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Re: [Phys-l] Weightless



Hi all-
John has evidently missed by construction of a consistent system of units where G is defined to be equal to 1 Nm^2/(kgg)^2; there is a g_g for calculating forces (g_g x gravitational mass), and a g_i which is the acceleration of any body in free fall; the gravitational kilogram, kgg ~.8x10^{-5)kg, where kg is the SIU kilogram.
This demonstrates that the usual identification of the gravitational kiogram with the inertial kilogram is nothing but a convention, handed down to us by Cavendish. The true equivalence principle, stressed in Weiberg's book on gravitation, is that the RATIO of gravitational to inertial mass is constant over all substances, protons, antiprotons, neutrons and electrons. This is the beautiful simplicity of gravitation which has recently been addressed in a number of short essays by Wilczek in Physics Today and Nature.
Reagards,
Jack




On Wed, 22 Nov 2006, John Mallinckrodt wrote:

Bob,

In response to my pointing out that, since g is not equal to GM/r^2,
one definition would have to be abandoned, you wrote:

I still see both definitions in common practice in high school,
first year physics texts and in engineering texts. So, apparently
neither has been abandoned yet. Please let me know when you have
convinced the authors of these texts to change their definitions.

and in response to John Denker's pointing out that "horizontal" is
not perpendicular to "toward the center of Earth" via an imaginary
situation involving a pool contractor you wrote:

If I were to hire a contractor to build a pool, I doubt that the
definition of weight would come into our conversation. I certainly
would ask for references and visit pools they have already built.
Good luck with your quest.

In both cases I don't really understand the point of your seemingly
dismissive comments.

Is it your position that there is something wrong with either of
those points? Is it, perhaps, that we should accept what
introductory textbooks say about such matters? More likely you
simply find the discussion overly pedantic and/or some of the
discussants including me arrogant. If the latter, I regret it
greatly, but I honestly don't feel the need to amend or apologize for
anything I've written in this thread.

For my part, I've never taken any serious issue with textbooks that
say that g = -GM/r^2 r_hat, because it's exactly correct in one
important highly idealized situation (within the framework of
Newtonian mechanics) and because it isn't a bad approximation in some
more realistic situations.

I've always figured that those students who go on to become
professional physicists will eventually make the necessary
adjustments. In other words, that they will come to appreciate the
fact that gravitational forces *are* frame-dependent and are not
generally determined by the masses and positions of nearby objects
*despite* what introductory textbooks may say.

I've always assumed that practicing physicists will understand (or be
easy to convince of) the deep significance and beauty of the
principle of equivalence and appreciate the breathtaking simplicity
of the world view that results from understanding that gravitational
forces *are* inertial forces, that they are always given by mg where
g is the local gravitational field, and where g is always easily and
operationally determined by simply measuring the acceleration of a
local freely falling object.

If that isn't the case, then I should probably revisit my relative
lack of concern about what is taught in introductory textbooks,
indeed, about what I myself teach. Perhaps it *is* time 100 years
after Einstein changed our view of gravity to start actually teaching
that view in a much more systematic way.

John Mallinckrodt

Professor of Physics, Cal Poly Pomona
<http://www.csupomona.edu/~ajm>

and

Lead Guitarist, Out-Laws of Physics
<http://outlawsofphysics.com>
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