West Caldwell, NJ

Revision Copyright- December 1997

All Rights Reserved

- The symbol "*" represents a multiplication.

- The symbol "^" represents the raising of a number to a power.

- The author relies upon the "No Break" command of HTML to prevent equations and expressions from being split between lines by the browser's wordwrap function.

**Redefinition:- Since the Lorentz Transformation, (1-V**^{2}/C^{2})^{0.5}, appears many times in the material which follows follows, the symbol 'B_{v}' will be substituted. Thus: B_{v}=(1-V^{2}/C^{2})^{0.5}.

- A:- If I had a microscope, I would observe the existence of germs.

- B:- The existence of germs does not depend upon the existence of the microscope.

- C:- If I could communicate using tachyons, I would be able to establish
absolute simultaneity between physically separated locations, measure my
velocity with respect to space itself, and thereby verify the Aether
Relativity Theory.

- D:- The validity of the Aether Relativity Theory does not depend upon my ability to communicate using tachyons.

- It must be a solid medium rather than a fluid. If it were not a solid
medium, transverse electromagnetic disturbances (light) would not propagate
since transverse disturbances cannot propagate through a fluid.

- It must have, as a minimum, a dielectric constant, a permeability, and
occupy a volume since these properties are readily observed.

- It apparently is absolutely continuous rather than composed of minute
particles. This continuity may well approach a zero size as a limit since it
behaves as if it had a "Q" which approaches infinity.

- A tuning fork made of steel will ring for a prolonged period after being
struck since steel is a high "Q" material. One made of lead will merely
"thunk" when struck since lead is a low "Q" material. Disturbances in the
Aether do not die out at a detectable rate while propagating through free
space suggesting that the Aether has a "Q" which is enormous and may well be
infinite.

- A tuning fork made of steel will ring for a prolonged period after being
struck since steel is a high "Q" material. One made of lead will merely
"thunk" when struck since lead is a low "Q" material. Disturbances in the
Aether do not die out at a detectable rate while propagating through free
space suggesting that the Aether has a "Q" which is enormous and may well be
infinite.
- Material particles must be constructed in such a way that it is possible for them to propagate through the solid Aether (Chapter 13).

Quantity | Dimensional Entity |
Parallel Transformation |
Transverse Transformation |
---|---|---|---|

Force |
F |
1 |
B_{v} |

Length |
L |
1/B_{v} |
1 |

Time |
T |
B_{v } |
B_{v} |

Quantity | Symbol | Dimensional Content |
---|---|---|

Force, F |
F |
F |

Length, L |
L |
L |

Time, T |
T |
T |

Energy |
E |
F*L |

Planck's Constant |
H |
F*L*T |

Velocity |
V |
L/T |

Acceleration |
A |
L/T ^{2} |

Incremental Mass |
M _{i} |
F*T ^{2}/L |

Momentum |
U |
F*T |

Angular Momentum |
J |
F*L*T |

Gravitational Constant |
G |
L ^{4}/(F*T^{4}) |

Ergo-gravitational Constant |
D |
1/F |

Temperature |
& |
F*L |

Charge |
Q |
L |

Dielectric Constant of Space |
e' |
1/F |

Permeability of Space |
u' |
F*T
^{2}/L^{2} |

- Current texts erroneously provide 1/B
_{v}as the Lorentz Transformation for Transverse Force.)

- The dimensional content for velocity is unaffected by the relativistic
correction term for the addition of velocities since that correction terms is
dimensionless.

- The dimensional content of the gravitational constant is determined from
the expression for Newtonian gravitational force,
F=G*M
_{i1}*M_{i2}/L^{2}.

- The ergo-gravitational constant is the conventional gravitational constant
defined in terms of the energy equivalents of the gravitating masses. It is
identical to Dr. Einstein's Cosmological Constant and is equal to
G/C
^{4}.

- Temperature is kinetic energy per available degree of freedom and has the
dimensional content of energy.

- Evaluation of the dimensional content of the expression for the
electrostatic force between charges provides
Q
^{2}/e'=F*L^{2}.

- Evaluation of the expression for the electromagnetic force between moving
charges provides Q
^{2}*u'=F*T^{2}. The velocity of light is given by C=(e'*u')^{0.5}.

