"Deterministic
Earth Mechanical Science" is a milestone in
the history of science. Earth Mechanical Science
is a deterministic field theory that is entirely composed
of physical laws. They are mathematically interrelated
by a few earth material properties coefficients.
The earth's surface is the outer boundary condition.
The first two essays explain the consequences of this
scientific advancement.
Energy
Minimization, Gravity,
Electrostatics, and Earth Mechanics.
by Phil Holbrook Ph.D.
The laws of mechanics, chemistry
and deterministic earth mechanics have much in common.
They describe the relationships of particles with finite
mass at minimum
energy. These are a subset of universal
laws which apparently operate simultaneously on and
within planet earth.
The lower atomic numbered elements tend to form into
minimum
energy molecules. Almost
all of the earth is composed of natural solid
and liquid
molecules. Energy
is continuous within and across the solidliquid
phase boundaries.
[Massenergy]
is apparently conserved within the earth and universe.
Energy minimization
on and in the earth primarily involves the weaker forces
of gravity and electrostatics its actions. These depend
upon two inverse square forceatadistance laws of
the same physicalmathematical form. Newton’s
Gravitational law and Coulomb’s electrostatic
law are;
Earth Gravitational
Attractive Force = G (Mass
_{1} * Mass _{2}
) / distance
^{<2>}
Electron Cloud Electrostatic Repulsive Force = k ( Charge_{1}
* Charge_{2} )/ distance ^{<2>}
Gravitational
forces extend to the edge of the visible universe. Molecular
electrostatic forces are 1038 times stronger than gravity.
But electrostatic forces don’t
reach beyond the next nearest electron cloud. Without
the repulsive force of neighboring electron clouds the
earth would be the size of a walnut with the density
of a black hole.
Both of the above laws are physically symmetrical
about their distance ^{<2>}
terms. The acceleration due to gravity
is a physically symmetrical
time ^{<2>}
term.
There is a direct connecting bridge across the fantastic
numbers of the universe and earth. Mass
and energy
are related by mathematically equivalent [stress/strain]
tie lines in the earth. Simple equations represent the
static elastic and plastic [stress/strain]
limits of molecular matter.
The bulk modulus and compressibility of natural minerals
and fluids
may be found in the Handbook of Physics and Chemistry.
The elastic constants and their energy
conserved PV/T variances are measurable
bulk material properties.
The equation matrix below expresses [massenergy]
conservation at minimum energy
conditions. Each line of this matrix is a physical
or conservation law that applies in Normal
Fault Regime tectonic settings in the earth.
Energy
terms and equations are background color coded tan.
Mass
terms and equations are background color coded light
blue. Bold blue are composite mineral
physical constants, and red is a composite bulk fluid
property. RETURN
TO TOP
Crust
General Governing Physics
This is how Gravity
(S_{v})
and Electron Cloud repulsive forces (S_{ave})
interact in the earth's sedimentary crust. Both forces
use the same solidfluid partitioning coefficient (1.0
– f) in the earth . The first
three lines of the explanatory matrices are the same,
applying to all tectonic regimes.
The solid
fraction of a rock bears the effective
stress load. Gravity
S_{v}
is an integral component of the total load. If effective
stress energy is minimized, S_{v}
could be the maximum,
intermediate, or minimum
principal stress. Physical minimization in the earth
crustal case requires that the ratio of the effective
stresses be of integer proportions that are symmetrical
about the positive integer ^{<2>}.
Newton's and Coulomb's laws are also physically symmetrical
about the positive integer ^{<2>}.
Gravitational
and electrostatic forces cross the [energymass]
(=) diagonal of this matrix. This equation matrix formulation
is a closed mathematical form as are Newton’s
Force
= mass
acceleration
and Einstein’s limit energy
= mass
c^{<2>}.
There are more parameters in the earth’s matrix
representation, because the earth’s interior is
different from the vacuum of space. All three expressions
are physically and mathematically symmetrical.
