johnreed-Math and Universe, Part 3, September 27, 2007
- From: johnlawrencereedjr <randamajor@xxxxxxxxx>
- Date: Thu, 27 Sep 2007 18:55:56 -0700
Research Results on Inertial Mass and Centripetal Force from The
Principia
Math and Universe Part 3 - September 27, 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, inertial
mass object, on a circular path of motion, at a uniform orbital speed.
The model was built in the following manner: Newton allowed the moving
inertial mass 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..." [1] (Principia)
Although Newton defined the least action planet orbits in terms of
inertial mass, we can perform no experiment that differentiates
between the atom and the mass of the atom, such that we can absolutely
conclude that the earth attractor (read gravity) acts on mass, and not
on the atom itself [2]. In fact, the earth attractor (1) allows
surface planet inertial mass objects to independently interact with
other surface planet inertial mass object. (which we qualify as)
quantitatively, in terms of inertial mass. And the earth attractor (2)
enables us to independently quantify the resistance we "feel" and work
against, as inertial objects, in terms of inertial mass. This
represents two sides of the same coin. Additionally, the freefall,
orbit velocity, and escape velocity, experimental data show that (3)
inertial mass "does not" enter into the controlling, earth attractor
mathematics. This represents the coin itself. I say that inertial mass
figures into "our" mathematics because we are inertial objects.
However, inertial mass does not figure into the earth attractor
mathematics, therefore the earth attractor does not act on inertial
mass.
Except for our tactile "sense" of attraction, which we feel as
resistance and quantify in terms of our inertial mass (m), as weight,
inertial mass is independent of the earth attractor action. "We are
certainly not to relinquish the evidence of experiments for the sake
of dreams and vain fictions of our own devising." (Principia) Even so,
these results have continued to center on the Newtonian explained
freefall, equal and opposite "inertial mass" impact (physical contact)
data [3], and today, provide the quantitative basis for Einstein's
observer dependent, postulated equivalence principle.
Consider:
Either our tactile sense of attraction to the earth (gravity), which
we feel as resistance, and isolate quantitatively in terms of our
'inertial mass', generates the least action, time constrained, planet
orbits, as defined by Isaac Newton, or the least action planet orbits
are the reason we can isolate the emergent quantity "inertial mass" on
the balance scale, and our tactile sense of attraction to the earth
(gravity), which we feel as resistance, and quantify as weight, is
caused by the earth attractor action on our constituent atoms [4],
holding us to the earth's surface. In other words; mass controls the
least action planet orbits; or the least action planet orbits allow us
to isolate the quantity inertial mass on the balance scale. Is this a
reasonable "either/or" proposition? Are they each mutually exclusive,
or can they both be true, as defined by Isaac Newton and postulated by
Albert Einstein?
It has been shown to an experimental accuracy of twelve decimal places
[5] that inertial mass "does not" enter into the earth attractor
mathematics during freefall, orbit velocity, and escape velocity
experiments. I can show that the least action planet orbits are the
reason we can isolate the quantity, inertial mass, on the balance
scale. The orbits function within the constraints of a least action,
time constrained principle. Freefall functions within the same
constraint (equal areas in equal times). Whatever the cause of the
shared least action principle, that least action principle allows us
to isolate inertial mass on the balance scale.
For:
If all objects did not fall at the same rate, when dropped at the same
time from the same height, we would be unable to separate the planet
attractor surface, accelerative action (g) from the mass of the
inertial object (m) on the balance scale. There would be no, specific
to each planet, common accelerative action (g) for falling objects, as
(g) would vary with the falling object's weight (w). In such a case
our "tactile sense of attraction" that Isaac Newton quantified
generally as gravitational force (gravitational force = weight = mg),
and that we feel as resistance, could be measured on the balance scale
only in terms of weight (w), and not in terms of weight (mg). In other
words, if all objects did not fall at the same rate when dropped at
the same time from the same height, we would have no emergent quantity
called inertial mass to investigate. In such a case, the idea for an
"unencumbered" field with respect to mass, required for Newton's first
and second laws, could not exist. Nor could we exist. Consequently, I
say that inertial mass is emergent in a field that does not act on the
property of matter we feel as resistance and quantify in terms of our
inertial mass, as weight. Therefore, and as experiment indicates, the
earth attractor acts on our atoms and not on the mass of our atoms. In
other words: the earth attractor acts on matter and not on mass.
