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Hi --
Evidently there are two approaches to thinking -- and teaching -- about
special relativity.
1) One approach is what might be called the "minimalist" approach,
making
as few conceptual changes as possible, using conventional D=3 space as
a framework, plus conventional notions of time, and then explaining how
SR requires corrections to the usual laws of motion. Quantitative
relationships are expressed using Lorentz transformations.
2) At the opposite extreme, there is the approach we might call
"feeling
at home in four dimensions". This emphasizes that four-vectors are
almost
like three-vectors, boosts are almost like rotations, rapidity is
almost
like an angle, et cetera. It makes heavy use of spacetime diagrams.
Quantitative relationships are expressed using four-vectors.
I remember back when I was a sorcerer's apprentice, Charlie Peck told
us "the purpose of this class is not to teach you how to do Lorentz
transformations; the purpose is to teach you how to avoid doing
Lorentz
transformations".
==========
Some people argue that approach (1) is the easiest, and the most
suitable
at the introductory level.
I'm not convinced. As a matter of personal preference, I like to
visualize
things. When I am trying to figure things out, and especially when I
am
trying to explain things to other people, I like to make pictures.
IMHO the spacetime approach is incomparably easier to visualize.
It also has the pedagogical advantage of reinforcing and deepening what
the kids already know about vectors and rotations.
Method (1) starts out trying to make the minimal number of conceptual
changes, but IMHO fails in the larger goal of being easy to learn,
because the few concepts that it does require are weird and
disconnected
from everything else the kids know. Knowledge doesn't "stick" unless
it
is well connected.
I recognize that different people have different tastes and different
pedagogical styles, and I don't want to get into an argument about
style
or taste.
But I think there is more than style involved. I think it is a matter
of
technique. It's like playing the piano: there is such a thing as good
technique. If you learn a bad technique, it is going to hold you back.
Maybe if your only goal is to play Chopsticks, then you don't need to
bother
learning good technique. But from a pedagogical standpoint, I don't
see
any advantage whatsoever in teaching people to play Chopsticks. The
job
market for Chopsticks-players is nil.
I find the pictorial approach so compelling that it is painful to watch
people struggling with the other approach. To me it is obvious that a
pencil does not get shorter if you rotate it, even though it make
"look"
shorter, projectively speaking, if you don't take the angle into
account.
Similarly it is obvious that a clock does not run slower if you boost
it,
even though it make "look" slower, projectively speaking, if you don't
take the rapidity into account.
A clock is a clock. A pencil is a pencil. The shadow of a pencil on
the wall of the cave is just a shadow; it is not a pencil.