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Re: [Phys-l] Sample relativity problem giving me fits...



In this thread the OP mentioned both time dilation and
length contraction, and several answers have taken the
same approach.

This is not, however, the only approach or even the best
approach.

It is usually the only approach mentioned in general-physics
textbooks, but it is not the only approach available. The
alternative was developed in the 1906--1908 timeframe by
some guys named Poincaré and Minkowski.

Length contraction and time dilation are emphatically *not* a
complete description of special relativity.

The alternative is to focus attention on rulers that do *not*
change their length, and on clocks that do *not* change their
tick-rate. Proper length and proper time. Spacetime.

Geometry and trigonometry in spacetime are not completely the
same as in ordinary 3-space ... but they are not completely
different, either. Just as we do not speak of "the" length
of a ruler being changed by a rotation, we should not speak
of "the" length being changed by a boost.

++ Vectors good.
++ Four-vectors in spacetime good.
++ Proper length good.
++ Proper time good.
++ Spacetime diagrams good.
++ Geometry and trigonometry good.
++ Hyperbolic geometry and trigonometry in spacetime good.
-- Fitzgerald-Lorentz contraction not so good.
-- Time dilation not so good.


This question is practically a poster-child for the disadvantages
of the dilation/contraction approach and the advantages of the
spacetime approach. Draw the spacetime diagram already!



For details on invariant clocks and rulers, see
http://www.av8n.com/physics/odometer.pdf

For a general discussion of the geometry and trigonometry of
spacetime, see
http://www.av8n.com/physics/spacetime-trig.pdf