Each line equates and balances mass
with energy.
The three different
tectonic regime minima
The fourth equation
in the matrix is the minimum energy effective
stress ratio in Normal Fault Regime Basins.
There are two companion equation matrices for strikeslip,
and thrust fault tectonic regimes.
Only the Normal Fault Regime will be discussed here.
Fault regimes are discussed at length in Chapter
13 of “Deterministic Earth Mechanical
Science”.
Each tectonic regime specific matrix has the same first
three lines mentioned in Crust General Governing
Physics. These three matrices are the simplest
and most general force balance
in the earth. RETURN
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Energy in Subsurface
Mechanics
The remaining four equations
of each matrix are rearrangements of terms that yield
the energies
pore fluid pressure
and fracture propagation pressure. Fracture
propagation pressure describes the action of
fluid pressure
release valves that are perpendicular to the minimum
principal stress. All the mechanical terms
in each [energymass]
matrix interact deterministically to explain the fundamentals
of earth mechanics.
There are circumstances such as [stress/strain]
hysteresis and two phase fluids that
occasionally come into play. These are second order
effects which can be resolved using the appropriate
second order physics. Energy
is locally conserved and minimized
through accepted physics on these levels as well.
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The similarity
of atoms, planets and stars
The Earth and other
planets in the Solar System have spherical shapes. The
Earth, Sun and Jupiter have an intermediate convective
layer. The stronger nuclear binding forces are not directly
involved in earth mechanics. Nuclear fusion generates
the Sun’s light and heat. Fortunately for us we
are near the Sun. Also fortunate is that the heat from
the earth’s molten core comes principally from
nuclear fission not fusion. The earth's natural radioactivity
generates heat but doesn’t propagate nuclear chain
reactions.
The mantle is mechanically decoupled from the
liquid metal core. Hence we have had frequent magnetic
polar reversals. Core to mantle mechanical
stickslip probably accounts for the magnetic
polarity reversals.
The mantle is coupled to the
overlying sedimentary basins over broad areas as evidenced
by the prevalence of minimum
energy stress ratios that are observed.
The shapes of all of the objects below are basically
spherical with physically explainable deviations.
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The
transfer of mechanical
forces (including acoustic waves) within
the earth is through molecular electron clouds.
There is two phase mechanics in the earth’s sediments
and sedimentary crust.
That is portrayed on the right of the collage above.
The surface of a SiAlic
clay mineral perpendicular to the caxis
is a layer of positively charged oxygen anions. Positive
charge falls off as distance ^{<2>
}from
the oxygen anionic surface. Water dipoles are aligned
for a short distance by this charged plate. Net neutrally
charged mineral
surfaces neither attract nor repel water dipoles.
The plastic drag forces from the convective mantle move
the continental and oceanic plates around as illustrated
by the earth cutaway model in the collage. Newton’s,
Hooke’s and Coulomb’s laws apply simultaneously
in the earth. Their images are superimposed over the
earth’s continental plates. The earth’s
crust is semibrittle on a geologic time scale. Continental
crust is SiAlic
and floats high on the turbulent mantle. Basaltic crust
is denser. It underlies the earth’s oceans that
are color coded blue.
Single element nuclear centered electron clouds tend
to be spherical. Niels Bohr and DeBroglie explained
the paths of individual electrons in any single atom.
Both won Nobel prizes. Continuous standing particlewaves
are the minimum energy
electron configurations in an atom.
The bright line or dark line spectra of each element
are symmetrical characteristics of each atom. The electrons
choose minimum energy
paths as do the spherical planets in the solar system
and universe.
