**
**

**COMPLETED
EINSTEIN GENERAL THEORY OF RELATIVITY (CGTR)**

Nimit Theeraleekul B.
Eng. (Communication)

(February 28, 2007,
3rd. revised July 1, 2011)

**Abstract:**** **Einstein general
theory of relativity (GTR) has been criticized for their philosophic problems
(both which came from STR and its own problems), despite of their**
predictability and accuracy.** Indeed all the problems could be eliminated by
using “Vacuum Mechanics” i.e. the mechanism of vacuum medium!

**Content:**** **1) Introduction. 2) **Mechanism
of gravity.**** **2.1) Why masses attract each other? 2.2) How
masses attract each other? 3)** **Philosophy behind space-time.**
**3.1) Newtonian space-time vs. Minkowskian
space-time.**
**3.2) Vacuum medium space-time. 4)
**Physical meaning of space-time curvature.**** **4.1) A new
view of curve surface.** **4.2) A better view of curved space-time**.**** ** 5) Modification of GTR.** **5.1) **Reinterpret**** the equivalence principle**. 5.2) Einstein tensor is vacuum tensor.** **5.3) Return of cosmological constant. 6) **Vacuum medium
universe – a better view of our universe.** 6.1)
Fulfilling the cosmological principle. 6.2) What is a
hypersphere?** **6.3) The origin of universe. 6.4) Our
universe is closed! 7)
Solution to some crucial problems of GTR**.**** **7.1) Problem with speed of gravity wave.** **7.2) Dark energy and dark matter
problem. 7.3) Mysterious
magnetic field in galaxies.**
**7.4) Gravitation time delay.** ** 8) Conclusion
& discussion. 9) References.

** 1) Introduction.** This article is
another expanding part of the author’s original article** “Vacuum mechanics a
New Approach to the Theory of Everything” **(VMTE) [1]. Einstein special
theory of relativity (STR) is one theory that has been expanded with the title **“Completed Einstein special theory of
relativity” **(CSTR). Here in
this paper, GTR will be expanded to “Completed Einstein general theory of
relativity” (CGTR) in a more
scientific detail. And because CGTR is related to some part of VMTE and CSTR,
so they are summarized as below.

** In VMTE**** **we
have started with the fundamental hypothesis that “**Vacuum medium is the fabric structure of vacuum space****”. **And it was proved that
vacuum space is not the conventional empty vacuum space; instead it is **vacuum
medium space!** In more detail it is the** privileged
absolute reference frame **of a
continuous isotopic homogenous medium and having a peculiar mechanical
property; it is very thin in mass density which is permeable by all matters,
and almost without any observed
resistance!

**“****Electrons and protons are **(something
like)** tiny black holes****”** is the consequence hypothesis, and they were
proved to be the** ****condensed **of** **vacuum medium.** **Both of them are the two elementary
particles which form to be **all kinds of the
material matters existed in the universe!**** **So
our universe is composed of material matters immerge in a huge volume of vacuum
medium space.

**Vacuum
mechanics – a new conceptual mechanics.**** **It is the **mechanism **of vacuum
medium, i.e. the action of condensed vacuum medium with vacuum medium, and the
interaction between condensed vacuum medium or vacuum medium themselves. All
the mentioned interaction is **responsible for all natural phenomena in our
universe!** Latter we will see how this vacuum mechanics is the key for
solving the philosophic problems in GTR.

** For CSTR,** we have derived the** Lorentz transformation **by using vacuum medium as the privileged
reference frame, and so** **we could understand its physical meaning! Then
we have showed that **“the increasing mass” **of the moving object** was
due to the inertial resistance **of vacuum medium (not the increasing of the
material mass of the object itself).

And we showed that **“time
dilation” **of the moving frame** was the slowing of the measuring clock’s
mechanism **(due to the inertial resistance of vacuum medium) and we have
called it as “relativistic clock”. ** **Also there is** no real “length
contraction”**, it is an appearance of **relative length** which occurred
in STR for trying to keep the constancy of light velocity referenced to the
moving observer! Finally we have shown how to solve the unsolved problem in
classical mechanics (as STR does), but with a more rational and understandable
way.

Now to** improve GTR to be
CGTR, **we will first point out
detail of the **philosophic **idea of the main parts that involved; the
concept of gravity, mass, space, and time. Next,** **using the new proposed concept of **vacuum mechanics **to solve the problems**.**** **Finally what we got after
modification is a more rational and understandable GTR; it is CGTR!

** 2)**** ****Mechanism of ****gravity.
**Sir
Isaac Newton had first provided us with his Universal law of Gravitation via
the formula (1) below, which state that two mass attract each other with the
force *F* that directly proportional with their masses _{}and
_{},
and inverse proportional to square of the distance r between them.

**
**

_{}…. (1), _{}…. (2), _{} …
(3).** **

But
Newton said nothing about “**why and how
masses attract each other**”. To solve the problem, modern physicists try to
explain it via gravitational field concept. And according to the formula (2)
that the gravitational potential _{} at any point around a source mass M is
direct proportion to the mass over the separate distance *r*. This seems
to be okay, but why and how? We could not visualize the working process; **it
is just an ad hoc solution**!

Lastly, while Einstein
said that **gravity
is the manifest of curved space-time** according to his famous field equation
(3) (where_{}is
Einstein tensor _{}is
energy-momentum tensor and *k* is a
coupling constant), but
why and how mass and energy cause space-time to curve is unexplained! Armed
with the concept of the mechanism of vacuum medium,** **i.e.** vacuum mechanics, **we are now going to see** **“why and how masses attract each
other”
together.

** 2.****1)**** ****Why**** masses attract each
other? **First of all, we will have to summarize (from the
original of matters in VMTE), what material mass is! In the first section that**
**vacuum
medium is the fabric structure of vacuum space, or we could say that “**space was created by using vacuum medium as
raw material**”. And the most special important intrinsic
property of vacuum medium is that**
every infinisimal part of them attracts each other with their own intrinsic
gravitational force** (contraction force)!

Also in VMTE we have verified that **“electrons and protons
are** (something like)**
tiny black holes of condensed vacuum medium”**.
(We could visualize them as two sizes of small solid spheres of the very
concentrated vacuum
energy; electron: a lighter one, proton: a
heavier one). So electron
and proton can attract each other (also with the
surrounding vacuum medium space) via their **black hole forces**, which is
much stronger attractive force than normal gravity (which created by masses
attraction). Actually, these black hole forces are the familiar forces** **known
as** electrostatic **or **Coulomb forces!**

(Please note that **all
size of tiny black holes always attracts each other.** There is only one
special case in which the same size (same type of charge) will repel, when both
of them closing to each other at a certain distance. This is because of the
repulsive stress in the vacuum medium between them is dominated (please see
detail in VMTE). And from now on** **when talking about the** **interaction
between charged particles** we will refer only to attractive force**,** **which
is the force **between electron and proton!**)

Now to see the action of **black hole force** (or
Coulomb force)
**within masses,** first we have to start with the most simple atom i.e. **hydrogen**
atom. We know that it was formed** **by electron and proton attract close together by black hole force. But notice that** **both particles** **are
still **not attach together** because** **the existing of** **vacuum
medium between them. To displace the medium between, some **external
additional forces** was used. This extra force must be strong enough to tear
off the medium which was called **weak force**! Next is **the nucleus of
helium atom** which composes of two protons and two neutrons. From the former
paragraph we could see that two protons will repel each other when they are
closing together enough, but not yet attach together. So some **external
additional force** must be used to overcome the repelling force, and this
extra was called as **strong force!**

Next talking about **the
attraction force between atoms within a molecule, and between molecules**,
are they also black hole force? Indeed they are; all categories of bonding
i.e. Val der Waals or molecular
bonding, ionic bonding, covalence bonding, metallic bonding and hydrogen
bonding **all are electrostatic forces** [2] i.e. **black hole force!**

Finally, we have to
point out one of the most crucial concept about the action of force; that is **“any interaction of forces between two
masses **which is not a direct
contact action**, **there must be some kind of mediums acting as
the** transmitting mechanism for
the force”! **For example when we want to pull an object we must use some
material such as rope as the transmission of force. And even within (or
between) atoms of rope’s material we would found that there are filled with
vacuum medium which acting as force transmitter.

