On 16/11/2013 6:04 AM, David Roberson wrote:
jwinter says:
/*"That is correct. However for us to measure how fast our signal
leaves our ship, we need 2 clocks - Say one at the back of the ship
where the signal is launched from and one at the front of our ship to
time how long it takes to travel the length of the ship. The signal
*only* leaves our ship at the speed of light *if* we have taken care
to re-synchronise our clocks (using the so-called Einstein method)
after reaching a steady speed. If instead we kept the same
synchronisation that we had before we started to accelerate, then we
would measure the same speed that any previously stationary observer
(remote or otherwise) measures (ie the light pulse would travel *much*
slower than c travelling from the back of our ship towards the front,
and *much* faster than c in the reverse direction! (this is not well
known and is a surprise even to many physicists).
The important thing here is that once we have reset our clocks to be
synchronous in our new high speed inertial frame, (or once we consider
ourselves to be at rest), then all distances with respect to our new
coordinate system have changed. In particular the 10 light year
remote star, has now instantly (with the synchronism or the
consideration that we are stationary) become only 1 light year away.
That is why it will only take us one light year to reach it.
Distances in the reverse direction (places behind us) are likewise
increased (instead of decreased) simply by the change of inertial
reference frame.
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."*/
Why would we need two clocks to measure the speed of light leaving our
ship?
Quite simply because that is how we measure the speed of anything
(distance travelled / time taken). When it is relatively slow (like a
100 meter dash) we can signal from end to end with light and only use a
single stopwatch. But if we want to measure the one-way speed of light
itself, then we need 2 clocks - one at each end, and read the time near
where the light pulse is launched, and read the time at the other end
when the pulse arrives. If we try to do it with one clock, then we can
only measure the round trip time. The round trip time of light is always
constant because that is how a clock ticks and is the definition of time
itself.
We were only subjected to a 10 G acceleration for the 1 year drive
period. Does the problem encountered accumulate throughout the entire
time that the acceleration is applied? For example, radiation emitted
by our drive engine at the very beginning of the trip would simply be
measured by all observers as having a velocity of c. Also, those on
board the ship plus every clock on board would determine everything
was normal except for the constant 10 G acceleration due to the drive.
It is normally assumed that the ship is rigidly constructed so that
the front remains a constant distance from the rear of the device.
Pretty much correct - but since it is a one-way measurement that is
"measured by all observers", you have assumed that they all have the
equivalent of two separated clocks which they have synchronised by some
means - and usually by assuming that they are stationary. So observers
moving with respect to each other synchronise their clocks differently -
and that is how they can all read the same speed (when it is obviously
not the same if they all agreed on synchrony!).
If the people on board ship (who are being accelerated) want to consider
themselves as being at rest, then they have a continually changing
synchrony. From the point of view of external unaccelerated observers
they are slowly acquiring a time-shear from the front of the ship to the
back. But the effect can also be measured by the people on board ship.
Clocks near the front tick slightly faster than clocks near the back. If
they transport one of clocks to be next to one that has long been
separated from it (so that their times can be compared directly without
light signalling between) then the one that has spent a while further
forward will be found to be fast in comparison to one which was located
further back.
The same effect happens in a gravitational field (since it is the same
as an acceleration) and has been measured on earth. If one clock is
taken to the top of the Eiffel tower (the front of the ship) then it
runs slightly faster than the one at ground level (the back of the
ship). With a careful measurement an observer at ground level could
measure that "light" from the clock at the top is slightly blue-shifted
(because it has fallen through a gravitational field and picked up
energy) and vice-versa. An observer at the back of the space ship could
measure the same effect - when the "light" from the clock at the front
was emitted it had a particular frequency, but as the back of the ship
accelerates to encounter it, by the time it is encountered it is blue
shifted.
This blue-shift / red-shift effect accumulates for the 1 year drive
period, so that at the end of it the clocks are significantly out of
sync. You can think of the time difference accumulation between the
separated clocks as simply accumulating your acceleration to provide a
velocity reading, which you could otherwise do electronically. When the
clock separation divided by the time difference accumulation is equal to
the speed of light, at that point (if your time had not slowed down) you
would be breaking through the speed of light barrier!