The light from each star reveals the chemistry of its
intermediate convective layer. The red shift of the
bright line spectrum from a star reveals how fast that
star or galaxy is receding from earth. It appears as
if the visible universe began with a singularity that
we call the “Big
Bang”. The composition of matter
evolved over time to form the 92
natural elements that we know of
today on earth. Elemental bright and dark line spectra
on earth provide scientists with elaborate natural compositional
and timing
devices. RETURN
TO TOP
In the short period since Isaac Newton, humans have
assembled a huge body of mathematically
deterministic interrelationships. Newton’s
scientific and philosophical explanations have been
extended by fifteen to twenty generations of subsequent
scientists. The mathematical forms of Newton’s
and ensuing laws have been verified by many scientists
through empirical observations. Scientists following
Galileo have looked into Nature
to determine the truth of a scientific argument.
I am happy and proud to make my contribution to this
body of knowledge. That contribution is that the earth
obeys the same physical
and chemical laws as the rest of
the universe. “Deterministic
Earth Mechanical Science” and
“Pore Pressure
through Earth Mechanical Systems”
are the two books that were written to demonstrate and
explain earth mechanics.
The books contain abundant data and sufficient technical
explanations. This explanation has the fewest
possible equations. It also uses the fewest
possible linking coefficients.
All of the linking coefficients are measurable
material properties. It simultaneously
explains a host of subsurface mechanical questions.
I give hundreds of earth scientists’ credit for
assembling a descriptive body of knowledge about planet
earth. I am most grateful to my doctoral advisor E.G.
Williams who taught me much of science and philosophy.
These two terms had the same meaning in Newton’s
lifetime. They still coincide at the highest
levels of science.
Significant scientific progress will likely be made
by those who let Nature be their guide. “The
Foundation of the Physical Sciences”
is being written to be popular reading for scientifically
curious people of all ages. RETURN
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Earth
Physical Limits; Minimum Energy pathways shown on selected
Two dimensional Mechanical Planes.
by Phil Holbrook Ph.D.
Minimum Energy
is the selection criterion for physical and chemical
laws. For instance the shortest distance between two
points is a straight line i.e. a minimum
energy pathway . The equivalent
pathways
inside the earth are hidden, but they meet the same
minimum energy
criteria.
Energy minimization
within the earth reduces the multidimensional problem
to that which can be described on two
dimensional planes.
These are analogous to the nodes of an n dimensional
standing wave. Minimum
energy increases away from these
nodes, but the average is smooth and continuous. [Massenergy]
is generally conserved. Energy
minimization on the most important
two dimensional planes
inside the earth will be discussed.
The pathway in space is through a vacuum. The pathway
in the earth is through the earth’s
matter. The fundamental
unit of energy
communication in the earth is the molecule.
Liquid phase
molecules
at earthly temperatures will be color coded bold red.
Solid
phase molecules will be color
coded bold blue.
Natural minerals
are the predominant minimum
energy phases of solid
matter in the earth. Fluids
have no shear strength. Everything below sea level or
the water table is a two phase (mineralfluid)
mechanical system. The two phases are in intimate contact
with each other through their contiguous molecular
electron clouds.
The earth is approximately spherical with all molecules
being attracted toward its center of mass. This is also
the earth’s geometric
center.
Vertical is the direction toward the earth’s center.
The two orthogonal horizontal axes are oriented by the
near surface [energymass]
field. The dominant factor affecting horizontal effective
stress orientation is the local tectonic
regime.
Continental plates shear past one another or are thrust
toward one another. These relationships are discussed
in Chapter 11 of Deterministic Earth Mechanical Science.
The [stress/strain]
response of solid
molecular electron
clouds is symmetrical.
The fluids
provide a neutral scalar supporting role in proportion
to their composite fluid
bulk modulus. The scalar fluid
and solid
bulk moduli are equally represented
in proportion to their abundance throughout the earth.
We need to first group the molecules
according to phase. The earth’s mechanical
energy can be represented by different
two dimensional planes.
One of the mechanical
planes will contain both the maximum
and minimum
principal
stresses.
Both the fluid
and solid
molecules have scalar mass
and energy terms.
