Some Idle musings whilst flicking through the Usenet Physics FAQ

Whilst idly thumbing through the Usenet Physics FAQ (http://
www.weburbia1.demon.co.uk/physics (v. Nov2006) and the and Charter
(http://www.weburbia1.demon.co.uk/physics/Administrivia/Charters/
relativity.txt) I came up with the following paradox which is closely
related to "If you go too fast do you become a black hole?" question.

Having read through the "Does mass change with velocity?" section and
seeing the explanation of relativist mass (m-r) and invariant mass
(m-0; sorry, these should contain subscripts as in the FAQ, but do not
transfer to plain text), it appears to me, please correct me if I
misinterpreted this, that any increase in m-r is counter-acted by a
slowing of time, so that F = d/dt(mv) (cf. Planck, Lewis and Tolman) -
am I correct in this thinking?

Anyway, here's the question, which as mentioned, is perilously close
to "If you go too fast do you become a black hole?":

Imagine two system in at motion wrt each other at a constant
relativistic velocity. If each system had a device similar to a
Newton's cradle but with a gap between the suspended balls, would
either system observe the balls in the opposing system change in mass
with a corresponding increase in gravitational attraction that then
manifests itself by moving the balls? Or would this effect be
cancelled out by F = d/dt(mv)? Or am I completely off-track with this
one?

I assume in this that there must be an agreement between any
corresponding solutions for Minkowski and Newtonian/Euclidean
geometries?

Comments, and no doubt abuse, welcome.



SCW

.

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