r } of the
earth’s orbital radius between perihelion
and aphelion, which amount to about 322 m/s over the 180 days, and (c) the tangential velocity V_{rev}
associated with the diurnal revolution of the earth on its axis, which is about 385 m/s at 34° N, the latitude
of Pasadena and Mount Wilson. These are not considered here.

In
any assessment of the results of the various interferometer tests, it
should noted that the observed data are
fringe shifts, except where masers were used, in which case the basic
observations are a beat frequency or frequency shift. In the classical
literature the test results are commonly expressed as ether drift velocity
which is just the basic fringe shift observation converted to an equivalent
drift velocity using Eq. (1). Early
experiments concentrated on attempts to detect the orbital speed of the earth
namely 30 km/s. Later, when only about
one third of this velocity was found, the approach changed fundamentally; the
fairly large fringe shifts observed at each rotation through 90° were discarded,
since they were too small to be explained by classical ether drift theory, and
efforts were directed instead at trying to find very small changes in the
fringe shifts at different times of the day so as to sample any effect of the
changing orientation of the instrument in space as the earth turned on its
axis. However, as we shall see, with
compressible flow and n = 9, the large discarded basic fringe shifts observed
at each 90 degree turn substantially
match the orbital speed of 30 km/s that was earlier thought to be
lacking.

Turning
now to other tests than those of Miller, there is first the original
Michelson-Morley test in 1887 at Cleveland [1,2] that used an optical path
length of 1100 cm and light with wavelength of 5.7 x 10^{-7 }m. They
reported an equivalent ether drift velocity of not more than 5 km/s to 7.5 km/s
in 6 hours of testing over four days in July. Based on compressibility
considerations with n = 9 this would corresponds to cosmic motions of about 15
to 22.5 km/s. Miller later recalculated
the results using a harmonic analyzer to retrieve the ether drift periodicity
(i.e. the effect which is periodic in each 180 degree turn of the
interferometer) and got 8 to 8.8 km/s, the corresponding compressibility
calculation then giving 24 to 26.4 km/s
(n = 9).

Morley
& Miller [2] in 1904, also at Cleveland,
used an optical length of 3220
cm, and in October observed a drift of 8.7 km/s (fringe shift 0.12)
corresponding to about 26.1 km/s in compressibility theory with n = 9.

Michelson,
Pease and Pearson [4] used an instrument similar to that of Miller, with an
optical length of 25.9 m, which was installed at Mount Wilson in a basement
room having small temperature or pressure variations. They reported their
results to be an ether drift velocity not greater than 6 km/s, which
corresponds in compressibility theory to 18 km/s.

Kennedy
and Thorndike [5] (1929-30) at Pasadena used an ingenious interferometer with
one arm longer than the other by only 0.16 m. They used light of wavelength
5.461 x 10^{-7} m. Their small instrument was completely enclosed in an
inert gas and could be maintained at a near constant temperature over long
periods of time. **The instrument was not
rotated** but, instead, observations were taken at a fixed azimuth
orientation daily over a full year, the fringe shifts being photographically
recorded. For the case of the diurnal
observations their average fringe shift was 0.000212, which, from Eq. (4) with
n = 9, gives an orbital velocity of 17.1 km/s. They also reported an annual
orbital effect of 10 ± 10 km/s, corresponding to 30 ± 30 km/s with n = 9, a
result in which they did not express much confidence

Illingworth
[6] at Pasadena used an improved instrument, originally designed and used by
Kennedy, which had a much shorter optical path length ( 2 meters) It was kept in an isothermal room. It was not rotated continuously but was turned
intermittently through 90 degrees, going from either north to west or northwest
to southwest. Observations were carried out for a period of 10 days in early
July. Illingworth observed a basic fairly large shift at each 90° rotation, which in his calculations he discarded, presumably
because on classical fringe theory it would
not have given the orbital speed of 30 km/s but only about a third as much. He
does not explicitly give the magnitude of this discarded rotational fringe shifts
except for a one hour period at 11 A.M on July 9, where he
tabulated a weight difference of 4.7 units
at each turn, and at 1/500 fringe shift
per weight, this gives a fringe
shift of 0.0094 with each 90° turn of the instrument. From Eq. (4) with n = 9 this corresponds to 32.6 km/s which is about
10% higher than the aphelion value of 29.557 km/s on July 3, but of course this
estimate rests on only the one 11 A.M.
observation. The small variations in the basic large background shift which was
observed at intervals over the day ranged from a maximum of 0.00036 at 5 A.M to
0.000008 at 11 A.M., 0.000082 at 5 P.M. and 0.00034 at

Joos
[7] (1930) at Jena used an elegant instrument with an optical length of 21 meters. His instrument was sealed and kept
at a near constant temperature. His observations were made during twenty one
days in May. Like Illingworth he
observed a large fringe shift at each rotation but searched only for variations
on this basic larger background during the day.
He does not give the magnitude of the larger rotational shift, but from
inspection of the fringe photographs reproduced in his paper it would appear to
be about 0.1 to 0.08 fringe per rotation. From Eq. (6a) shift of 0.083 would correspond to 29.557 km/s, which
is the orbital speed at aphelion on July 3. He reported an average fringe shift
of 0.001 for the small diurnal
variations with changing orientation.