**
**

**Figure 1 Attraction mechanism between masses**

By the way, unfortunately in our daily
life,** **we could not see vacuum medium, so we seem familiar that** no
medium is required for gravity force **as in diagram fig.1 (a). And when we
look at diagram1 (b) for the first time, **it would look crazy!** But after
considering for a minute we would found that **it would be crazier **if
there is nothing pulling between them** **(here, spring was used for
representing contraction force of vacuum medium)**.** Why? Because **gravity is physics **(science of nature)** not
a magic **(unscientific)!** **

In conclusion,
**masses attract each other** because all the
matters in the universe compose of two elementary charge particles** **i.e. electron and proton**. **And because both of them are
something like tiny black holes of condensed vacuum medium (which have their
own intrinsic gravity property), so it is inevitable that **gravity is also
the property of material masses. **Anyway, we have to** **make clear** **that
the gravity between masses is different from the gravity inside masses. All
attraction forces** **at molecular level within material mass are** black
hole forces, **while** **the attraction force** **between pieces of
material masses are** normal gravitational forces!**

** **

** 2.2) ****How masses attract
each other?** When
physicists use gravitational field concept to explain the attraction force
between masses, they are wondered why it is so similar to electrostatic field
concept. And they seem to believe that they are **different thing**s. Armed with the concept of vacuum mechanics,** **we could understand without difficulty
that** both fields are the same thing; it
is the contraction force field (internal stress) in vacuum medium!**

**
** ** **** **

**Figure 2**** ****Attraction mechanism between two
charges**

Before seeing “how masses attract each other”, it is easy to start with **“how
****charges attract each other****”** by using the idea of “the flux of E (electric
field)” explained by Richard P. Feynman [3].

According to diagram 2(a), flux of E emanate from charge +q (proton) in
a spherical shape (shown in circle) around the charge, and at any distant r
from center of charge,

_{} ….. (4).
(where _{}is the permittivity constant).

** **Actually** E
is the force **that will act on a unit charge placed anywhere in the electric field E. So the total flux of force from charge +q
is as follow.

**
**

**Total flux of force** through closed surface = _{}…. (5).** **

Note, even “flux” means “flow” but “flux of force” does not mean “flow
of force”, instead** it means “emanating
of attractive force” via the internal stress of vacuum medium”** around the
charge sphere +q. Or we could say that at a distance *r* from charge *+q*,
there is an attractive force (a contraction stress in vacuum medium) per unit
area equal to_{}. And if
-q charge is placed at r, then **the attractive force per unit area is equal
to**_{}as showing
as the** contraction spring** in fig.2 (b).

And
to make it easy to understand “how charges attract each other”, look at
diagram 2(c) and 2(d) for analogous concept. **While water is draining from
sink, the tiny ball immersed in water was sucked via water and moving forwards
the drain!**

** **

Now in the similar way of charge,
we can calculate **the total flux of force
from the normal mass M** in fig.1 (a) (Readers could found the detail in
“Gauss’s law for the gravitational field” [4].) as follow.** **

**
**

**Total flux of force **through closed surface =_{}.. (6).** **

**
**

[Where _{} … (7) is the force of the gravitation
field which acts at a unit mass placed at the surface of the sphere with a
radius r and *G *is the gravitational constant. (g
is the same thing as the acceleration of a unit mass.)]

.**
** ** **

To interpret the meaning of formula (6) we have to look at its unit, which* *is force^{ }*
area / mass (newton^{.}meter^{2}/Kg.). So the formula say that** **M Kg. of mass** creates gravitational force multiply by the enclosed area is equal to **_{}** **(newton^{.}meter^{2})**
around the mass sphere **via the internal stress of the surrounding vacuum
medium**.** Or we could say that, at any point r
from the mass M there is a gravitational force act at a unit mass placed there**
per unit area =**_{}. And** **if mass m was placed at r then **the****
****gravitational force** between M and m **per unit area =**_{}, which shown as** **the contraction springs in fig.1 (b). ** **

Now let us come back to explain more detail
about diagram fig.1 above. For diag.1 (a),** **when considering it** scientifically
**we would found that** it is a magic.** The reason is because there is no
mechanism for gravity (for explaining how it works) so it is **a supernatural
phenomenon!** Instead if we accept that there are infinite numbers of **unseen**
spherical concentric shells of internal stress in vacuum medium around the
earth.** **Then** each shell**** ****represents different value of gravitational
force **which is** the manifest of internal stress in vacuum
medium. **

** **While the closer shells to the earth mean
the stronger of the gravitational force, and the far away shells mean the weaker of the gravitational
force according to formula (7). So if we understand the mechanism which just
explained,** **then the** mystic view of the unseen gravitational force is
not mystery anymore!**** **Anyway,
for someone who is not familiar with the unseen “internal stress in some
material medium” it is still difficult to visualize. So the **contraction
spring** in diag.1 (b) would give a better view, even though** **it may
look strange and unfamiliar to us!

**
** ** ** ** **

**
In conclusion**;
in this section we have explained the mechanism of gravity which is the action
of the internal stress in vacuum medium between masses. While in the former
section we have shown that mass which was formed from billions of tiny black
holes (condensed vacuum medium), so it also has gravity as its own property. Then
by using the concept of vacuum mechanics, we could say that **“masses create gravity and manifest it via
the internal stress in vacuum medium”**, couldn’t
we?

** ** ** ** ** **

** 3) Philosophy behind ****space-time.** All of us live in the universe that involved with “space” and “time”. So everything,
all natural phenomena and human activities can not be separated from space and time.
Nowadays we have two types of space-time; the first one is classical**
Newtonian space-time** and another one is relativistic **Minkowskian space-time.** Anyway, it is interesting to note that** **both
concepts of space-time still have** their own problem until now!** So
we have to clarify them first before we could improve and got a complete GTR.

**3.1) Newtonian
space-time ****vs. Minkowskian
space-time.**
Let us consider detail of Newtonian space-time with absolute three dimensions
spatial space and one universal time. It is the same thing as Euclidean space
in which the square of Euclidean “distance” between
two adjacent Cartesian coordinates is

**
**

_{} _{} …… (8).

** **Note that each spatial distance term and time interval of (8) is** invariant **(constant).

**
**

But according to STR, where the constancy
of speed of light (referenced to any moving initial observers) was used to link
these three dimensions of space and one dimension of time, then what we got is
a four dimensions space-time called **Minkowskian
space-time**. And the square of space-time “interval” between two events is

_{} …… (9).

** **Note that each term of spatial distance and time interval in the right
hand side of (9)** is not invariant **(not constant)!

