# Section 14 Draft - johnreed

Discussion in 'Undergraduate Math' started by johnreed, Dec 20, 2010.

1. ### johnreedGuest

Consider a pure, one isotope element. On a balance scale, imagine that
we can place one atom at a time in a pan. We have a standard
calibrated mass in the other pan. We can (theoretically) place one
atom at a time in one pan until it is balanced against the standard
mass in the other pan. When we lift either the pan with atoms or the
pan with the standard mass we feel weight. We feel the combination
represented quantitatively as the product [mg] at location [g]. The
quantity [g] represents an acceleration that is dependent solely on a
distance from a center.

In this thought experiment, we observe that the balance scale compares
the resistance of a quantity of atoms to the resistance of a quantity
of matter calibrated in mass units. Given that the thought experiment
is valid, we feel (work against) at location [g], the cumulative
resistance (mass) of the number of atoms in the pure object pan at
that location.

The action of the balance scale, on balance, speaks only to the
uniform attractive force on the contents of each pan. The balance
scale does not tell us what kind of force is acting on the pans. We
can look at it as though it is a uniform attraction on mass, (as
Newton did) or a uniform attraction on atoms (where Newton did not
require any greater distinction than mass). In either view, mass units
are conserved. Question: What is it about mass that allows this?

I asked how we derived the quantity mass in the first place. Mass is
the scalar component of force, where F=mg and F=ma. In the case of
[mg] it comes from the balance scale. Each atom in the pure object
pan is uniformly acted upon by the planet attractor. If this is
correct we should be able to deduce the number of atoms in the pan by
dividing the total weight by the weight of one atom, since in this
gedanken all atoms are identical by definition. However, since the
total weight includes [g], an outside influence, and the weight of one
atom includes [g], also an outside influence, which outside influence
acts uniformly on the balance scale as well, and on us as we observe
the action, we can eliminate the quantity [g] from the frame of the
balance scale action (adding it back in at any specific location to
describe the force we must apply).

Since [g] is the same magnitude depending on location before and after
we obtain a balance, the equation on balance where [mg]1=[mg]2 can be
divided by [g] to yield [m]1=[m]2 on balance. This shows that the
balance scale compares mass [m] (resistance) since the quantity [g] is
a variable influence dependent on any location such a measurement can
be made, the quantity [mg] represents a variable resistance, a
magnitude of matter that we feel as weight, at any location we can use
the balance scale.

Here it appears that we have defined gravitational force in terms that
are subject to what we feel at any location in space. In this case we
define the universe in terms of the force we feel and apply to a
resistance and we generalize that force to the entire universe
because we feel it everywhere. Since the resistance we encounter at
any location [g] is equal and opposite to the force we apply at any
location [g], the subject is closed. That's all we require to
successfully operate within the least action universe.

What we feel is the product of resistance [m] at an accelerative
location in space [g]. Where the balance scale solely compares the
resistance [m], independent of any location [g]. But we always knew
that, didn't we?

If you wish to review some of the foundational logic for the
ideas expressed herein, do a Google.group search on: "The Least
Action
Consistent Stable Universe and the Mathematics, Sections 1 through
9",
or "Randaminor", "Randamajor", "Thejohnreed", "Earth Attractor" or
"Planet Attractor". To exhaust the search on the internet take your
search back to 1998. To exhaust the copyright information take it to
1988 and "Pi and Angular Momentum in Perspective", "The Anti-Billiard
Ball Hypothesis", and "The Physics Preview for the 21st Century".

I have made it easier to reference my supporting work by creating a
Google Science and Technology Group titled: "The Least Action
Consistent Universe and the Mathematics". Currently it contains
Sections 1 through 9 as noted above. The many sub-sections and work
prior to 2007 has not been included. I will develop it further as I
gain familiarity with the venue.

Meanwhile it is available for public review to all, and open to
criticism and discussion by any person who joins the group. No
restrictions or requirements to join.

Endnote:
[1] Section 5 and 6 as listed above provide a more comprehensive
explanation of least action. For my purpose here the reader may
substitute the word "efficient" for the phrase "least action
consistent".

johnreed, Dec 20, 2010