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Re: [Phys-l] Teaching Special Relativity



On 07/02/2009 06:04 PM, Richard Tarara wrote in part:

.... but really, how are our gen-ed students, with the hard won idea that
momentum is mass x velocity (actually work to convince them that they
instinctually have a great feel for this) supposed to deal with the
observations.

I don't think anybody is asking students to give up the idea
that momentum is mass × velocity. In spacetime, the 4-momentum
is mass × 4-velocity. And you can be sure I mean the invariant
mass (i.e. rest mass) in this expression.

There has been a long discussion of the mass × velocity issue,
based on the utterly false assumption that using the spacetime
approach makes this more complicated. It doesn't! I seems that
people who have never tried the spacetime approach are presuming
it guilty of a crime it did not commit, indeed a crime that never
took place.


While we're on the subject, it strikes me as beyond bizarre that
anyone would ask students to give up the idea that the length of
a ruler is /the/ length of the ruler ... and that the length is
invariant with respect to rotations. The spacetime approach says
the length is invariant under rotations in the XY plane and also
rotations in the XT plane, i.e. boosts, i.e. changes of velocity.

If the component you get by _projecting_ the ruler onto this or
that set of axes is shorter than /the/ length of the ruler, that's
fine. The foreshortening of the projection has got nothing to do
with how the ruler is constructed, and everything to do with the
geometry of the projection.

In contrast, the contraction/dilation approach says that rotation
changes "the" length of the ruler ... not just the length of its
shadow, but "the" length of the ruler itself. It says rulers
can't be trusted, and clocks can't be trusted either. You've got
to be kidding!


Some 2300 years ago, Plato pointed out that the shadow of a thing
is not the same as the thing itself. This has been understood in
simple (!) quantitative terms in the context of relativity since
1908. I think it's time to put contraction, dilation, and velocity-
dependent mass where they belong, in the same bin as conservation
of caloric and phlogiston.