CHAPTER 9
SUMMARY
Relative and absolute motion, an overview
The true Universe?
Building blocks of Nature
Nature is an interplay between mass, charge, time and length. It produces
acceleration and velocity generating the most precious commodity of all, namely
energy, which can be stored (potential energy) or used (power). Stored energy is the
product of mass (
m
) and tension (
蠁
)
. Spent energy or power always involves
radiation Charge (
q
) and mass (
m
) are related through the constants
蔚
0
and
渭
0
. The
change in energy with time (power) is nature鈥檚 gift of life. Without change in energy
nothing would ever happen.
9.1 Relative and Absolute Motion, an overview
Isaac Newton, the ground breaker of modern physics and mechanics,
summarized physics in three laws of motion which are still in broad use
today. He believed the Earth was orbiting the Sun through a fixed
space or ether so that our frame of reference, the Earth, would have an
absolute velocity with respect to stationary space. If Earth in its orbit
is moving around in stationary space, which acts as a medium for force
fields and the propagation of light waves, then space must have some
physical properties. It should be possible to perform an experiment that
could detect the Earth's motion through stationary space or the so
called "ether". Michelson and Morley (1887) were first to attempt such
an experiment using sensitive optical interference methods. It was
thought that the travel of light waves, from a light source to a mirror
and back, would be different along the direction of the Earth's orbital
THE DEADBEAT UNIVERSE
122
motion through the ether than at right angles to it. The result was
that no difference in travel time was detected. Ritz explained the null
result by suggesting that
c,
the speed of light, is always constant with
respect to the light source, but other scientists at the time favored the
idea that our Earth is dragging the ether along in its motion. This is
perhaps closer to the truth since the gravitational tension of all matter
in the Universe is what constitutes the ether and serves as a medium
for force fields and electromagnetic waves.
As long as the
gravitational tension is constant the speed of light stays
constant
. There is no change in the gravitational tension
univ
蠁
at the
surface of the Earth, regardless of its orbital motion around the Sun,
that will change the speed of light in any direction along the Earth鈥檚
surface except in the vertical direction where the Earth鈥檚 own
gravitational tension changes with altitude. The change in the Earth鈥檚
gravitational tension with altitude (acceleration
g
) will change the
speed of light, see Appendix C. Fitzgerald (1889) and, independently,
Lorenz (1892), on the other hand, believed that the null result could be
explained if one assumed that the length of the measuring instrument
shortened in the direction of motion. This turned out to be an
appealing approach and it had its origin in the discovery, at that time,
that matter could not accelerate to exceed the speed of light
c.
It had
been observed that velocity
v
, (
=
v distance
per
time
) did not increase
proportionally to the square root of kinetic energy as envisaged by
Newton but seemed to shrink at high values, never to reach the speed of
light
c
. This behavior was attributed to the shrinkage of
distance
and
was assumed to affect anything moving at high velocity. The proposed
shortening in the length of objects, including instruments and
measuring rods in the direction of velocity
v
relative to the ether,
was attributed to a factor
尾
which limits the velocity to the speed of
light
)
/
(
1
2
2
c
v
鈭
=
尾
.
(
none
) (128)
SUMMARY
123
This shortening of length is known as the Lorenz-Fitzgerald
contraction and the idea has been widely used in situations where
energy and velocity are transferred from coordinates in one frame of
reference to another, which are moving with a velocity of
v
relative to
each other
.