There
were two tests of space anisotropy and special relativity carried out using
masers shortly after they became available. The basic observations in these
experiments were beat frequency shifts upon rotation of the instrument, this
quantity being proportional either to uV/c_{0}^{2} or (V/c_{0})^{2}. In reassessing these tests with compressible
flow theory and n = 9, these two velocity ratios are to be divided by 9.

1) Cedarholm and Townes [8] (1959) used
an ammonia maser to look for an ether drift effect in the Doppler shift. They compared the frequencies of two such
masers with their opposing beams run in parallel, and when the apparatus was
rotated through 180°. Their tests were run at intervals over a year. The expected beat shift f, based on an ether
drift effect, was f = [4uV/c_{o}^{2}] where V = 30 km/s, u
the speed of the ammonia molecules is 600 m/s, and the frequency of the
excited molecules is 2.387 x 10^{10} /s. The expected beat shift was
19.8 cps, so that the actual expected frequency shift was about 10cps. The
observed shift was only 1.08 ± 0.02 cps. Their conclusion was, since the
observed shift of 1.08 was far less than the predicted 10 cps, that the speed
of light was thereby shown to be unaffected by the orbital motion of the earth
in space of 30 km/s.

However, if compressible flow with n = 9
is included, then the predicted
frequency shift becomes instead f
= 10/9 = 1.11 cps , which agrees well with the observed value of 1.08.

(2) Jaseja, Javan, Murray and Townes [9]
(1964), using two rotating masers positioned at right angles to one another,
tested for the ether drift second order effect in (V/c)^{2}. They reported on a short six hour test in
January. Upon rotation through 90° they
got a basic, repeating frequency shift of 275 kc/s plus a variation of not more
than 3 kc/s. They discarded the observed repeatable frequency shift on rotation
of 275 kc/s as presumably due to magnetostriction, and concluded that there was
no evidence of any frequency shift effect arising from the from the earth’s
orbital motion of 30 km/s

Their expected frequency shift equation
was 2 (V/c_{o})^{2}
, which for V = 30 km/s gives 3000 kcs expected frequency shift on rotation.
Only about 275kcs shift was observed and was discarded. However, when the compressibility parameter n
is included, we get 2 (V/c_{o})^{2}
/9_{ }which gives 3000/9 = 333 kcs predicted versus 275 observed or
only about 20% high. Expressed in
relative motion terms this corresponds to about 27.2 km/sec.

Compressible
photon flow theory is self-consistent and moreover it matches the experimental
data, thereby fulfilling the two essential requirements for viability. We can then, from this new standpoint,
evaluate classical Galilean addition of
velocities, the Lorentz/Fitzgerald contraction factor and the special
relativity theory of Lorentz
transformations.

Classical
or Galilean addition of velocities uncritically extended the addition of mass
particle velocities to the case of addition of particle velocity to the wave
speed of light c in the formulation of the classical fringe shift equation for
the Michelson-Morley experiment. Fortuitously, the two-way going-and-coming
design of the experiment involves forming the quantity ( c^{2} - V^{2})
= (c + V ) (c- V) which, if c is identified with the static speed wave speed c_{o},_{
}agrees _{ }correctly with
the compressible flow Eq. (2) for n =1. It is important to realize that with n
= 1 all of the velocity adds to or subtracts from the wave speed c, whereas
with n larger than unity only a fraction of V adds to or subtracts from c which gives
(c + V/√n)( c - V/√n) = (c_{o}^{2} - V^{2}/n).

The
classical formulation with n =1 predicted the impossibly large fringe shifts
which posed a major problem to the science of the day. The Lorentz/Fitzgerald
solution was not just to reduce the
fringe shift but to eliminate it entirely. This was accomplished by inserting
into the velocity transformations an ad hoc reduction factor [1- (V/c_{o})^{2}]^{-1/2}
which simply cancelled the large shift completely.

The
special theory of relativity succeeded
in putting the ad hoc formulation on a theoretical basis by assuming, first,
the classical Galilean addition of particle and wave velocities as before, and
second by postulating the constancy of the speed of light in all relatively
moving inertial coordinate systems. When this is done the Lorentz/Fitzgerald
contraction factor emerges automatically. The price of an apparent
inconsistency was eventually felt to be
justified since the unacceptably large fringe shift predictions were now
eliminated. On compressible flow theory, such an addition of the entire
relative velocity V to the wave speed c
would be interpreted as being an adiabatic photon flow with n = 1, while the
postulated constancy of c = c_{0} would necessarily be seen as an
isothermal flow (n = ∞); the two assumptions taken together now become
physically inconsistent.

