Is Mass an Emergent Quantity in an Electromagnetic Universe?
- From: johnlawrencereedjr <randamajor@xxxxxxxxx>
- Date: Sat, 29 Dec 2007 16:03:30 -0800 (PST)
Is Mass an Emergent quantity in an Electro Magnetic Universe?
Research Results on Centripetal Force, Part 2
Math and Universe, Part 4
modified December 29, 2007
John Lawrence Reed, Jr.
Isaac Newton defined centripetal force in terms of his second and
third law, to act at a distance, by setting his first law object on a
circular path of motion, at a uniform orbital speed. Newton allowed
the moving inertial object to impact the internal side of the circle
circumference at equidistant points to inscribe a regular polygon. He
dropped a radius to the center of the polygon from each vertex (B) of
the polygon to describe any number of equal area triangles. "...but
when the body is arrived at B, suppose that a centripetal force acts
at once with a great impulse..." (Principia)
To argue for his supposition, Newton took the triangle base length,
toward the infinitesimal limit approaching zero. The base length, and
the infinitesimal arc of the velocity driven and time consuming
trajectory of the moving inertial object, can then be represented as
arbitrarily close in length as desired. The velocity acceleration
vector (v/t), or (dv/dt) at the vertex (B), is by definition
consistent with the continuous and efficient curvature of the circle,
and is ultimately directed along the radius toward the center of the
circle and represented as centripetal acceleration (v^2/r). This time-
space mathematical property of the perfect circle and perfect motion
serves as the assigned carrier for "inertial" mass, as the cause of
the defined centripetal acceleration and is designated as centripetal
force (mv^2/r). Note again that Newton used a perfect circle and
perfect motion to derive his supposition for a mass driven centripetal
force from instantaneous acceleration (velocity) where the only change
in velocity is direction. Here the equal areas in equal times falls
out of the perfect orbit as a mathematical artifact of the efficient
area enclosing circle itself.
Consider:
A circle is an efficient enclosure of area. That is, the circle
circumference is the shortest line length to enclose the greatest
area. Equal arc lengths from the same circle will radially enclose
equal areas, just as equal time intervals from the same orbit will
radially enclose equal areas. When we take the efficiency ratio of
the circle as the quotient [circumference/area] or [2pir/pir^2] and
reduce it, we have [2/r]. When we take the quotient of a circle's
[arc segment length to its radially enclosed area] we also reduce that
to [2/r]. This is an efficient area enclosing, symmetrical property
of the circle itself. This is, on the face, trivial and rather
mundane, as it follows from the perfect symmetry of the circle.
With the real world orbits this symmetric efficiency is retained in
terms of time and space. We have the efficiency ratio here as the
quotient [the period/the area enclosed by the orbit]. The reduced
quotient here when we take [r] as the average distance of the planets
from the sun, is [2/rv]. This is a real world orbit, time-boundary to
enclosed space analog, of the circle's length-boundary to enclosed
area, efficiency quotient [2/r]. I'll leave it to the reader to show
that Kepler's law of areas proves that the analog of the symmetry of
the 'circle' efficiency, in the real orbits, is maintained. All you
need to show is that the efficient symmetry quotient for any Kepler
swept out area is [2/rv]. [Arc segment interval length to radially
enclosed area].
oOo
We can see that the efficient symmetrical property of the circle
analog is reflected in the real elliptical orbits as Kepler's law of
areas, where acceleration includes change in both the magnitude and
direction of the object's motion, and that the magnitude changes even
as the direction changes, such that the efficient symmetrical, area
enclosing property of the orbit is maintained. Newton generalized the
efficient equal areas in equal times property of the supposedly
inertial mass driven object's perfect circular path, together with his
centripetal force, to any curved path directed radially around a
point. "Every body that moves in any curve line... described by a
radius drawn to a point... and describes about that point areas
proportional to the times is urged by a centripetal force... to that
point" (Principia)
Newton extended the mass generated property to include the trajectory
of two bodies in elliptical orbit. "Every body, that by a radius
drawn to the center of another body... and describes areas about that
center proportional to the times, is urged by a force..." (Principia)
Newton tied his "least action" mathematical model for a supposed mass
driven centripetal force to gravity (our tactile sense of attraction
to the Earth that we feel as resistance and quantify as weight [mg]).