Einstein's idea that Newton's first law applies to planet orbits
because the planets travel a least action curved space-time geodesic,
extends Newton's definition of a circular (least action), inertial
mass generated view of planetary motion, by further co-opting the
least action planet orbits, within an extended 4D spacetime
mathematical model. While maintaining our centrist view for a mass
generated notion for gravity, Einstein backed into a more accurate,
partially electromagnetic, least action mathematical frame. Where a
defined curved spacetime is designated as the cause of the least
action orbits. For now, I'll leave it to the reader to contemplate the
argument that the earth attractor acts on our constituent atoms and
not on their mass, and to:
1) Consider how well blackholes, curved space-time, and the big bang,
will survive theoretically where the earth attractor acts on our atoms
(matter) and not on our mass. 2) Show that the balance scale measures
inertial mass and that, "gravitational" mass does not exist. 3)
Consider possible reasons for the Pioneer anomalies. 4) Consider
possible reasons for the Foucault pendulum anomalies during total
solar eclipses. 5) Consider non-Newtonian alternatives for dark matter
and energy (See johnreed Take 23 - Dark Matter).
Endnotes:
[1] The verbal argument Newton used to connect his inertial mass
driven centripetal force to Kepler's laws is, by my notes here, vague.
So far I have traced it from the balance scale through the pendulum to
Jupiter's moons and the Sun. Newton used the third law which provided
the equal and opposite, attraction-resistance pair. Though as Einstein
was "happy" to learn later, we feel no resistance during freefall
(excluding air resistance). Which would be the case if the earth
attractor acts on our atoms and not on our mass. This from old notes.
Must re-check the publication. So I'm still working on it in that
sense. However the sole purpose of my argument here is to show that
Newton defined centripetal force in terms of inertial mass. This
explains the assumptive equivalence directly. The reason inertial and
so called gravitational mass are quantitatively the same will be
further entertained in another post, shortly.
[2] This is not to say that the earth attractor acts on atoms and not
on particles. The earth attractor acts on all material objects. The
atom is the fundamental unit of matter that is proportionally
equivalent to mass with respect to pure stable elements. The atom also
serves as a basis for an electromagnetic explanation for the
resistance Newton felt and called centripetal force, and set
equivalent to the a priori human notion for "gravity". And the fact is
we cannot discern which of the two, mass or atoms, are acted upon by
the earth attractor. Should I declare an equivalence principle here?
Say, since the observer cannot tell the difference they are the same.
Call it the 2nd observer dependent equivalence principle? :-/
[3] Isaac Newton's interpretation of the freefall phenomenon; Albert
Einstein's interpretation of the freefall data; and my interpretation
of those data; lead to entirely different conclusions.. Einstein
postulated that because he could not feel his own weight (resistance)
in freefall, and because he could not tell if he was in an accelerated
frame, or in a gravitational frame, and because the measured, so
called gravitational mass, and the measured inertial mass are
quantitatively the same, they are in fact, the same. I will expand on
this in my next post.
[4] Again this should not be read as an exclusion of particles. I say
that the earth attractor acts on matter and not on mass. We cannot
perform an experiment to prove otherwise because the mass of an atom
and the atom itself are directly proportional. In the case of pure
elements the number of atoms is directly calculated from the mass.
This can be directly calculated from any object provided we know the
precise composition of the object. However, measuring the mass of a
shovel full of dirt will provide no precise information on its
composition and therefore no information on what is being acted upon
by the earth attractor. If the earth attractor acts on atoms,
independent of their mass, we can expect a small deviation in our
calculations to occur in extreme cases.
[5] Many of my notes were compiled years ago. The degree of accuracy
here has increased since then. The reader may find up to date and
comprehensive data on this at Uncle Al's website.
johnreed
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