Esfand Theory Commentaries
1
–
Gravity
Written and translated from Persian into English by :
Ftolah Esfandiar
Ed. Rev
>
2
.
0
June,
201
3
Copyright
©
2011 ,
Copyright disclaimer : May
be copied, or quoted
unconditionally
Keywords
:
Esfand theory
,
stress, strain
astronomy, theory of everything,
acceleration
, speed
of
light
,
ether
, particle, photon, electron,
gravity,
elasticity, elastic modulus
, star, gravitational speed
Esfand Theory Commentaries
–
1

Gravity
Contents
1

Alternate physics theories of 21st century. page 3
Synopsis , Abstract
2

Free trembles versus confined wave systems
travel in ether continum.
page 5
Free trembles within ether , Elementary particles motion
in gravity field , Basic elements of gravity
3

Elementary gravity.
page 1
0
Elementary gravit
ational elasticity , Intermediate particles
motion in gravity field
4

Advanced gravity.
page 2
0
Intermediate ether elasticity , Superelastics in action : rubber ,
Advanced
gravitational elasticity
5

First steps to probe gravitational waves
page 4
2
Gravitational wave detecting by light interference,
Recommended remedies
6

Conclusions.
page 4
4
7

Internet references.
page 4
5
2
In addition to standard physics
(
similar to most
academic programs
)
,
t
here
is
a
lso a
small percentage of altern
ate
research presented by
limited
n
umber of physicists, mathematicians, engineers,
. . .
Most of these alternate physics works or theo
ries are based on reviving
c
oncept of ether : a super

elastic medium to carry light. Corresponding
t
heories may be called EBOL (pronounced as : E

Toll), standing for
“Ether Borne Light” theories.
As early as nineteenth century, Nicola Tesla
considered common matter
a
s trembles
within
ether. However, today few theories consider common
matter
a
s wave sub

systems within ether.
These theories, which this
(
Esfand)
theory also belongs to, may be called “ EBLAM “, standing for :
“ Ether
Borne Light And Matter “ theories.
Though,
Esfand Theory is not in full conformity with any other EBLAM
o
r EBOL theory, a list of closer Internet papers / sites are listed in chapter
seven
, for quick reference.
3
Some of the old, as well as new riddles of physics are shown solvable by
Esfand Theory
, in these corresponding commentaries.
Chapters two thru f
our
deal with
:
elementary,
…
to
advanced
gravity
,
With its main theme : proof of general law of gravity, based on this theory
Alone, and not from the way planets rotate around the sun
, also
showing
–
with touchable and simple facts
–
how gravity gradually
deviates from Newtonian values
as speeds exceedingly increase.
Referring to micro

world;
part of chapter three shows

that
modeling
subatomic particles is just
at the beginning

needing many researchers,
along several decades,
for acceptable
m
odels generation.
4
Any disturbance within infinite
elastic medium, by any reason, causes
elastic waves ( somewhat similar to earthquake waves in earth’s crus
t )
spreading to many directions, similar to
fi
gure
2
–
1
, below :
As in Fig 2

1, an elastic wave is assumed to spread from point
“A” on surface
S2
.
S1, S2, and S3 are assumed
“
equal longitudinal wave speed “
surfaces in
near steady ether space, where
wave speeds
increase as we
go from S1 to S2 …
Etc.
I
so

tension surfaces may be of little help for ether and a few super

elastic
materials as will be shown in chapter four.
Of all directions that elastic wave spreads, the one along A

B is more
Important
, :
the line or curve perpendicular to equipotential surfaces, in the
direction of
longitudinal wave speed
increase, as this is the direction of gravity ( or
sometimes
:
electrical, nuclear, or a particle’s core ) force, where forces act as
accelerations
on particles ( or trapped wave systems ).
If elastic wave speed, or gravitational wave speed, hereinaf
ter abbreviated to
“ gravitational speed “,
is shown as Q ; and small path increment A

B , as “ds”,
then, part of the free wave that propagates along gravity direction, will have a
change in speed, or acceleration of :
Since we are working mainly on gravity, length “s” may be replaced by
“r” : distance to center of a star, to reach Eq’n. (2

1) below :
(
)
=
with subscript “ G “ standing for
“general”.
Eq’n. (2

1) , may be called “ General Acceleration Law “, which may be
interpreted as :
“ Accelerations generally (except for transverse wave inducing
parts such as photons and magnets; in rapidly changing conditions
; or very high
speeds );
are equal to g
ravitational speed, multiplied by gravitational speed
gradient.
”
Please note, that dQ, and dt , refer to changes by location (
unless
noted otherwise
) , and major bodies with their gravity fields
, are considered to be
near steady :
.
6
2
–
2
Elementary particles motion in gravity field
From Esfand Theory, it is assumed that particles are made of one or more
tensile
, and
( relative ) compression trapped waves. Each lump of trapped elastic
wave may be considered as a point

lump, postulated at center of corresponding
elastic wave cloud, suitable for some applications.
For example, an electron’s 2

dimensional model
may
be simplified as two
points : “A” (tension), and, “B” (relative compression), as trapped lump

wave

points, in Fig. 2

2 .
Going back to acceler
ation of gravity, and
how it works, we notice that
,
7
particle’s internal wave

lumps, are superimposed over ge
neral ether space tension.
Principle of superposition, if applicable, states that motion of lump

wave

points
may be found by just algebraically adding several components ( internal motion or
spin + inertial + gravity acceleration ). But we need to confirm
applicability of
principle here.
2
–
3 Basic elements of gravity
As will be shown later in examples 2