These scalars are contributing factors to the [stress/strain]
slope. That mechanical energy slope will be greatest
on that two dimensional
plane.
The difference of any measured effective stress from
the deterministic energy
minimum is a measure of the effective
stress energy that is accumulated
in the molecular electron
clouds. If there is no difference,
there is no tendency toward movement within any mechanical
system.
The first and most fundamental
in situ [stress/strain]
relationships of the most abundant
natural minerals
are shown below. This two
dimensional plane shows mineral
specific compactional equilibria. RETURN
TO TOP
This
two
dimensional plane is a mechanical view
of the plastic [stress/strain]
relationships inside the earth. The scalar
effective stress energy
is on the ordinate or “y” axis. Solid
mass
(solidity)
is the scalar on the abscissa
or “x” axis. [Massenergy]
is conserved on this plane. Any combination of mathematical
operations that comprise a [stress/strain]
relationship will be a straight line on this two
dimensional plane.
Over 90% of the earth’s SiAlic
crustal matter is contained in the five mineral
types shown. Quartz, SiAlic
claystones, calcite, anhydrite and halite
are in a decreasing order of compaction resistance.
The crossover between Quartz
and SiAlic claystones
is due to an additional compaction resistance between
individual clay
particles. This is a particle size phenomenon that is
peculiar to clay minerals. The plastic compactional
[stress/strain]
response of water wet clay minerals is green
on this plane.
The [stress/strain]
relationships of the nonclay
minerals are subparallel. They are
offset in rough proportion to their scratch or indentation
hardness.
The offsets reflect differences in the mineral’s
internal scalar average electrostatic
bond strengths. Quartz
is the hardest and halite
is the softest of the abundant
natural minerals.
The mineral Quartz
has about ten times the compaction
resistance of Calcite.
A great deal of empirical data was assembled and analyzed
to arrive at these straight
lines. Extreme edge effects have
been removed. The fit was better than five percent (5%)
over the entire range of porosities that are represented
in natural sediments
and sedimentary rocks.
The porosity data ranges from several feet below an
undisturbed mud line to total solidity.
All of the major non clay
minerals occur as supporting grains
or intergranular cements. The effects of post compaction
chemical cementation were removed by fitting to the
highest porosities at any given effective
stress.
The empirical straight lines have additionally been
tested against observed pore
pressures in over 300 wells worldwide.
The straight line
curves shown are natural [stress/strain]
loading limb pathways
on this two dimensional plane. Effective
stress (energy)
and solid
(mass)
conserved strain
are balanced scalars on this plane. Hence the figure
title is “First Fundamental
in situ [stress/strain]
relationship”.
The straight lines
shown represent plastic loading limb data. Effective
stress unloading
involves a different [stress/strain]
pathway. Elasticity is a limit for effective
stress unloading
and reloading. Hooke’s
law as expanded by Cauchy is a relationship between
bulk modulus and shear modulus summarized on the next
two dimensional plane.
This plane describes the natural elastic
coefficients for sedimentary rocks with
randomly oriented natural flaws. RETURN
TO TOP
Both
bulk and shear moduli include a density i.e. (mass
term) as a devisor. These elastic moduli have mathematically
related energy
terms. The positive offset of all the straight lines
is the bulk modulus of the pore
fluid. It is NaCl
brine in this case.
This represents a macroscopically static mechanical
system. Any combination of fluids and gasses in the
pore space of a granular solid would have a composite
fluid
bulk modulus
property. This would be lower
limit of an elastic [stress/strain]
lever.
The upper limit
of the lever
would be the weighted average of the solid
elastic moduli. The entire ranges of
porosities from zero to 100% lie on a straight
line lever with these
mineral and
fluid end
points. Any preferred orientation
of flaws would affect these relationships.
There is a smooth scale change along the straight
line on this two
dimensional plane. This owes to
the transition from a matrix supported granular solid
to a suspended solid slurry. The [stress/strain]
of slurries are explained by the Woods equation which
is a degenerate form of Hooke’s law. The assemblage
of these equations on this
two dimensional plane is attributed
to Michel Kreif. Many authors have measured the elastic
moduli of clay minerals.
