Re: Apparent weight

[David Bowman <dbowman@tiger.gtc.georgetown.ky.us>]

A. R. asks:

> So am I correct in concluding that in your approach *any* acceleration
> relative to *any* frame always has a force corresponding to it?

Not exactly.  Rather, any expression contributing to (the equation of
motion solved for the) rate of change of the momentum of an object in
any frame is identified as a force.  If any expression is an acceleration
(I would say *the* acceleration here, since in any given frame an object
has only one acceleration at any time) then that expression (barring
relativistic effects) is the *total* force on the body divided by the
body's mass (Cartesian component by Cartesian component). 

>                                                                 To be
> specific, since I clearly measure myself to have big accelerations
> relative to yonder stunt pilot doing maneuvers in the sky, if I wish to
> calculate in that frame I gain a force acting on me that I do not feel,
> but which "mathematically functions" as the cause of the accelerations?

Yes (if this is a question).

> Why does mathematics require such a cause?

Without those forces on you your acceleration relative to frame in which
the stunt pilot's plane is at rest would be zero, and you just agreed that
you had those accelerations.  Therefore, the mathematics requires them in
order to get your acceleration  (i.e. the equation of your motion) correct
in that frame.

> I can't help but notice that you make no mention, here or in all that
> follows, of inertial reference frames or inertial trajectories (the
> geodesics of either Newtonian flat or Einsteinian curved spacetime).  Is
> that by design.  Do you ever include such in your teaching.  If so, I
> would be intrigued to hear how.

Yes.  I already answered this in a previous post.  I must admit that I do
not include the part about "the geodesics of either Newtonian flat or
Einsteinian curved spacetime" in introductory courses when Newton's laws
are being discussed.  In addition, I do tend to emphasize that inertial
frames *are* special in that in such frames the only forces acting on a
body come from physical interactions with other dynamical entities.  Thus
if a body can be isolated from all such other interacting entities then
those forces that remain after such an isolation are due to the non-
inertial motion (i.e some combination of rotation and acceleration of the
origin) of the reference frame wrt an inertial frame, and a transformation
to such a frame will eliminate all these remaining forces.  Once the
physical interactions are turned back on in the inertial frame description
there are only forces acting on the objects coming from those physical
interactions.  I make a big point of emphasizing that those forces
appearing in non-inertial frames due to the frame's non-uniform motion wrt
an inertial frame (which can be eliminated by transforming to such an
inertial frame) are always directly proportional to the body's mass.  This
gives us an opportunity to discuss the Equivalence Principle (at the
appropriate limited level of the students) since, by the time this
discussion about frame-generated forces takes place, the class will have
already been familiarized with Newtonian gravitation and the fact that
the gravitational force on an object is always directly proportional to 
the object's mass.

> Very interesting.  Now I see where the big differences in approach arise
> from.  To me forces are very real and powerful physical phenomena, whose
> properties and effects can be *described* mathematically. I don't conceive
> their existence as purely mathematical, and so I take there ontology very
> seriously, as I am sure you have noticed from previous posts.

And as you can see from my previous posts, I don't.  This is not to say
that I don't believe in the reality of actual forces (in your sense of the
term 'force').  Rather, it is to say that my position allows me to remain 
comfortably noncommittal and agnostic on such a philosophical issue
without having the actual ontological situation affect how I do or
formulate physics.  This way if physics advances to some other level such
that the very idea of an actual force is found to be as mistaken as the
idea of caloric, then its no skin off my nose.  I prefer to leave the
sticky philosophical issues to philosophy, and not let them clog up physics.
My approach to physics is very utilitarian.  (When I want to commune with
Ultimate Reality I go to church.)

>                                                               I thank you
> for your candor and clarity.  It at last clears up where the differences
> lie.

You're welcome.  And thank you for your exposition of your position.

Since I have spent too much time on this discussion after getting sucked
into it (despite my protestations to resist) I hereby quit.  I need to get
back to other pressing uses of my time.  I hope the next time the topic of
'fictitious" forces comes up (and it will) that the one who raises the
issue will consult the FEB 98 archives thoroughly before posting his/her
questions/comments and setting off another round of this interminable
debate.
 
David Bowman
dbowman@gtc.georgetown.ky.us