"For if a body by means of its gravity revolves in a circle concentric
to the earth, this gravity is the centripetal force of that
body." (Principia) Note that Newton accepted as an a priori given,
the resistance he worked against and called gravity, as a fundamental
(now mass driven universal gravitational) force. Where that
resistance is either his own inertial mass or the inertial mass of
another inertial mass object.
oOo
It is of special significance that Newton generalized Kepler's law of
areas to the entire universe as the carrier for his mass driven
centripetal force. "...because the equable description of areas
indicates that a center is respected by that force... by which it is
drawn back... and retained in its orbit; why may we not be allowed...
to use the equable description of areas as an indication of a center
about which all motion is performed in free space?" (Principia)
Newton used Kepler's law of areas, as the mathematical carrier for his
solely mass driven centripetal force. Therefore I conclude that
Kepler's laws are required for Newton's mass driven centripetal
force. Since this is in fact the case, how is it we say that Kepler's
laws "require" Newton's mass driven centripetal force? That is, how
is it we say that prior to Newton, Kepler's laws were entirely
empirical and that these empirical laws can be derived from Newton's
universal law of gravitation? As I see it, the brief answer to this
question shows the importance of acquiring a clear and unambiguous
conceptual understanding of the applied mathematics. Consider:
1) F=GMm/r^2
Outside a perfect circle and uniform motion, the "equable description
of areas indicates" more than just a center "respected by that
force". Kepler's laws show that a time function accompanies the
force. Where is the time function in Newton's universal law of
gravitation (1)? Where is the time function in Newton's perfect
circle and uniform motion derivation for centripetal force?
Newton defined a universal gravitational force between two objects as
a function of the product of their mass where the function is
attenuated by the inverse of the square of the distance between the
masses. I note that [1/r^2] is an efficient quantitative, general
least action property. I also note that the mass density of the
objects is an "invisible" shared variable, dependent on the inverse
of the square of the distance [1/r^2] between the objects, and that
the scale is set by the local quantitative measure of (our subjective)
inertial mass [m], and the constant of proportionality[G], also
measured as a function of the local inertial mass [m]. Consider:
2) F=4pi^2mr/T^2
The right side of (2) reflects the efficient least action properties
of perfect circle and perfect motion orbits, where inertial mass is
included by using the mathematical technique of multiplying both sides
of an equation by one (not shown here, but trust me on this). Then
the introductory text will set (1) equal to (2) as:
3) GMm/r^2=4pi^2mr/T^2
Where on rearranging and simplifying we have:
4) T^2/r^3=4pi^2/GM
The introductory physics text will now argue that (4) shows that
Kepler's third law [K = T^2/r^3] is merely a result of Newton's
gravitational law, and "... although this derivation uses perfect
motion and perfect orbits, it applies equally well to real orbits in
real motion provided we use the average distance from the sun to the
planet for [r]." (Paraphrased)
The introductory physics text states that the derivation here uses
perfect circles in perfect motion (where we have the efficiency
quotient as either [circumference/area] or [the period/area]). And
then it states that the derivation applies to real orbits as well,
provided we use the average distance from the sun to the planet for
[r]. So that the efficiency quotient in the real orbit case is: [2pir/
pir^2] or [T/pir^2]. Clearly, nothing has changed mathematically.
They each reduce to the efficiency quotients [2/r] or [2/rv]. Where
the time function remains joined to the perfect circle in uniform
motion.
oOo
In (2) we have the perfect orbit and perfect motion where we allow our
quantity for resistance (inertia) mass [m], a free ride. Then we use
(3) and (4) to eliminate inertial mass [m] from the derivation while
including inertial mass [m's] empirical "scaling" measurement (G) and
the measurements that accompany the least action orbits, to define the
magnitude for [M]. In other words, we arbitrarily assign as a
proportionally controlling property of the celestial body least action
orbits, the quantity (G) measured as a function of a quantity that is
independent of the Earth attractor mathematics, inertial mass [m].
Since inertial mass is an influential quantity in our mathematics, but
is an independent quantity in the Earth attractor mathematics, how is
it we measure [G] as a function of inertial mass and assign it as a
constant of proportionality that applies to all celestial bodies? Are
we not defining the universal order after our own inertial image? The
Earth does qualify as a celestial body. If inertial mass is
independent of the Earth attractor action, it is a reasonable
generalization to conclude that inertial mass is independent of the
action of all celestial attractive bodies [Endnote 1]. Or am I being
too speculative here?
oOo
The introductory physics text approximates the orbits as circular and
notes that a circular orbit implies a centripetal force. The
introductory physics text should note that a time controlled circular
orbit implies a time controlled centripetal force. It is important to
note that while a time controlled least action orbit implies a time
controlled centripetal force, it 'certainly' does not imply a so
called "gravitational mass" generated centripetal force, nor does it
imply 'any' force of the type we feel and quantify, solely in terms of
the resistance we work against, as inertial mass objects.
