Re: a question on the relativity of lengths and times (need help)
- From: "Androcles" <Androcles@ MyPlace.org>
- Date: Tue, 26 Jul 2005 18:00:11 GMT
"francisco" <paco1955@xxxxxxxxxxxxx> wrote in message
news:h_sFe.998$kk6.909@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| let there be given a stationary rigid rod; and let its length be l as
| measured by a measuring-rod which is also stationary. we now imagine
the
| axis of the rod lying along the axis of x of the stationary system of
| co-ordinates, and that a uniform motion of parallel translation with
| velocity v along the axis of x in the direction of increasing x is
then
| imparted to the rod. we now inquire as to the length of the moving
rod, and
| imagine its length to be ascertained by the following operation:
|
| by means of stationary clocks set up in the stationary system and
| synchronizing, an observer ascertains at what points of the stationary
| system the two ends of a rod to be measured are located at a definite
time.
| the distance between these two points, measured by the measuring-rod,
is a
| length which may be designated "the length of the rod".
|
| how can i, by means of stationary clocks set up in a stationary system
of
| coordinates, physically locate two points on the axis of x of the
stationary
| system (in order to measure the distance between them with a
measuring-rod
| which is also stationary) which correspond (at a definite time) with
the two
| ends of a rigid rod (which is moving at a constant velocity v along
the axis
| of x in the direction of increasing x)?
Several ways, depending on how long the rod is and what accuracy you
require.
Suppose the "rod" is a mile long train, and passes over railway ties.
You place a clock at one railway tie, then roughly a mile down the track
you place a whole bunch of clocks, all reading the same time as the
first,
one per railroad tie. If you can afford it, you can place as many clocks
as there are ties, one per tie. Next you synchronize the clocks. You
pick up
your cell phone and tell your buddy Albert "The time is 12:00 pm, there
is a train due in 5 minutes, make sure all the clocks are set to 12:00"
Now you wait for the train. If it's British Rail, it'll be 15 minutes
late.
When the train reaches your clock, you shout "NOW" into the cell
phone and your buddy looks at which tie the back of the train is over.
He places his left foot on that tie, his right on the next and commences
walking, following after the train, counting ties as he goes.
When he gets to you, the length of the train is the number of railway
ties he counted.
Hmm.... I guess you didn't need to buy all those clocks after all.
Silly Albert. I bet he put you to up to this, huh?
Androcles
.
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