Re: CAUSATION IN PHYSICS

[Tucker Hiatt <hiattu00@USFCA.EDU>]

I don't know who first said it, and I don't even know that I'm quoting it
correctly (please help me if you DO know), but consider:

"Mathematics describes all possible universes.  Physics describes THIS
universe."

Mathematically speaking, "a = F/m" and "F = ma" are equivalent.  Physically
speaking, they are not.  I think it's helpful to tell our students that, in
this universe, acceleration is PHYSICALLY DETERMINED by force and mass.

At 7:47 PM -0700 10/14/00, John Denker wrote:
> The thing that confuses me most about this discussion is this:  Why bring
> up "causation" at all in an introductory mechanics course?

Please allow a slight digression...
In discussing simple waves, lots of physics books tell us the following:

wave speed = wavelength x frequency.

Then, when we ask our students, "What happens to a slinky wave's speed when
the wave's frequency is doubled?", they dutifully report that the wave's
speed doubles!  They're living in the "wrong universe."

This is why we might want to emphasize causation in wave production and
propagation, and why it's causally-correct ("CC", as opposed to "PC"!) to
write:

wavelength = wave speed x period.

First, students recognize this version of the formula as a simple
application of "distance = rate x time," and, second, students can infer
that wave speed and period PHYSICALLY DETERMINE the wavelength.  If I'm
lucky, I can even get them to see that wave speed is PHYSICALLY DETERMINED
by properties of the wave *medium*, and that period is PHYSICALLY
DETERMINED by the wave *source*.

By the same token, a = F/m describes the causal link between force and
acceleration while F = ma does not.  (Acceleration is PHYSICALLY DETERMINED
by acceleration and mass; and physical determination is a necessary -- but
not sufficient -- component of causation.)

I agree with John Clement when we writes, "The real reason for establishing
the causation link between forces and acceleration is ultimately
pedagogical."  The formulas "a = F/m" and "lambda = vT" are thick with
causational meaning (physically speaking, of course, not mathematically
speaking).  To leave out the causation decreases the chance that our
students will understand these relationships in their full, physical
richness.  It also decreases our students' appreciation of the fact that
physics isn't just math -- and that *this* universe isn't just *any*
universe.

- Tucker Hiatt