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[Phys-L] proper acceleration, proper time, proper length, spacetime geometry and trigonometry

On 11/02/2014 12:27 PM, Ken Caviness wrote in part:

_proper_ acceleration

In all generality: Very often there is more than one way of
looking at things.
a) The expert will be able to see it in more than one
-- Sometimes the expert will be able to translate back
and forth.
-- Sometimes one viewpoint will be prohibitively inconvenient,
and the expert will have to make a choice.
b) The non-expert will be able to see it in only way.
Different non-experts will have incompatible views.
c) The beginner might not be able to see it at all.

So it is with special relativity.
++ The modern (post-1908) view emphasizes proper time,
proper length, proper acceleration, invariant mass,
four-vectors, spacetime diagrams, geometry, trigonometry,
et cetera.
-- The archaic (pre-1908) view emphasizes dilated time,
contracted length, various notions of velocity-dependent
mass, et cetera.

The archaic viewpoint is not necessarily wrong. In simple
situations, it can be used to obtain correct answers. In
more advanced situations, it can be prohibitively inconvenient.

There are pedagogical and practical reasons for preferring
the modern (post-1908) approach. It is simultaneously easier
to learn, easier to teach, easier to use, and more powerful.
It can be used to explain the archaic viewpoint easily ...
whereas the converse is not so easy.

In the modern approach, you can get along just fine without
any contracted lengths, without any dilated times, without
any notion(s) of velocity-dependent mass, et cetera.

If you rotate a ruler in ordinary Euclidean space, "the"
length of the ruler does not change. The length of the
shadow that the ruler projects on the floor might change,
but that is not "the" length of the ruler.

Similarly, if you boost a ruler in spacetime, the modern
viewpoint says "the" length does not change. That is to
say, the proper length does not change. The /projection/
of the ruler onto the lab frame might change, but that
is not "the" length of the ruler.

Let's be clear: "the" length -- the proper length --
does not undergo Fitzgerald-Lorentz contraction.

Meanwhile, if you rotate an object in such a way that the
shadow should get shorter, but it doesn't, it means the
object must have stretched.

When I wrote up my notes on relativistic acceleration of
an extended object, I used the modern (post-1908) approach
exclusively. I wasn't consciously trying to make a point;
that's just how I think about it. That's how I was trained.
The professor told us quite explicitly: "The point is not
to learn how to do contractions and dilations. The point
is to learn how to /avoid/ doing contractions and dilations."
That's the sort of pronouncement that gets your attention.
I didn't fully understand what he meant, but I could tell
it was important.

However, today I am trying to make a point: the modern
spacetime viewpoint is not the only way of looking at
things, but it has treeeemendous advantages.

I can perfectly well follow the contraction/dilation
approach, but all the time I am saying to myself, wow,
is that clumsy and archaic.

I know there are plenty of introductory-level textbooks,
web sites, and TV "science" shows based on the premise
that the history of relativity began /and ended/ in 1905,
but that is just wrong. Wildly wrong.

The point I am making today is only tangentially connected
to the "acceleration" issue; it applies to all of relativity.
OTOH since the acceleration puzzle is a tremendous magnet for
misconceptions, there are big rewards for a clear, careful
modern approach.

For the next level of detail, see

That stands in contrast to a bunch of dirty laundry that
I would *not* inflict on introductory-level students: