Re: Derivatives

[Roger Haar <haar@soliton.physics.arizona.edu>]

Hi,

        If you want something that will appear as a discontinuity in
velocity try a
relatively small steel ball against a relatively large steel plate.
Unless you have
very fast instruments, the bounce will appear instantaneous.

        As  I understand the 4 force of nature, none of then can be
turned on or off
instantly.  For example, electrostatic forces depend on the distance
from charges
and charges can only be moved about not created instantly.  The case is
similar for
gravity and the nuclear forces.  Magnetic forces imply moving charge, if
this charge
is something like an electron in a vacuum then the strength of the
magnetic force varies
with distance.  If we try to start an current in a wire there is some
inductive impedence
and the current does not change instantly.  I think this inplies that on
the macroscopic
scale velocity and probably acceleration are smooth and continuous .

        At the QED level where exchange of bosons is the source of
forces, it might seem
that then there are discreet changes in velocity ( for example, when an
exchange  virtual
photon is absorbed).  But one must always integrate over all of the
exchange processes
and velocity and acceleration along with everything else are a bit fuzzy
at this level.  I think
in quantum mechanics the notion of instantaneous change in velocity is
probably
meaningless, because it cannot be measured.

Thanks
roger haar





Thomas L Wayburn wrote:

> You might describe a model train track that changes from straight to
> an
> arc of a circle suddenly.  I am sure you will get many better
> responses,
> however.  - The Amateur
>
> P.S.   I have read a number of other responses, which I regard as
> quibbling.  Obviously, they are not helpful to achieve your goal.
> But,
> perhaps, you ought to explain that physics is not done in the real
> world
> - rather in a world of ideals that often closely approximates the real
>
> world and always closely enough to be useful.   In the meantime, I
> would
> like to see a really helpful answer to your question!
> *****************************************************
> *******************
> On Tue, 28 Oct 1997 22:08:23 -0500 David Abineri
> <dabineri@dot-net.net>
> writes:
> > I have always pointed out in my Physics classes that a Displacement
> vs
> > Time graph must always be differentiable if it is to represent a
> > "real"
> > situation since one cannot change instantaneously from one velocity
> to
> > another.