Re: Newton's laws +- logical completeness

[John Denker <jsd@MONMOUTH.COM>]

At 11:37 AM 9/15/00 +0500, D.V.N.Sarma wrote:
> Another funny thing. In order to determine whether the testbody
> is moving equal distances in equal intervals of time we need a clock
> i.e., a body whch moves equal distances in equal intervals of time.
> Is there not something circular here?

All these questions about "circular logic" arise from the notion that
Newton's laws are, by themselves, the basis of a logical system.  But they
are not.  Newton's laws are _not_ by themselves analogous to the handful of
axioms that form the basis for Euclidean geometry.

If you approach high-school physics the same way you would approach
high-school geometry, you are going to have innumerable "funny" problems.

In particular:
   -- we need rulers,
   -- we need scales to measure mass,
   -- we need clocks,
   -- we need reference frames,
   -- we need to know that forces act like vectors, and
   -- we need other things...

The things on this list are not trivial, and they are not guaranteed by
Newton's laws as they are usually stated.

 -- Rulers have been around for thousands of years, but logically they
cannot be taken for granted.
 -- Scales have been around for thousands of years.  Again, logically they
cannot be taken for granted.
 -- Galileo established that a pendulum makes a good operational time
standard.  This is totally nontrivial!
 -- Galileo established the idea of reference frames and the relativity
thereof.
 -- Et cetera.

The mechanics curriculum usually starts with Galileo, not Newton.  It
starts with a lot of conceptual, operational stuff -- not axioms.

You _could_ teach mechanics using an axiomatic approach -- but that is
appropriate for grad school, not high school.