Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: (d/dt)ACCELERATION



In a message dated 9/14/00 10:52:04 AM Eastern Daylight Time,
jsd@MONMOUTH.COM writes:

<< There are very few things in physics that are truly discontinuous. >>

I would suggest an important distinction here. If we think of "physics" as a
consistent system of models for describing the physical universe, then
"physics" is indeed full of discontinuities, one of which is the
instantaneous change in acceleration that occurs in the basic model of
kinematics which we teach our freshmen. If we refine this, and include the
"jerk", we have a discontinuity in the jerk to deal with. We've seen
persuasive arguments why this too is "unphysical". But I think similar
arguments will occur (albeit referring to a shorter and shorter time scale)
if we try to include a continuous "snap", "crackle" and "pop" in our system.
Perhaps a Fourier transform could be used to handle this infinite series of
problems we run into when we try to remove discontinuities from our system -
but this introduces other "unphysical" phenomena.

Our model is getting more and more clumsy and complex as we pursue our goal
of a complete description of nature, and the value of this endeavor is
dubious. For purposes of analyzing collisions and designing devices, the
jerk is usually as far as we need to go, I would imagine, before we have a
model which has adequate predictive power. And so we keep our discontinuity
and live with it. But we should be humble enough to remember that it is
<our> discontinuity, not Mother Nature's.

What has very few true discontinuities is "nature", not "physics". Compared
to the vast subtlety and complexity of what actually happens when systems
consisting of trillions of trillions of atoms collide, for example, our
models are but crude things at best, but they are a light by which we can see
more clearly the essence of what happens.

The good news is that as our need for more detailed knowledge about nature
grows with the sophistication and miniaturization of technology, the need for
physicists to build more complex models will spring eternal.

Chris Horton