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Re: Newton's first law



At 10:48 AM 9/13/00 -0400, Carl E. Mungan wrote:
I'm interested in how folks introduce Newton's first law (N1) to
their classes.
...
A typical textbook says something to the effect that "N1 gives us a
criterion for determining if a reference frame is inertial"
(paraphrasing from Tipler). I have several problems with that:

(1) I like to distinguish "laws" (things about the world that do not
follow from mathematical deduction using definitions) and
"definitions" (useful but ultimately arbitrary decisions physicists
make). The above phrasing seems to reduce, maybe not to a logical
definition of "inertial frame" itself, but certainly at least to an
operational one.

I agree with your observation that there is an element of arbitrariness
here. The arbitrariness is real. Some of the arbitrariness is inescapable.

In mathematics the situation is more clear:
-- there are undefined (and undefinable) terms such as points, lines,
and planes
-- there are axioms that assign (with considerably arbitrariness) the
properties of the above, and then
-- there are theorems which are derived from the axioms.

To return to the world of physics, the term "force" starts out as an
abstraction, essentially as abstract as a mathematician's "point", until it
is given meaning -- implicitly -- by being used in the laws of motion.

Alas the physics situation is messier than the math situation, because
physicists have not been careful to distinguish what are the terms, the
axioms, and the theorems. Many of the things that you would need to say in
order to axiomatize the notion of "force" are left unsaid in the usual
formulation of Newton's laws -- notably the fact that forces are vectors,
and obey the vector laws when you superpose them, rotate them, et cetera.

For an introductory class, it may help to give an example of a force --
such as a string tied to a pulley and a weight. Then you can say "Feel
this. We _choose_ to call this a force. Anything that acts like this is
also a force."

You can speak of force, time, and distance.
Or you could speak of torce, dime, and fistance.
There is no magic in the names; the words would not mean anything unless
and until they are used in _consistent_ ways by the laws of motion. The
interesting thing is that the laws are consistent to an astonishing
degree. Predictions can be made with astonishing accuracy.

Even as an operational definition, it puzzles me. Suppose I plunk
you down in some cubicle attached to some reference frame. ... Your
assignment, should you choose to accept it, is to
*experimentally* determine if your reference frame is inertial using
NI alone.

Alone???? That's an over-extrapolation of what Tipler was saying.

As far as I can tell, of all the laws of physics, there is not a single one
that means anything _by itself_. It's like a big geodesic dome; any
single strut, out of context, is structurally unsound and would fall down
immediately.

how do you know you've measured every last force on it?

Philosophically speaking, you don't.

This boils down to a replay of Joel's questions about perturbations of the
speed-of-light experiment.

The only truly essential thing is that physicists need to be able to
replicate each other's experiments. It turns out that over the years, we
have seem to have identified all the forces that are significant for
kinematics experiments (gravity, friction, electromagnetism, outgassing,
etc.) and there are widely-known techniques for reducing their effects on
our experiments. But in principle, there could be a rash of
replication-failures starting tomorrow, because of N-rays from the planet
Krypton; you can't rule it out.

=======

Another philosophical point is the choice to regard absence of friction as
ideal and natural -- in contrast to the Aristotelian view that friction
(and decaying velocities) is natural. This is an important invention. It
is a choice. But it is a good choice, so it can't quite be considered an
arbitrary choice. It is a good choice because it makes for good
communication and good replication. One physicist can tell another that
the experiment has negligible friction, and we know what that means. We
know how to replicate that. We know how to account for nonzero friction
starting from the zero-friction abstraction.

Again this is a replay of Joel's question: for the speed-of-light
experiment, you never really have a chamber where the walls have exactly no
effect, and the residual gas density is never exactly zero. But those
idealizations are easy to communicate, and form the unshakeable foundation
to which correction terms can be attached.