3

1, thru 3

1

1 , extra
or net gravitational
speed
imposed by gravity fields(with respect to
base gravitational speed
)
,
namely
increment
dQ =
of gravitational speed,
is
usually very small compared
with general ether space
gravitational speed:
(assumed near uniform before
presence of star).
Rewriting general acceleration law (
2
–
1
) , for acceleration of gra
vity :
(
)
Noting that we are still working with
part of
assumed free waves ( and not yet
with trapped wave systems : common matter )
moving
in the direction of gravity :
towards a star
(
)
and
are usually small as will be shown in example 2
–
3
–
1 and last
term of Eq’n (2
–
2)
may
normally be neglected, to yield a simpler Eq’n (2
–
3)
, that
may be called “normal
gravity acceleration
law” :
(
)
with
subscript ,
“
g
“ standing for
= gravity
,
is
base
gravitational speed
(
before presence of star
)
, assumed uniform: and
8
, is net or excess gravitational speed due to presence of star (depends on distance
)
So, “normal acceleration of gravity law”, Eq’n (2

3), states
that
:
“In normal conditions, acceleration of gravity is the product of net
gravitational
(
speed
)
gradient by base gravitational speed.”
Applicab
i
lity of the law for common matter :
to be dealt in
section 3
–
2 .
Initially, V
<
0.00
3
C
is recommended by author, as criterion for “normal
condition”, as this is the case for major bodies within solar system. Nevertheless,
depending on application, normal condition criteria need adjustment. Therefore
E
q’ns (2
–
2), and (2
–
3), are not suitab
le for locations such as near supernovas,
black stars ( commonly known as black holes ), or near big

bang, unless if errors
are estimated first.
Gravity accelerations are directed towards stars, or any major body. In case of
presence of several sourc
es of gravity, they may be dealt separately, and then
superimposed
, if being in normal conditions.
Example 2
–
3
–
1
Find net gravitational speed gradient
at earth’s surface,
(where gravity acceleration is 9.8
⁄
assuming base gravitational speed
to be
144
,
500.
T
times the speed of light
. The reason for estimating
very
high
gravitational speeds will be given in chapter
5
.
Solution :
from (2
–
3)
:
(
)
(
)
So, net gravitational speed gradient at earth’s surface is :
(
)
9
3
–
Elementary gravity
3
–
1
Elementary
gravitational elasticity
In section 2

1 general acceleration law, Eq’n (2
–
1)
;
and
normal gravity law
, Eq’n
(2

3), were introduced. We may now try to find
details of
gravitational speed
gradient
, as a major step to find acceleration of gravity of
major
objects.
Initially, it seems that presence of a major body results in extra ether tension,
and tension gradient, directly bringing in gravity; however, due to unusual
properties of ether, we will see that through a secondary effect, a slightly different
mechan
ism is the main cause ( of gravity ).
Net gravitational speed gradient due to presence of a star, or any
massive
body,
may be shown as :
(
)
[
]
Where
is a reference distance to star’s
center. Its more convenient
value
is
star’s radius, making star’s surface as reference point.
Then “normal
g
ravity
acceleration law”, Eq’n (2

3); may be written for this location as Eq’n (3
–
2)
(
)
[
]
For
farther points acceleration of gravity reduces by inverse of distance squared.
(As will be shown in next chapter 4 .) Then :
(
)
; and
(
)
1
0
Integrating
from
to any required distance
, net
gravitational speed
, may be found :
∫
∫
=
∫
[
]
It further can be shown that at any distance “r” to star’s center, net gravitational
speed
,
may be found from Eq’n (3

5) :
(
)
Equation (3

5), that may be called
“ net
gravitational speed rule “, states that :
“
Net gravitational speed at normal conditions and outside of a star, is
equal to gravitational speed gradient at that point, multiplied by distance
to star’s center.”
( Off course, this being for free waves t
ravelling along gravity,
until we show its application extent covering common matter
in normal conditions,
in next
section 3
–
2
)
Or Equally
: “
Net gravitational speed at normal
conditions and outside of a star, is equal to product of
acceleration of
gravity at that point and distance to star’s center, divided by base
gravitational speed.”
Example 3
–
1
–
1 Find net gravitational speeds at A) 6371 Km and B) 40000
Km from earth’s center (roughly at earth’s surface and at geosync
h
orb
it) :
Solution :
Assuming
a base gravitational speed similar to example 2

3

1
:
,,
( 3
–
6
)
,,
(
A)
From example 2
–
3
–
1 :
(
)
Then for
r = 40000 Km :
1
1
(
)
Net gravitational speed
:
(
)
3
–
2
Intermediate particles motion
in
gravity field
Recalling Esfand theory, where Fig. 4
–
3 was presented to give a two
dimensional preliminary model of electron, the electron profile therein may
be further improved as shown in Fig 3

1
:
1
2
From section 2
–
2, we can replace two (relative) compression and tension
pack of elastic waves with two lump

wave

po
ints “A”, and “B”. The extent
of rotating elastic wave clouds can not reach near the center of electron,
because frequency of any part of waves would approach infinity as turning
radius approaches zero.
The obvious solution is
not having any waves nea
r center at all.
Therefore, Fig. 3
–
1 is presented here as one step improved version of
Fig. 4

