On 16/11/2013 12:25 PM, leaking pen wrote:
/*However if we consider ourselves using our initial clock
synchronisation, then we know our true accumulated speed because we
can see that the light pulse is only just travelling a bit faster than
us (it takes the pulse a very long time to travel from the back of the
ship to the front) and so we are travelling just a shade slower than
c. Also since any clock tick rate is given by an oscillation time, if
we use the round trip time of a light pulse travelling from the back
of the ship, to the front and back again, as our oscillation tick
time, then we know that our time is ticking a lot slower than it was
before we accelerated. If we divide the known distance (10 light
years) by our speed measured this way (~0.99c or thereabouts) then we
know how many ticks of our (slowed down) clock will happen in that
distance - and it will be 1 years worth. Since our clock seems to us
to be ticking at its normal rate, we will get there in what feels to
us like a year."
*/
Wouldnt the light take the same amount of time per our observation to
travel the ship? Isn't that fact basically defined by relativity?
The question is how do you measure the time? If you measure the round
trip time, then Yes it never changes - because that is our definition of
time. But if we want to measure the *one-way* velocity so that we can
compare it with the other *one-way* velocity, then we need two clocks -
one at each end. If we synchronise these clocks by any means just
before we make the measurement, then Yes - again it takes exactly the
same amount of time to travel in each direction along the length of the
ship. That is guaranteed by our synchronisation technique.
But .... if we keep the initial synchronisation that was established
before we started accelerating, then using this time at each end of the
ship and pulses of light traversing this distance, we can discover our
speed relative to when the clocks were initially synchronised - and this
can indicate a speed in excess of c!
Consider the Eiffel tower experiment. The clock at the top runs faster
and the time difference accumulates until a light pulse sent from the
top when the clock reads say 10am, could arrive at the bottom clock when
it reads 9:59:59 - which is before it left! This same effect occurs
without any gravitational field to mess with time, and only with the
help of acceleration. If you got a reading like this from your space
ship measurement, you would know that you had accelerated such that your
accumulated speed relative to when you synchronised your clocks was
greater than c.
