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?
Maybe you are asking whether, or how, we can get a different time for
the light round trip time - since that is guaranteed by relativity. If
we measure with the one clock, then as per relativity, we always obtain
the same round-trip time = (twice dist between clocks)/c where the
distance remains fixed to the observer travelling alongside but is
shrunk and the clock ticks slower according to a stationary observer.
However with the separate clocks that were synchronised in the
pre-acceleration frame, we have more options (and this has made me
scratch my head a bit!). But the fact is that if a light pulse is sent
from one clock at a particular time, then the time it arrives at the
second clock can be read out by instrument, and the time it arrives back
at the first can also be read out by instrument, and so these times are
a matter of common agreement for both a travelling observer and a
stationary one. What is interesting is how does the stationary observer
see the case where the light pulse arrives at the back of ship before it
leaves from the front of the ship (as determined by the clock
readings). It is clear from symmetry that for an overall trip, clocks
that were initially synchronised will after acceleration and
deceleration remain synchronised - from both travelling and stationary
observers point of view. However while ever the ship is accelerating,
according to the stationary observer its length is shrinking and so the
clock at the rear is travelling faster than the clock at the front and
must tick slower losing time. The opposite effect occurs upon
deceleration and so the clocks get back into sync. It is remarkable
though that this time difference can increase without limit.
Given the separate one-way times of flight of a light pulse as
determined by pre-synchronised clocks, I believe the travelling observer
can duplicate the calculations of the stationary observer for whom the
distance between star systems remains 10 light years, and get the same
answer. That was my point in the first paragraph above, although I
agree that there is something quite wrong with the way I have described it!