3 of Esfand theory. So lump

wave

points “A” and “B” actually tend to
be at periphery of electron core, with centrifugal acceleration overcome by
(
gravity

type
)
radial
gravitational speed
gradient
⁄
as
in Fig. 3
–
1 ,
and following paragraph
s
.
Time averaged stresses and gravitational speeds will be applied here, so
there will be no concern for time variations, and direction of accelerations
(centrifu
gal and
radial
g
ravitational speed
gradient) , as these accelerations
are exactly, or nearly along particle’s radial direction
, with balance of
accelerations equal to zero along circles of lump

point

waves travel ,
.
Trying to find
particles
’
quasi static equilibrium
conditions,
we may
notice that centrifugal acceleration
,
⃗
⃗
⃗
⃗
;
for a
trapped lump

wave

point is :
(
)
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
In which “
” is angular velocity, “
⃗
⃗
“ is just a unit
length
vector
towards particle center, and “ R “ is effective radius for lump

wave

rotation.
A
cceleration,
due to gravitational gradient (
from “general acceleration
law”
)
is :
(
)
Making 3
–
10 and 3
–
11 equal :
1
3
(
)
( similar to y’ = y / x : just a line )
Defining characteristic slope “ S “, as
quasi

gravitational

speed gradient
[
]
:
(
)
[
]
( similar to y’ =
y / x : just a line)
Example
3
–
2
–
1
is presented below
, to estimate characteristic slope of electron
:
Example 3
–
2
–
1 Assuming electron’s effective core radius of
meters,
and
a
base gravitational speed
of :
to be
144500 times speed of light
( as will be recommended in chapter five)
:
144500 x 299792458
Or 43320 million
kilometers per second
; find an approximate initial estimate of
electron’s characteristic slope.
Solution
:
(
)
[
]
Note
: In addition to approximati
ons involved, higher core gravitational
speeds were not considered in above example 3
–
2
–
1 .
Preliminary two dimensional particle modeling might start by
Rather flat core
gravitational speed at
center, combined with core periphery
characteristic slopes
;
then
connecting
characteristic
slopes
to surrounding
base
gravitational speed v
ia
a repelling ; lower

than

base gravitational speed
curve (sometimes called
compression shield
, or compression cloud)
. Having
reasonable
magnitude for
characteristic slop
e
a
nd radius seems
t
o be among
criteria that makes sub

atomic particles stable
.
1
4
Now let’s consider a simple subatomic particle ( in 2
–
D model ), as the one
shown in Fig. 3
–
2,
in a near uniform gravitational gradient along X direction.
Considering one of the lump wave points, such
as “A” in Fig. 3
–
2, and
, as first
step :
assuming no gravity ( uniform
gravitational speed
), simplified location of
“A” will be :
1
5
(
)
(
)
and
are inertial components of particle velocity.
Before considering a particle in gravity field, let’s check the differences between
free waves and
particles motion in ether space : the main difference is particles’
velocity may have varying angle
s with acceleration.
1
6
In general,
time variations, such as change in inertial and other velocity
components due to
any rapid changes
, need be accounted for , therefore :
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
The last term denotes spatial component of
particle’s
general acceleration
, but
direction of “ ds “ along velocity, differs with “ dr “ along acceleration,
or
as
suggested by Fig
3
–
3
.
From there :
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
with
⃗
⃗
being just a unit
length vector
along
acceleration.
Therefore :
⃗
⃗
⃗
⃗
⃗
⃗
(
)
⃗
⃗
Unified force
–
acceleration
equation is resulted as Eq’n ( 3
–
17 ) excepting
at
electro

magnetic fields
( for common matter
, assuming acceleration
⃗
⃗
⃗
⃗
) .
(
)
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
with
⃗
⃗
⃗
⃗
⃗
being
(steady)
free wave’s
general acceleration spatial component, as introduced by Eq’n
(
2
–
1)
.
similarly, unified force
–
acceleration equation ( 3
–
18 ) may be found for light
(photons) , excepting
at
electro
–
magnetic force fields. :
(
)
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
⃗
with
⃗
⃗
⃗
being
photon’s
acceleration, and
:
photons’ velocity
.
Further developing of unified force
–
acceleration rules is beyond the scope of
this paper.
1
7
Going back to inside of a sub
–
atomic particle at normal conditions, where :
and ether’s gravitational gradient being much less than particle’s
characteristic slope “ S “ ( as shown in Eq’n (3
–
13) , and just as a
n arbitrary
comparing base )
to imply low gravities
:
:
velocity
and acceleration
of lump wave points (and not of a whole particle) remain more or less
perpendicular to each other at these conditions, and a small term due to gravity
may be int
roduced as a
linear adjustment based on principle of superposition.
For superimposing gravity components of velocity, assumed along X
direction, we might make use of acceleration of gravity being
(
)
,
and
noting that
( ignoring
difference of gravitational speeds inside of particles )
, following
(
3
–
1
9
)
Eq’s
are found for lump

wave

point “A”
‘s velocity
:
(
)
(
)
And location
coordinates
, with particle’s center at
:
(
)
(
)
(
)
Above Eq’ns (3
–
19
), and (3
–
20
) are not exact; do not include some less
significant values, and need be worked more if required
: only to show that in
normal conditions gravitational and other ( such as inertial ) components of motion
may be dealt sepa
rately, then superimposed.
1
8
W
here normal conditions do not exist :
at
high speeds and accelerations, such as
near supernovas or
black stars (commonly known as black holes)
changes
become
significant and x coordinate in Eq’n. (3
–
20
)A shows nonlinearity
in
gravitational
section
;
besides
,
some other concerns
need be considered,
such
as
r
apid changes
, which acts through
temporal partial derivatives
;
as well as
other
points possibly associated with high speeds or accelerations.
Not included above are effects of being part of atoms and solids, also probable
tending of particle axes to be aligned
with
velocity, at high speeds.
Similar expressions may be written
for particles with axis along gravity, or
inclined angles.
19
4

