Re: Apparent weight

["A. R. Marlow" <marlow@loyno.edu>]

On Sun, 22 Feb 1998, JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL 60439 wrote:
> ... I seem to have a somewhat different view of Newton's Laws, so I'll
> take this opportunity to record them.  This view is somewhat closer to that
> espoused in MECHANICAL UNIVERSE by Olenick, et al.  The problem is to keep
> the three laws from being trivial:
> N1:  There exist inertial frames.  The test for an inertial frame is that
> an object that is not acted upon by a force is not accelerated.
> 	Comment: This leaves the notion of force undefined.  It also insures
> 	that N1 is independent of N2.
>
> N2:  F=dp/dt
> 	Comment:  The 4 forces of nature are given.  N2 then permits one to
> 	measure mass (definition of mass).  Otherwise, N2 is empty because
> 	force and mass are defined in terms of each other.
>
> N3: Any part of a system may be analyzed in isolation, using N2, replacing the
> 	remainder of the system by the forces exerted by that remainder.
> 	Comment:  N3 is just a computational device.
>
> 	As far as GR is concerned, the key point is that one can always find
> 	a local inertial frame in any curved universe.  In that frame Newton's
> 	laws, being local laws, take on the same form that they do in special
> 	relativity.  The problem of GR is how to get from one local frame to
> 	another one.  This view is especially emphasized in Misner, Thorne and
> 	Wheeler's book.
> 				Regards,
> 					Jack


I second your view fully, and must confess that I have been very surprised
at the amount of debate it seems to arouse.  I had thought that the view
expressed above had become rather standardly accepted in the last 15-20
years as general relativity became better known and its implications more
clearly interpreted (largely due to work by Misner, Thorne and,
especially, the magnificant pedagogy of John Wheeler and his coauthor
Edwin Taylor  --  more recently, the Princeton Series book "Gravitation
and Inertia" by Ignazio Ciufolini and Wheeler makes the argument even more
strongly), but that doesn't seem to be the case, as is evidenced by the
recent posts.

I now think I understand why the debate arises.  There seem to be deeply
different metaphysical presuppositions that are actually showing up in
physical interpretations.  If one regards forces as a purely mathematical
constructs, then of course what governs their appearance or disappearance
must be mathematical esthetics, logic and convenience, and you are free to
manufacture them mathematically subject only to those rather liberal
constraints.

If, on the other hand, you regard forces as real *physical* phenomena with
measurable properties which our mathematical constructs must attempt to
describe as accurately as possible, then a more restrictive set of
constraints comes into play, and one is not free to have them come into
existence or go out of existence as we change our kinematic perspective.

I'm not sure, but I think the first view also seems to give greater weight
to the visual perception of reality and less weight to the tactile
perception, while the second view gives about equal weight to both types
of perception.

As far as GR goes, I believe the first point of view would probably
interpret the stress-energy density tensor ("matter tensor" on the right
hand side of Einstein's equation = source of curvature) as a purely
mathematical construct, and so would allow parts of what Misner, Thorne
and Wheeler would call the Einstein curvature tensor to be moved under the
umbrella of the matter tensor freely.  One who regards the matter tensor
as a mathematical description of a preexisting physical reality would not
feel so free.

It has to be emphasized that none of this has anything to do with whether
you are using inertial or noninertial frames.  Once you have chosen a 
nonzero matter tensor, it will be nonzero whatever frame you decide to
use.  The choice is rather whether you want to move nontensorial "pieces"
from one side of an equation to another and still call the resulting
nontensor a valid representation of mass-energy-momentum density present
in spacetime.  The analog in Newtonian space is: once you have settled on
the physical net force vector acting in a situation, and have written the
vector equation <m dv/dt = F> to describe the situation, is it legitimate
to call the second half of the splitting <m(dv/dt)rot + w x v> (that
results from the product law of calculus when we introduce rotating axes)
a "force."  The "purely mathematical construct" school sees no problem;
the "representation of physical reality" school sees problems, not least
of which are that there is no assignable source of the new "force" nor any
third law counterpart, and the new term is not a proper partial
derivative, but only half of a derivative. 
 
I must admit that I see no resolution of the differences, once the
metaphysical differences are recognized, as well as the fact that purely
mathematical considerations will not resolve the issue.


A. R. Marlow                          E-MAIL:  marlow@loyno.edu
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