Now by comparing
Newtonian space-time with Minkowskian
space-time we would found that in the former, **space is absolute **(constant)
and** independent from time, **while in the latter** space and time are
dependent. **And notice that** **both of them** **are the concept of**
empty vacuum space **not physical space**.** There is also a weak point
about universal time in Newtonian space-time; that is the concept of
instantaneous action at a distance. Then it means that **any action of force
or traveling of light signal occur with infinite speed**. But this is what it
should be because it is correspond to Newton’s concept that **space is empty**!
The reason is that light speed is infinite in any medium with zero density
(Wave speed in any medium is proportion to square root of elasticity over
density).

Minkowskian space-time also has a weak
point about **the distortion of both space and time; **that is** **there
is both** the time dilation and length contraction! **The reason** **is because Einstein
mixed them by keeping “constancy
of speed of light referenced to any inertial moving observers” for his derivation of Lorentz transformation (Please see detail in CSTR). Up to now we
have seen the problems which involved with both Newtonian and Minkowskian
space-time. So
what we want now is** a better view
of ****space-time which has no side effect **mentioned above;** **that is** ****“Vacuum medium
space-time”.**

**3.2) Vacuum medium space-time. **Based on “vacuum medium is the fabric structure of
vacuum space”, vacuum medium space **is a physical space, **not an empty
one. It is the
same concept as Newtonian absolute space with universal time; the only **difference**
is that vacuum medium space is a physical space**
**not an empty as
Newtonian space do. This means that** the distance between any two points in
space is constant,** while the
universal time means** at any
instant, ****time is the same and it flows evenly
everywhere****.**** **So** **what was defined as the continuum of four
dimensions space-time,** **actually **it is the continuum of three spatial spaces at any instant time! **

**
**

Another point** **that vacuum medium space-time** different **from** **Newtonian space-time**
**is that** ****speed of**** any action or speed
of ****light
signal is c, not infinity **(according to vacuum mechanics, any disturbance in vacuum medium
propagate with light speed c).** **And when** **measurement** **was made**
**by a moving observer** **referenced to vacuum medium, **space and time
could be mixed by using the constancy of light speed in vacuum medium
space-time without any distortion! **So every term in equation (9) is **invariant**.

Below is **how ****the dynamics of a moving inertial frame work in vacuum medium
space-time**, in which it is working according to **Lorentz transformation!** In the diagram of fig.3, a light
source was placed at the origin O of the stationary absolute privileged vacuum
medium referenced frame S, at time *t*** **=* x = y = z* = *0*.
Then light signal propagates radial outward as a sphere. And at any instant
time_{}, what we got for the event at P_{} is the sphere formula;** **

**
** ** **

_{} …….. (10).** **

**Figure 3 Vacuum medium space-time**

Now, let us place the
light source at the origin O’ of a moving frame S’ (referenced to vacuum medium
rest frame). Again when O’ is at O and at *t*
= *t*’ = 0, while light source is start
emitting, S’ is also moving with speed *v*
(less than c). When S’ is passing P’ toward Q, the emitting signal from P’ will
reach P at the same instant that S’ is at Q. And if we consider only for the
co-ordinate x, then the time* t’* at P’
and the distance *x’* (distance between
P’ and P) **are the time and the distance
according to Lorentz transformation!**

To see the **physical
meaning** of the invariance _{} in S defined in (9), by comparing to _{}of (10) in S’, we would found that

_{}.

Someone may say that
it is just the concept of STR that “the constancy of speed of light referenced to
any moving initial observers”. But when consider the above diagram carefully we
will found that, it is the emitting light signal from P’
that reaches P not from Q (the actual position of S’ at time t). **So it means that the constancy of light
speed is reference to absolute vacuum medium space, not to the observer in a
moving inertial reference frame!** That is, the propagation time of light
signal from P’ to P is t’, not the time from the present position Q (of S’) to
P. Then**
there is no real time dilation and no true length contraction!**

**
**

Finally if there is **no real**
time dilation and **no real** length contraction,** ****are**** ****proper time and proper
length still necessary?** The answer is yes; because both of them are **relative values**
and still useful for some propose such as Doppler Effect. Besides that, we
still have the **relativistic clock** instead of the conventional time
dilation. And for length
contraction, because it is only a **relative length**,
so we must be careful** not to use the ****length contraction**** for guiding to the increasing density of ****mass! **

** **By the way, **proper
quantity** was defined as **the
intrinsic quantity** when measuring was done by an observer on his own
reference frame. But according to STR & GTR, all reference frames are
moving relative to each other. So **we could not find any “true” intrinsic
quantities in our universe. **Instead
according to vacuum medium space-time,** **we** **could preserve the meaning of** **“intrinsic quantity”
because **it is only the same one true invariance measured quantity in any reference
frame!**

**4) Physical meaning of space-time
curvature.** According** **to GTR,** **our
universe was built with four-dimension space-time (three spaces plus one time),
but it is impossible to visualize how a curved space-time is. Let’s refer to a famous professor in physics nowadays,
Stephen W. Hawking word [5] **“It is
impossible to imagine a four dimensional space.”** Or (again) referenced to
Richard P. Feynman word [6] “We live in three-dimension space and we are going
to consider the idea that three-dimension space is curved ……, we can’t imagine
space being bent in any direction because our imagination isn’t good enough.
(Perhaps it’s just as well that we can’t imagine too much, so that we don’t get
too free of the real world.)” Is this word still
being true forever? **Could we understand
three****-dimension space being curved while we still live in the real
world?** For my opinion, **the
answer is yes we could!** And let’s us find out together by starting with a two-dimension space below.

**Figure 4 Comparing a curve surface with
a flat surface**

**
**

**4.1) A new view of
curved surface.****
**All of us are familiar with a two-dimension curve
surface such as a portion of elastic spherical surface sheet of a basket ball
shown in the diagram fig.4 (a). After we flatten it out by making an appropriate cut where
necessary, then what we got is **an incomplete flat sheet** as shown in (b).
Next, we complete the cut-off parts by pulling the neighboring parts together
(while keeping the sheet’s thickness to be the same everywhere). Then what we
got is **a completed flatten surface sheet** as in (c). Actually, we could
get the flattened sheet (c) just by pressing the curved surface sheet (a).

Note that the**
flattened surface sheet **(c)** is not the same thing as a true (ordinary)
flat surface **(d) which made from the same elastic material**!** But, what is the difference?

The difference is that the area density of
elastic material is** uniform in a true flat surface sheet** (d), while **it
is not uniform in the flattened surface sheet **(c), i.e. the area density vary from high
density around the center to the lower density at the rim of the sheet. So **the
uniformity of material density of a physical space area of sheet is the crucial
point** for considering whether it is a flat sheet or a curve sheet. Thus from this point of view**, **we may say that **a curve
surface sheet is a non-uniform of material density of a flat surface sheet!**** **

** **

** ****4.2) A better
view of curved space-time.**** **Now we will extend the concept **“non-uniformity of the
material density of a sheet” **(two-dimension curve sheet) to a
three-dimension curve space (curve of** volume space**). First we start with a simple analogy of the atmosphere which covers the surface of our
earth. We know that air density is higher near the earth’s surface and
decreasing to a lower density when the altitude is increasing. This non-uniform density of air was caused by the earth’s gravity which
is higher near the
earth’s surface and decreasing at a higher altitude. So we
could say that** the atmosphere space (physical space of air) is curved.** But suppose that, if the gravitational
attraction of the earth to the atmosphere is the same at any altitude, then the air’s density
will be uniform. **In this case we could say that the (three- dimension)
atmosphere space is flat! **(Note, both the words “curve” and “flat” used
for volume space may come from curve and flat sheet which we are familiar.)

