Re: johnreed take 1C --- 2005
- From: Joe Fischer <efischer@xxxxxxxxx>
- Date: Fri, 23 Dec 2005 21:57:38 -0500
On 22 Dec 2005 randamajor@xxxxxxxxx wrote:
>As I continued with my analysis of Newtonian gravitation (see Take 1B),
The format and presentation is great, thanks.
>I noted that:
>
>Newton set mass [m] as a component of a force "we feel":
I don't think "feel" had anything to do with the mechanics,
which likely came before the gravity theory, but used as the
basis, the work of Galileo and others, like the inclined ramp
experiments, for the mechanics.
The inclined plane slows the effect of gravity and
provides a constant force to experiment.
>(1) F = [m]a
>
>and Newton set mass [m] as a component of a force "we feel":
>
>(2) F = [m]g
Not as "a force we feel", rather as a quantity of matter
which resists acceleration.
>On the basis of his "feel" of force, Newton assigned mass two
>manifestations. He called the "feel" part in (1) inertial mass. He
>called the "feel" part in (2) gravitational mass. It is useful to
>recognize that in both cases we feel the same mass regardless of the
>cause. Newton defined inertial and gravitational mass the same, each as
>a component of a different force we feel. One mass. Two forces.
They are not two forces, But modern PPN writers
and gravitational experimenters get even more silly,
with "target gravitational mass", "target inertial mass",
"source gravitational mass" and "source inertial mass".
Four names for the simple quantity of matter.
>I noted that Einstein used an imaginary elevator to argue that we could
>not tell the difference between (1) and (2),
It really isn't good to use the word "elevator",
I used to do that, and people seemed to think I meant
an elevator on Earth in Earth's gravity.
Scientists knew before Newton that all things
fall equally, but it was the ones that thought heavier
things fall faster that coined the term "gravitational
mass".
Newton made gravitational mass equal to
inertial mass in the formulas.
>and, essentially on that
>basis, Einstein called this the principle of equivalence.
I could talk for hours about this popular misconception,
the fact that gravitational mass and inertial mass are equal
was called the equivalence principle well before Newton.
What Einstein did was postulate a situation where
gravitational mass absolutely _MUST_ equal inertial mass,
because it is obviously inertial mass that is being measured.
But the beautiful thing that resulted is that freefall
and orbits are then inertial motion.
Another misconception is that observed freefall
acceleration equals rocket acceleration., but it doesn't,
just the opposite in fact, freefall is inertial motion, and
it is surface gravity acceleration that equals rocket
acceleration.
>Since they
>feel the same, they are the same, and, according to one interpretation,
You really haven't defined what you mean by
"they feel the same".
And a force does not even mean there is acceleration,
so it doesn't feel the same.
>they are the consequence of a curved space-time, and have nothing to do
>with what we feel, but have something to do with mass. I had to
>investigate this.
Spacetime does not cause a "consequence",
it is a map of motion.
>As I progressed on several fronts, I noted that if Newton wanted to
>define a force that functioned from mass, as did his weight, because he
>had discovered that the apple and the moon "fell" at the same rate. And
>if Newton believed that the force operated between objects at a
>distance, even though his weight was undetectable unless he was pressed
>to some surface, he could set the force proportional to the product of
>the masses, and inversely proportional to the distance between them.
"Force is a term used in other ways besides relating
to gravity. And it should be "inversely proportional to the
square of the distance".
>So, he could arrive at a preliminary relationship on the order of:
>
>(3) M[m]/r
He was prompted by Hooke and a couple of other
people. The important thing was to make the gravity
theory work with the mechanics. The mechanics surely
came first, and was the most important.
>I noted that, as a result of the moon and the apple, Newton extended to
>all matter in the universe, a gravitational attraction consistent with
>the force "we feel", and consistent with the planet orbits. This
>was formulated as:
>
>(4) F = GM[m]/r^2
Orbits use a + A = G (M + m) / r^2.
>It would be useful to again note that Newton defined a force, based on
>his "feel" of attraction to the earth, and quantified the force in
>terms of acceleration and mass. I noted that in (4), the quantity [G]
>was determined by Cavendish as a result of a horizontal measure of
>torque.
Determining G was important in estimating the
weight of the Earth, and Cavendish did it long after
Newton.
>This at best served as a scaling mechanism, where the actual
>measure could result from the surface area of the sphere as an atomic
>attraction, more easily than as a result of the mass of the sphere.
Newton knew gravity was not like a magnet.
>As near as I can tell, Newton had no clearly definable concept of
>"least action". Therefore it would not be apparent to Newton that
>the apple and the moon, and his formulation in (4), each operate
>consistent with a principle of least action. Least action can take many
>mathematical forms. For the academic humanist the easiest to understand
>form, is probably the static representation of a Euclidean circle. It
>is the shortest line length to enclose the greatest area. Kepler's
>laws are also easy to grasp in this regard (see Take II). The
>Lagrangian and the Hamiltonian are other classical forms, and
>Feynman's sums of histories, yet another, albeit, quantum mechanical
>form. Even the roll of a pair of dice can be shown to derive from a
>least action principle.