- If one accepts the precept that the exponent of a dimensional entity
must be an integer, there are two possibilities. The first possibility is
that the dimensional content of Q is equal to L, the dimensional content of
e' is equal to 1/F, and the dimensional content of u' is equal
to F*L
^{2}/(L*T^{2}). The second possibility is that the dimensional content of Q is equal to unity, the dimensional content of e' is equal to 1/(F*L^{2}), and the dimensional content of u' is equal to F*T^{2}. The dimensional content for charge, Q, must equal to the dimensional content for length, L, in order for the Principle of Relativity to apply, and this value, and its related values for e' and u' is chosen for Table 7.8.1.

- If one accepts the precept that the exponent of a dimensional entity
must be an integer, there are two possibilities. The first possibility is
that the dimensional content of Q is equal to L, the dimensional content of
e' is equal to 1/F, and the dimensional content of u' is equal
to F*L

- In attempting to use mass as a fundamental observable entity, care must be
taken to insure that the observation of mass does not require knowledge of
another mass(es), unless that mass(es) has been determined by an independent
means. Otherwise, such an observation defines mass in terms of itself, an
obvious absurdity.

- When one determines mass by "weighing", the necessary independent means is
available. The laws of orbital mechanics allow the determination of the mass
of a primary object to be determined in terms of the orbital period of a
satellite and the gravitational constant. The gravitational constant, in turn,
can be measured in terms of inertial mass by means of the Eotvos Experiment of
Figure 8.1.

- In order to determine the mass of an object by counting its particles, a
similar independent means of measuring the mass of the particles is required.
This process is complicated by the fact that the mass of a compound particle
(e.g..- an atom having an atomic weight greater than 1, or a molecule) does
not equal the sum of the masses of its component parts (e.g.- the mass of a
helium atom is less of the mass of four hydrogen atoms due to the energy
released during its fusion). A mass spectrometer could be employed to
determine the mass of every particle, atom, or molecule of interest, but, as
is the case of "weighing", such usage would define mass in terms of its
inertial effects.

*It would appear, then, that a refinement of our understanding is required. There are only two primary means of observing mass. It may be observed by the energy released during annihilation and it may be observed by "shaking". "Weighing" or "counting" are a secondary means of observation which rely on the primary means for their validity.*

L=1/(1-$)

T=(1-$)

L=1

T'=1/(1+$)

S =1/(1+$)

Quantity |
Parallel Velocity |
Transverse Velocity |
Gravity Relativity |
General Relativity |
---|---|---|---|---|

Force F |
1 |
B_{v} |
1 |
1 |

Length L |
1/B_{v} |
1 |
1/B_{g} |
1 |

Time T |
B_{v} |
B_{v} |
B_{g} |
B_{ge} |

Space S |
1 |
1 |
1 |
Bge_{} |

Stiffness K' |
B_{v} |
B_{v} |
B_{g} |
1 |

Quantity |
Symbol | Parallel Velocity |
Transverse Velocity |
Gravity Relativity |
---|---|---|---|---|

