Re: [Phys-l] bound vectors ... or not

[John Denker <jsd@av8n.com>]

On 09/05/2010 02:58 PM, LaMontagne, Bob wrote:

> At first blush it appears that the concept of a bound vector is not
> required for angular momentum, but it is useful for torque.

Lost me there.


1) Since 
  torque = (d/dt) angular momentum
it would seem to me that whatever is required or useful for 
torque is equally required or useful for angular momentum 
... and vice versa.


2) I think we all agree that in many situations when dealing
with a force, we need the idea of direction-and-magnitude of
the force and also the idea of point-of-application .....
That's not the question.

The question is simply whether we want to express those two 
things using one "vector" (i.e. a so-called bound vector) 
or using two vectors (i.e. plain old vectors, aka free 
vectors).

My reading of the math and physics literature going back 50+
years is that vector means free vector exclusively, so that
a so-called "bound vector" is not really a vector at all, but
rather a pair of vectors, like two persons inside a horse 
costume.

I'm sure Banesh Hoffmann didn't write about bound vectors on
a whim. He was not a lightweight; the Einstein-Infeld-Hoffmann 
equation is named after him.  But my hypothesis for today is 
that when it comes to bound vectors his book is out-of-date 
and/or represents a negligible minority view.

I'm not sure, so I offer it as a hypothesis for discussion.

As a subsidiary hypothesis I suggest that many of the things
that people are tempted to call bound vectors can be more
easily and more correctly expressed as _bivectors_.  I'm pretty
sure Banesh Hoffmann was not up to speed on Clifford Algebra.
  http://www.av8n.com/physics/clifford-intro.htm

Maybe it's just me, but I cannot visualize a bound vector.
Every time I try, I get a bivector instead.  I can easily
visualize bivectors!  Maybe somebody could suggest an example 
of something that is a bound vector but not a bivector.