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

[John Denker <jsd@av8n.com>]

On 10/03/2006 01:21 PM, Dan MacIsaac wrote:

> ....  KE is not in the object but  
> also depends on other objects; velocity is measured relative to a  
> system.  A thrown baseball on a moving train has a different KE in  
> the frame of the train than it does according to an external  
> stationary observer.  Even KE requires a system.

That is, of course, 100% true as stated.  However, it leaves out
something important.  I would have said something like:

  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.

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.