Force |
F |
1 |
B_{v} |
1 |

Length |
L |
1/B_{v} |
1 |
1/B_{g} |

Time |
T |
B_{v} |
B_{v} |
B_{g} |

Energy |
E |
1/B_{v} |
B_{v} |
1/B_{g} |

Planck's Constant |
H |
1 |
B_{v}^{2} |
1 |

Velocity |
V |
1/B_{v}^{2} |
1/B_{v} |
1/B_{g}^{2} |

Acceleration |
A |
1/B_{v}^{3} |
1/B_{v}^{2} |
1/B_{g}^{3} |

Incremental Mass |
M_{i} |
B_{v}^{3} |
B_{v}^{3} |
B_{g}^{3} |

Momentum |
U |
B_{v} |
B_{v}^{2} |
B_{g}^{3} |

Angular Momentum |
J |
1 |
B_{v}^{2} |
1 |

Gravitational Constant |
G |
1/B_{v}^{8} |
1/B_{v}^{5} |
1/B_{g}^{8} |

Ergo-gravitational Constant |
D |
1 |
1/B_{v} |
1 |

Temperature |
& |
1/B_{v} |
B_{v} |
1/B_{g} |

Charge |
Q |
1/B_{v} |
B_{v} |
1/B_{g} |

Dielectric Constant of Space |
e' |
1 |
1/B_{v} |
1 |

Permeability of Space |
u' |
B_{v}^{4} |
1/B_{v}^{3} |
B_{g}^{4} |

Stiffness |
k' |
B_{v} |
B_{v} |
B_{g} |

A

A

- The primary difference between the axioms of Riemann geometry and Euclidian geometry is that Riemann's geometry does not require that parallel lines never meet while Euclidian geometry does have that requirement. The writer understands that both geometries define a straight line as the shortest distance between two points.
- Since the non-Euclidian geometry of N dimensions can be contained within a
Euclidian geometry of N+1 (or N+3) dimensions, the
shortest distance between two points does not lie within the non-Euclidian
geometry. lt leaves that geometry between the two points and travels through
the Euclidian geometry of N+1 (or N+3) dimensions. (To
illustrate, if one considers the surface of the Earth to represent a two
dimensional non-Euclidean geometry, the shortest distance between New York and
Los Angleses is not a great circle, it is through a tunnel which passes almost
two hundred miles beneath the Mississippi River.)

- The straight line of non-Euclidan geometry is the shortest distance
between two points which
**remains**within the non-Euclidian geometry (e.g.- the great circle path between New York and Los Angeles.) Since the straight line of non-Euclidian geometry does not meet the rigorous definition of a straight line, it seems reasonable to question the rigor of non-Euclidean geometry except as a convenient means of describing the properties of a curved "surface" contained within a "volume" defined by Euclidian geometry.

*The author asserts that a rigorous theory should not be based upon Riemannian geometry without an adequate and relavent treatment of the higher order Euclidian geometry it implies.*

- It will predict the cessation of contraction at the radius where the
velocity of fall from an infinite distance is equal to the velocity of
light.

- It will be consistent, in the absolute sense, with the Law of Conservation
of Energy.

- It will be consistent with the Principle of Relativity.

- It will be consistent with the Principle of Equivalence.

- It will yield predictions which are consistent with
observation.

- The mass of the object is contained in an infinitesimally thin shell which
is at a constant radius from the center. All of its gravitational mass and its
entire internal volume is at the same gravitational potential.

- This model is structurally unstable and will collapse in response to the
slightest deformation, just as a plastic soft drink bottle will collapse
under a slight external pressure even though it can withstand considerable
internal pressure. This instability does not limit its usefulness in
analyzing the gravitational field.

- This model is structurally unstable and will collapse in response to the
slightest deformation, just as a plastic soft drink bottle will collapse
under a slight external pressure even though it can withstand considerable
internal pressure. This instability does not limit its usefulness in
analyzing the gravitational field.
- Where it is necessary in the discussion to eliminate the effects of energy loss by radiation, the surface of the object is considered to have zero emissivity.

R

The term, #, is added to the expression for the Horizon Radius derived in "Gravity" because, as that text shows, energy in the form of radiation gravitates at twice the rate as energy in the form of matter. The portion, #, of the total energy of a contracting object which is in the form of radiation changes as the object contracts due to the release of gravitational energy as radiation or the conversion of radiation into matter. The material which follows has been simplified by normalizing the radius of the object in terms of R/R

- As the object contracts, the velocity (as a fraction of the local velocity
of light) and the kinetic energy of a particle falling to the object from an
infinite radius increases.

- The increase of kinetic energy of the falling particle raises its
temperature until its kinetic energy becomes equal to its rest mass energy. At
that point, its temperature no longer rises because the creation of additional
matter is a higher entropy path for the absorption of the energy of fall than
is an increase in the temperature of existing matter. The locally observed
temperature then remains constant at about 4.25 trillion Kelvins until the
final portion of the locally observed expansion phase.

- The simulation assumes that once the matter creation stage is reached,
internal pressures balance gravitational pressures and the velocity of fall
no longer increases. The simulation was also run without allowing the
creation of additional matter by allowing the actual contraction velocity to
increase to the velocity of light. The only difference in the results
obtained was a reduction of less than one second in the time for the process
to go to completion. It seems reasonable, therefore, to accept that any
effects resulting from having erroneously assumed that the velocity of
collapse is limited by matter creation may be ignored.

