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

["RAUBER, JOEL" <JOEL_RAUBER@SDSTATE.EDU>]

> I'm confused.
>
> Displacement is change in position, no?  Has there been any
> disagreement
> about that?

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.

> 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.

> I think that is what JSD is saying.  If so, what is the
> problem?  If not,
> please help me.

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

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.

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.

It isn't the usual definition AFAIK.  See references in previous posts. IMO
the concept of displacement precedes the concept of position, as it is a
more general notion.  BTW in the lexicon I'm espousing both displacement and
position are vector quantities as JD mentions in other strands of this
thread, and location is not a vector quantity.

Side note:

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.  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.