Newton's third law is based on the behavior of impacting (physically
contacting) inertial mass objects, which behavior is independent of
the Earth attractor action on the objects. So exactly what is equal
and opposite? The resistance we feel and quantify as force (mg)? The
resistance we feel allows the falling billiard ball weight (mg) to be
set equal to the imaginary but theoretical Earth weight (Mg), where
(m) operates independent of the Earth attractor action and figures
quantitatively solely as resistance to our effort? Here equal and
opposite force applies to the interaction between inertial mass
objects [ma(1) = ma(2)], which we qualify as. Impacting billiard
balls are interactions between inertial mass objects, as is the
comparative measure of mass on the balance scale, where on balance (g)
divides out. We have assigned this property beyond the interaction
between the inertial mass objects (and ourselves, also inertial mass
objects), to the Earth attractor and we have generalized that
assignment to the entire universe as the controlling cause of the
least action order we observe in the celestial universe. The
functionality of the entire construct rests solely on inertial mass,
the resistance we work against, and least action motion.
We are inertial mass objects. We can feel the Earth attractor action
on our bodies as resistance. Therefore, we conclude that the Earth
attractor acts on our mass [m] as a function of our quantified weight
[mg], which we measure on the balance scale against a known inertial
mass that operates independent of the Earth attractor action. The
Earth attractor action is anonymous with respect to the action of the
balance scale. This action compares two masses where each mass is
equal and opposite to the effort we expend in lifting an inertial mass
object with weight [mg]. We say that the earth attractor applies just
the necessary amount of our notion of force to equal our weight and
our effort. We assign as a property of force to the Earth attractor,
the resistance we feel as an inertial mass object where [m] operates
independent of the Earth attraction action. If what we feel operates
independent of the Earth attractor action, how is it we can assign
what we feel as the controlling cause of the order we observe in the
time controlled least action celestial universe?
Consider:
In (1) where [M] represents the mass of the Earth and [r] represents
the distance to the center of the Earth from the Earth's surface, the
resistance we work against at the Earth's surface is formulated as:
5) F=mg
We must exert effort to lift, to overcome the resistance of the Earth
surface inertial object. We quantify the resistance to our effort in
terms of mass as weight [mg], where the focus of the Earth attractor
can be explained using functional mathematics (without recourse to an
equal and opposite force (weight) with respect to the Earth attractor,
to account for the resistance we work against), as an action on the
atom. We already know that the quantity inertial mass is independent
of the Earth attractor action. Whereas the Earth attractor action on
the atom unambiguously explains why all objects fall at the same rate,
again without recourse to the third law, which law defines force [mg]
solely in terms that are consistent with the resistance (our effort)
that we quantify and work against, as inertial mass objects [mg]. We
call our effort force. The Earth attractor pulls on atoms and we pull
back. We have assigned our quantified inertial mass defined "pull
back" to the entire universe and we call it gravitational force (or, a
consequence of a curved space-time). So that we set (5) equal to (1)
as:
6) mg=GmM/r^2
Although we have defined two formulations here for a mass generated
force, when we set them equivalent in (6), mass [m] again appears to
not be a functional part of the formulation. We see this as a
consequence of the fact that all objects fall at the same rate.
Whereas the reason little [m] divides out of the equation is because
we have defined force as a function of inertial mass [m] in both
cases. Where such a definition applies to us as inertial mass objects
and our interaction with inertial mass objects, but fails to address
the time controlled aspect of the least action universe.
Consider:
The fact that inertial mass objects fall at the same rate independent
of their mass means that with respect to celestial bodies inertial
mass is anonymous, operating within time controlled least action
parameters. We can define the least action behavior of the celestial
universe in terms of the force we feel and quantify as (mg) (which
also operates within least action parameters), and set both
formulations equivalent in (6). So mass [m] divides out of the
calculation as a matter of definition, not because all objects fall at
the same rate, which in this view is a convenient and obscuring co-
incidence that completely excludes the causal nature of the time
function. Which time function, when it does eventually appear,
appears as another dimension in general relativity as a "space-time"
curvature. A consequence of its original invisible joined inclusion as
an artifact of the circle itself.
