Re: Anyone want to have fun with time dilation calculations?
- From: The Ghost In The Machine <ewill@xxxxxxxxxxxxxxxxxxxxxxx>
- Date: Wed, 08 Feb 2006 15:00:17 GMT
In sci.physics, Spaceman
<Realspace@xxxxxxxxxxx>
wrote
on Tue, 7 Feb 2006 16:20:29 -0500
<RdqdnYdeGLGJknTeRVn-oA@xxxxxxxxxxx>:
Please figure supposed actual speeds if using time dilation
if you dare.
:)
0.999c = what speed according to time dilation?
0.7c = what speed according to time dilation?
0.5c = what speed according to time dilation?
0.3c = what speed according to time dilation?
0.1c = what speed accordingto time dilation?
OK, follow along closely.
O and A are the customary two observers. O has a small
steady light (about LED or peanut bulb size, maybe; it
doesn't matter too much). A has a rod, L=1 meter in length.
A knows this rod is 1 meter in length because it's actually
a meter-stick, a common appliance in the more intelligent
countries, presumably. (It's marked off in centimeters and
maybe millimeters; yardsticks in slightly less intelligent
countries are marked off in maybe 1/16th inch increments.
But I digress.)
A also has a small mirror affixed to the end of his rod.
This mirror is mounted at a 45 degree angle so that A
can see the light as the rod passes over it.
A diagram of course in ASCII is problematic, but here's
an attempt:
L
A: v <= T------------------\
O: *
A also has a sophisticated timer unit (T) mounted
at the other end of the rod. This unit will measure
the difference in time between the light passing under
the timer, and the light reflected by the mirror on the
moving rod. The velocity can then easily be measured, once
lightspeed (a time factor of L/c) is taken into account.
We now move the rod over the light at a speed v, any of
the speeds above. The rod will be moving timer end first.
At time t_A = t_O = 0 the timer starts. At time t_A' the timer
detects the lightpulse coming from the mirror and stops.
The velocity is now given by v = L/(t_A' - t_A - L/c), since
in SR lightspeed is c relative to all observers, regardless
of its source. This calculation is unaffected by time dialation.
If O has a similar rod and timer unit (and furthermore both
timers have light sources) his measurement of the velocity
would agree with A's.
--
#191, ewill3@xxxxxxxxxxxxx
It's still legal to go .sigless.
.
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