I appreciate the thorough response and would like to seek clarification of a couple of issues discussed.
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? 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. I admit that I fall into the same confused group as the many physicists about this issue. Is there any special reason that we would synchronize our clocks by taking into account our original 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? 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 normally consider the clock rate that I measure as the correct one. I realize that it can be compensated or synchronized to others by means of formula, but my local world works with my clock. My heartbeat is always proportional to the local time, my laser sends out beams that are tightly locked to atoms that are around me. It does not matter to me that perhaps a long time ago some super nova exploded and sent everything in the local region recoiling at nearly the speed of light as compared to before the event. jwinter says: "...the observer near the star concludes that he is the one moving rapidly toward us and we are stationary. From his perception the Lorentz contraction of the distance between both parties is the same as we located upon the high velocity ship calculated earlier. He therefore determines he and the nearby star will close the gap in much less than 10 years of time passing. This is not correct. This observer has had no reason to re-synchronise his clocks to match the inertial reference of the space ship (because he has experienced no acceleration). So nothing changes for him. It will still take 10 years for the spaceship to travel the distance because it is still 10 light years away." If this is correct then all of the time dilation and distance contraction appears to result from the acceleration of the parties involved. The relative velocity is merely calculated from the acceleration encountered. Since velocity is defined as the integral of the applied acceleration this might seem plausible. Distance is the second integral of acceleration so again any modification to distance by dilation could be traced back to some past acceleration of the subject. It is not clear that this assumption is accurate at this time. I cling to the concept that all motion is relative which has been observed up to the present time. The CMBR might ultimately be a factor that must be considered, but I am not aware of any physics measurement that is based upon some fixed zero velocity assumption required to make it function. All of the ones I have seen allow for relative measurements. Any one else have important insight to share? Dave -----Original Message----- From: jwinter <[email protected]> To: vortex-l <[email protected]> Sent: Fri, Nov 15, 2013 2:00 am Subject: Re: [Vo]:Local Calculated Velocity of Space Ship On 15/11/2013 12:44 AM, David Roberson wrote: ...Since we knew the original distance to the star was 10 light years, it suggests that we should reach it within 1 year our time at our calculated velocity. Is this what should actually occur? Yes this is correct and this is the essence of the twins paradox. There is no limit to your accumulated velocity as measured by yourself using your clocks that are slowing down the faster you go. If you were a photon (or had no rest mass) you could travel the 10 light years in an instant of your time but still take 10 years of observers time. I realize that an observer located near the star and stationary to it would determine our velocity as less than light speed and thus take longer than 10 years to reach his location. Also, the observer would detect that time passes slower on our ship due to our relative velocity. We of course would see his time as passing slower by the same factor during our high velocity trip. Yes. I also understand that we can measure the distance to the star once we reach our stable velocity by using radar signals for example. The signal would leave our ship at a velocity of light relative to us and head toward the star which appears to be significantly closer to us by Lorentz contraction. Our high specification radar beam would reach the star and some would reflect back toward us. The frequency of the reflected beam would be shifted by the velocity of the star relative to our velocity and we could thus accurately calculate the star's relative velocity which would be the same as the velocity the observer sees us moving toward him. 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. The observer near the star has his own radar which he directs towards us. He also determines the same relative velocities by measuring the reflected signal from our ship, so everyone is in agreement that the space between us is closing at a velocity that is somewhat less than light speed. Yes. Since velocity is relative, This is an assumption which cannot be proved. Given a peek out the window at the CMBR, we could determine our velocity with respect to the rest of the matter in the universe - which conceptually at least is an absolute value. ...the observer near the star concludes that he is the one moving rapidly toward us and we are stationary. From his perception the Lorentz contraction of the distance between both parties is the same as we located upon the high velocity ship calculated earlier. He therefore determines he and the nearby star will close the gap in much less than 10 years of time passing. This is not correct. This observer has had no reason to re-synchronise his clocks to match the inertial reference of the space ship (because he has experienced no acceleration). So nothing changes for him. It will still take 10 years for the spaceship to travel the distance because it is still 10 light years away.
