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

[John Denker <jsd@av8n.com>]

On 10/04/2006 06:22 PM, R. McDermott wrote:

> should we 
> expect answers to be frame independent as a general rule for Newtonian 
> physics?  

It depends:  answers to _what questions_?

If the question involves only physical observables, the answer
should be frame independent.  Example:  Does the red billiard
ball collide with the black billiard ball?   That reeeally ought
to be frame independent.

> Should the calculation of KE be consistent regardless of frame? 

No, for two reasons.

1) If you want to take the geometric view of energy, it is only one
component of the energy-momentum four-vector.
 -- If (big if) you want to just project off the energy component,
  that requires a frame of reference.
 -- The alternative is to maintain the geometric (as opposed to
  component) viewpoint which would involve taking the dot product
  of the object's energy-momentum four-vector with some other
  *physically relevant* four-vector, so as to pick out the energy
  in a physically-relevant i.e. frame-independent fashion.

2) Picking out the KE part of the total energy is an even dodgier
proposition.

>  If answers 
> should/must be frame independent, what characteristics are we talking about? 
> Forces?  Momentum?  Energy?

Forces and momenta, considered as 3-vectors, are well behaved with
respect to rotations in 3D ... but not well behaved w.r.t boosts.  The
corresponding four-vectors are well-behaved w.r.t rotations in 4D,
including boosts.