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Re: [Phys-l] Minkowski in the classroom (splinter from "how to prove relativity")



On 08/03/2010 02:47 PM, Jeff Loats wrote:

I am curious if you (or others) know of textbooks for Modern Physics that do
SR using spacetime rather than what seems to be the more standard "time
dilation & length contraction" version.

For an upper-division "Modern Physics" textbook, there are a number
of options. (This is in contrast to the introductory textbook
situation, which is dismal.) For an overview, you might want to
take a look at figure 5 in the paper by Gary Oas:
http://www.arxiv.org/pdf/physics/0504110
Actually the whole paper is worth a look.

If you don't want to buy a whole textbook, and just want a book on
this one topic, there's always Taylor & Wheeler _Spacetime Physics_.

They don't do things exactly the way I would (as of today)
recommend. They spend too much time IMHO making contact with
the old-style length-contraction/time-dilation/variable-mass
approach. I've made this mistake enough times to know it's a
mistake. I recommend sticking tightly to the spacetime approach,
using clocks that keep proper time, rulers that measure proper
length, invariant mass, four-vectors, and spacetime diagrams.

The old-style stuff should be postponed as long as possible,
which is very long indeed, if you ask me.

In any case, if you use Taylor & Wheeler selectively rather than
slavishly, you can get everything you need. Also the book has
some style and some class, which is worth something, IMHO.

I certainly gain a lot of insight from it, and as I contemplate teaching SR
to a new batch of physics sophomores in about a month I am left wondering
why it is that few textbooks have taken that path.

Again: At the upper-division level, the spacetime approach is
/more/ common than the other approach, if the survey by Oas is
to believed. (The problem is at the introductory level.)

Generally it is bad luck and bad manners to speculate on other
people's motivations, so I'm not going to have much to say about
this. But I have two or three theories:

a) Some people are unduly attached to the "historical" approach,
using history to organize and motivate the study of physics. If
length-contraction/time-dilation/variable-mass was good enough
in 1905, it "should" be good enough today, so they say.

But the fact is, it stopped being good enough in 1908. For 102
of the last 105 years, people who know what's what have known
that spacetime is the right way to think about relativity.

Special relativity is the geometry and trigonometry of spacetime.

b) Kissing cousins to the "historical" approach is the "cult of
personality". There are folks out there -- folks who ought to
know better -- who think that evolution is all about Darwin and
relativity is all about Einstein. If length-contraction/time-
dilation/variable-mass was good enough for Einstein, it "should"
be good enough for us, so they say.

But the fact is, Einstein changed his mind! If Einstein had not
adopted the spacetime approach, he never would have been able to
progress from special relativity to general relativity.

And no, there is no good reason why we should follow Einstein's
footsteps, step by step. By way of analogy, we do not need to
learn all about phlogiston before being introduced to modern
ideas of energy and oxygen. To say the same thing another way:
"There is no law that says pedagogy must recapitulate phylogeny."

Especially in an introductory course, students need to learn the
best way of doing things, not the most ancient way.

c) It seems that the folks who write introductory textbooks are
not the people who do relativity for a living. Furthermore, as
far as I can tell, most of them never pursued the subject as far
as general relativity. I reckon that almost anybody who was up to
speed on general relativity would insist on the spacetime approach
from the get-go.

The question is not whether you can "get by" teaching special relativity,
strictly speaking, using the length-contraction/time-dilation/variable-
mass approach. You can. If the only goal is to check off the "special
relativity" box on some checklist, it doesn't matter which approach you
use. But that is the sort of phoning-it-in that gives ivory towers
a bad name. Any student who wants to actually /do/ modern physics as
opposed to merely reading about it will need to unlearn all the length-
contraction/time-dilation/variable-mass stuff.

This is why the teacher who is teaching subject X (or writing a text
about X) needs to know a lot more than just X. It is important to
know about more-advanced topics Y and Z, so that proper decisions
can be made about /how/ to teach X, so as to lay a proper foundation
for what comes later.