Henry Wilson DSc
2010-02-11 23:33:09 UTC
next to an optical fibre that encircles the planet, WHICH IS NOT ROTATING. Its
circumference is 40 million metres.
//===================C======================// optical fibre around equator
_____________v<-_____p___q_______________________surface (actually curved)
(the surface is drawn flat for convenience. The fibre goes right around the
Paul's clock emits light pulses every 3.33 nanoseconds through both ends of the
fibre. The pulses are labelled according to their emission times and move at c
wrt the fibre and the clock. The linear distance between each pulse is
therefore 1 metre. Each pulse takes ~4E7/3E8 (0.133) seconds to pass through
the fibre in either direction.
Since the planet is not rotating, the pulses returning to C were emitted and
detected by Jerry at point p. At any instant, 40 million pulses are in transit
around the planet in each direction.
Tom observes that the pulses arriving simultaneously from both fibres carry
Using powerful rockets, the planet is sent into rotation with a period of 1
day, (86400 seconds). Its surface rotation speed 'v' wrt the nonrotating frame
is 465 m/s.
In this new situation, the pulses that arrive at C when it is at point p, were
not emitted at that point but rather from an imaginary point q, which is at
rest in the nonR frame and moving away from C at speed -v in C's R frame.
Each pulse takes still takes (0.133) seconds to pass through the fibre in
Therefore the distance p-q = 465.(4/30) metres.....or 62 metres.
Since the distance between pulses is still 1 metre in the C's frame, there are
now 40000062 pulses moving through the fibre in one direction but only 39999938
moving in the other.
"That's odd", says Tom, "now, for some reason, the pulses coming from the left
fiber left Paul's clock 0.266 seconds ahead of those arriving from the right.
Which one should I use to synch my clock?"
"This is great", says Jerry after some deliberation, "now we can build a ring
gyro that will detect absolute rotation, based entirely on Henry Wilson's
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