- The simulation assumes that once the matter creation stage is reached,
internal pressures balance gravitational pressures and the velocity of fall
no longer increases. The simulation was also run without allowing the
creation of additional matter by allowing the actual contraction velocity to
increase to the velocity of light. The only difference in the results
obtained was a reduction of less than one second in the time for the process
to go to completion. It seems reasonable, therefore, to accept that any
effects resulting from having erroneously assumed that the velocity of
collapse is limited by matter creation may be ignored.
- The locally observed velocity of the expansion stage is limited to the
velocity of light.

- This limitation is not imposed by Velocity Relativity because the locally observed expansion is not caused by velocity. The particles which are observed to be separating from each other are essentially stationary. It is the reduction in the actual velocity of light which makes them appear to be separating at a high velocity.
- This limitation would result if the propagation velocity of
gravitational effects is limited to the velocity of light. Since the
gravitational force producing collapse propagates through the interior of
the object, the force causing the collapse would then cease to act once the
locally observed expansion velocity became equal to C.

- Since gravitational energy is released from the energy contained in
the matter and radiation within the field rather than from the field
itself, there is no reason to believe that the gravitational field itself
contains energy in any form. Velocity Relativity then does not impose its
velocity limits of +/-C on the propagation velocity of a
gravitational field. To the author's knowledge, there has been no
experimental determination of the velocity of propagation of gravitational
effects.

- Since gravitational energy is released from the energy contained in
the matter and radiation within the field rather than from the field
itself, there is no reason to believe that the gravitational field itself
contains energy in any form. Velocity Relativity then does not impose its
velocity limits of +/-C on the propagation velocity of a
gravitational field. To the author's knowledge, there has been no
experimental determination of the velocity of propagation of gravitational
effects.
- The computer simulation was run both with and without a limitation on the velocity of propagation of gravitational effects. The only significant difference was, that without this restriction, the expansion phase, as locally observed, is so rapid that nucleons begin receding from each other at faster than light velocities within a second after the expansion phase starts. Since our Universe is most certainly an ancient gravitational object which is expanding and which contains a large number of observable nucleons, the author accepts that gravitational effects propagate at the local velocity of light.

Gravitational Pressure = R

Radiation Energy Density = 3R

And, since radiation pressure is proportional to the energy density of the radiation, the radiation pressure, P

Radiation Pressure = 3R

Equating the expressions for the gravitational pressure and the radiational pressure enables the relationship between the gravitational potential, R

(1-R

The characteristics of a collapsed object in which all of its energy has been radiated to space has also been derived in "Gravity". Actually, the object has shrunk to the size of a mathematical point which contains zero energy. As observed locally, the object has shrunk to the radius of its original Event Horizon and contains an amount of energy which is equal to the energy originally contained in the matter from which it was formed. This energy, however, will be entirely in the form of radiation.

- The object consists of mostly empty space filled with radiation.
- Nucleons within the object are organized in strings of varying lengths up
to a significant portion of the size of the object. If the object is
sufficiently large, these strings eventually contain stars and
galaxies.

- Workers in the field of plasma physics have shown that electric and
magnetic fields in space are capable of organizing matter in this manner.
("The Big Bang Never Happened" by Eric Lerner, Times Books.)

- Workers in the field of plasma physics have shown that electric and
magnetic fields in space are capable of organizing matter in this manner.
("The Big Bang Never Happened" by Eric Lerner, Times Books.)
- The object will be observed to be expanding towards an infinite radius
with the fraction of its total energy which is in the form of radiation, #,
approaching unity.

- Extrapolation of observations of the expansion process backwards in time
will lead to the conclusion that the object began with an eruption of matter
into existence. Simplistically, it would be concluded that the matter was
created from nothingness at a single point in space.

- The radius of the object will appear to be increasing at the velocity of
light.

- The object will be composed entirely of normal matter or of anti-matter
but it will not contain both types.

- Mutual annihilation will cause matter and anti-matter in the original
cloud to annihilate each other until only the predominant type of matter
remains.

- Mutual annihilation will cause matter and anti-matter in the original
cloud to annihilate each other until only the predominant type of matter
remains.