The results indicate a high level of uniformity.
This two dimensional
plane is physically
symmetrical i.e.^{<2>}.
Vp^{2}
is proportional to Vp^{2}
for body waves on this
two dimensional plane. These acoustic
waves can be remotely generated and recorded either
from the surface or from the inside of a borehole in
the earth.
The plastic and elastic limiting [stress/strain]
relationships are shown together on the following two
dimensional plane. Effective
stress (energy)
is on the ordinate and solid
mass conserved
strain is on the abscissa. This follows the thread of
governing physics through the
earth. RETURN
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Realistic
units are shown on this plane. The [massenergy]
and [stress/strain]
values are equivalent if you insert the color
coded mineral coefficients. The
slope of the plastic compactional relationship alpha(a)
is that of the average mineralogy
present. The intercept sigma_{max}
is that of the average mineralogy
as well.
If compaction does not reach its sigma_{max}
limit, there will be an intermediate peak
loading limb point. Any subsequent
unloading or reloading will be between the two straight
line limits that are shown. There
may be time dependant hysteresis loops about the straight
line. At sigma_{max}
and beyond, the solid
material behaves as a plastic and yields to all stresses
equally with no change in porosity. The change in volume
beyond sigma_{max}
stress
is entirely in the spacing of molecular
electron clouds.
Failure of materials on a two
dimensional plane was introduced
by the German engineer Otto Mohr in 1874. Energy
minimization inside the earth allows
for three dimensions to be shown on this Mohr
two dimensional plane
without loss of information.
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Mohr cleverly portrayed stress
as circles with the average
stress (scalar) at
the center. In Normal Fault Regimes the maximum principal
stress is gravity.
The blue
circle shows the maximum
and minimum
vectorial stress on the circle’s circumference.
The scalar average
stress is the center point.
Shear stress (t)
is on the ordinate. Average
confining stress, as well as the
maximum
and minimum
vectorial stresses are on the abscissa. The color code
purple
is assigned to gravity.
A tangent to a Mohr
circle is a rock or sediment's failure
condition. It is the coefficient
of internal friction for a porous
granular solid. Sedimentary grains resist both compaction
and shear with all that they have i.e. their contiguous
molecular electron
clouds.
Each of the three Mohr
circles shown is physically
symmetrical, i.e. <2>
. Their circumferences are even number multiples of
their mean stress.
Gravity
is the maximum principal
stress in Normal Fault regimes.
Gravity
is the intermediate
principal stress in Strikeslip
Fault regimes. Gravity
is the minimum principal
stress in Thrust Fault regimes.
This closed and minimized
mathematical system has actually reduced the earth’s
multi dimensional mechanical systems onto a two
dimensional plane.
The coefficient of
internal friction (t) is a different
measure of average mineral's
electrostatic bond
strength. This describes the behavior
of composite macroscopic bodies based upon the average
mineral
electrostatic bond
strengths.
The energy
transfer between continental plates or fault blocks
is through the same contiguous electron
clouds. There are transition zones
in the earth between normal, strikeslip, and thrust
fault tectonic regimes. These zones could be up to several
hundred miles wide, but the crust is not that deep.
The earth’s surface area is huge by comparison.
The more general case is that the molecules
of the earth will move toward one of the three
deterministic minima. The answers
to minimum energy
questions outside local transition zones are to be found
on the appropriate two
dimensional plane.
The preceding discussion was broad but not comprehensive.
These two dimensional
planes illustrate the interactions
of the governing laws of physics in the earth’s
sedimentary crust. If history repeats as Niels Bohr
predicted, there are many more answers to be found under
this same physically
deterministic bridge!
