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__Part XI__** **

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__Nov. 2020__** **

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__Three Cosmic Equations of State: Visible Matter,
Dark Matter and E/M Radiation__** **

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__“Dark” E/M Radiation__** **

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__The Possibility of Detecting__** **

__‘Visible to Dark’ Matter Transformations__** **

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__Some Cosmological Adjustments__** **

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**1. ****Introduction
**

**2. ****Properties
of Three Main Equations of State**

** ****General
**

**
Equations of State**** **

**
The Curvature Criterion **

**3. ****The
Elliptical Dark Matter State ( p ^{2} /b^{2} + v^{2} / a^{2}
= a^{2}b^{2}): The Dark Matter as a Rarefaction ‘Form’ **

**General **

**Proposed Elliptical Equation of State for Dark
Matter **

**Properties of the Proposed Elliptical Dark Matter
**

**4. ****The
Linear State: ‘Dark ‘ E/M Rarefied
Radiation, Does It Exist?. **

**5. ****The
Possibility of Visible-to-Dark Matter Transformations **

**6. ****Some Cosmological Consequences **

**7. ****Summary
**

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__In
Part X: The Big Bang: Visible Matter and Dark Matter Origins____]__ [ Feb. 2020] [1] ,we
re-examined our earlier proposal that
visible cosmic matter (hadrons
and leptons) are ** compression**, dynamic forms which originated at the Big Bang in a
hyperbolic

We then proposed in the same document that the ** dark matter** of the cosmos consists
of

We now continue our
examination of rarefaction compressibility to yield more detail on the nature
of the Dark Matter World __including the
possibility that a form of ‘dark radiation” exists and is its ‘illumination’,__
__as well as a proposal for a visible to dark
matter transformations.__

First, we put this in context with a look at three cosmic Equations of State.

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** Equations of State** are equations which link the thermodynamic ‘state’ variables of
pressure, p, specific volume (v = 1/ρ) and temperature T. [

These “states” are the dynamic, compressible entities in which waves travel and in which shock waves of either compression or of rarefaction form and produce elementary forms or particles of matter, visible or ‘dark as the case may be, but which so far have appeared to be almost completely separate and noninteracting .

** **

For
example, we have (a) the Ideal Gas Law
as the **hyperbolic** equation of state describing the production
of visible matter [ pv = const. = RT] :
(b) the **elliptical** equation of state
[p^{2}/b^{2} + v^{2}/a^{2} = a^{2}b^{2}
= const] which we propose to describe the dark matter of the cosmos., and
(c) the **linear** equation [p = ±Av]
which will be seen to describe
both Maxwell’s Electromagnetic waves, as well as newly proposed ‘dark’
electromagnetic waves to irradiate the
dark matter world.

These three equations of state are depicted on pressure p, versus –specific volume ( v = 1/ϼ) diagrams, as in Fig. 1, Quadrant 1.

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**Figure
1: Equations of State for Visible
Matter, Dark Matter and Linear Waves **

__2.2 Equations of State and Wave Types
Supported by Each State:__** **

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**(1)
**** The hyperbolic state supports compression waves only**; rarefaction waves die out but

The properties
of our ordinary ** visible matter** are, of course, well known and in voluminous
detail. The state is one of condensed energy forms, i.e: elementary mass-particles, atoms,
molecules.

For ** visible
matter**, the equation of state is

The visible
matter interacts intimately with a linear wave state via the electro- magnetic
force and via absorption and emission of __condensed
e__lectromagnetic radiation ( i. e of
photons).

**(2)
**** The linear state **supports

** **

The ** linear equation of state [p =
±Av ±B]** supports the condensed photons of
electromagnetic radiation and its interaction with visible matter. Theoretically this equation also supports ** rarefaction
waves**
and so the possibility of

**(3)
**** The elliptical state, we now propose,
pertains to the dark matter. This state supports rarefaction waves only. Waves of finite
amplitude grow to form rarefaction shocks ** in which we propose dark matter ‘forms’ emerge to produce a
rarefied kind of matter.

(Since the
assigned ** elliptical
equation of state** for

**Note: **We should point out
here that the three curves in Fig. 1 are
for illustration of ** equation type** only. That is to
say, the relative sizes of the areas ( pv) under each curve ( pv represents an
energy amount) are not representative of
actually existing relative total energies; this would require expert assessment.

** 2.3 The Curvature Criterion for the Three Equations of State **[Ref.
(5) Shapiro. Vol. 1]

Pulses or changes in flow rate in compressible fluids cause pressure fluctuations which result

in traveling disturbances called ** pressure waves**. These waves can be of either compression or
rarefaction depending on the physical nature of the compressible fluid as
expressed in its equation of state. Waves in material gases of visible matter
(hyperbolic equation of state) are always compression while rarefaction waves
are damped and die out. For the elliptical state the reverse is the case and
rarefaction waves prevail.

If the wave
amplitude is ‘infinitely’ small, the waves are stable and are called ‘**acoustic** waves’. If the wave amplitude
is finite to begin with then, in both the hyperbolic and elliptical states, the
waves grow rapidly to form shocks or shock wave, respectively of compression
and of rarefaction.

**The criterion for wave behavior is the curvature of the equation of state [d^{2}p/dv^{2 }]^{ }on the pv diagram**.

**P **

** **** **

**Fig. 2. Hyperbolic and
Elliptical Equations of State with
opposite curvature**

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**1.
**If the curvature is
positive [d^{2}p/dv^{2} **>
**0] as in the hyperbolic, visible matter case, then the compression waves
are non-linear and steepen with time to form compression shocks; rarefaction
waves die out.

**2.
**If the curvature is
negative [d^{2}p/dv^{2} ‹ 0], as in the __elliptical____ __dark matter, then their rarefaction waves are non-linear and
steepen with time to form rarefaction shocks while compression waves die
out.