However, instead of changing length of coordinates in
moving frames by
尾
it is just as easy to modify the rate at which time
flows by
尾
or to change both. This variation of the Lorentz-Fitzgerald
idea is exactly what Einstein (1905) had in mind when he introduced
his Theory of Special Relativity which led to the concept of space-time
尾
/
0
0
E
E
E
=
+
)
/
(
2
2
t
ml
(129)
or
[
]
2
2
0
1
)
/
(
1
1
1
尾
鈭
=
+
鈭
=
c
E
E
c
v
,
(
l/t
) (130)
where
E
is the kinetic energy of a mass
m
due to its relative
velocity
v
and
2
0
mc
E
=
is the rest mass energy of an object. The
interesting but perhaps troublesome outcome of Einstein's theory is
that it eliminates the use of length when transforming velocities from
one coordinate to another thus abolishing the concept of a fixed space
and the existence of an ether. Einstein's velocity equation (130)
improved Newton's law of motion to the point where it can precisely
describe the behavior of particles with high relative velocities such as
found in high energy particle accelerators. In fact, Einstein鈥檚 equation
is only accurate in situations where matter has gained velocity due to
gain in energy. The diagram in Fig. 17 shows how Einstein鈥檚
relativistic formula differs from Newton鈥檚 law of motion when used to
calculate velocities of high energy electrons. Einstein鈥檚 energy-
velocity formula has been verified numerous times in particle
accelerators where matter has gained energy and is perhaps one of the
greatest successes in physics of the 20th century. But one problem still
remains, namely that neither Newton鈥檚 law of motion nor Einstein's
THE DEADBEAT UNIVERSE
124
relativistic equations work satisfactorily for the high relative velocities
found in atomic orbits, where velocities are created by loss of rest mass
energy. In fact, Newton's laws of motion offers a slightly better fit
for the energy-velocity relationship of atomic energy spectra than does
Fig. 17. Velocity of high energy electrons as a function of Energy according to
Newton and Einstein.
Einstein's theory, see Fig. 12, Chapter 6.
The reason why both Newton's law of motion and Einstein's theory
of relativity do not work for atomic orbits has to do with the fact
that both theories consider us at rest (thus the term rest mass energy)
and therefore ignore the influence of our own motion with respect to
the rest of the Universe. Einstein's theory goes as far as to state that
everything is relative and that no observer occupies a privileged
position in the Universe because there is no absolute space or ether to
reference our position or velocity to. Although our Earth, the solar
system and our galaxy, are moving relative to other astronomical
objects the theory claims that it is just as valid to say that other
astronomical objects are moving relative to us and that we, therefore,
can consider our frame of reference here on Earth to be at rest. By the
SUMMARY
125
same token an observer at any other galaxy can consider her or himself
to be at the center of the Universe and at rest. Herein lies the snarl
with Einstein's relativity theory since it essentially places ourselves as
stationary observers in a mathematically centralized position. As
previously explained it creates the same difficulty that haunted our
predecessors for thousand of years when they firmly believed that our
Earth was at the center of heaven and at rest and how an impossible
task it was to understand any mathematical equation describing the
planets including our Sun orbiting the Earth. It is for this same
reason that both the Lorentz-Fitzgerald transformation of velocities
and Einstein's relativity theories are difficult to understand and why
they have always been a subject of debate. Even though the
mathematical equations, in some cases, provide correct numerical
answers there is still a small number of investigators who cannot
accept a mathematical theory unless it makes physical sense; while
many mainstream scientists of today seem to feel that a
mathematical equation, which gives a correct numerical answer,
constitutes a physical law. Even if Lorenz-Fitzgerald and Einstein's
equations give correct answers, it is the interpretation of the physics
that is amiss because it does not take into account our absolute motion
in the Universe and, therefore, breaks down when applied to atomic
and astrophysical orbits where velocities relative to us are generated by
loss of potential energy (see Appendix C). To illustrate the importance
of absolute motion consider, for example, the Earth's orbital velocity
0
v
around the Sun using standard Newtonian mechanics
km/s
30
/
.
0
=
=
orb
sun
R
GM
v
.
(
l/t
) (131)
Adding energy in the amount of
E
螖
to the Earth's orbit would sling
the Earth out to a higher orbital radius but slower orbital velocity of
earth
orb
M
E
E
v
v
)
(
2
0
螖
鈭
=
螖
鈭
(
l/t
) (132)
THE DEADBEAT UNIVERSE
126
where
v
螖
is the change in orbital velocity due to the added energy
E
螖
. However, should the Earth's orbit on the other hand, experience
a loss in potential energy it would fall closer to the Sun, but with an
increase in orbital velocity of
earth
orb
M
E
E
v
v
)
(
2
0
鈭
+
=
鈭
+
,
(
l/t
) (133)
where
v
鈭
is the change in orbital velocity due to
鈭
E
, the loss in
energy, see Fig. 18.
Fig 18. Diagram illustrating change in Earth鈥檚 orbital velocity and frequency
螖
谓
and
鈭
谓
as a function of change in orbital energy
螖
E
and
鈭
E
respectively.
