Re: [Phys-L] speed of light .. foundational issues

[John Denker <jsd@av8n.com>]

On 07/08/2016 03:42 PM, Derek McKenzie wrote:

> Meanwhile though, I still have a serious pedagogical issues with the
> language, and I don't believe I'm just being pedantic.

Fair enough.

> the speed of light, as if that were any different to any other speed.

The speed of light *is* in some ways different from any other speed.

At the very least, you can say that the speed of light is special
for rotations in the xt plane, in the same way that a radian is
special for rotations in the xy plane.

 -- trig functions like sin() and tan() are nice and linear when
  the rotation angle is small compared to 1 radian, but they
  exhibit significant nonlinearity for larger angles.

 -- trig functions like sinh() and tanh() are nice and linear
  when the rotation angle (i.e. the rapidity) is small compared
  to 1, but they exhibit significant nonlinearity for larger
  rapidities.

Actually the speed of light is even more special than that,
because anything moving at the speed of light in one frame
is moving at the speed of light in any other frame.  In 1905
Einstein showed that you can more-or-less derive all of special
relativity starting from this one observation (although that
is IMHO more of a show-off stunt than a reasonable pedagogical
derivation).

> Students already think that strange things happen to you as you approach
> the speed of light,

Well, that's because they've been taught to think about it in a
clumsy, archaic way.  The modern (post-1908) way is much simpler,
namely:
 *) Special relativity is the geometry and trigonometry of
  spacetime ... nothing more and nothing less.
 *) *THE* length of a ruler is its proper length, defined in
  the frame comoving with the ruler.
 *) *THE* timing of a clock is its proper time, defined in 
  the frame comoving with the clock.
 *) *THE* mass is the invariant mass.
 *) The physics does not care what frame (if any) is chosen
  by whatever observers (if any) are involved.
 *) The /projection/ onto this-or-that frame will depend on
  the choice of frame, but that's just the projection;  that's
  not the real physics.  The shadow of a ruler changes if I
  rotate the ruler, but that's just the shadow;  *THE* length
  of the ruler is invariant.  This is not entirely a new idea;
  it has been understood for 2300 years that the thing that is
  most easily observed is not necessarily the best representation
  of the underlying reality.
    https://faculty.washington.edu/smcohen/320/cave.htm

 *) If special relativity seems weird and paradoxical,
  you're doing it wrong.  Most of the predictions of special
  relativity are prosaic and well known.  Mostly special 
  relativity serves to give a unified view of things that
  otherwise would have to be learned separately.
   -- unification of space and time
   -- unification of rotations and boosts
   -- unification of mass, momentum, and energy
   -- unification of electricity and magnetism
   -- et cetera

These ideas are developed in more detail, with diagrams, at
  https://www.av8n.com/physics/spacetime-welcome.htm

Special relativity is the geometry and trigonometry of spacetime
... nothing more and nothing less.