Advanced gravity
4
–
1
Intermediate
ether elasticity
Before developing advanced gravity rules, it is
necessary to review some basic
elastic stress / strain
( or force / deformation )
relationships, and fit them into
spherical / gravitational equations. Then, with the help of some experiments results
on one of common super
–
elastic materials ( rubber ) ,
general
gravity laws are
re

discovered.
It has been shown, that by the action of particles trapped wave action, ether is
slightly stretched into a star or any major body.
From this
“ shrinkage “
of ether
(more near the star
–
less farther away )
, a secondary
extra or net tension
–
superimposing on general space tension
–
appears as gravity
( with a mechanism as
will be shown in this chapter )
, as particles tend to move to faster speed zones
.
Ne
vertheless,
primary tension gradient is unable to induce the gravity, as
will be
shown to be the case for super

elastics such as ether, in this chapter
.
Readers already familiar with structural, mechanical engineering; or with
elasticity ( statics,
+ elastic wave propagation in solids ), might want to skip part of
following few paragraphs, as they probably are over

described.
Within a very large elastic solid body in q
u
asi

static conditions, and assumed of
linear elasticity at vicinity of point
of interest, there are some expressions relating
different stresses and strains. Stresses are forces divided by area of applied
surfaces. For example : kilonewtons per square meters tensile or compressive
stress :
And strains are deformations per un
it length of any assumed part :
For example, if a solid bar is in tension, Eq’n
(
4
–
1
)
applies :
2
0
(
)
⁄
Where “ E ” is
Y
oung modulus ( or modulus
of elasticity ).
While a bar is in tension, it elongates with a strain of
. But it also becomes
narrower in diameter ( two directions perpendicular to length ), with a smaller
transverse
strain :
u
.
u
( Greek letter “nu” ) is called Poisson’s
ratio
and
from this point is shown with
, in this paper.
Poisson’s ratio,
is between 0.29 to 0.37
for
most
strong and high stiffness
solids, but it approaches 0.5 , for a few solids that include superelastic materials
( reviewed in secti
on 4
–
2 ), as well as for liquids.
In an ( approximately ) infinite elastic body,
stretching (tension) in one
direction is partly resisted by lateral stiffness of the body. As a result, expressions
(4
–
2)A thru (4
–
2)
C
are found as relation
ship
s between stress
, strain
,
poisson’s ratio
, and modulus of elasticity “E”, (
in 3 principal directions where
no shear exists
) :
.
(
)
(
)
(
)
(
)
(
)
(
)
Going to spherical circumstances around stars, Eq’ns (4
–
2) may be re

written as
Spherical point strains :
Eq’ns (4
–
3)A, and (4
–
3)B; for any point outside of a star,
such
as
point “A”
in Fig 4
–
1 .
2
1
2
2
(
)
(
)
(
)
(
)
Where subscript “ r “ stands for : radial, and “
t
“ for : tangential.
We also note
a complete symmetry
, around the star, including a tangential
symmetry for local coordinate
tangential axes
at point “A”, as far as they are
perpendicular to each other and corresponding radius.
Eq’ns. (4
–
3)A and(4
–
3)B, show
general relation between solids stresses and
strains, ( or forces and deformations ) at one point. Unfortunately, th
ese Eq’ns will
be shown

most probably

to lose validity for super

elastic materials; and
specifically, for ether.
This chapter 4’s goal : w
e a
re
trying to re

find general gravity law, and
s
pecially
its most difficult part :
inverse of distance (to star center) squared. as
the first step,
we need to find how different relevant parameters vary with distance “r” .
We may note
that most parameters : stresses
, strains
, and net gravitational
speeds
, (but not young
or elasticity modulus, “E”), are
net : normally very
small parameters superimposed
–
by presence of a star
–
over general space
ethereal tension
(or other corresponding gross parameters)
.
To follow their changes
by distance to star’s center, we need to co
nstruct their corresponding differential
Eq’n
s
, before trying to solve
them.
Now
considering a crustal segment of ether (part of ether between two
successive hemispheres), at distance “ r “ to “ r+dr “ from star center as in Fig.4
–
2
, we can write balance of forces (
∑
) for the quasi

static case.
2
3
2
4
Trying to add vertical ( along
downward “ Z “ axis ) components of forces :
Crustal compressive force :
(
)
Component of
crust’s
internal tension :
(
)
Component of
outer tension, below crust :
(
)
(
)
(
)
As resultant of all components should be zero :
(
)
(
)
Dividing by
, and omitting infinite small magnitudes of higher order,
the
“
quasi

static equation
”
( 4
–
7 ) is resulted. :
(
)
(
)
In order to better handle the stresses and strains, we have to introduce another
parameter : shrinkage
( not to be mistaken
with
structural shrinkage; nor
with
“dr” , or
, small increments of
radius
).
Shrinkage
, may be defined as the
a
mount that radius “ r “ of an assumed ethereal sphere is shortened, as ether is
pulled by
particles’ internal waves
action
into a
star, as in Fig 4
–
3 .
2
5
2
6
Off course, Shrinkage
, normally is very smaller than radius “ r “.
From Fig 4
–
3 ,
(
)
As the surface of sphere with r
adius
is
:
(
)
Net tangential strain ( relative shortening ) of ether sphere due to gravitational
shrinkage is equal to area increment
, divided by area
S
(assuming
is
entered as a positive value of radius shortening)
:
(
)
Thus “ Shrinkage