The diagram in Fig. 19 shows a curve labeled "Energy gained", which
is constructed from Equation (132) and a curve labeled "Energy
lost" which is constructed from Equation (133). The two curves,
"Energy gained" and "Energy lost" demonstrate that for an equal
change in energy
E
E
鈭
=
螖
the velocity
v
螖
does not equal
v
鈭
or
2
鈳
鈳
鈳
鈳
鈳
鈳
鈭
螖
鈮
鈭
螖
v
v
E
E
,
(
none
) (134)
SUMMARY
127
which informs us that two different equations must be used depending
on whether energy is lost or gained, for the simple reason that our
frame of reference, the Earth, is not at rest. The same is true for objects
seen from our point of reference relative to the rest of the Universe, a
reality which has been neglected and explains why existing theories
fall short in accurately predicting velocities of atomic orbits where
electrons have lost energy to radiation. Therefore, it cannot be ignored
Fig. 19. Change in the Earth's orbital velocity as a function of change in energy.
that we ourselves are in motion when trying to determine motion of
matter relative to us. We have to abandon the doctrine of both
Einstein鈥檚 relativity and Newton鈥檚 concept and accept the fact that we
are part of a Universe in which all matter has its own peculiar position
and absolute velocity with respect to the center of mass of the system.
The intention of this book has been to show that it is possible to
construct equations of motion that are both conceptually clear and
physically sound, and that will work for both energy gained and energy
lost, as well as for absolute and relative velocities. For example, if we
use Newton鈥檚 Equation (131), that was used to describes the Earth's
THE DEADBEAT UNIVERSE
128
orbit around the Sun, but change the mass and radius to that of the
whole Universe we obain
c
R
GM
v
Univ
Univ
abs
=
=
.
.
/
,
(
l/t
) (135)
where
c
v
abs
=
can be considered our absolute velocity relative to the
rest of the Universe. At our frame of reference in the Universe, the
potential energy of matter equals
2
0
mc
E
=
. The absolute velocity as a
function of gain in potential energy is therefore
E
E
E
c
v
abs
螖
+
=
0
0
.
(
l/t
) (136)
As previously shown relative velocities of bodies in the Universe, that
have gained kinetic energy relative to our frame of reference, are
obtained from the vector sum
2
0
0
2
2
2
鈳熲師
鈳
鈳
鈳溾帨
鈳
鈳
螖
+
鈭
=
鈭
=
螖
E
E
E
c
c
v
c
v
abs
,
(
l/t
) (137)
which can be reduced to Einstein's relativistic Equation (130)
[
]
2
2
0
1
)
/
(
1
1
1
尾
鈭
=
+
鈭
=
c
E
E
c
v
.
(
l/t
) (138)
On the other hand, when energy is dissipated relative to our frame of
reference, such as when electrons or astronomical bodies are captured
in orbits and where potential energy is lost relative to us , the above
Equations (137) and (138) are invalid. The correct equation for
velocities relative to us that are produced by loss in potential energy is
therefore
2
0
0
2
鈳熲師
鈳
鈳
鈳溾帨
鈳
鈳
鈭
鈭
鈭
=
鈭
E
E
E
c
c
v
.
(
l/t
) (139)
SUMMARY
129
The curves in Fig. 20 show the velocity of an electron relative to our
frame of reference as a function of energy gained and energy lost. The
straight line represents Newton's law. The curve labeled "energy
gained" is constructed from Equation (137) and which also conforms
with Einstein鈥檚 Equation (138). The curve labeled 鈥渆nergy lost鈥 is
constructed from Equation (139) and fits perfectly situations where
absolute energy has been lost such as in atomic orbits, see detailed
description in Chapter 6, section 6.3. The energy-velocity Equations
(138) and (139), identical to Equations (5) and (10) in Chapter 3, which
were developed from the cosmic harmonic model pictured in Fig. 4,
Chapter 2.
Fig. 20. Change in energy of an electron as a function of its change in velocity.
In summation, consider two observers, one at Earth and one outside
the Universe. The outside observer will see our galaxy and Earth fall
with an absolute velocity of
c
toward the center of the Universe. The
outside observer will also see our galaxy being accelerated at a rate of
THE DEADBEAT UNIVERSE
130
0
a
toward the center of mass of the system. Contrary to the cosmic
observer, the observer on Earth tends to see himself at rest relative to
the bulk Universe. Both observers however, will find that potential
energy of matter at Earth equals
2
0
mc
E
=
.