[Note: In all
states, if the pressure disturbances are of infinitesimally low amplitude then
stable waves of either compression or rarefaction called *acoustic* waves can persist without growing to shocks].

**3.
**In the case where the
curvature is zero [d^{2}p/dv^{2} = 0], the pv curve is ** linear**
, i.e. it is a straight line, [p = ±Av ±B]
and waves of both compression or rarefaction, and of any amplitude large
or small, are all stable and can propagate unchanged. This linear case can also
be visualized as the tangent case linking the hyperbolic and elliptical state
equations.

__To repeat, __waves large or small, in this
linear state, are all stable and all can propagate unchanged. ** Growth to shock waves is not possible in the linear case.**
[Ref. (5) Shapiro. Vol. 1]

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As we have shown in Part X, the formation of the elementary
particles of our __visible universe__

can be described by compression shocks in the hyperbolic state [pv = constant] occurring in the Big Bang event.[1,4].

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** We now propose that the
dark matter’s elliptical state should
produce rarefaction shocks and rarefaction forms,**
and that this rarefaction property --as opposed to compression
properties-- may then explain both the dark matter’s invisibility
and its apparent non-interaction with visible forms of matter, except by
way of gravity.

Our elliptical equation of state for the dark matter is :

/.

If the curvature
is positive [ d^{2}p/dv^{2}
› 0] as in material gases, then hyperbolic state compression waves steepen to form compression shocks and
rarefaction waves die out.

If the curvature
is negative [d^{2}p/dv^{2} ‹ 0], as __in the proposed elliptical dark matter case__, then __rarefaction__ __waves
would__ steepen with time to form rarefaction shocks while compression waves
would die out.

**P **

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**Fig. 3. Hyperbolic and
Elliptical Equations of State with
opposite curvature**

We understand a great deal about ordinary hyperbolic matter ( 4.9% of the cosmos), but very little about the much more abundant dark matter (27%). The dark matter apparently occurs everywhere and has a strong influence on the structure, dynamics and the physical evolution of the cosmos. It does not appear to interact with ordinary matter, nor with electromagnetic radiation. Its interaction with our ordinary matter is apparently only by gravitation, although there is some thought that the dark matter may interact very weakly with matter by some application of the weak nuclear force.

Some other explanatory candidates have been that the dark matter is some new kind of unknown baryonic elementary particle, or involves weakly interacting WIMPS. Currently theories also distinguish between Cold, Warm or Hot Dark Matter.

However, ln this Report we have assigned to the dark matter a rarefaction nature, with its cosmic origin being at a strong rarefaction shock wave occurring in the sudden and massive inflationary expansion that occurred right after the Big Bang’s enormous compression state.

As a background to this new
rarefaction shockwave proposition, we mention that we have earlier proposed
that the ordinary matter’s elementary particles are routinely formed in
compression shockwaves in linear accelerators, and that this is verified in the
predicted mass ratios which are in good agreement with the experimentally measured mass ratios. __[Appendix A: Formation of Visible Baryonic Matter
in a__* Hyperbolic Compressible Shockwave] *

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Figure 1: Equations of State for Visible Matter, Dark Matter and Linear Waves

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__4.0 The Linear
State: Dark E/M Rarefied Radiation, Does
It Exist?__** **

The linear state equation [
p = ± Av ±B] is pre-eminently a stable **wave
equation**. These linear waves can be
of either compression or of rarefaction, but all are stable, propagating
without change in amplitude, so that shocks are impossible. The linear compression
waves interact with our compression visible matter as observable E/M photonic
radiation.[17].

It seems reasonable
therefore to propose then that there may also exist linear__ ‘dark’ rarefaction__ wave forms i.e.
‘rarefied photons’ which parallel the linear E/M __compression__
photons which interact with our compression visible matter as E/M radiation.

A
further question which arises is whether rarefied dark matter can interact with
rarefied linear radiation? This would parallel the interaction of visible
compression matter with the Maxwell’s compressed photonic electromagnetic
linear radiation [ 17]. If so, the
resulting ‘dark matter’ and its associated ‘dark’ radiation’ World would lie
all about us. It is known through its gravitation to be five times as abundant
as our own visible world, but it is as yet undetectable by any known means
apart from its mentioned gravitational attraction. [** **

__This then raises the possibility
that a ‘dark linear E/M to dark
matter interaction’ may be__ __detectible by some means yet to be discovered.__

__To summarize: The linear equation of state__ [p = ±AV] is here taken as describing sets of linear waves, not
only of photonic compression but of ‘photonic’ rarefaction as well. And so, we may now explore the possibility
that “dark” leptons expressing ‘__dark’ electromagnetism may also exist.__

The proposal is a valid scientific proposition. It does however as yet lack some testable effects. We suggest that such effects may lie in some small numerical discrepancies in the experimental data of existing cosmological and quantum experimental testing.

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__5.0 The Possibility of Visible to Dark Matter
Transformations: Is the Concept of Dark__** Energy Necessary? **

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Astronomical
observations, of a large increase in the Cosmic Microwave Background Radiation
( CMB) discovered \around 1998. was interpreted as showing the universe to be
undergoing an __accelerated__ expansion. In
explanation, the concept of an all
pervasive ** “dark
energy**” exerting an expansion pressure was introduced. The amount of
this new hypothetical energy needed to explain the CMB increase was enormous,
constituting some 69% of the known universe compared with only 4.9% for the
visible universe.

Towards a
simplification, ** we now propose a transformation from World A matter to World B matter**.

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. This transformation of World A visible matter to World B dark matter A would logically take place at a common tangential point having a common critical pressure p* ( Fig. 3.).

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