Re: Displacement and position (was: displacement and graphs)

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

At 01:33 PM 10/10/01 -0500, RAUBER, JOEL wrote:

> I do not think that JR or JD disagree that Displacement may be calculated by
> calculating change in position.  It is a convenient way to calculate a
> coordinate independent quantity via the intermediate step of subtracting two
> coordinate dependent quantities.

I agree with that as stated.

It _may_ be done this way, not necessarily to the exclusion of other ways.

> > It seems to me that people will naturally assume you mean the
> > displacement
> > relative to the initial (fixed) position, wherever that happens to be.
> >
>
> Sure (I'm not sure of the "fixed" part), but that is not how I interpret
> John's definition, see below.

There is a difference between "fixed" and "initial".

Example:  when discussing thermal phonons in a crystal lattice, the natural
and reasonable reference is the "rest" position of the atoms, even though
(at nonzero temperature) precisely none of the atoms is !initially! at that
position.

> Where I (JR) have a problem with JD is his definition of displacement,
> namely "displacement generally means position relative to some arbitrary
> reference."
>
> It strikes me that what he has defined is the position vector not a general
> displacement, He defined displacement from the origin (the arbitrary
> reference).

I never required the reference to be the origin.  I never said that.  I
never even imagined that.

> This is a less general case of a general displacement. One need
> not establish an arbitrary reference in order to construct a displacement.

The process of constructing the displacement also constructs the reference,
whether you like it or not.

> E.g.
>
> Let's stipulate that it is sufficient for this discussion to consider a two
> dimensional flat space.
>
> Then without indicating a reference point; draw a dot at the initial
> location of a partical, then draw a dot at its final location.  Next take a
> ruler and draw a line between the two dots then draw an arrowhead at the end
> of the line located at the final location of your partical.  You now have
> the displacement vector and there was no need to establish a reference point
> to construct it.

Huh?  The initial position was chosen as the reference point.  That is a
perfectly reasonable choice, well within the envelope of possible
reasonable choices.  But it is still a choice, and it is still a reference,
perfectly in line with everything I've been saying.

> JD is perfectly free to define displacement the way he has!  But he is then
> forced to calculate changes in position in a non-coordinate independent
> manner.

That's not true.  I can't imagine how anything I've said would lead to such
an inference.

> If JD means by "arbitrary reference" the initial position of the object,

That's a subset of what I might choose as the reference.

> If JD means by "arbitrary reference" the initial position of the object, I
> agree with him, but find it ugly and not part of the usual vocabulary, where
> the arbitrary reference point is usually the origin.

Usually?  Says who?  I didn't say that.  It was JR who assumed the
arbitrary reference was the origin;  see his parenthetical remark above.  I
never said any such thing, and in fact gave arguments and examples
countering this notion.

I won't debate the alleged ugliness of something I never said.

> Notice, that this
> requires you to change your arbitrary reference for each succeeding interval
> of motion of your object that you wish to consider.  Sure you can do that in
> a consistant fashion, but UGH.

De gustibus non disputandum.  A glance at the literature will confirm that
using a succession of references is utterly standard procedure:
 -- for sound propagation in crystals in fluids,
 -- for considering incremental displacement,
 -- et cetera.