Re: [Phys-l] teaching energy +- reference frames

["R. McDermott" <rmcder@gmail.com>]

----- Original Message ----- 
From: "John Denker" <jsd@av8n.com>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Wednesday, October 04, 2006 1:20 PM
Subject: Re: [Phys-l] teaching energy +- reference frames


>  KE requires a frame of reference ... but the frame doesn't matter.
>
> Students should understand that the laws of physics are independent
> of the choice of reference frame.  This is important ... arguably
> about as important as the idea of energy itself.
>
> I like to say that if you get an answer that is frame-dependent, you
> were asking the wrong question ... or at best a not-very-fundamental
> question.  There must be a frame-independent way of restating the
> important part of the question.

To piggyback off of this response (which is kind of where I thought Dan 
MacIsaac would go next), I'm interested in this whole idea of choice of 
frame and the results that derive from the choice:

If I'm reading this correctly, John (or whoever wants to jump in), should we 
expect answers to be frame independent as a general rule for Newtonian 
physics?  Should the calculation of KE be consistent regardless of frame? 
If so, of course, this would pretty much require energy to "reside" in a 
system of particles (since performing the calculation on an object could 
yield a different answer - Dan's example).  But DO we require that?  And 
what of the previous LONG discussion regarding centrifugal force wherein 
this force only appears in SOME frames and not in others?  Wouldn't a demand 
that answers be the same in any frame be tantamount to asking what is the 
answer "really"; much as my asking which are "real" forces?  If answers 
should/must be frame independent, what characteristics are we talking about? 
Forces?  Momentum?  Energy?



> This is a tricky pedagogical problem, because it arises only at
> _intermediate_ levels of sophistication.  The most unsophisticated
> students will just pick a frame -- the lab frame -- and will not be
> concerned with the possibility that "KE requires a frame".  At the
> other extreme, sophisticated students will know how to talk about
> energy in terms that are manifestly invariant w.r.t the choice of
> frame (four vectors and all that).  We can discuss the details if
> anyone is interested.
>
> ========
>
> One very common way to generate frame-dependent and therefore non-
> fundamental questions is to ask for the _components_ of a vector
> in a particular frame.
>
> In my mind, it is very important to distinguish between a vector
> and the components that represent that vector in a particular
> frame.  Similarly it is important to distinguish between an
> operator (e.g. tensor) and the matrix elements that represent
> that operator in a particular basis.
>
> I know this is a sophisticated distinction.  I remember reading
> about it as a youngster and not appreciating it until years later.
>
> The terminology on this point is messed up, which creates further
> barriers to understanding.  For more discussion of this, see
>  http://www.av8n.com/physics/two-vector.pdf
>
> There exist vectors that have geometric and physical reality
> *independent* of the choice of basis ... vectors with tip and
> tail, vectors with direction and magnitude.
>
> It is important to be able to switch back and forth between
> the geometric viewpoint and the component viewpoint.  Neither
> should be allowed to ride roughshod over the other.
>
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