9.2 The true Universe ?
What has been described so far is a Universe based on the harmonic
model shown in Fig. 4, Chapter 2. This model is basically a
mathematical model which appears to works well for a stationary
observer here on Earth using standard physical units for energy, time,
velocity and mass
etc
. However, these units are not the same
everywhere in the Universe but will change drastically with location.
Time flows slower at the Sun鈥檚 surface than here on Earth and faster on
the planet Pluto. This means that fundamental constants such as the
gravitational constant
G
and Planck鈥檚 radiation constant
h
, which
both have physical dimensions involving time, are not the same
everywhere and as a result the relationship between energy and
velocity can not be the same at different locations in the Universe. The
reason for this is that the cosmic gravitational tension
univ
univ
univ
R
GM
/
=
蠁
, which determines the energy of matter, varies with
the cosmic radius and can therefore not be the same everywhere. At
our position
0
x
in the Universe
2
c
univ
=
蠁
and the potential energy of
matter is
univ
m
E
蠁
0
0
=
.
The fact that energy per mass , inertia of mass and consequently time
(see section Chapter 2, section 2.4), change proportionally with tension
makes it difficult to exactly evaluate physical events at other localities
in the Universe, using the same standards for physical constants as
here on Earth.
Although the harmonic model of the Universe presented in this book,
seems to function satisfactorily there are some questionable features
SUMMARY
131
which need to be addressed. For example, should we not be able to
add velocities linearly in the same direction as we are accustomed to
rather than by vector summation and is the edge or the end of the
Universe really at exactly
m
10
6674
.
1
28
脳
as predicted by the
harmonic model in Chapter 2?
Absolute velocity and potential energy per mass of matter as a
function cosmic radius predicted by the harmonic model are shown in
Fig. 21. Absolute velocity and energy and absolute radius were
obtained from the Equations in Fig. 4, Chapter 2. The diagrams also
Fig. 21. Calculated absolute velocity, observed velocity and energy per mass as a
function of Cosmic radius using the standard mathematical model presented in
previous chapters.
show the observed relativistic velocities
v
螖
and
v
鈭
as seen from our
vantage point here on Earth, and which are also predicted by vector
summation see Equations (137) and (139) and Einstein鈥檚 Equation
(138). However, it does not seem natural that there should be two types
of velocities, absolute velocity as predicted by the harmonic model and
relativistic velocity according to Equations (137, 138, and 139). In the
THE DEADBEAT UNIVERSE
132
authors opinion velocities should add linearly in the same direction and
by vector summation only if they point in different directions. I
therefore believe, that in the relativistic energy-velocity Equations (137)
and (139) and Einstein鈥檚 Equation (138) it is not the velocity but the
energy that appears both as absolute and relative. In Chapter 3 section
3.1, it was shown that energies do not always add linearly as
demonstrated by the examples of the tennis ball and rocket. Doubling
the energy of a rocket at the launching pad does not make the rocket go
twice as fast but increasing the energy in flight by two will double the
velocity. Changing the diagram in Fig. 21 to reflect the idea that both
relative and absolute energy can exist and how it will relate to the
observed velocity is accomplished by mathematically replacing the
components in Fig.21 and construct a new digram such as Fig. 22.
Fig. 22. The standard cosmic model modified to show both relative and absolute
energy as related to observed velocity.
The Diagram in Fig. 22 presents a more sensible view of our
Universe where relative energy is energy of matter as seen from our
vantage point in space and absolute energy as seen from an observer
SUMMARY
133
outside the Universe. Both absolute and relative energy will equal
0
E
at
our galactic reference point
0
x
in space. The observed velocity at
0
x
, or
our velocity relative to the rest of the Universe, is
c
and increases or
decreases by
v
螖
or
v
鈭
on either side of
0
x
. The increase and decrease
in observed velocity as a function of cosmic distance is not linear as
suggested by Hubble鈥檚 law but follows a quadratic function.
The other problem with the harmonic model presented in Fig. 4 is
that at maximum amplitude
A,
the radius is precisely
m
10
6674
.
1
28
脳
where the gravitational tension; potential energy of mass; and length of
time become infinite. This is purely a mathematical solution which
stems from the fact that we only know the amount of mass in our
Universe within our radius of
x
0
and not how mass is distributed
outside
x
0
.
A close examination of the diagram in Fig. 22, shows that
relative energy of matter increases linear with radius up to our
galactic position at .