tangential strain equation” (4
–
11) ,
is found as :
(
)
or :
Tangential strain is equal to minus twice of shrinkage, divided by
radius “ r “ ( distance to star center ).
( net
–
gravitational ) .
Minus sign indicates
a compressive tangential strain.
In contrast with positive or
(net gravitational) te
nsile radial strain,
.
In order to formulate radial strain
, as per shrinkage
, we may note
that
any small radial increment “ dr “ , is strained by
difference in shrinkage
, at two
ends of this “ dr “.
2
7
Thus “ Shrinkage

radial strain equation” (4
–
12) , is found as :
(
)
(
)
or :
Radial strain is
equal to minus derivative of shrinkage with respect to
radius
“ r “ ( distance to star center ).
( net
–
gravitational ) .
Minus sign indicates a positive or tensile radial strain, as
(
)
is also negative.
It is noteworthy to highli
ght a point regarding signs here. In elasticity equations,
such as set of Eq’ns (4
–
3), positive
numerical
values stand for tension, while
negative
numerical values
: for compression or compressive parameters. While in
static equilibrium Eq’ns, such as
quas
i

static Eq’n (4
–
7), direction of coordinates
rule the signs. Therefore sometimes ( but hopefully not in this case ) sign
corrections / changes may be necessary while working with both groups of Eq’ns.
Summary of resulting Eq’ns appear as ( 4
–
13 )
named Eq’ns
below :
(
)
(
)
quasi static equation
(
)
(
)
shrinkage

radial strain Eq’n
(
)
shrinkage

tangential strain
Eq’n
Equations ( 4
–
3 )A and ( 4
–
3 )B will be shown
–
most probably

not valid
for ether. Besides, more
exact solutions require replacing “r” with
in
some of the above
Eq’ns ,
as the latter value is the real radius for some of the
parameters evaluation as suggested by Fig’s
4
–
2 and 4
–
3 . This will be done in
section 4
–
3 .
As this theory is mainly involved in touchable, physically clear
expressions
,
interpretation of qua
si

static Eq’n (4
–
7)
, or (4
–
13)A,
would be of great help in
its further development.
2
8
If shrinkage
had not induce
d
any
net
tangential (compressive) stress
,
then Eq’n
( 4
–
7 ) would reduce to
:
(
)
Which when solved, a main solution as
( A : a constant ) would be
found for radial stress. T
his kind of connection between
and “ r “
–
as will be
shown later
–
would bring us one step closer to : “ inverse of distance squared “
part of general gravity law
”
.
But shrinkage reduces radii
, and therefore
compressive tangential strains and stresses are expected. This
point
is
further
developed with reference to
Eq’n
(4
–
13)A
( same as Eq’n ( 4
–
7 ) )
as follows
:
Since numerical value of compressive stress
is expected to be negative,
in ( 4
–
13 )A would be positive, meaning that :
Reduction of radial tens
ile stress
,
by
increasing “ r “ is further
accelerated
by tangential stress.
This is very undesirable, as it will lead to
gravitational gradients
,
and from there gravity accelerations reducing by
, with “ n “ much greater than 2
(as may be shown; or will partly be shown).
At this point, the author brings readers’ attention to the point that : knowing
very little
about ether elasticity, many expressions are deduced
assuming similarity
with common matter. Therefore it is expe
cted to be very helpful
to review one of
the most studied
–
most superelastic of common materials : rubber
,
in forthcoming
section
4
–
2 .
But before then, let’s review some of very important effects of shrinkage, that
will be required to re

find g
eneral gravity law.
Looking at Fig’s 4
–
2 , and 4
–
3 , we may notice that we have a kind of pre

stressed, or pre

strained
condition upon presence of a star
( pre

meaning : after
considering “shrinkage”, but before considering other elastic factors
) .
29
A point at distance of
,
has been
at a distance of
, at no
star condition. Therefore
, tangential strain is slightly more than what is found from
Eq’n ( 4
–
11 ) . Also, noting that shrinkage
is normally very small compared
with
, it can be assumed the same for
, or
.
Shrinkage corrected tangential strain, therefore, is :
(
)
(
)
Radial strain needs no shrinkage correction
. :
(
)
(
)
Also referring to Fig 4
–
2 , and applying
instead of
, verti
cal
components of forces are
found as :
(
)
(
)
(
)
(
(
)
)
(
)
Dividing by
(
)
, and omitting smaller quantities of higher order,
:
(
)
(
)
, or
(
)
(
)
(
)
:
Shrinkage corrected
quasi
–
static Eq’n.
4
–
2
Superelastics in action : rubber
One of the most studied / highest superelastic materials is latex ( or
vulcanized
natural ) rubber. It is elastic within more than 6
0
0% tension. Before going through
its mechanical properties, it will be useful to review general expressions relating
those for all solids as set of Eq’ns ( 4
–
19 ) :
3
0
( 4
–
19 )A Young or elasticity modulus . . . . . . . . . . . . . . . . . E
( 4
–
19 )B Shear modulus
. . .
. . . . . . . . . . .
. . . . .
(
)
( 4
–
19 )C Density . . . . . . . . . . . . . . . . . . . . . . . . . . .
( 4
–
19 )D Poisson’s ratio . . . . . . . . . . . . . . . . . . . . . . .
( 4
–
19 )E Lo
ngitudinal modulus . .
.
.
(
)
(
)
(
)
(
)
( 4
–
19 )F Longitudinal (or pressure/tensile) wave speed .
(
)
√
( 4
–
19 )G Shear wave speed .
. . . . . . . . . . .
.
(
)
√
( 4
–
19 )H Wave speed (pressure to shear) ratio .
√
(
)
( 4
–
19 )I Longitudinal to elastic moduli ratio
.
(
)
(
)
( 4
–
19 )J
Bulk
modulus
(mostly for liquids or uniform
) . .
(
)
More details may be found by searching with “elastic constants”, or similar
keywords, at wikipedia.
org
, or other web sites with wide range of elasticity
coverage.
(More description on
and
in
section
4
–
3
)
.
Example 4
–
2
–
1 Find ether Poisson’s ratio
, if gravitational speed is :
Q/C =
144500
( base of this selection will be presented in chapter five )
Trying to find
from ( 4
–
19 )H yields :
3
1
Looking at Eq’ns ( 4
–
19 ) , we may notice ( though
is between 0.29 to
0.37 for most
strong
solids ) that if Poisson’s ratio
, approaches
½
, bulk
modulus and longitudinal ( pressure / tensile ) wave speed become extremely large.
These properties
normally
belong to
liquids : “Negligible shear resistance, but
strong in compression”.
It follows that they are called “ incompressible ”.
Actually, liquids are also compressible, though with comparatively very high
modulus. F
ro
m common solids, rubber resembles liquids in this respect : Poison’s
ratio close to 0.5 . This is equivalent to saying that : it ( as for liquids ) changes
volume very little while under strong stresses.
But rubber has

