Is accessible at the intro level. If you want a more descriptive level
book, take a gander at Ellis & Williams "Flat and Curved Space-Time"
________________________
Joel Rauber
Department of Physics - SDSU
Joel.Rauber@sdstate.edu
605-688-4293
| -----Original Message-----
| From: Forum for Physics Educators
| [mailto:PHYS-L@list1.ucc.nau.edu] On Behalf Of David T. Marx
| Sent: Friday, September 09, 2005 2:44 PM
| To: PHYS-L@LISTS.NAU.EDU
| Subject: Re: relativity: style +- technique
|
| John,
| Is there a book you might recommend for the
| introductory level or even general ed. level that presents SR
| using approach #2?
|
| Thanks,
|
| David Marx
| Illinois State University
|
| John Denker wrote:
| > 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.
| >
| >
| >
| > --
| > No virus found in this incoming message.
| > Checked by AVG Anti-Virus.
| > Version: 7.0.344 / Virus Database: 267.10.19/93 - Release Date:
| > 9/8/2005
| >
|
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