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Re: [Phys-l] light clock relativity experiment



On 04/30/2008 07:58 AM, marx@phy.ilstu.edu wrote:

In many textbooks today, you'll find the light clock thought experiment in which on a high speed
spaceship an astronaut observes a vertical light pulse emitted each second that is reflected from a
mirror to a photo detector. The earth-based observed is shown observing the same light pulse as the
ship moves some distance; and the observer measures a much longer time than one second for the
travel time of the light pulse.

So far so good.

First, he was concerned because the book was showing that the two observers could even see
the light pulse as described in the text. I agreed with him that observers looking from the side would
see no light, since there in none traveling in the direction of their eyes (without some scattering
occurring).

That's a fair objection, but it is possible to repair the experiment to
remove this objection. Let's take "seeing" the light to be a sloppy
metaphor for "observing" or "measuring" the light. We could depend on
scattering some of the light. Or we could have an ensemble of N copies
of the experiment. In each copy we put a camera with a fast-acting
shutter in some place of interest. This messes up the downstream part
of the experiment, but other members of the ensemble will take up the
slack. Considering the ensemble as a whole, we can measure everything
we need to measure.

The key concept here -- as always -- is _spacetime event_. The arrival
of a pulse at time (t) at location (x,y,z) is an _event_ (t,x,y,z) ...
so it's fair game.

Then, he failed to see how the light has a horizontal component, even though the light
source is moving at the speed of the ship. How does light gain the horizontal component of the ship?

I can't say much about this without seeing the diagram in question.
Many diagrams of this kind are wrong, and small changes do not suffice
to repair them. Trying to depict on the /same/ diagram what is seen
by /different/ relativistic observers is possible, but there is AFAIK
only one way it to do it, namely by use of a _spacetime diagram_.
(Except maybe in trivial cases.)

For an example of spacetime diagrams put to good use, see
http://www.av8n.com/physics/twins.htm
Don't overlook the "combined" figure farther down the page:
http://www.av8n.com/physics/twins.htm#fig-twins-combined

Note: If you want to make your own spacetime diagrams, you may find it convenient
to start with prefabricated spacetime graph paper:
http://www.av8n.com/physics/spacetime005blue.pdf
http://www.av8n.com/physics/spacetime005red.pdf
http://www.av8n.com/physics/spacetime005redblue.pdf
Then all you have to do is add the events.


Also:
Situations that involve three spacetime dimensions (horizontal, vertical,
and time) are particularly hard to get right. Light-clock situations
often fall into this category: horizontal motion, vertical separation,
and time. If one of the spatial directions has no motion (only fixed
separation) it simplifies the calculations, but still the diagram is a
pain to draw. Here's an example:
http://www.av8n.com/physics/magnet-relativity.htm#fig-wire-bivector