Re: transfer of momentum

["John S. Denker" <jsd@AV8N.COM>]

On 11/18/2003 11:52 PM, Bob Sciamanda wrote:
> I realize that the concept of momentum flow is put to good
> calculational use by mechanical engineers in static stress
> situations.

And by fluid dynamicists, and astrophysicists, and others.

> I might remark that N2 says that it is the NET force on an object
> which is equal to the time rate of change of the object's momentum.
> To associate a momentum rate of change (or flow) with each of several
> forces acting on an object is a bit of a conceptual stretch, although
> of no calculational harm.

If means what I think it means, I must remark that the
"stretch" is not only harmless but mandatory.

In particular, consider a chain.  Not a metaphorical
chain, a real chain with N metal links.  Place it
under tension.  Neglect gravity.  Momentum will flow
into link #1, flow *through* each of the other links,
and flow out of link #N.

The links do not accelerate because they are not
accumulating any NET change in momentum ... but
even so the fact that momentum flowed *through*
the link has great physical significance.  It
represents the tension.

Momentum is a real, conserved quantity.  This is
a big deal.  Each little NtSec of momentum has its
own world-line which is endless.  The momentum-flow
is divergence-free in four dimensions.

> Perhaps one might distinguish, and associate each individual force
> with a "virtual" momentum change (flow) and associate only the NET
> force with the actual momentum flow.

Better, and more simply, associate the NET force
with the NET momentum flow.

There is nothing "virtual" or non-"actual" about
the momentum-flow through a link.

It's just like electricity:  suppose there are
five wires attached to a node.  Some of them
dump in positive current, while some of them
dump in negative current.  Charge will accumulate
on the node if-and-only-if there is a net current
into the node.  But even if there is no such
accumulation, there will be a current flowing
*through* the node and this is of great physical
significance.

It is not a "virtual" current.  It is the plain
old garden-variety current.

Charge is conserved, just like momentum.  The
four-current is divergence-free.

If you can visualize charge flowing in circuits,
you can learn to visualize momentum flow.  The only
change is that whereas electrons may be imagined
as shiny round little scalars, you need to imagine
the momentum-carriers as holding little pointy
arrows, representing the vector character of the
momentum.  The momentum-carriers also have little
feet, representing their direction of motion,
which in general is not parallel to the momentum
they are carrying.