0
x
It seems likely then that relative energy should
Fig. 23. A more realistic description of the Universe. Velocity and potential energy
of matter shown as a function of cosmic radius seen from our vantage point in space
and expressed in Earth units.
THE DEADBEAT UNIVERSE
134
continue to increase in a linear fashion past our position
x
0
to its
maximum radius or amplitude
A
as shown by Fig. 23. Allowing the
relative energy, or gravitational tension of the Universe, to increase
linearly with its radius beyond
0
x
means that the mass of the Universe
must increase proportional to its radius squared (
2
U
U
R
M
鈭
) which is in
exact agreement with the Large Number Hypotheses and the Virial
Theorem described in Chapter 8, see page 116 and 120.
The increase in inertial mass as a function of radius squared hints
to a Universe with a non-uniform mass density, unless pancake
shaped, as suggested by several investigators. A pancake shaped or
disk shaped Universe could possibly represent the ultimate structure of
cosmos completing the hierarchical system from atoms, solar systems,
galaxies, cluster of galaxies to a meta galaxy of near infinite size. The
diagram in Fig. 23 portrays, in the author鈥檚 opinion, such a Universe
in a authentic way. It shows our distance from the cosmic center
and for comparison a distance of 15,000 Mpc centered around our
galaxy.
At the present time a distance of 15,000 Mpc is still far beyond the
reach of our telescopes. The diagram in Fig. 24 zooms in on a
small section of Fig. 23 spanning 400 Mpc along the cosmic radius in
each direction of
x
0
. Note that the observed velocity of nearby galaxies
appear linear with distance but then further deviates with distance.
This explains why the illusive 鈥渓inear鈥 Hubble鈥檚 law has never been
established. In fact, several astronomers (A. Dressler (1987), (1994),
Riess et al. (1996) and Perlmutter
et al
. (1998) ) have recently
discovered that Hubble鈥檚 velocity-distance relationship is not linear but
changes slightly with distance which they ascribe to a small amount of
acceleration caused by some unknown force. The force is of course
generated by the gravitational mass of the Universe and the observed
acceleration is the cosmic acceleration
0
a
(see Fig. 15. Chapter 7)
SUMMARY
135
Does the radius of the Universe and the gravitational tension and
potential energy of matter increase forever? There must be a limit to
the size and mass of the Universe otherwise the laws of physics break
down. But if there is a limit to the Universe how do we describe empty
space beyond the boundaries of our Universe? Empty space contains
nothing and we cannot assign properties to nothing or nothingness.
This is a difficult subject since it is practically impossible for most of us
imagine empty space as nothing or something that does not exist.
We seem to understand that we cannot visit or live within the
boundaries of a country that does not exist but yet we seem to find it
possible to visualize a boundless void outside our Universe where
nothing exists, a place filled with an infinite amount of nothing!
Fig. 24. A small section along the radius of the Universe centered around our Galaxy
showing the change in velocity, tension, time and potential energy of matter as a function
of cosmic radius.
One point of view is that since space outside the Universe is filled
with its gravitational field which decreases to zero at infinity, one could
THE DEADBEAT UNIVERSE
136
argue that the Universe together with its gravitational field is infinite
and boundless. Alternatively, if the energy of the gravitational field is
quantized and divided into a finite amount of small energy/mass
packets, like sand pebbles on the beach, then one could expect the
number of energy packets to eventually run out before reaching infinity,
thus favoring a finite Universe.
9.3 Building Blocks of Nature
Length
:
As mentioned in Chapter 1 the building blocks of nature are
mass, charge, length and time or
m, q, l
and
t
.
Length
or distance is
probably the one building block that is easiest to understand.
Length
however, has no physical significance unless joined by any of the other
three building blocks. For example,
length
per
time
is velocity and
mass
per
length
determines the strength of gravitational tension
(
r
Gm
/
=
蠁
).