That diminishes the image of least action in my mind.
>Consider the falling apple. It plummets straight to the ground with
>respect to the earth and the tree. If we roll a small glass marble at
>velocity, off a platform that is the same height as the apple at the
>instant the apple starts its journey, both the apple and the marble
>will hit the ground at the same time. The marble is less massive than
>the apple, and the marble travels a longer, curvilinear distance, yet
>both the marble and the apple reach the earth at the same time. This is
>also an example of least action. It does not depend on mass, and
>neither does the moon.
The moon certainly does do things the apple doesn't,
the moon is .012 the mass of the Earth, and changes the
motion of the Earth quite a bit.
>Where the force Newton felt as attraction to the earth results from the
>same cause as a least action event. Where Newton and the apple were
>inertial objects, if inertial objects are to be found anywhere. Where
>Newton and the apple were both being acted on by the earth attractor.
>And where mass had nowhere been shown to be causal. I determined that I
>should analyze in greater detail, what it is exactly, that I feel.
Mass is nothing but the quantity of matter.
>I sought to better understand why all objects fall at the same rate,
>when dropped at the same time, from the same height. I noted that orbit
>velocity and escape velocity, reflected the same property as freefall.
Sure, inertial motion, Newton knew this, but
he needed freefall to be acceleration so the mechanics
and gravity used the same simple formulas.
>Mass does not figure mathematically, with respect to the earth
>attractor, into any of these 3 processes.
I dont know what that means, mass needs to be
in the formulas if better precision is needed.
>These separate, and
>apparently unconnected* facts had been well documented. However,
>connecting the 3 earth processes in order to identify mass as an
>independent and defining, emergent quantity, within the attractor
>field, had not been done. In my view, the single aspect of mass that
>appeared unresolved in this context, involved the balance scale.
The balance scale was used by Newton and many
before him to compare masses in commerce.
>I studied the balance scale in order to define its action more
>precisely. I noted that the balance scale compares the relative
>"resistance" of inertial objects, with respect to the earth
>attractor, the moon attractor, and by implication, with respect to any
>other attractor. I tentatively offered an imaginary experiment in Take
>16, using a balance scale in a magnetic field, to isolate the quantity
>mass. In all cases, the quantity [g] divides out, leaving only the
>quantity [m].
You didn't post where the other takes can be found,
I find this one interesting, even if not historically correct.
>After much contemplation, I noted that we could not use a balance scale
>if all objects did not fall at the same rate. In such a case we could
>not divide [g] out of the equation. We would be unable to isolate [g]
>from [m] on the balance scale. We would have a single quantity, weight
>[w]. I noted that the balance scale measures what we feel, as a
>function of our inertia and the pull of the earth attractor. A spring
>scale is calibrated to our feel of weight and reads in terms of [mg].
>We calibrate the balance scale and use known weights where [g] divides
>out on each pan. Weight [mg] is dependent on our feel of attraction and
>on our location. Mass is independently isolated on the balance scale
>regardless of location.
Except for the fact that the Earth does not attract,
a balace scale does accurately compare masses.
>Again, after much contemplation it became clear to me, that if the
>earth attractor did act on mass, we would not be able to peel ourselves
>from the earth's surface, nor could we even exist. I concluded that
>the earth attractor did not act on mass.
If the Earth acted by attraction, many things would
be different.
>I was rather stunned to learn this because we had used a balance scale
>for some 3000+ years before Galileo. Apparently, from Aristotle on
>(2000 or so, more years) we expressly believed heavier objects fall
>faster than lighter objects. And even today, with another 300+ years,
>we still believe that the earth attractor acts on mass. I recognize
>that hindsight is our strong suit and that the balance scale was used
>as a practical tool rather than as a scientific tool, for much of this
>time. I also recognize that our progress is slow**. However, 3000+
>years and Aristotle, and 300+ years to boot? With the evidence clearly
>before us, had we chosen to examine it?
The balance scale is and always been one of the
most important scientific tools.
>I concluded that inertial mass is an emergent quantity. A property of
>matter that arises in a force field, the cause of which, does not act
>on inertial mass. I also concluded that there is no quantity called
>gravitational mass. Later I determined that the earth attractor acted
>on the atom rather than on the mass of the atom (see Take 13).
The Earth does not attract, and the Earth attractor
does not act on anything.
>* We have devoted a voluminous amount of research on Galileo's
>initial discovery that all objects fall at the same rate if dropped at
>the same time from the same height. The related fact that mass does not
>enter into the earth attractor mathematics during escape velocity and
>during orbit velocity, though well known, has generated little or no
>similar interest.
You can be certain that a heavier object requires
a different formula than a light one, the Earth has a mass
greater than 10^22 and we can only measure about 10^14,
so obviously all things fall equal.
A heavy enough mass falling would also cause the
Earth to fall up, causing the two masses to accelerate
together faster.
> MERRY CHRISTMAS 2005, folks.
>johnreed
And a H A P P Y N E W Y E A R
Joe Fischer
.
- References:
- johnreed take 1C --- 2005
- From: randamajor
- johnreed take 1C --- 2005
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