Re: [Phys-l] Relativisitic mass vs Invariant mass

[John Denker <jsd@av8n.com>]

Bob Sciamanda wrote:

> I applaud speculations into possibly subjecting "relativistic" time and length notions to the 
> same treatment which "relativistic mass" has endured.

:-)

> I would like to bring the discussion to bear upon what seems (to me) to be the beginning seed of
> the whole idea of frame dependent kinematical quantities: the relativity (frame dependence) of
> the notion of the simultaneity of events.

> If John, on a moving train, flashes a point light source, the set of simultaneous light arrival
> events (a wavefront) is a sphere centered on John, just as if he were not "moving".  For Mary,
> "stationary" on the platform,  a different set of simultaneous events forms a sphere centered on
> the point of origin of the flash on the "stationary" train track.
>
> Are we to base all of these invariant quantity notions on some invariant simultaneity notion?  It
> seems to me that therein lies the root of everything.

I agree.  Maybe it's not the root of "everything" in the world,
but yes, it's the heart and soul of special relativity.

I address this point in section V of the spacetime-trig paper (i.e.
starting near the bottom of page 13).
  http://www.av8n.com/draft/spacetime-trig.pdf
In equations 15 and 16, the matrix element that makes a boost
different from an ordinary rotation is precisely the element
that describes the breakdown of simultaneity at a distance.

Also: students who have been subjected to the non-geometric approach
to relativity are notoriously likely to remember the FitzGerald-
Lorentz contraction and the time dilation, but forget the breakdown
of simultaneity at a distance.  This is yet one more argument against
the contracted/dilated approach, and in favor of the geometric
approach.  On a spacetime diagram, the breakdown of simultaneity is
easy to see:  one observer's contours of constant t are angled
with respect to the other observer's contours of constant t-prime.

Geometry good.  Spacetime diagrams good.  Invariant time, invariant
distance, and invariant mass good.  Contraction and dilation bad.
Treating space and time on the same footing good.  Treating boosts
and rotations on the same footing good.  Four-vectors good.