...Is there any special reason that we would synchronize our clocks by
taking into account our original velocity?
If we had two clocks, and synchronised them at the start of the trip
(before we started to accelerate), then whatever process you choose to
do it by assumes our original velocity to be zero. It doesn't matter if
we keep the clocks separated and signal between them through wires or
with light, or if we put them together to synchronise them and separate
them afterwards. All presently available methods take into account our
original velocity and assume that it is zero. If we signal between them
with light, and if we are "really" moving with respect to an absolute
reference frame then our signals are delayed differently in different
directions and we have synchronised them with a built-in time-shear. If
we synchronise them when the are next to each other and then separate
them, then during the motion of separation one clock travels faster
w.r.t the "really" moving absolute reference frame and so ticks slower
for the period that the separation motion occurs and acquires a
time-shear offset from the other. It turns out (as it always does!) that
these methods have the identical effect and if we are "really" moving
during clock synchronisation, we cannot avoid synchronising them with a
time-shear that matches our initial velocity.
Since that could have been any velocity, it is not clear why it is
important. Suppose we happened to be going at a velocity of c/2
relative to some observer. No one can determine that he or we are at
any particular velocity. Was that not one of the rules guiding SR and GR?
It doesn't matter what velocity it is. By synchronising your clocks you
have simply calibrated your present speed to read zero. Comparing the
ongoing synchronisation of separated clocks then simply indicates to
what velocity, and in which direction you have accelerated with respect
to that initial reference frame.
If we adjust our calculations in such a manner as to take into account
what other at rest observers determine, then we leave the local frame
which I am attempting to analyze. Let's remain on board the ship
until we can milk as much knowledge as possible from this location.
We should assume that we have reached a static constant velocity
state once the acceleration period has ended. Then we look at the
world from that point of view to determine our fate. We are aware of
the distance measurement conducted before our acceleration that the
star was 10 light years distant. This information is important and
allows us to calculate the time it should take to cover it at our
assumed velocity. Any distance contraction can now be measured by
sending a radar probe toward the star. The reflected beam yields both
velocity as shown in the Doppler shifted signal as well as distance
calculated by the time delayed return. At this point the ship is
essentially stationary in space and the observer and star are heading
towards us.
Do you see a way that this paradox can be resolved without prior
knowledge of absolute velocities?
I don't actually see a paradox. Unless different observers agree on a
what reference frame to use, then they cannot even agree on the order in
which two events separated in distance happened in time. This is
because the time-shear effect that occurs during synchronisation of
slightly separated clocks, when extended to great distances produces
very different "now"s. Observers on earth will consider that "now" on
the 10 light year distant star is ~9 years different from the "now" that
observers on the space ship contemplate. After all they will be there
in 1 year and so only a years worth of history will pass while they are
travelling. But to earthbound observers 10 years worth of history will
pass while the ship makes the journey.
Supposing that according to observers on earth who are in (very slow)
communication with the remote world (which shares the same reference
frame), a nuclear holocaust occurs 5 years after the ship departs on its
journey. According to the travellers who have just started their trip
and just reached top speed, when they arrive they will find that it
happened 5 years ago. So in their time-sheared frame of reference at
the start of the trip the holocaust had already occurred 4 years ago
before they left earth! So the travellers in their travelling reference
frame say that the holocaust preceded their departure by 4 years,
whereas the earthbound observers say that the departure preceded the
holocaust by 5 years. Can they both be right? According to Einstein's
relativity they are both as right as each other because there is no
preferred reference frame.
Here is an interesting question. Supposing one of the travellers had a
dearly beloved relative on the distant planet who dies in the
holocaust. And supposing, as is so often reported as happening on
earth, appears in the traveller's bedroom momentarily after death. At
what point before or during the trip should the apparition occur? If
you want that this occurrence should be almost "immediate" regardless of
distance then you need tohave a preferred universal reference frame -
such as the CMBR. Then all can agree on simultaneity, and instantaneous
mental telepathy and suchlike over large distances become non-problematic.