**
** ** **** ** ** **

Up to now we have
found that it is easy to visualize and understand “flat and curve space” by
using concept “uniformity of density of the material that constitute the
physical space”. So for** vacuum medium space,
it is the uniformity density of vacuum medium energy that was used for
considering the curvature. **But we have to be careful** **because** **there are two part of vacuum
medium energy.** **The** **main part is
the energy** **that
constitutes and maintains the isotopic fabric structure of space (flat space).
While the additional part is the internal stress energy in vacuum medium that
occurred due to the existing of the near by mass (gravitational potential
energy). To visualize** **the internal stress energy occurred in vacuum medium, it
is easy to look at **“internal stress created in incompressible
fluid such as water**, when** **it** **(the water) was subjected to external force.
In this condition we would found that
volume of the water is not change (mass density is the same as in the water
without external force), but there is an additional stress energy occurred in
the water!

To show formally** **how the concept of**
“non-uniformity of energy density of vacuum medium space” **could explain**
“curve space”**, we will go back to
the three last paragraphs in section 2.2. There, we have said that
gravitational force is the manifest of internal stress in vacuum medium space
near the center of earths mass. While the stress in vacuum medium that closed
to the mass is higher due to the stronger force of gravity, the far away part
will be lesser due to the weaker gravity according to equation (7), that is_{}.

Actually we could view
the surrounding vacuum medium as **infinite numbers of unseen** **spherical concentric
shells with ****different constant value of stress in vacuum medium **around the center mass.** **In this way, each shell would represent
different value of some constant **“Gaussian surface curvature”.** Also each
shell represents
different layer of **“Geodesic
closed surface”.**
The closer layer of the shells to the mass means the larger curvature of the
Geodesic path, while the
far away shells mean the smaller curvature of the Geodesic path.

Below are the diagrams
which show the deviation of light ray path through curve space-time. In a) the
bending of light ray path follow **the imaginary curve
space of rubber sheet**, while in b) the bending of light ray path follow
the Geodesic path of the** **Gaussian surface curvature. So we could see that **it is more rational
for curved space-time with non-uniformity of the internal stress created in vacuum medium space, rather than
the conventional curved space-time of empty space!**

Figure 5 Light ray path through curve space-time

** For an example, **we will show how the
concept of “uniformity of the internal stress in vacuum medium space”** could
explain “curved space” in GTR by using Schwarzschild exterior solution**
below.

_{} …. (11).

It is the metric
equation of line element (square of interval) of curve space-time
surrounding a spherical body mass M. And we can approximately express it in rectangular coordinate (and may be called isotopic) [7] as
below

_{} ….. (12).

** When there is no
gravitating body (M = 0) equation (11) and ****(12)**** reduce to ****a flat
space-time** as below

_{}….. (13),
_{}…. (14).

Now consider the
coefficient of time component_{}of (11) which is equal to_{}. And we could
see from (2) that the gravitational potential_{}, so _{}[8]. When we compare _{} in (11) with _{} in (12) which is a flat space-time then
we would see that** the additional term **_{}**is the additional energy arisen from the
gravitational potential due to M.** Also this
additional energy is greater near mass M, and it will be reduce to zero when r
is infinite.

Based on Vacuum
medium space-time we could equally say that internal stress energy in vacuum
medium is greater near mass M, while it will be reduce to zero when r is
infinite. Or we could say that the** non-uniform of internal stress energy in
vacuum medium create the curvature in space around mass M!**

In conclusion** **we
could say** **that** a three-dimension flat space-time **is the space**-**time
**with uniform internal stress of vacuum medium, **while** a
three-dimension curved space-time **is the space**-**time** with
non-uniform internal stress of vacuum medium! **This is more rational and understandable space-time,
isn’t it?

** **

**
5) Modification of GTR.** Up to now we have seen how the concept of vacuum mechanics
(mechanism of vacuum medium) gives a better view of gravity, relativity and
space-time. It let us to visualize and understand the mechanism of gravity, it
gave us a more natural concept of space-time and it let us understand clearly
what the curved space-time is. So if we want a complete GTR, we have to improve
it by using this new better concept.

**5.1) Reinterpret
principle of equivalence.** Since GTR was
extended from STR in which the principle of relativity is valid only in the
realm of inertial system, so the principle of equivalence was created by
Einstein to cover system with **noninertial **reference frame in GTR.

Conventionally
according to the
principle of relativity of STR, two inertial observers will experience the
universe in exactly the same way (laws of nature is the same for them), even
though their observations are made relative two entirely different inertial
systems. In GTR, the principle of relativity was generalized to include the
observer in noninetial system forming to be **the principle of equivalence,
i.e. laws of nature is the same for**** observer
in any system!**

Under the concept of vacuum
medium space which is absolute privileged reference frame, we have
reinterpreted the
principle of relativity of STR from “physics is the same in any inertial frame”
to “physics is the same in any inertial frame referenced to vacuum medium space”. In the same way for GTR, we have to
reinterpret the
principle of equivalence from “physics is the same in any system” to **“physics is the same
in any system referenced to**** vacuum
medium space****”****!**

**5.2) Einstein tensor is vacuum tensor.** Let’s look again at Einstein field
equation (3) below

_{} … (3).

The formula said that Einstein tensor _{} is curvature tensor_{}, which
provides a complete description of space-time curvature. And it **is equal to** energy- momentum tensor _{}of all matters and energy involved (except the gravitational energy
created by the matters itself) in
the system. But there is** no way to deduce the connection (between the two
parts) from more fundamental principle** [9]**!**

When considering it in detail, the above **space-time geometry** _{}** is a geometry of “nothing”**;** it
is the geometry of an empty vacuum space.** So it is difficult to visualize how to deal with the tensor of
“nothing” which is unphysical. In the real world we normally use tensor for
solving the problem with something which is physical such as electromagnetic
field, fluid or solid materials. **It is
Einstein’s genius that he could imagine **(guided by Mach’s principle and the principle of equivalence)**
how to link an energy-momentum tensor **(physical tensor)** to
describe the abstract geometry of space-time! **** **

**
** ** **

But if we consider the energy-momentum tensor _{}in the
view of the whole universe, we would found that it consists of all the matter
and energy that irregularly distributed across the universe;** it** **is not a continuous physical medium which
contains all the necessary information for Einstein tensor.** So he had
designated a new kind of material field with mass, energy and momentum
densities at each point in the system; that is the energy-momentum tensor
required.

**
**

Now we have learned above that** **actually** space-time geometry is the physical geometry of vacuum medium.** And
this vacuum medium is the main part of mass (energy) that pervaded across the
huge universe. So all the observable matters of galaxies, stars, dust clouds
etc. are the minor part that are immerged in the sea (of uniform distribution)
of vacuum medium through out the whole universe. Then** **Einstein tensor
which originally was an imaginary **becomes a real tensor of physical geometry
of space-time.** So we could say that **Einstein
tensor is vacuum medium tensor **(tensor
of vacuum medium space)**!**

**
**

**
5.3)**** Return of cosmological constant. **Someone who familiar with GTR would
found that the total
matter and energy existed in the form of energy-momentum tensor_{}, which is
the source that create the curvature of space-time **does not include gravitational energy **(which created form the total matter
and energy)** itself. **So it means that** the total energy in
the system is not conserved! **This is the crucial weak point of GTR**. **

** And to solve the
problem,** it was proposed
a quantity which play the same role as a gravitational potential; a 4x4
pseudotensor _{}(the
gravitational potential energy of the field) by adding it to_{}, to assure the energy
and momentum to be conserved. How ever _{}is merely
a pseudo-tensor, it does not have** a convincing physical
presence **(or absence) [10].** **Armed with vacuum medium space, it is easy to solve the problem**. **We start with **general form **of the full field
equation with** cosmological constant _{} **as (15) follow.

