Section 14 Draft - johnreed

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

  1. johnreed

    johnreed Guest

    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.

    Current web address: http://groups.google.com/group/thejohnreed

    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
    #1
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