Re: [Phys-l] three central misconceptions about relativity

[John Denker <jsd@av8n.com>]

On 10/14/2011 10:34 PM, Hugh Haskell wrote:
> [the students] are simply not ready for the 
> 4-d stuff at this point.

So don't do that then!

Take it two dimensions at a time.  At the level of introductory
special relativity, and a lot of levels beyond that, it suffices 
to understand the tx plane.  That's only two dimensions.

> ... are simply not ready for the 
> 4-d stuff at this point.

That's true, just not relevant.  Forsooth, most professional
physicists have a hard time visualizing relationships in three
dimensions, let alone four.

You can do the experiment:  Ask somebody to consider 90 degrees
of pitch followed by 90 degrees of yaw.  Ask them to describe
the compound rotation as a single rotation:  What is the angle?
What is the plane of rotation?

Again:  For the purposes of introductory special relativity, and
a lot of purposes beyond that, it suffices to understand the tx 
plane.  That's only two dimensions.

  There are some more-advanced topics, e.g. the aberration 
  formula, that are intrinsically higher-dimensional ... but 
  that's beyond the scope of the introductory course ... and 
  attacking such topics with contracted rulers and dilated 
  clocks would be a truly terrible idea.

  Ditto for general relativity:  Correctly visualizing gravitation
  in terms of spacetime curvature necessarily requires more than 
  two dimensions.  It is, however, doable:
    http://www.av8n.com/physics/geodesics.htm#fig-darts
  This is further support for my main point:  Unlearning everything 
  you ever heard about dilated clocks and contracted rulers is a 
  prerequisite for getting anywhere with general relativity.

===================

I take it as axiomatic that no matter what you are doing, the
are wrong ways of doing it.  I will happily stipulate that there
are lots of wrong ways to teach about spacetime ... lots of ways
of making it seem more complicated than it is.

So don't do that then!

I'm beginning to sound like Henny Youngman's doctor, but it's true.
If special relativity looks complicated, paradoxical, and weird, 
you're doing it wrong.  Don't do it that way.