**
**** **** **

_{}…. (15), _{} ….
(16).

**
**

Then after rearranging
(15) and write out the 00-component as show in (16), where_{} was** **replaced
by_{} (_{}= mass density). So reference to (16), _{}**functions as a constant mass density of
vacuum medium energy, **and acting as** **the**
**“**ambient mass**”** **which **spread through out space** [10’]**!**

Einstein first
introduced ** _{}**to act

In VMTE, we have said
that the **ambient mass** of vacuum medium energy is so dilute. So it is
insignificant on a planetary or local galactic scale, but **it will be
dominant on the cosmic scale** (because the huge volume of the universe). As
for an example, we could see it from** **Schwarzschild exterior solution derived including ** _{}**[7’] as below

_{}…. (17).

Comparing (11) and
(17) we could see that the effect of ** _{}**term on the field surrounding the central
mass M would increase with the size of the region considered. Hence, since the
motion of the planets are actually given with great accuracy by (11), we can
conclude that

Finally **we have solved the
problem and fulfill the field equation **(3) by just add vacuum medium to energy-momentum tensor in term
of** _{}**.

**
6)**** ****Vacuum medium universe – a better view of our universe.** The most interesting application of Einstein field equation (3)
is that it was used to describe our universe; the story of cosmology. Anyway**,
there are several weak points about the assumption for developing model of the
universe **and also the problem about the model itself.

**Figure 6 ****Vacuum
medium universe**

In section 5.1 we have
shown that Vacuum tensor is a better view for Einstein tensor. Here we will
show that Vacuum medium universe (the universe which was built
from vacuum medium) is a better view of our universe. All the observable matters of galaxies,
stars, dust clouds etc. are the minor part that are **immerged in the sea (of
uniform distribution) of vacuum medium throughout the whole universe **as
shown in the diagram which we will talk in detail later.

**
**** **** **** **** ** ** **

** 6.1) Fulfilling the
cosmological principle.** While the relativity
principle was the foundation of STR, the equivalence principle provides the
physical basic for GTR. In cosmology **cosmological principle was introduced
to let the field equation manageable.** Note that the first two principles
were modified to get a more rational meaning under the concept of vacuum
medium; now this new concept will also **give the cosmological principle to be
a more meaningful!** Let’s start with the amended and presently accepted form
of the cosmological principle [10’’] which state that:

**
**

“The general overall
features of the universe are the same relative to any local observer at
corresponding epochs in the evolution of the universe”.

What does it means for
the principle is to take **all the existing matters (galaxies and stars)
uniformly distributed across the universe.** But we know that actually the
matters are irregularly distributed, so how could we improve this weak point?
Armed with the existing of vacuum medium, the principle could be strengthening.**
**The reason is because the** total mass of vacuum medium energy **(which
uniformly distributed) is much more than that of the visible existing matters!
And when we compare them in term of mass density, it is the ratio >20:1 (see
section 6.4). So it doesn’t matter how the tiny part of visible matters was distributed;
**the total masses distribution in the universe is still uniform! **

** ****
6.2) The origin of universe.** Nowadays, main part of cosmologists believes in the hot big
bang with inflation universe. **“But the universe is the ultimate free lunch”**,
this is Stephen W. Hawking’s word [5’]. The mentioned universe was suggested to
start out from the hot infinite dense singularity; then it had expanded with
acceleration (inflation) up to the present universe. **The big problem is that
where did the huge quantity of the increasing matter come from, it contradicts
to Law of conservation of energy (mass)! **To solve the problem, team of
experts in astronomy & astrophysics has proposed a new cosmological model
called “quasi-steady-state model” [12].

According to **the
new theory “quasi-steady-state model”, the major development is that matter
creation occurs with energy conservation.** Their thesis that matter is
created and ejected in the form of quasi-stellar objects and matter in other
forms from the nuclei of galaxies are the observational evidences. In summary
the general equation of the theory was derived from the friedmann-Robertson-Walker
model **by introducing a scalar field C**. The role of C - field is to act
as **a negative energy and negative pressure for the effect of matter creation**,
and the matter creation is to accelerate the expansion of the universe. **So
there is no need a hot big bang with inflation scenario!**

** ** By the way in this new model, it
was explained that the existence of **near – black hole** in the center of
galaxies **is an indication of the creation events have taken place**. And
to visualize such events in physical terms, the suggestion conceptual
explanation is from the basic fabric of space-time. They are well-used to
thinking that particles creation occur in association with a transition that
involves space-time in a physical way, not just as a passive medium in which
particles are supposed to exist. **In graphic language, particle creation
would be associated with an opening-up of space-time!**

** ****Now according to Vacuum medium space-time**, in which we have mentioned early that it
is the fabric structure of space-time created out of vacuum medium energy. Or
we could say that **vacuum medium is the raw material for constructing the
fabric structure of space-time****!** This means that at the starting moment, the
universe is zero** **size (no space-time) there is no vacuum medium either**. **When the universe is expanding its size, vacuum medium must be increased for
expanding the fabric
structure of space-time. And when the universe is reducing its size, it means
that vacuum medium is decreasing. Then we could see that** ****vacuum medium universe is possible without ****hot big bang and inflation universe****!**

Note that actually
vacuum medium is just the contraction (gravity) energy that try to encounter
its expanding (please see detail in VMTE). So if we view **the existing of
vacuum medium as positive energy, and its intrinsic property (gravity) acts as
negative energy, then the total energy of the universe is conserved!**

** **Finally we could see that vacuum
medium** **universe** **and** **quasi-steady-state
model **may be classified
in the same group. **Both of them were created** ****without
****hot big bang and inflation! **In technical detail, vacuum medium energy
in vacuum medium universe could be though as C-field in quasi-steady-state model. And in vacuum medium universe** **vacuum medium** **energy
create space-time, while in quasi-steady-state model,** **particle
creation would be associated with an opening-up of space-time. So in the future**,
when we combine both models together,** **we may get a more complete theory
of our universe!**

** 6.3) What is a hypersphere?**
Under the cosmological principle, a simple model of the universe was developed.
A positive** **(spatial) **three-dimensional curve surface **called**
“hypersurface” **which is embedded in** **a (spatial)** four-dimensional
“hypersphere” **was introduced** **to be** a model of the universe.**
To grasp it intuitively it was suggested looking at an analogy of the
two-dimensional curve surface of our ordinary three-dimensional sphere balloon
as the model of the universe.

Anyway it is very
difficult for anyone to visualize such an extra spatial dimension surface of
the balloon as our universe, and then a question arises immediately: is it any
other** simple view of the universe which we could understand it? **Indeed
the answer is yes, because the concept of vacuum mechanics helps us as below.

After the big bang in
which the universe was born, and while all the observable matter i.e.** gas
cloud** **stars, dust and galaxies etc **were created from vacuum medium,
they are flying apart from each other after originated from a single common
point. From this point of view, **the universe will look like a simple
ordinary expanding sphere ball of vacuum medium. **It is** **not just only
the ball’s surface of a spherical shell enclosed with empty vacuum space!

Actually, we can use
Newton gravitation law to develop the **simple sphere ball universe **[12’],
and indeed, the **Friemann model of the universe** (standard model of the
universe) was derived by using Newton gravitation law in Newtonian cosmology
[11’].

