Re: (d/dt) ACCELERATION

[John Denker <jsd@MONMOUTH.COM>]

At 10:14 AM 9/14/00 -0500, Jack Uretsky wrote:
> Sudden change of velocity implies infinite acceleration, which is infinitely
> destructive and therefore unphysical.  Sudden change of acceleration
> does not violate any physical principle, although it may be difficult
> to achieve in particular cirmumstances.  So the displacement-time graph
> need be only twice differentiable.

I'm skeptical of this argument, for dimensional reasons among others.

Preliminary remark:  One must always be careful with the meaning of
"infinity".  In situations like this, the only safe procedure I know of is
to use it to denote the result of a limiting process, where something grows
without bound as we pass to the limit.

In this way I take Jack's statement to mean that there are physical
processes which in some limit can be extrapolated to give an unboundedly
sudden change in acceleration, i.e. an infinite jerk.

Let us, for now, hypothesize that this is true.

The interesting thing is that the same sort of argument supports the idea
of sudden changes in velocity, i.e. infinite acceleration.

The argument goes like this:  The yield strength of materials has
dimensions of pressure, i.e. force per unit area.  Acceleration, in
contrast, has dimensions of force per unit mass.  If we have something that
has a small mass per unit area, we can give it an arbitrarily large
acceleration without exceeding its yield strength.  This is easy to achieve
if we have something that has very small extent in the direction of the
acceleration vector;  this could be a thin sheet with a pressure applied to
it, or just a small particle.

In particular, the collision of small particles gives an unboundedly large
jerk _and_ an unboundedly large acceleration, in the limit as particle size
goes to zero.

I know of no physical law that allows infinite jerk but forbids infinite
acceleration.  The laws of electromagnetism essentially prohibit infinite
acceleration of charged particles, but have nothing to say about neutral
particles.  As far as I can tell, the laws of gravitational radiation do
not forbid infinite acceleration, although they place severe restrictions
on it.

If somebody knows of a law that clearly forbids infinite acceleration (in
the limit of small particles), please explain.