Re: [Phys-L] Question on special relativity

[John Denker <jsd@av8n.com>]

On 12/20/2015 09:35 AM, I wrote:

>  Make the analogy to playing pesäpallo.  A ball hitting a moving
>  bat is not at all the same as hitting a moving bat.

I meant to say:
   A ball hitting a stationary bat is not at all the same as hitting
   a moving bat.


One other thing:  The reference mentioned "length contraction".  That
is a relic from the archaic (pre-1908) way of thinking about relativity.
It is a recipe for confusion.  The proper length has a clear physical
significance.  In any given situation, the "contracted" length may or
may not have any significance.  It's like measuring the shadow of a
building.  It does not directly represent the true height.  Sometimes
the shadow allows you to infer the height, but you need additional
information and additional effort.

It is better to formulate the problem in terms of proper length,
proper time, invariant mass, four-vectors, and spacetime diagrams.
As a specific example:  Rather than using length-contraction to
evaluate the angle of the mirror, express things in terms of dot
products of four-vectors, such as the four-velocity of the light
(dot) the four-velocity of the car ... and the four-velocity of
the light (dot) the four-velocity of the mirror.  There's a lot
less that can go wrong this way.

Also I wrote:
>     Draw the spacetime diagram.

I realize that is not super-easy in this case.  The problem involves
two spatial dimensions, so the spacetime diagram is three-dimensional,
which is hard to draw and hard to visualize.

As a warm-up exercise, draw the spacetime diagram for reflection from
a moving mirror at *normal* incidence.  This doesn't answer the original
question, but it's a step in the right direction.

Also ... it may be advantageous to not analyze the spacetime positions
in any great detail, but rather to focus attention on the world-line
of a particular point in space, namely the center of the mirror.  Most
of the interesting physics is in the velocities at that point, immediately
before and after reflection.

Note that figuring out the direction of the incident light in the frame
comoving with the car is nontrivial, because the light is moving in
one direction and the reference frame is moving in another direction.
This is the famous "aberration" phenomenon.  The formulas and diagrams
can be found at:
  https://www.av8n.com/physics/spacetime-welcome.htm#sec-doppler-2sd