The distinction between these two approaches is artificial.
They both subscribe to the fundamental dicta that
1) physics is conceived, constructed, and tested in the form of assertions
of quantitative relations among humanly defined measurables.
2) special relativity asserts that the four dimensional (spatio-temporal)
interval between two given events is a Lorentz invariant ( numerically the
same for all inertial observers).
3) the spatial and temporal components of these four dimensional intervals
are what we humans define, and measure, as distance and time. These
measurements are what are *real* to us - these are what correspond to our
immediate sensory experiences and our most sophisticated laboratory
measurements.
4) The numerical values of these components (measurable properties of
reality) are observer dependent. The measurements of different inertial
observers are related by the Lorentz transformation of the space-time
coordinates of each event from one observer's frame to another's. No ONE
observer's measurements are any more objective or "true" than another's.
5) There is no other meaning to a time or space interval. These are humanly
invented concepts. There is no supra human "isness" to these properties;
they are undefined outside of the context of a specific human observer.
----- Original Message -----
From: "John Denker" <jsd@AV8N.COM>
To: <PHYS-L@LISTS.NAU.EDU>
Sent: Friday, September 09, 2005 3:32 PM
Subject: relativity: style +- technique
| 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.
|
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