also

other interesting prop
erties that
justifies its comparing
with ether. Of those, superelasticity is of more concern here : able to stand more
than 600% tensile strain while staying near elastic
(rebound if released)
.
In case of
interest in more details
, referring to
page 33.5
of “Chapter 33, Mechanical
properties of rubber“
by “Schaefer“ is recommended (
re
f
e
rence
s
listed
at the end
of
this
section
).
Summary : latex rubber, with superelasticity (within more than 600% tensile
strain), and Poisson’s ratio of near 0.5 , i
s probably the nearest common matter to
resemble ether.
As this section was concerning a different subject, its references are listed
separately here.
Notes : 1

Some manufacturers use word “modulus” instead of “ultimate tensile
stre
ss” for rubber.
2

Most papers
regarding
tensile test
s
on rubber specimens, treat tensile
stress
, without correction for cross section reduction.
Latex rubber references :
(
1
)

Search web under keywords “The viscoelastic properties of rubber under a
complex loading” , and “Nutthanun Suphadon”
3
2
(
2
)

Search web under keywords “Chapter 33, Mechanical properties of
rubber”, and “Ronald J. Schaefer” ;
of main interest here : page 33.5 .
(
3
)

Scincedirect.com ,
“
On the response of rubbers at high strain rates
–
I
simple waves
”
, by J. Niemczura ,
and K. Ravi

chandar .
4
–
3 Advanced
gravitational elasticity
From section 4
–
2 , first trials to estimate mechanical properties of ether, would
include similitude w
ith
latex
rubber and similar superelastic materials.
In this regard, we may solve the set of spherical point

strains E
q’ns (4
–
3) for
stresses, to find “spherical point

stresses equations” (4
–
20) :
(
)
[
]
spherical point

(
)
[
]
stress eq’ns
As
approaches 0.5 , denominators of (4
–
20) Eq’ns approach zero ,
most
probably :
making those Eq’ns unreliable . This could have been guessed, as
Poisson’s ratio near
½
belongs
mainly
to liquids, not solids ( with some exceptions
such as rubber an
d ether )
.
Continuing interpretation of quasi

static equation (
4
–
7)
, ( or Eq’n ( 4
–
13 ) A )
from section 4
–
1 , let’s assume radial stress to be :
(
)
With n : a positive digit showing how fast radial stress reduces by distance,
and A : a constant.
F
rom quasi

static Eq’n (4
–
7 ) ,
(
)
(
)
It follows that most probably
, tangential stress is o
f the same general form of :
(
)
with B : a constant
Substituting
assumed
and
in (shrinkage

uncorrected) quasi

static Eq’n
3
3
(4
–
7)
yields :
(
)
(
)
(
)
or :
(
)
(
)
Dividing sides by
results in :
(
)
(
)
Most trials on “n” lead to inconclusive results, such as tangential tension ,
…etc.
Trying n=3 gives a ratio of
, interpreted as : compressive
tangential stress with absolute value : half of radial tensile stress. But as specifie
d
at the end of section 4
–
1 , any value of
, except
near zero, ends with
excessively low accelerations of gravity, proportional to
inverse of higher ( than 2 )
powers of distance. Trying n=2 , on the other hand,
brings in compatibility with
gravity and other requirements :
“Almost equal sign” is used, since the uncorrected
quasi static Eq’n used does
not include minor shrinkage correction of
(
)
(corrected version
was
(
)
) . As a result :
and :
(
)
So, we had three reasons for considering
net
tangential stress as being of
insignificant quantity :
First,
approaching
of denominato
rs of (4
–
20) Eq’ns
to zero
, with apparently a tendency of ether
to act similar to liquids in some aspects.
Second : similitude with common superelastic materials such as rubber. And third,
from above two paragraphs. The last
reasoning
, off course, had been a loose one.
As we ruled out an option ( significant value for
) because it contradicted (yet
to be proved) gravity laws. Nevertheless, it is
probably not decisive, as any
“
theory
of everything”
claiming to unify all forces
,
has to pass dozens of tests before a
general admittance.
3
4
Going back to
elastic waves in solids, and recalling a transverse wave speed of
( 4
–
19 )G Shear wave speed . . . .
. . . . . . . . . . .
√
Also, longitudinal wave speed within a very large body is :
( 4
–
19 )F
Longitudinal (or pressure/tensile) wave speed
:
√
Although shear,
Young (elasticity), and longitudinal moduli change as tension
varies in ether, their ratio is expected to stay quite constant most of the times, as
this is the case with common superelastic materials, and these
( moduli or speeds )
ratios are confined by t
he Poisson’s ratio.
Now
the ratio of longitudinal modulus to
shear
modulus
, from (4
–
19)E
:
(
)
(
)
And from
( 4
–
19 )H Wave speed (pressure to shear) ratio
is:
(
)
√
(
)
, where this (
) may be called
“M” ratio.
Having Q and C , we may find
,
from
example
4
–
2
–
1
adopting
gravitational speed of
, is equivalent to a Poisson’s
ratio of :
(
)
with
(
)
.
Also,
may be called “N” ratio,
with its square value equal to
,
as per
Eq’n
(4