By the way, we will
explain **why a simple expanding sphere ball turn to be a four- dimensional **(not
include time)** hypersphere** (when it was involved GTR, which is just a
relativistic gravitational)? To answer this question, we refer to
Roberson–Walker metric equation which was derived from the concept of “four-
dimensional hypersphere”** **below

_{}………. (20).

(Where R
is the radius of the hypersphere, k = 1, 0 or -1 according to three models;
closed, flat and open respectively.) Then we will compare it to the metric
equation of “Einstein static universe” model, **which was derived from the
spherically symmetrical static form of conventional space-time geometry** as
below

_{}…… (21).

** **Here we can see that when the term _{}in equation
(20) was ignored, then (20)** is the same pattern **as (21)!** **Indeed
in the reverse, equation (21) can be changed to the form of three-dimensional
spherical surface which embedded in the four-dimensional Euclidean space (as
shown in the reference); that is the starting point of Roberson – Walker metric
equation.

**6.4) Curvature of the universe.** According to the hypersurface model of the universe, it was
divided to three types of space-time’s curvature depend on the value of k in
Roberson – Walker metric equation (20). First where k = 1, it represents**
closed universe **or the universe with positive curvature (something look
like the earth surface), second where k = 0, this will represent** flat
universe **or the universe with zero curvature (something look like ordinary
flat surface) and third where k = -1, it represents** open universe** or the
universe with negative curvature (something look like saddle shape surface).
Indeed, all these three types of the universe are very difficult to visualize **how
they are look like**!

**
**

**Based on the
concept of sphere ball of vacuum medium universe, **it is easy to understand
all three types of space-time curvature. As mentioned early that vacuum medium
is uniform everywhere across the whole universe.** This doesn’t mean that it
make the universe flat.** The reason is because vacuum medium is just act as
the background fabric structure of space-time** **(i.e. the ambient mass
mentioned in section 6.1)** **which will** handle the internal stress
energy **(gravitational potential energy) within!** **So when we talking about the** **mass
density of the universe**, **what we mean is the **total energy** which **equal
to the ambient mass plus the observable mass **(i.e. all the existing masses
we are familiar)!

According to the new
concept, when the universe is close (where k = 1). It means that** the average
mass density is higher near the center of the universe and lower in the area
far away**. Next when the universe is flat (where k = 0), its means that**
average mass density is uniform through out the whole universe**. Lastly when
the universe is open (where k = -1), this means that** the average mass
density is higher near the rim and lower when approaching the center. **So
now we could see that it is easy to visualize whether the universe is curved or
not by using the new concept; that is **the uniformity of mass density is the
indicator of space curvature!**

** **Now we come to the most**
popular**** ****question**; whether our universe is close or open? Does it will expand forever,
or at a certain time it will collapse back to the beginning again? Up to now, cosmologists found that **the universe seems to
expand to the cold dead end rather than contract back to the hot big crunch
singularity!** This is because the observed existing mass density was found to be around_{}. This is far from the critical density of
mass _{} [10’’’] which was needed to close the universe. (Note _{}means closed universe, _{} means flat universe and _{} means open universe.)

Anyway, the calculated critical mass density above was made on
the assumption of zero value of cosmological constant. **Here we will
recalculate by including the cosmological constant** that was found in
section 5.2 above by using formula (22) [8’’] below

_{}. …. (22).
(Where *H* is Hubble constant.)

After calculation what we got is
the **new calculated** value of critical mass density (A)_{}. And from the end part of section 6.1 **we
found that the**** ****mass density**** of vacuum medium **_{}, which is the unseen ambient mass of
space-time. When it was included with the observable existing mass density_{}plus its equal amount of gravitational
potential energy within itself, then we will get a **new** **existing mass
density **(B)_{}.

Now we could see that,
based on concept of vacuum medium, **the new total mass density (B) is close
to the new critical density (A)**. So these would give us a new possibility
that **our universe is no need to be only the open universe. It may be a flat
universe or a closed universe **depending on the accuracy of the parameters
involved.

And if the observable
mass density is about 30%
of the critical density (_{}) which was reported lately [10’’’’], that
is about_{}. Then we will get a new bigger value of (B),
that is_{}. So finally we will get_{}, which means that** our universe is
closed!**

** ** Anyway, according to
the concept of vacuum medium that space-time was created from vacuum medium
energy. And** if the universe is flat or open, **this would mean that it
will expand forever.** **Then what will follow is** the created amount of
mass (energy) would be infinite** which seem crazy**!** So in this sense,
the only possible choice is that the closed universe**,****
**isn’t it?** **

**
7)**** Solution to the crucial problems in GTR.** Let’s start with a famous physicist S. Chandrasekhar (1980)
word (when he had talk about problems in GTR) as “The element of controversy
and doubt, that have continued to shroud the general theory of relativity to
this day, derived precisely from this fact, namely that in the formulation of his
theory Einstein incorporates aesthetic criteria; and** every critic feels that
he is entitled to his own differing aesthetic and philosophic criteria**. Let me simply say that I do not share these doubt; and I shall
leave it at that” [13]. In this paper** the author doesn’t dare to do
something like that**, the only aim is to complete GTR. Then this will make
GTR to consistence with QMT and **paving the way to the theory of everything**
as mentioned in the original paper!

** **

**
7.1) Problem with speed of gravity wave.**** **Einstein had showed that the existence of
gravitational wave radiation is a natural consequence of the GTR. By
considering the case of weak field equation (space-time curvature is small), he
got a linear wave equation (of gravity) which is transverse wave traveling with
velocity of light resemble to electromagnetic wave.

But, why gravity wave traveling with speed of
light,** it is just his guessed
that it would be the same speed**
[14]. For electromagnetic wave it is obvious that we could prove that it
traveling with velocity of light by using Maxwell equations, while we could not
do the same thing with gravity wave! This may be the reason that most of the
text books about GTR tried to avoid talking about it.** **

According to GTR, we known that **space-time
is just an empty space without any physical entity, **so it is very difficult and even impossible to** **explain how gravity wave
could propagate **without something
act as the medium.** (Indeed there is no exception for every kind of waves,
and in CEMT we have shown that it is unreasonable for electromagnetic wave
traveling without vacuum medium.) Some author such as I.R. KENYON [8’] who has
an insight; he tried to explain gravity waves via stress-strain relation of
space-time. He said that **“gravitational waves are quite simply the vibration
of space-time itself”**. Unfortunately we could not easily to visualize how
space-time (which is just an empty space) could act as the mechanism of wave! ** **

Instead, if we accept the vacuum medium concept, then it is easy to
understand that **gravity wave is just the vibration (mechanism) of vacuum
medium **which is the same thing as electromagnetic wave. Of course we must
not expect to get everything for gravity the same thing we do with
electromagnetism. This is obvious because the source of gravity is different
from one of electromagnetism; **that is normal masses could not create all
phenomena as electrons do! **

Now
let us explore some more detail for gravity wave by using the same concept as
of electromagnetic wave;

**
**

_{} …… (1), _{}…….. (13).