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On
“The Foundation of the Physical Sciences”
by Phil and Marie
Holbrook
Forward
Physical laws are continuous mathematical functions
that describe the relationships between discrete entities.
These can be aslargeas galaxies to subatomic particles
in size. There are forces between all sizes of particles
that govern their spacing, speed and motions. These
apply at different distance scales. The governing laws
describe mathematically how the forces interact.
Isaac Newton gave the laws for macroparticles in 1687.
Niels Bohr explained Quantum Mechanics in 1925. Richard
Feynman understood Newtonian mechanics, Quantum Electrodynamics
and was working on subatomic particles at the time
of his death.
Isaac Newton, Niels Bohr and Richard Feynman had deep
understandings of physical law. It is revealed to us
in their science and through their writings. “The
Character of Physical Law ”
is a milestone summary of our accumulated knowledge
of physics given by Richard Feynman in 1965.
Newtonian mechanics is the core of the deterministic
sciences. Newton’s laws are an interdependent
set of postulates that apply to macroscopically distinct
objects. [Massenergy]
conservation embraces physics, inorganic chemistry and
earth mechanics. The laws of these sciences are symmetrical.
They all describe natural minimum energy seeking systems.
The most stable forms of motion and matter are minimum
energy configurations.
A common pattern with respect to physical laws is evident.
That pattern includes a simplest
method for expressing physical and inorganic chemical
laws given the tools of mathematics. One could learn
this common pattern concurrently with the scientific
facts as they are being taught.
“The Foundation of the Physical Sciences”
is an exposition of the physical facts related to a
common straightforward pattern. This book uses our most
important physical laws as examples to demonstrate the
foundational pattern. They are
arranged in a logical order where one law leads to the
next. Newtonian mechanics is followed by Quantum mechanics
which explains how we know what we do about the “Big
Bang”.
The book follows a logical progression that leads to
the most current physical answers. This accumulation
of deterministic equations has
occurred over three centuries. Einstein’s theory
of relativity is the physical limit of
Newtonian mechanics.
The motions of our Solar System was causally
explained by Isaac Newton. The details
of planetary and satellite orbits have first order gravitational
explanations. The rings of Saturn are a smaller scale
example of our disc shaped Solar System. Gravitational
pulls over billions of years have shaped both Saturn's
rings and the Solar system.
The Periodic Table is a masterpiece
of atomic matter organization. The properties and reactivity
of each atom can be predicted from its position on the
table. Chemical equations balance perfectly about an
equal (=)
sign. The number of elements on each side of a chemical
reaction equation are exactly equal (=)
discrete integers. This is mathematically perfect electrical
charge <symmetry>.
Only 14 elements compose over 96% of the earth’s
SiAlic
crust. Five simple molecules make up the bulk of this
total. These molecules are late stage matter that has
evolved in stars since the “Big Bang”. We
can know all of this by combining our knowledge of the
quantum spectra of starlight with chemical and spectral
analyses measured now on planet earth.
The hierarchal order of physical laws is approximately
the order in which we perceive them from birth. Infants
can recognize symmetry and sequential
order. The governing physics can be consciously
taught in parallel with our natural order
of perception. Every person can become consciously aware
of the foundation of the physical sciences in elementary
school. The foundational pattern
unifies many observation and may be as important as
the physical and chemical laws themselves.
This book will highlight our most famous physical and
chemical laws. The intellectual and personal lives of
the discovering scientists are interesting in themselves.
Original scientists have an unusual common characteristic.
They are passionate in their search for the truth. We
hope that all readers will enjoy looking into the heart
of Natural Science and the original
scientists that looked into it. RETURN
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About
the Books Cover
All
that we see is the interaction of light with the matter
of the Universe. The Earth is the third planet from
the Sun in the Milky Way Galaxy. At night the sky is
black and by day it is blue with occasional white clouds.
The Sun radiates photons of light as do the rest of
the Stars in the Universe. The peak frequency of the
Sun is yellow
but it radiates all colors. The planets and moons reflect
the Sun’s light.