19)I . F
rom Eq’n
s
(4
–
19)E ,
and
(4
–
19)F,
it
follows that
:
(
)
√
with
√
(
)
(
)
We are looking for values of
, to apply
it to general acceleration law of :
3
5
(
)
Differentiating
(
)
:
[
√
√
√
√
]
or :
(
)
[
]
Most efforts to
apply
(4
–
32) , in finding gravity laws leaves us with extremely
small gravity
accelerations ( details not given to save space )
, unless we include
shrinkage effect
, which brings in a
secondary
type of
stress

wise, non

uniform
overlay, superimposed
over base ether tension,
by presence of
a
star.
Before
going any further, it
will be very helpful to
make a certain distinction
between two groups of parameters :
First, the
gross parameters, such as
and
( Young
modulus, before and
after presence of a star )
; or
:
base gravitational speed
.
And, second “ very small parameters “ , such as
: net gravitational speed,
net stresses:
,
; net strains :
,
, or shrinkage
; that may
approximately be considered as differentials
, in normal conditions.
Now, recalling shrinkage

corrected quasi

static Eq’n (4

18) :
(
)
(
)
(
)
and
that
Poisson’s
ratio of super

elastic
ether approximately being one

half :
, let’s assume a shrinkage proportional to inverse of distance
(subject to later verification) :
3
6
(
)
,
which is an initial
assumption compatible with
n=2 in Eq’n (4
–
2
5
) . Though a
constant,
“ I “ has dimensions of
. From Eq’n
(4
–
21) radial stress may be estimated as :
(
)
Though a constant, “ A "
has dimensions of force
.
Noting that in Eq’n
(4
–
18), shrinkage

changes of the left side is smaller of higher orders, and this
term
’s variations
may be assumed
insignificant
while checking shrinkage effects
;
f
rom Eq’n (4
–
18) it may be found t
hat
or
is slightly
modified by small
shrinkage ratio of
, within their
shrinkage

correcting
coefficient
.
Therefore
has a shrinkage

effect

correction proportional to
.
C
onsidering
negligible
, and small changes of most parameters upon
presence of star, a star
–
present
Young ( or elasticity ) modulus of
( by
approximate definition )
may be derived as proportional to :
(
)
(
)
Where subscript
“ c “ stands for “corrected”; and “ u “ for “ uncorrected for
shrinkage “ , it also follows that :
(
)
(
)
Thus small increment of elasticity modulus is :
(
)
W
hich is to say : small changes of modulus of elasticity are proportional
to
inverse of distance ( to star center ) squared.
Also from Eq’ns (4
–
19)E , and (4
–
1
9)F
:
√
√
(
)
(
)
or :
(
)
√
combining with (4
–
32)
, and (4
–
37) ,
but
omitting insignificant
effect of
density
changes
,
–
as
the change
3
7
excessively
decreases as Poisson’s ratio
approaches on
e

half
–
, which means :
negligible volume and density changes :
(
)
(
)
or :
(
)
,
but
acceleration of gravity is :
(
)
, it follows that :
(
)
The result
:
In normal conditions ( small to medium speeds
and
accelerations) acceleration of gravity is proportional to inverse of
distance, squared.
The general interpretation of above
clause
is as follows :
Gravity summarized :
A
star
’s, or any major body’s
gravity is formed
through a
secondary effect of shrinkage, affecting
corresponding net radial stress and
net
tangential
strain
s
, (tangential stress
remaining very small
) , superimposed over
general space’s
base tension
and tensile strain.
Example 4
–
3
–
1 Assuming s
un’s surface acceleration of gravity around :
(
)
gravitational speed of
,
( from example 4
–
2
–
1)
coinciding with :
,
and equivalent ether
density of
:
(
)
in
SI units, as
suggested by
“Gorbatsevich” 2007, in “ The ether and universe “ , pages
31 to 33,
3
8
A
at :
h
ttp
\
bourabani.narod.ru
\
ether

e.html
, and other sites,
estimate
order of
magnitude for
shrinkage
, and net tangential strain at sun’s surface.
Solution : Shear modulus is found from (4
–
19)
G
as : ( All units : SI )
(
)
and with Young modulus
from
(4
–
19)B :
(
)
(
)
knowing sun’s
radius of
, recalling
(
)
or
:
(
)
(
)
(
)
, with sun’s surface shrinkage of :
,
which is
possibly the order of magnitude
of
how much ether is drawn from sun’s surface inwards, by the action of gravity
(particles’ waves).
Shrinkage effect is more realized as
(Shrinkage
ratio
)
, :
(
)
or
around one ten

thausandth
of billion
shrinkage effect at sun’s surface; where net tangential strain
is :
(
)
or :
39
(
)
With, several approximations
i
nvolved,
figures derived in this example may be
un