- Separately, the photons must be electromagnetic impulses propagating at
the velocity of light.

- The net electric, magnetic, and mechanical effects of each impulse must equal zero when averaged over time.
- When a sufficient number of these impulses are superimposed with the appropriate timing and phasing, they must produce the apparently continuous electromagnetic wave of Figure 13.1.

- In its observable form, energy is not continuous. It appears only in the
form of discrete packets which may be photons, neutrinos, protons, neutrons,
or their anti-particles, and which are designated as quanta.

- Each quanta, whether it be a photon, a neutrino, or a material particle,
has a frequency equal to its energy content divided by Planck's
Constant.

- Each quanta couples to the Aether. Any quantum stress induced in the
Aether by that coupling pervades all of space at a quasi-infinite velocity and
probably obeys the inverse square law with respect to distance.

- Some quanta, such as photons which have been created in pairs, have
quantum numbers (the axis of polarization in the case of photons) which are
permanently coupled. This coupling is infinitely stiff, virtually
instantaneous, and is unaffected by the distance between the paired
particles.

- Information as to the state and position of each quanta is transported at
a quasi-infinite velocity and with infinite resolution by quantum stress in
the Aether.

- The stress pattern in the Quantum Field at any point in space is
modified by the configuration of obstacles in the path of the particles
producing the stress.

- The stress pattern in the Quantum Field at any point in space is
modified by the configuration of obstacles in the path of the particles
producing the stress.
- Particles in motion follow a path which is consistent with the path of the
information transported at a quasi-infinite velocity by the stress in the
Quantum Field.

- Since the Quantum Field is continuous and the particle is quanticized,
the transport of information by the two effects cannot match on an instant
by instant basis. The match becomes proportionately more precise when the
number of particles observed becomes large enough to allow their positions
to be a statistically accurate representation of the information represented
by the stress in the Quantum Field. The instantaneous peak to peak error in
the information match is equal to the energy of the
quanta.

- Since the Quantum Field is continuous and the particle is quanticized,
the transport of information by the two effects cannot match on an instant
by instant basis. The match becomes proportionately more precise when the
number of particles observed becomes large enough to allow their positions
to be a statistically accurate representation of the information represented
by the stress in the Quantum Field. The instantaneous peak to peak error in
the information match is equal to the energy of the
quanta.

- Each quanta must apply a quantum stress to the Aether.

- Quantum stress in the Aether must propagate in all directions at a
quasi-infinite velocity.

- Quantum stress in the Aether probably must obey the inverse square
law.

- Quantum stress in the Aether must be refracted by the geometrical
configuration of matter.

- The quantum stresses imposed on the Aether by multiple quanta located
throughout all of space must superimpose to produce a single quantum stress
level at any given point.

- A quanta moving in a free trajectory follows a path consistent with the
diffraction pattern of the quantum stress it generates in the Aether.

- Since a quanta represents a discrete amount of energy while its
contribution to the stress level in the Aether is continuous, the path of a
particle cannot follow its diffraction pattern in the Aether exactly. A
residual quantum stress level remains after the arrival of each
particle.

- The Aether minimizes its residual quantum stress level by adjusting the
paths of subsequent particles to produce the observed diffraction pattern in
the rate of particle arrival.

- Since a quanta represents a discrete amount of energy while its
contribution to the stress level in the Aether is continuous, the path of a
particle cannot follow its diffraction pattern in the Aether exactly. A
residual quantum stress level remains after the arrival of each
particle.
- Since the localized stress in the Aether results from the superposition of
all of the stress sources in the Universe, the diffraction process affecting
individual particles is extremely noisy.

- While quantum effects appear random, they are more correctly described
as deterministic but enormously chaotic. Dr. Einstein's statement that "God
does not play dice with the Universe" is correct after all. (As an example,
the variations in the paths of objects in the Asteroid Belt are
deterministic, but those variations are sufficiently chaotic as to prevent
rigorous analysis of their orbits, forcing them to be considered as having
quasi-random deviations about their nominal orbits. Occasionally, those
quasi-random orbital interactions are sufficient to throw an asteroid out of
the Asteroid Belt completely. Occasionally, a radioactive atom throws one or
more of its component nucleons from its nucleus.)