Blue skies
originate from Nitrogen
atoms which are about 80% of the Earth’s
atmosphere. Nitrogen
absorbs photons of blue
light and reradiates
them in all directions. Atmospheric water coalesces
into colorless spheres and crystals in the atmosphere
forming white
clouds.
These water particles are colorless and refract
light of all colors. Rainbows result from the direct
incidence of sunlight by colorless spherical water droplets.
We can only see short distances through clouds, rain
or snow because solid particles scatter whatever light
is present. Interestingly, grass is green because it
absorbs all other colors. Bricks
are red for the same reason.
The movement of all celestial objects is governed by
Newton’s Law of
Gravity. Stresses and fluid pressures
within the earth involve electrostatic interactions
with gravity.
The electron clouds of the molecules that compose the
earth repel each other. Coulomb’s Law of electrostatics
has the same physically symmetrical
<2>
formulation as the Law
of Gravity. Physical symmetry,
[massenergy]
conservation, and mathematical equality
(=) are
the foundations of the physical sciences that are shown
in the center of the books cover.
We actually see photons which are particlewaves that
have no mass. They can travel
up to the speed of light which is the limit of the universe
that is visible from planet earth. There is strong
indirect evidence of dark matter
and dark energy within the visible universe.
Spheres are the highest symmetrical forms
in the Universe. We see macrospheres in the dark night
sky. Stars, planets, moons, and atoms have a basic spherical
symmetry that is modified slightly their internal forces.
Convection causes bubbling Sun spots, the drift of continents
on earth, and the swirling Giant Red Spot of Jupiter.
The rings of Saturn and Uranus have planar symmetry
about these planets due to local variations in the force
of gravity over billions of years. The planar disc shape
of our Solar System results from many pulls of gravity
from the larger solar system objects over time.
Physics explains what we perceive and see. The radial
tie lines in the Venn diagram represent direct physicalmathematical
connections. There are abundant reason for understanding
"Foundation of the Physical Sciences".
The foundation is mechanically simple and yet profound.
The physical sciences are mathematical combinations
of A)
continuous mathematical functions; B)
real number constants; and C)
integers. Mathematical operations are symmetrical about
the (=)
sign. The physical meanings of the A
B C’s
and mathematical (=)
symmetry can be fully taught in elementary school. This
book presents the foundation of the physical
sciences that also apply at the highest
levels of education.
For more information on how “Deterministic
Earth Mechanical Science”
springs directly from the Foundation of the
Physical Sciences. You click the hyperlinks
or browse this website starting immediately below. Most
of the website material is focused on geomechanical
science. The poster immediately below shows how seemingly
complex the superposition of a few accepted physical
laws can be.
It is not complex for a mindless electron. It simply
chooses the minimum energy path between the other electrons
that also orbit the same positively charged nucleus
of an atom. The earth is built of these simple components.
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___________________________________________________
Geomechanics
in the Gulf of Mexico conference in conjunction with
OTC May 2, 2001 (NOTE; this is a large 3092
KB file that loads slowly over phone lines. It is copyrighted
and contains a pictorial summary of the relationships
between the Extended Elastic, and GrainMatrix Compactional
Mechanical systems. If you have a slow system, scroll
down in this window. It will eventually upload after
you get below the thumbnail explanation.
This
poster reproduction summarizes the relationships between
the earth's endmember geomechanical systems. The primary
loading limb compaction of sediments is portrayed from
left to right across the top. Graphic documentation
of the grainmatrix compactional mechanical
system go from top to bottom on the left.
Graphic documentation of the Extended Elastic
Equations of Hooke's law go from top to
bottom on the right. The in situ fracture
pressure limit to pore
pressure is in the lower left.
The
force balanced equations that explain both grainmatrix
compaction and low frequency acoustic waves are in the
center. You can click on [massenergy]
conservation laws in the earth for an explanation.
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