reliable :
order of magnitude at best.
Showing the gravity proportional to both involved masses is rather simple, :
Imagining having three one kilogram masses at
earth’s surface, the total weight (or
gravitational force) , by principle of superposition,
is
three times each weight.
Also, imagining two earth halves with same radius of earth are absorbing a
small mass; again, upon principle of superposition, a whole earth would
enforce
twice gravitational force than two halves.
Thus :
(
)
Similar to Newton’s general law of
gravity.
From above discussion,
it follows that forces are proportional to masses of
subject bodies.
So in normal conditions, where base gravitational speed,
,
may
be assumed constant
in
general gravity law
Eq’n
( 2
–
3 )
:
(
)
gravity
force is proportional to subject
mass, as well as to concerned acceleration, or
( as may be shown with similar to
above gravity discussions, : for any force )
:
(
)
We
would not apply above expressions where
massive objects enforce
considerable change in base gravitational speed
, or at rapidly changing
conditions
,
unless if errors are estimated first.
A coefficient would be required in
Eq’n ( 4
–
5
0
) , unless if we adopt a suitable system of units, such as “ SI “ .
Important conclusion
of
part 4
–
3
:
In Esfand theory,
we deal with
accelerations rather than forces; however,
most corres
ponding forces may be found
from Eq’n ( 4
–
5
0
) at normal conditions.
4
0
Example 4
–
3
–
2
:
Prove or show Newton’s first law of motion by Esfand
theory.
Solution :
Inertial
movement of pa
rticles were briefly reviewed in section 3
–
2 .
It is further added that
inertial movement
of bodies(
as a complex set of elastic
wave systems within ether space )
is probably best described by comparing it with
an elastic wave travelli
ng along a stretched spring ( but with no friction ).
4
1
Chapter 5
–
First steps to probe gravitational waves
5
–
1 Gravitational wave detecting by “ Light
Interference “
Somewhat similar to proof of Esfand Theory ( section 2 on absolute change of
light color at its reflection ) ,and referring to below Fig 5
–
1 , (relative)
expansion/contraction is induced at passage of transient gravitational wave.
From research on CBR (cosmic background radiation), we know that
light/photons expand with space ( therefore also expand/contract at passage of
transient gravitational wave). Again, length A
–
B
of Fig. 5
–
1
remains
constant
at
passage of transient gravi
tational wave;
if expressed in terms of (divided by)
corresponding instantaneous absolute (with respect to ether) wavelength.
The result : gravitational waves may not be detected by simple interference of
light, partly sent back and forth along line A
–
B, presumably fixed in space.
5
–
2
Recommended remedies
How to detect gravitational waves by effective methods may be subject of more
research by interested researchers
, though some preliminary estimates follow :
Summary
of last
section 5

1
: a light beam running thru space does not
gather any information from transient gravitational waves.
An alternate / indirect
method

based on average observed dark matter accelerations

for estimating
approximate gravitational speed ( thou
gh with extra

ordinary high value ) is
available at chapter 6 of “Esfand Theory commentaries 4
–
Secrets of Dark
Matter” at this site.
As
this indirect
guess
starts from a secondary parameter
(
arbitrary
;or mean

observed
dark matter accelerations
) and
estimates a primary
parameter (gravitational speed), errors are subject to be magnified; with
numerically
unreliable answers. A better estimation of gravitational speed
may be
made by accepting its equivalence with quantum
entanglement
state
transfer spe
ed
: around 144500 times speed of light , as reported
by “
University of Science and
Technology of China in Shangha
i”
In
"spooky action at a
distance" travels at least
10,000 times faster than light
, by Brian Dodson; March 10, 2013 at :
www.gizmag.com/quantum

entanglement

speed

10000

faster

light/26587/
,
which is the base of most examples in this paper.
Nevertheless, this chapter 5 is not limited to Esfand theory, and may be adopted by
most “EBOL” ( Ether Borne Light ) theories.
4
3
6
–
Conclusions
These commentaries are
released with author’s trusting
that Esfand theory is
compatible with most current physics
rules
.
Also, the author believes in maintaining all
–
state of the art
–
branches of
modern physics, such as relativities.
His recommendation is just based on looking
at the world from a different angle : what really is the world made of ? , therefore
impr
oving
progress in next decades
( in case the general outlook of this theory
seemed qualified for further work ) .
Example :
After confirmation of earth’s rotating around the sun, everybody
(even the astro

physicists) say ( e.g. ) : “ at 11.
5
0 A.M.
, when sun rises from east to
max height “ , and not : “ the earth rotates from west
and sun seems to rise “ ;
because in time keeping
, we hadn’t need import all newer concepts at the price of
discomfort.
Above words may be summarized as : it is su
ggested that all
current
theories
and branches of modern physics with valuable and enormous extent they cover,
stay where they are
, but in the meantime, we need to know the real world for
improving future trends.
4
4
7
–
Internet references
(1)
–
Dodson, Brian,
"spooky action at a distance travels at least 10,000 times faster than
light"
,
www.gizmag.com/quantum

entanglement

speed

10000

faster

light/26587/
(
2
)

Duffy, M.C., “ The
E
ther
, Quantum Mechanics, and Models of matter “ , at
www.molecularstation.com
,
and some other sites.
(
3
)

Gorbatsevich, F.F., “ The Ether and Universe “ ,
at
http
\
bourabani.narod.ru
\
ether

e.html , and some other sites.
(
4
)

Karlsen, Bjorn Ursin, “ The Great Puzzle “ , at www.scribd.com , or
http://home.online.no , and some other sites.
(
5
)

Mountainman Publishing, many papers on
ether available at :
www.mountainman.com.au/aetherqr.htm
.
(
6
)

World N.P.A. (Natural Philosophy Alliance ), many papers on alternate physics
available at : www.worldnpa.org .
4
5
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