- One would expect that the summation of quantum stresses from all of the events occurring throughout the Universe would occasionally combine to produce extremely large momentary quantum stresses at a given point. The effect would be analogous to the production of an unexpectedly large wave, called a rogue wave, in the ocean by the combination of a large number of different waves of considerably lower amplitude.

- While quantum effects appear random, they are more correctly described
as deterministic but enormously chaotic. Dr. Einstein's statement that "God
does not play dice with the Universe" is correct after all. (As an example,
the variations in the paths of objects in the Asteroid Belt are
deterministic, but those variations are sufficiently chaotic as to prevent
rigorous analysis of their orbits, forcing them to be considered as having
quasi-random deviations about their nominal orbits. Occasionally, those
quasi-random orbital interactions are sufficient to throw an asteroid out of
the Asteroid Belt completely. Occasionally, a radioactive atom throws one or
more of its component nucleons from its nucleus.)

- The planets were formed by the collision of smaller objects circling the
Sun in eccentric orbits. The collision process continued until the Solar
System was virtually cleared of objects in non-circular orbits.

- During the planetary formation stage, the planets could not acquire
atmospheres because the bombardment which was forming them made their
surfaces extremely hot. Any atmospheric gases which impacted the planet from
interplanetary space would boil away immediately.

- During the planetary formation stage, the planets could not acquire
atmospheres because the bombardment which was forming them made their
surfaces extremely hot. Any atmospheric gases which impacted the planet from
interplanetary space would boil away immediately.
- Once the rate of bombardment forming the planets reduced to the point
where the planets could cool sufficiently, they proceeded to collect
atmospheres from the gases which remained in the Solar System.

- For Venus to have its present atmospheric density, all of the planets,
including the Earth, must have acquired enormous (by Earth standards)
atmospheres.

- A planet gains atmosphere by sweeping up gases from interplanetary
space. It losses atmosphere through evaporation of those gases to that
same space from its uppermost layer.

- A planet gains atmosphere by sweeping up gases from interplanetary
space. It losses atmosphere through evaporation of those gases to that
same space from its uppermost layer.

- For Venus to have its present atmospheric density, all of the planets,
including the Earth, must have acquired enormous (by Earth standards)
atmospheres.
- In order for a molecule of gas to be lost to the planet, it must acquire a
thermal velocity greater than the planet's escape velocity. This must occur at
an altitude at which the atmosphere is sufficiently thin so that it does not
strike other molecules while escaping.

- The rate at which atmospheric gases are lost to space is determined almost entirely by the rate of energy input from the Sun and by the escape velocity of the planet at the top of its atmosphere The rate of atmosphere loss is virtually independent of the amount of atmosphere the planet owns.

- Without a conceptual model we cannot know to whether our mathematical
analyses are relevant and what information our experiments have provided. (As
an example, consider the experimental measurement of the velocity of light, as
discussed in Chapter 6. The experiment measures something but it most
certainly does not measure the velocity of light.)

- Without a valid mathematical analysis of the model, it cannot be known
whether the model will function in the anticipated manner and what
experimental results are required to validate the model and its mathematical
analysis.

- Without experimental verification, one cannot be sure that the model and its mathematical analysis represents reality or delusion.

- Everything he accepts as true must agree with everything else that he
accepts as true.

- In the event of contradiction, the validity of the relevant information,
both old and new, must be considered to be tentative.

- If the information is more than trivially important, the necessary
effort must be made to resolve any inconsistencies by correcting the new
and/or the old information.

- The more items of information processed in this manner, the closer one's
store of knowledge will approach absolute validity. (It will never be
perfect, no one lives that long.)

- In the event of contradiction, the validity of the relevant information,
both old and new, must be considered to be tentative.
- One must never assume that his source of information, no matter how
revered, is correct.

- Where necessary in an academic or business situation, one must keep two
sets of books. One set of books must contain the information expected by the
individuals possessing power over your future and the other set must contain
the information you have determined to be true.

- Where necessary in an academic or business situation, one must keep two
sets of books. One set of books must contain the information expected by the
individuals possessing power over your future and the other set must contain
the information you have determined to be true.
- One must never allow himself to be brainwashed or bullied into not following the preceding rules.

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