**
**

By considering equation (1) for gravity and (13) for electrostatic, we
would found that **both are the result of the same attraction force arisen in
vacuum medium** between two pieces of mass. The only difference between them
is that while the first one is a weaker force (normal gravity) due to the
neutral masses, the second is stronger force (black hole force) due to charged
masses. So **both of the two constants ***G* **and**_{}**are the
same property, i.e. it is the modulus (of elasticity) of vacuum medium!**

Next, how could we find magnetic field for gravity which was called **gravitomagnetic
field **[15] or** cogravitational field **[16]? We know that the flowing
of electric current create magnetic field around the carrier wire, but how **could
we find mass current to create gravitomagnetic field?** Actually we know that
a single moving electron also create magnetic field. (Note that when an
electron is moving, it will rotate and drag surrounding vacuum medium creating
magnetic field as explained in VMTE.) Then** a rotating (moving or not) sphere
of mass should also create gravitomagnetic field**!

And show below is the formula for cogravitational field K (mentioned
above) which was generated from a rotating sphere of mass moving with constant
speed [15’],

_{} ….. (14), where _{} ….. (15).

While *K* in
(14) corresponds to in *B *(16) and *g* in (15) corresponds to* E*
in (17) for a point charge moving with constant speed as below

**
**

_{} ….. (16), where _{} ….. (17).

By comparing (15) and (17), **what we got is** that *G* correspond to** _{}** or

**Finally
we will try to find** **mass density**** of vacuum medium** **energy **as mentioned in section 5.2. Referenced to the
formula (m) in the derivation of Maxwell equation of CEMT, this will rewrite as
equation (18) below,

_{}…… (18). _{}…… (19).**
**

**
**

(Where *c* is the velocity of
light, *M* (elasticity) = ¼*k* (twist modulus), _{}= mass density,

_{} = permeability and_{} = permittivity of vacuum medium.)

Replacing *M*
with *k/4* and_{},_{}in term of *G* in (18) what we got is
(19). Then comparing the second and third terms of (19)** we will get**
_{}which is** mass density**** of vacuum medium**** energy!** Also we could found
from (19) that **the twist (shear) modulus of vacuum medium is**** _{}**which is very low!

**
7.2) Dark energy and dark matter problem.** Dark energy** **& matter
seem to be today’s most hot issue in cosmology**. **And nowadays,
cosmologists still **do not know what it is**! Why it is so mysterious and
what prevent them from finding it?**
**Armed with vacuum mechanics (the mechanism
of vacuum medium), we could solve these problem without difficulty here!

**
7.2.1) Dark energy problem.** Let us start with modern cosmologists which found that nowadays our universe is expanding!
But when they make some calculation by using the conventional** **(non-ether
based) general relativity (without the cosmological constant), they found that** dark
energy** is needed to give enough** mass density** to do the acceleration
of the expanding of our universe.

** **

To explain and solve
the problems about the dark energy, first let’s start with the
Friedman-Lemaitre-Robertson-Walker Universe as explained by the equations;

_{}...... (4)
_{}...... (5)

Where the **size of
the expanding universe** measured by a relative cosmic scalar factor *s(**t)*, λ is the cosmological constant which
correspond to the **repulsive force** that counteracting the conventional
attractive gravity as required by Einstein for **static universe**.

For static flat
universe in which_{}, then equation (x) and (y) give_{}, and then_{}which mean that the **cosmological
constant** has **a positive energy density with negative pressure**! And
at present time, the term _{} is what was so-called as “**vacuum
energy density**” [17] (while_{}), and its main part is the **dark energy**
density. But, unfortunately we **do not know **what it is, and why it has
such a strange property (negative pressure)!

Reference to the new
concept of **vacuum medium universe** (section
6) in which all the **visible matters **(condensed vacuum medium) are
immerged in the **sea of vacuum medium**** space** as show
in the diagram fig 6. (Please be careful that what which was
shown in the diagram is not true scale, it just showing how the overall view of
the universe looks like for us who located at the center!)

Now we could see that
actually **the dark energy is vacuum medium energy** which is the fabric
structure of our universe and it is the main part of the total energy of our
universe. And the** **vacuum medium energy has a **constant** mass
density _{}(calculated from the mechanical property of
vacuum medium in section 7.1), which we have
called it as “**ambient mass **(energy)** density**”. Indeed, the value
of this** **ambient mass density is the same order as the **critical
density** of the** vacuum energy** mentioned above (i.e._{})!

To see the reason of the “**negative pressure**” of the dark energy
is easy, it is because vacuum medium energy has the **internal** **gravity**
(contraction force) as its intrinsic property (see detail in VMTE)! If we
interpret that the** **existing of vacuum medium (space) as positive
energy and its internal gravitational force as negative energy, then the total
energy is zero, i.e. **the principle of conservation of energy of the universe
is ****preserved!**

Now we can show mathematically how the** negative pressure** works
via its** internal** **gravity** in **vacuum medium universe** while
preserving the** principle of conservation of energy** as follow.

For the **adiabatic
expansion process** in the early state of the universe, its volume ** V **and
the energy

_{}

From (9), we can see
that **vacuum medium density ****r**** has internal** **gravity
(negative pressure) = -p**. Also from (8), we can see that when
the universe’s size is zero, both

Finally, someone who familiar with the “**inflation**” concept in the
**early universe** would found that** scalar field** concept was just an
ad hoc solution; it is a hypothetical matter without any of its own
property! Also it is facing with
the severe problem of “**infinite hot dense amount of energy” **(at the
beginning of the **big bang**)** **which **contradicts **to the**
conservation of energy**!

But again, **armed** with **vacuum medium energy** which acts as
the **scalar field** **energy**, it gives us a more physical meaningful
and also the **new inflation** process in the beginning of the universe is **not
violate** the** **principle of conservation of energy i.e. there is no
need the **infinite hot dense amount of energy **for creating** **inflation**
**of the** **big bang! Indeed, **vacuum medium** with its** internal**
**gravity** will act as the inflation in **de Sitter universe**. But
unlike the conventional de Sitter universe which is empty universe, vacuum
medium universe is a physical one with **positive **vacuum medium energy
together with its **negative** pressure within!

**
7.2.2) Dark
matter problem.** Up to now
we have found that actually the** **dark energy is the same thing as vacuum
medium, but what about dark matter, is it also the same thing as the vacuum
medium?

** **First let us look more detail about **dark matter** in which cosmologists found that all galaxies
have an abnormal rotation, i.e. their orbital rotational velocities do not obey
**Newton law of gravity** (the velocity should **decease** while the
distance from the center increases). Instead, the galaxies orbital rotational
velocity is **uniform** for any distance from their center. So it seems as
if there is something like **a halo of dark matter **of the galaxy!

Also there is missing mass for forming of galaxies into cluster of
galaxies. And it was calculated that **the missing mass is 10 – 100 times the
total amount of visible matter in the galaxies **[18]**.** This missing
mass was thought to be the invisible dark matter, but no one knows what it is.

By the way, some
cosmologists have try to explain the galaxies rotation problem by invent “**modified
Newtonian dynamics** (MOND)” theory, but it is not so successful! Here, we
will see how the aether based Einstein general theory of relativity could **lead
to solve** the dark energy problem.

Armed with the concept of vacuum medium, we will see that actually**
the missing mass **is also the same thing as **vacuum medium energy! **But
the problem is that we just said that for the scale of
galaxy’s size, the vacuum medium** **(as dark energy) has a **negligible **effect
on it, then how could the medium could has a **significant** effect on
galaxy as the** **dark matter? The answer is because **galaxy’s rotation**
causes a drag of the surrounding vacuum medium!

As we have mentioned
early that vacuum medium have a **peculiar mechanical** **property**;
while it is uniform, transparent** **and** **continuous medium, with very
thin in mass density. But in other side, it has **very large elastic
coefficient** and sensitive to shear force (rotational force) while not to
compressive or longitudinal force!