Length
脳
width
is surface area and is an important spatial
dimension when dealing with pressure, temperature or radiation. Mass
per unit surface area (
2
/
l
m
) is often used as a measure of pressure
although a more sophisticated term for pressure is newton per unit
surface area (
)
/(
2
l
t
m
). The surface temperature of a body is determined
by the power radiated per unit surface area of the body or
蟽
A
L
T
/
4
=
where
蟽
is Stefan-Boltzmann鈥檚 constant
. Length
脳
width
脳
height
is
volume or space and is also quite meaningless unless filled with
gravitational
tension
,
mass
or
charge
. We can imagine empty space but
it is doubtful it can be detected. It was believed that gravity could
warp space or bend world lines. I do believe that light rays will bend
inside a volume filled with a non-uniform gravitational tension and that
measuring sticks can shrink or expand, but I do not believe that the
elements of space itself 鈥
length
脳
width
脳
height
鈥 can change. The fact
that light bends near gravitating bodies is, therefore, not due to warped
space or bent world lines but is caused by the same effect that bends
SUMMARY
137
light in glass, namely Snell鈥檚 law. A peace of glass does not warp space
or bend world lines, see Chapter 4, section 4.7.
Mass
: If the units of
length, width
and
height
do not change what
about
mass
? In scientific terms
mass
is often referred to as either
gravitational mass
or
inertial mass
. Many are of the opinion that both
are equal, which is a subject of debate. Let us follow the historical
progress that led to the concept of
inertial mass
which starts with
Galileo Galilei 1564-1642. It is said that Galileo obtained his ideas for
his famed experiments while attending a church service during which
he also observed and timed the swing of a chandelier hanging from the
ceiling. One experiment that followed is here described in Galileo鈥檚 own
words:
I had one ball of lead and one of cork, the lead ball being more
than hundred times heavier than the one of cork, and suspended
them from two equally long strings, about four or five bracchia in
length. Pulling each ball away and releasing them at the same
instant from their vertical point of rest, they fell along the
circumferences of their circles having the strings as radii swinging
back to near the same vertical height of origin and then returned
along the same path. This free pendulum motion, which repeated
itself more than hundred times, showed clearly that the heavy
body kept time with the light body so well that neither in hundred
swings, nor in thousand, will the former pass the latter by even an
instant, so perfectly do they keep step.
The experiment clearly showed that the pitch of a pendulum does not
change with
mass
or weight even though gravity exerts a much
stronger force on a heavier weight. The next test was to see whether a
heavier weight would fall faster than a lighter weight. Galileo is said to
have dropped different weights from the tower of Pisa, see Fig. 25, and
found that they reached ground at the same time. In modern terms,
two different weights are accelerated at exactly the same rate even if
THE DEADBEAT UNIVERSE
138
the Earth鈥檚 pull is stronger on the heavier
mass
. It is often said that
since inertia of
mass
is the same as resistance to acceleration, then
although twice the
mass
means twice the pull by the Earth鈥檚
gravitational field, the resistance to the pull will also double, thus
canceling any effect of change in
mass
leaving the acceleration
unchanged. This explanation is not quite right because the Earth鈥檚
gravitational field does not care about the
mass
of an object but
bestows the same rate of acceleration on any object immersed in its
field. This is simply
Fig. 25. Galileo鈥檚 experiment and discovery of acceleration at the tower of Pisa.
explained by the fact that the Earth鈥檚 acceleration
g
is solely
determined by the gradient of the Earth鈥檚 own gravitational tension or
Earth
Earth
R
g
/
蠁
=
and not by the
mass
of the body being attracted to it.
However, the view that the inertial force of a body (the force that resists
acceleration) exactly balances the gravitational force that attracts it,
SUMMARY
139
did stick in the mind of scientists for a long time and has led to some
questionable theories. One such theory concerns the 鈥渆quivalence
principle鈥 which goes as far as to state that inertia of
mass
is the same
as gravitational
mass,
since gravitational force cannot be distinguished
from inertial force. The proof given is Einstein鈥檚 famous example of an
observer inside a windowless elevator. Two conditions are considered,
one where the elevator is stationary suspended by a cable in the
gravitational field of a gravitating body such as the Earth, and the
other where the lift is being pulled by the cable at a steady rate of
acceleration far outside any gravitating body. In both cases the
observer will feel his feet pressed to the floor and inside his windowless
elevator the observer would supposedly not be able to tell whether he is
subject to a gravitational force or an inertial force, since they both are
considered equivalent. This is not quite right, because for one thing,
the lines of force inside the elevator, when subject to a gravitational
force are not parallel but always converge to a point which coincides
with the center of
mass
of the gravitating body. When pulled at a
steady accelerating rate, the lines of force are always parallel. Also, a
steady change in clock rate and a change in the velocity of light will
take place in the latter case caused by the steady increase in velocity
and tension
)
(
2
v
螖
鈮
螖
蠁
, see Appendix C. Another problem with the
鈥渆quivalence principle鈥 occurs when it is applied to the bending of light
near gravitating bodies. Here the 鈥渆quivalence principle鈥, which
assumes that any substance (including photons) will accelerate towards
a gravitational center at an equal rate regardless of
mass
(whether zero
or infinite), predicts that a massless beam of light will accelerate and
bend in the same manner that the path of a massive projectile will
accelerate and bend when passing near a gravitational source. The
angle of deflection is determined by Newton鈥檚 law of gravitation. In
reality, massless light beams, contrary to massive objects, do not
accelerate, they slow down and decelerate when entering a gravitational
field and the bending of light in gravitational fields is better explained
by Snell鈥檚 law (Chapter 4, section 4.7).
