A question has been on my mind for a long time and I am hoping that someone among the vortex crowd has found time to give it consideration. Acceleration is one of the measurements that can be relatively easily calculate by folks traveling within their space ship. And, since the calculated velocity obtained by our ship when subjected to a large acceleration can be accurately determined, the following mind experiment should be possible in theory.
First, we are stationary and determine that a nearby star is 10 light years distant. Then, we apply a very large acceleration to our ship and begin to calculate our velocity relative to the stationary starting point. After a modest period of time, we calculate that our super rocket engine which uses anti matter as fuel and attached ship, has reached a calculated velocity of 10 times the speed of light. This number is calculated by integrating the acceleration that we can easily measure in the reference frame around our ship that is also constantly accelerating. 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? 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. 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. 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. Since velocity is relative, 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. I have a strong suspicion that something is not quite correct about this experiment and hope that others would explain where it is wrong. If the concept as presented is accurate then travel above the speed of light would be possible provided an engine of enough power were possible to construct and the occupants could survive very high levels of acceleration that would be required to make such a journey possible within a reasonable time frame. For example, to reach approximately one times the speed of light from start with one "G" acceleration takes a year of time according to my calculations. Thus, it would require at least 10 "G's" applied for over a year to make the above 10 light year journey practical. And, a reverse acceleration at the far end of the journey would be required unless passing the observer were the only requirement. Perhaps this subject has been discussed earlier on vortex, but it might be interesting to bring it back up as a refresher in relativity. It is always interesting to better understand the relationship between time and motion as we ponder the strange behavior of LENR systems. Dave