The
development of compressible theory in the last half-century permits the
alternative solution outlined here, which not only explains the partial success
of previous attempts, but which, instead of incorrectly eliminating the fringe
shift entirely, reduces it to the experimentally observed values by postulating a relative
photon flow with n = 9.

The
transformations between relatively moving inertial coordinate systems in the
new theory are made by replacing the static speed of light c_{o} with
the reduced local speed of light c required from Eq. (2), by computing c = c_{o
}[1- 1/9(V/c_{o})^{2}]^{1/2} = c_{o} . Alternatively, if desired or more familiar,
the compressibility could be ignored, with the wave speed arbitrarily taken
at the static speed of light c_{o} ( 3 x 10^{8} m/s) in all coordinate systems as before, but then
the factor of special relativity
theory ( = [1- (V/c_{o})^{2}]^{-1/2})
must be replaced by the factor where 1/ = c/c_{o} =
[1- (1/9)(V/c_{o})^{2}]^{1/2} in the transformation
equations. If this computation method is chosen, the space and time coordinates
and the various physical quantities must then be altered to: = l'/l_{o} =
dt_{o}/dt' = m'/m_{o,}
etc.

In
the case of a material gas, the energy partition is among random kinetic motion
of molecules in three space dimensions plus perhaps rotation and vibration, and
these random motions give rise to pressure and compressibility. For photons, however, there are no obvious
equivalents to thermodynamic pressure, random kinetic motion, and so on, and
therefore the precise physical nature of a photon flow that could give rise to
the observed agreement with compressible flow theory remains to be established.
However, it does appear possible that three space dimensions, each with
associated states, plus vibration states
might provide the nine-dimensional energy partition required to explain
the results summarized in Table 1.

**Table 1.
Observed interference fringe shifts and corresponding computed flow velocities.**

---------------------------------------------------------------------------------------------------------

Observer Observed
“Ether drift” __Compressible
flow (n = 9__)

fringe
shift velocity V ^{a} Orbital

() (km/s) velocity V ^{b}

(km/s)

---------------------------------------------------------------------------------------------------------

**Michelson-Morley** 0.01 5 - 7.5 15
- 22.5

(1887) Cleveland (Miller
revision) 8- 8.5 24
- 25.5^{}

**Morley & Miller** 0.09 8.7 26.1

(1905)

**Miller** 0.122 (avg) 10.05 30.1 ^{}

(1925-6)

**Michelson et al.** 0.01 (max) ≤6 ≤18

(1929) Mt. Wilson

**Kennedy-Thorndike** 0.000212
(daily) 17.0 ^{c}

(1929-30) (annual) 10 ± 10 30 ± 30^{}

Pasadena

**Illingworth** 0.0094 (rotational) 32.6 ^{c}

(1927) Pasadena 0.000195 (orientational)

**Joos** 0.083 (est.) (rotational) 29.56 ^{c}

(1930) Jena 0.001 (orientational)

---------------------------------------------------------------------------------------------------------

**Cedarholm & Townes** Maser 1.08 ± 0.02 cps (30 km/s ± 556 m/s)

(1959)

**Jaseja et al.** Maser 275 ± 3 kc/s 27.2 km/s (29

(1964)

^{a} Computed
from Eq. 1; ^{b} V = (‘ether
drift’)x√9; V computed
from Eq. 4;

**References**

[1] A.A. Michelson
and E.W. Morley, Am. J. Sci*.***
34**, 333 (1887).

[2] D.C.
Miller, Rev. Modern Physics, **5**, 203 (1933).

[3] H.A.
Lorentz, Astrophys. J*.* **68**,
395 (1928).

[4] K.K
Illingworth, Phys. Rev*.***
30**, 692 (1927).

[5] A.A.
Michelson, F.G. Pease, and F.
Pearson, Nature, **123**, 85 (1929).

[6] G.
Joos, Ann. d. Physik,** 7**, 385 (1930).

[7] R.J. Kennedy and
E.M Thorndike, Phys. Rev. **42**, 400 (1932).

[8] J. P.
Cedarholm and C.H. Townes, Nature, **184**,
1350-51 (1959).

[9] T.S.
Jaseja, Javan, J. Murray, and C.H. Townes*, *Phys.
Rev*.*** 133**, A1221 (1964).

[10] R.S. Shankland, *et al.* Rev. Modern Physics*.* **27**,
167-178 (1955).

[11] A.H. Shapiro,
*The Dynamics and Thermodynamics of
Compressible Fluid Flow. *(John Wiley & Sons, New York, 1954).

[12] R. Courant and K.O. Friedrichs, *Supersonic
Flow and Shock Waves. *(Interscience, New York, 1948).

**Copyright © 2004
Bernard A. Power, Consulting Meteorologist (ret.)**