THE DEADBEAT UNIVERSE
140
Our concept of
mass
is not very clear. How is gravitational
mass
g
m
related to inertial
mass
i
m
? In our frame of reference at Earth we
often define the
mass
of a body by its inertia or resistance to
acceleration
a
F
m
i
/
=
i.e
. if a body accelerates by
a
=
1
meter per
second per second when subject to a force
F
of one newton (nt) its
mass
is 1kg. We can, therefore, determine inertial
mass
from Newton鈥檚 laws
of motion
2
2
v
E
m
k
i
=
, Newton
(
m
)
(140)
where
E
k
is the kinetic energy involved in accelerating the body to a
given velocity of
v
relative to us. There is one problem here, namely
that at high relative velocities a relativistic increase in inertia of mass
becomes notable. This relativistic mass increase, which was discovered
by Einstein, makes Newton鈥檚 law obsolete so Equation (140) needs to be
changed to
2
0
c
E
E
m
k
i
+
=
, Einstein
(
m
)
(141)
where
2
0
0
c
m
E
=
is the
mass
equivalent energy of the body at rest
relative to our frame of reference. Since
0
E
and
2
c
are constants and
k
E
is a variable it means that
i
m
must increase proportionally with
k
E
. It is also important to remember that the rate of
time
in a system
that has been accelerated changes proportionally with the energy of the
system, see for example, Equation (1) and the 鈥渢win paradox鈥 Chapter
2 section 2.4.
Gravitational
mass
on the other hand is determined by Newton鈥檚
law of gravitation
蠁
g
g
g
E
GM
R
E
m
=
=
, Newton
(
m
)
(142)
SUMMARY
141
where
R
is the distance of
g
m
from the center of a gravitating
mass
M
and
g
E
is the energy required to move
g
m
from
R
to infinity. The
gravitational tension generated by
M
at
R
is
蠁
. Since
g
E
is directly
proportional to
蠁
it means that the gravitational
mass
g
m
will always
remain constant. In contrast to inertial
mass
gravitational
mass
does
not change with energy. However, the rate of
time
changes
proportionally with gravitational tension. For example, we have seen
that the rate of
time
is slower at the Sun鈥檚 surface than here on Earth
due to the Sun鈥檚 higher gravitational tension. The result is that all
physical processes on the Sun are slower, including processes involving
acceleration. This slow-down of acceleration can be interpreted as an
increase in inertia. This leads to the argument that the relativistic
mass
increase discussed above is really not an increase in
mass
but an
increase in the length of
time
thus retarding or slowing down the rate of
acceleration which we interpret as increase in inertia of mass. By the
same token we can say that gravitational energy increases the length of
time which is not reflected in Equation (142).
Conclusion: Whether the tension of
mass
(
m
E
/
) is raised by an
increase in velocity relative to our frame of reference or by an increase
in a surrounding gravitational field
mass
stays constant but inertia will
change due to the change in rate of
time
.
Time:
From the above it appears that out of the three main building
blocks of nature
length,
mass
and
time,
only
time
is a variable. A
meter is always a meter and a kilogram is always a kilogram and will
remain unchanged anywhere in Cosmos but the unit of
time
, the
second
, varies at different locations in the Universe. Most interestingly
is that length of time is determined by the combination of
mass
and
length
(
M/R
) which is proportional to Tension and Energy. Time
therefore must be related to Tension and Energy. The question is:
Does tension or energy determine the rate of time or does the rate of
time determine the amount of energy?
THE DEADBEAT UNIVERSE
142