Yes we divide the quantity mass [m] out of the equation but we retain
the proportionality of the attendant time controlled least action
properties that define the independent, inertial mass magnitude [m],
as a function of the local measurement of the universally general time
controlled least action kinematics. Its like saying since two
triangles are similar they are congruent. The fact is, Newton defined
gravitational force in terms that are dynamically proportional to the
local empirical measurements accompanying mass [m]. This includes the
equal and opposite comparative behavior of impacting inertial mass
objects, the comparative measure of inertial mass on the balance
scale, the uniform time controlled planet specific property [r] and
[t] dependent, accelerative action (g), and the gravitational constant
[G] measured as a function of inertial mass [m]. The magnitude of [g]
varies from location to location so that the attraction between
celestial bodies is defined in dynamic terms that are proportional to
the resistance we feel, using the similarity of measurements
accompanying time controlled least action motion, where the
quantification [m] of that resistance is independent of the celestial
attractor action. Little [m] divides out because we have defined
force as a function of [m] in both cases. However, the so called
universal gravitational force is solely defined in terms that are
proportional to the resistance we feel, which does not divide out.
oOo
7) g=GM/r^2
To close for now, again consider [6]. Where when we divide little [m]
out, we are left with [7]. Note again that [G], [g], and [1/r^2] are
empirical measurements that accompany least action processes. Note
too that the law of areas is a consequence of a time controlled least
action orbit. So, when we divide [m] out, the result in [7] leaves
[M] proportionally hardwired to our empirical measurements that
accompany the time controlled least action physical processes
involving [m], and extend to [M] via [1/r^2], also a property
attendant to a time controlled least action process.
In other words we have defined a universal time controlled celestial
force solely in terms of the resistive properties of inertial objects
(which we qualify as and which we work against) that function
"anonymously" with respect to celestial bodies, solely within time
controlled least action parameters. The time controlled least action
parameters are today extended within a 4D mathematical framework
called general relativity. These parameters are now known as
"geodesics". A term that simultaneously clarifies even as it further
obfuscates the underlying time controlled least action principle.
oOo
Endnotes
[1] This is not to say that celestial bodies have no mass. Rather,
their inertial mass while causing the eccentricity of the super
electromagnetically Sun, time controlled orbits, and possibly causing
the planet precessions, and the "least action" inclination of Uranus,
have no further consequence, at the present time. And it is in part,
to propose as one alternative possibility, that in the case of active
stars and some planets, their present inertial mass is a consequence
of the structural build of their super electromagnetic cores, which
super electromagnetic cores would be the primary source of the
celestial controlling attractor action. (See johnreed Take 23 - Dark
Matter and johnreed Take 24 - What is Super Electro-Magnetic
'Gravitation').
oOo
Author's after note:
The reader's indignation runs high with this post. I can understand
that. It challenges the very foundations of physics, as we know it.
I am only the messenger and if the message is valid, personal attacks
on me serve no purpose. If the message is invalid, then again, the
message should be attacked, not the messenger. I encourage such an
attack and I will embrace a rational argument, as readily as I have
embraced the {severely governmentally constrained} intellectual
freedom provided to me by the framers of the United States
Constitution. However, to merely avoid the issue by saying the post
is too speculative because it opens a rational, factual based door for
thought, IS without merit. The proper questions to consider are: Are
my base arguments valid or invalid? If they are valid, are they
significant or insignificant? At present I note, but do not limit
these arguments, to the following:
Argument 1: Isaac Newton defined a mass generated centripetal force in
terms of his first law object moving along a perfectly circular
trajectory at a uniform (perfect) speed. I show that this is true
directly from The Principia.
Argument 2: The law of areas falls out of a perfectly circular
trajectory and uniform speed as a property or artifact of the
efficient area-enclosing circle itself. I see this as self-evident
but I have explained it on the first page.
Argument 3: Kepler's law of areas is an efficient symmetry analog of
the circle. I show this by first showing that the efficiency quotient
of the circle reduces to the efficiency quotient of any radially
enclosed area of the circle. Then I show that Kepler's law of areas
proves the analog case for the real orbits.
Argument 4: Isaac Newton connected this efficient property of the
circle to its analog in the real orbits and used Kepler's law of areas
to carry his idea of centripetal force, mathematically, to the entire
universe. I show that this is true directly from The Principia.
Argument 5: I show that our mathematical derivation of Kepler's laws
from Newton's universal law of gravitation ultimately rests solely on
least action motion. The fact that all objects fall at the same rate
also shows that mass operates solely within least action motion,
"anonymously" with respect to celestial bodies.
Argument 6: I show that setting the quantity we work against and call
weight [F=mg], equal to Newton's universal law of gravitation [F=GMm/
r^2] co-opts the least action properties attendant to an anonymous
object in motion, and proportionally renders these properties solely
in terms of the resistance we work against and call force.
johnreed - Thursday, December 27, 2007
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