According to the
stress** **action in any very large elastic coefficient medium, it means
that large **stress energy** was created in the medium. Then **galaxy’s
rotation** creates a huge** stress energy** which is then makes the
galaxy’s** abnormal** **orbital rotational velocity** as if there is a
large halo of matter around the Milky Way galaxy as shown in the diagram fig.6.
So we can conclude that the large** stress energy** vacuum medium is acting
as what which we called it as the** dark matter**, can’t we?** **

**
7.3) Mysterious magnetic field in galaxies.** Magnetic field with strengths of _{}is widespread in the cosmos – in galaxies
extended radio sources and in cluster of galaxies [12’’]. And according to**
the reference;** “most of the cosmological models have been **devoted to
explain the amplification of an initial seed field by dynamo action in spiral
galaxies.** Also our understanding of magnetic field in spiral galaxies is
very limited”.

“An observation which we
believed is highly significant is that for many nearby spiral galaxies the
measured interstellar magnetic fields falls off much more slowly with radius
than the matter density, i.e. in the outer parts of such galaxies the magnetic
stress become comparable to gravity. Not only is this hard to understand in
theoretical modeling, but it is taking place at distances where the rotation
curve is flat and the flatness is usually interpreted as **evidence for the
presence of a halo of dark matter**”.

The above paragraph
has explained** the magnetic field pattern **that occurred in** the
rotation spiral galaxies, **but we still could not understand** why it is
something like that**. Armed
with the concept of vacuum mechanics, it is easy to see that this is the
appearance of the rotational stress of vacuum medium around the rotation of
spiral galaxies! The reason is as mentioned in the above
section that a big rotating mass will drags the surrounding vacuum medium with
it. And what followed is** the ****rotational stress occurred in vacuum medium around**** is the manifest of the created magnetic field!**

**
7.4) Gravitation
time delay.**** **We
know that in STR there is no explanation why a moving observer has a time
dilation. And in the first section we have explained that **actually the
conventional time dilation is just the slowing of the measuring clock **(due
to the slowing of the moving clock mechanism). For GTR there is also no
explanation why an observer in a stronger gravitational field has a time dilation
(compare to observer in a weaker gravitational field or no gravitational
field). **Based on the concept of internal stress in vacuum medium** (as
explained in section 4.2), it is easy to explain why time dilation occur!

A
measuring clock will run slower in stronger gravitational field (internal
stress energy in vacuum medium) than the weaker one. This is because the
stronger resistance of gravitational field energy, the more slows down the
mechanism of the clock (compare to one in weaker gravitational field or no
gravitational field). **This is a rational and understandable explanation of
what was called “time dilation”!**

** ** ** ** ** **

**
8) Conclusion & discussion.** Up to now we have seen how GTR
was improved by adding it with rational philosophical idea (which tell how the
theory work); **the mechanism for relativistic mechanics **i.e.** the
mechanism** **of vacuum medium** (or vacuum mechanics)! Indeed it is the
same mechanism used in improving STR and extends to cover GTR. Here are their
additional important points;

a) The crucial idea
which **vacuum mechanics** give to GTR, are the mechanism of gravity, physical
space-time, physical meaning of curve space curvature and how gravity wave
propagates etc. All these things **could not be understood in the conventional
GTR**, armed with the new concept, it is easy to visualize and explainable!

b) Comparing with STR, we would see that the topic in GTR is much wider
and more complicate, and we could not go into more detail in this paper. For
example, the topic such as conventional black hole topic was not mentioned
here. Indeed the author fell that it is** unconvincing for the huge massive
star to collapse into a singularity of mystic black hole **in which we could
not imagine** how it is something like that!** (Note that even Einstein
himself did not believe in the black hole [20].)

c) It is interesting
to note that recently, it was reported by Stanford and NASA
researchers that the “Gravity Probe B” experiment test has confirmed the
prediction of “**frame-dragging**” of space-time (which is the effect that a
spinning object pulls space and time with it as it rotates) according to GTR.

Anyway, this positive result of “frame-dragging” got from GTR is **contradicted** to the negative result of **Michelson-Morley** experiment which was used to verify the “aether dragging” in STR. Now,
what is wrong and how could we solve the paradox? Armed with our aether based
relativity, it is not difficult to see that the conventional interpretation of
M-M is wrong, isn’t it?

d) By the way, we know
that there is one big problem for combining GTR with quantum mechanics in order
to get successful **quantum gravity.** So our modified theory - Completed
Einstein general theory of relativity (CGTR) would provide a new way to the
desired theory!

e) Lastly, we could
see that what was written in this paper is not fully mathematical rigor.
Anyway, it is not a toy theory; what we have done **is just enough **to give**
the new idea **to the readers** **with some** confidences. **So what
was left here should be the work of professionals who are involved in the
matter to complete it** **for** the virtue of academic merit and the progress of our world’s knowledge!**

**9) References.**** **

(**Precaution;** Several GTR text books with different
authors were used as the reference and each author used different pattern and
different notation for the same formula. Here in this paper, the author has
made some change of the original pattern and notation for the readers
convenient, so please be careful!)

** ** [1] Nimit Theeraleekul, the articles are now presenting in www.vacuum-mechanics.com.** **

[2]
Michael de Podesta, “Understanding the Properties of Matter”, p.126-127 and

p.246-247.

[3] Richard P. Feynman, Robert B. Leighton and
M. Sands, “The Feynman Lectures on

Physics” Vol. 2. p.
4.7-4.10.

[4] Reese,
Ronald Lane, “University physics”, p.264-267.

[5] Stephen W. Hawking,” A Brief History of
Time”, p.25. For [5’] p.136.

[6]
Richard P. Feynman, “Six-not-so-easy pieces”, p. 123.

[7]
Richard C. Tolman, “Relativity Thermodynamics and Cosmology”, p.334-338.

For [7’] p.202-205.

[8] I.R.KENYON,
“General Relativity”, p.45. For [8’], p. 5 and p.124-143.
For [8’’] p. 158.

[9] Richard P. Feynman, Fernando B.
Morinigo, William G. Wagner, “Feynman Lectures

on Gravitation”, p.135.

[10] Richard A.
Mould, “Basic Relativity”, p. 336-338. For [10’] p. 394, for [10’’]

p. 393, for [10’’’] p. 405-406, and for [10’’’’] p. 422.

[11] Ray d’Inverno, “Introducing Einstein’s Relativity”, p.171-173.
For [11’] p. 310-312.

[12] F. Hoyle,
G. Burbidge and J. V. Narlikar “A Different Approach to Cosmology, From a

static universe through the big bang towards
reality”, p.189-196 and p. 311- 320. For

[12’] p.14. And for [12’’].
p.321-325.

[13]
Bernard F. Schutz, “A first course in General Relativity”, p.197.

[14] Richard P. Feynman, “The Character of
Physical Law”, p.53-54.

[15]
Ignazio Ciufolini and John A. Wheeler, “Gravitation and Inertia”, p.1-9.

[16] Oleg D.
Jefimenko,”Causuality Electromagnetic Induction and Gravitation”, p. 83-84.

For [15’] p. 88.

[17] Matts Roos
“Introduction to Cosmology” p. 54.

[18] Robert Resnick,
David Halliday, Kenneth S. Krane,”Physics” Volume 1, Fourth

edition, p.361-363.

[19] Tian Yu Cua, “Conceptual Development of 20PPPPPPPPP^{PP}^{th}^{PPPPPPPPPPP}
Century Field Theories” p.119.

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