* 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?
On Fri, Nov 15, 2013 at 7:57 PM, <[email protected]> wrote: > 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 to have 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. > >
