Re: [Phys-l] Relativistic elevator

[John Denker <jsd@av8n.com>]

On 03/25/2008 08:46 AM, Savinainen Antti wrote:

> there are three figures regarding a relativistic elevator & the
> equivalence principle in Strobel's Astronomy Notes:
>
> <http://www.astronomynotes.com/relativity/s3.htm> (Scroll down)


To answer a question that wasn't explicitly asked:  Those figures
are hard to interpret -- and possibly very misleading -- because 
they are drawn partly in the lab frame (the guy holding the 
flashlight) and partly in the elevator frame (the guy riding 
the elevator).  In the middle figure, the sloping beam is *not* 
what the lab-frame guy would see.

Actually, using an ordinary flashlight, the figure doesn't show
what the elevator guy would see, either.  He would need to take
a snapshot of the flashlight beam, and that is very tricky to
do.  There would be significant "breakdown of simultaneity at
a distance" just considering the distance across the elevator
cabin.  This would be significant because the beam is moving so
fast.  The snapshot process in the elevator frame would be
significantly different from the snapshot process in the lab 
frame.

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

There *are* ways of depicting things in two different reference
frames without such inconsistencies:

A) You can put together a flipbook as in
   http://www.av8n.com/physics/img48/relativity-flipbook.png

Here we don't have a continuous flashlight beam, but rather 
one pulse of light, a wavepacket represented by the round 
green blob traveling from left to right.  You can verify that 
in the lab frame, the wavepacket moves strictly horizontally
across the frame, i.e. it is always at the same altitude as
the flashlight.

Meanwhile you can verify that relative to the elevator frame,
the wavepacket moves from upper left to lower right.

You can, if you want, cut out the four sub-diagrams and staple
them together to make a flipbook.  Then flipping through the
book uses time to represent time (appropriately scaled down).

There is a fundamental principle at work here, a principle
that will keep you out of trouble in this example and in a
thousand others:  Focus attention on *events*.  In relativity,
an /event/ has a definite location in spacetime.  It can
therefore be represented (in any given frame) by definite
values of t, x, y, and z.

  By way of contrast, the flashlight beam is not an event,
  because it has huge extent in the x direction, and extent
  in the t direction as well.  This makes the beam incomparably
  harder to analyze than the wavepacket.  In each panel in
  the flipbook, the wavepacket has a definite position in
  spacetime, i.e. definite values of t, x, y, and z.

Focus attention on *events* !!!!!!

=====

B) You could also draw a spacetime diagram.  Usually such diagrams
have only two axes (x and t), which takes some of the fun out of
it.  Note that the elevator diagram has three dimensions (horizontal,
vertical, and time) ... so it is not easy to directly represent the 
main idea, namely the spatial slope of the beam in the elevator frame.
There are ways to get around this, perhaps using two spacetime diagrams
(x versus t and y versus t).

The advantage is that spacetime diagrams allow you to see things
(and quantify things) using multiple reference frames at the same
time, such that you can switch back and forth and see the relationship
between the various frames.

The disadvantage is that it it's not as visually appealing, not as
cute as a cartoon of the elevator.