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

[John Denker <jsd@av8n.com>]

On 09/06/2010 06:14 AM, treborsci@verizon.net wrote:
> One might say that a vector field (e.g. the electric field E(r,t) ) defines 
> a vector (E) associated with, "located at", (or "bound to") each space-time 
> point.

We all agree that idea of vector fields is a good one.

This does not however shed any light on the "bound vectors" 
issue.  The vectors in a vector field are not "bound" the
way a "bound vector" is bound.

  I misunderstood this point yesterday.  If there is any
  confusion on this point, it's partly my fault.  Sorry!

===============

I am increasingly confident that the terms can be translated 
as follows, translating from terms that are unfamiliar to us 
to terms that are familiar in the math and physics literature:

  "bound vector" --> pair of points
  "free vector"  --> vector
                     i.e. plain honest-to-goodness vector
                     i.e. direction and magnitude only


Given a vector u from A to B, and a vector v from C to D,
we say u=v if and only if they have the same direction and
magnitude.  Commonly u=v even though A does not equal C
and B does not equal D.

Given a pair of points (A,B) I can construct the point A, 
the point B, and the vector from A to B.  The converse
absolutely does not hold.  The fact is, given a vector u I 
cannot reconstruct the points A and B, because there are 
innumerable pairs of points that all give the same vector.