Harry, I am currently supporting the idea that acceleration is the main reason for the clock differences because it would not appear reasonble to expect a difference in clock readings if both observers continued to move at constant velocities. They need to eventually come to rest at the same location to make an accurate comparison. Some might argue that a signal could be sent between then, but I prefer to have a solid legitimate measurement that can not be faked.
My visualization of the system is fairly simple to follow. Initially, both brothers are at rest and can synchronize their watches. In this state, we can assign the location as 0,0,0,0. The 3 space dimensions are zeroed out as well as the clocks synchronized to read zero time. >From this initial state everything concerning their velocity, position and of >course instantaneous acceleration can be totally determined by one >measurement, which is acceleration. This parameter can be measured >relatively easily and also is not influenced by any relative motion of the >remainder of the universe. In other words, the spaceman on the ship knows >exactly what his acceleration is at every point in time. Now, the first integral of acceleration is velocity. The magnitude of the instantaneous velocity as well as its direction can be accurately calculated by the space guy. Next, he can perform a second integration of the acceleration to obtain an accurate reading of his position with respect to the initial coordinate system reference point where his brother is located. This collection of data representing his instantaneous velocity and position can then be used to calculate any time dilation or distance contraction effects that he expects to measure. If the spaceman controls his acceleration carefully, he can pass very close to his brother at a high velocity. If no additional acceleration is applied, then we would expect the balanced time dilation effect that we have been considering a paradox. But keep in mind that there had to be quite a bit of behind the scenes acceleration applied in order to get to this condition. So far I have not pursued an exact calculation of this type of case and therefore can not speak with authority that the numbers add up. Others claim that they have done this and you might wish to locate some of their proofs. If I recall, there was an article in Scientific American a few years ago where they claimed to have done that. Dave -----Original Message----- From: H Veeder <[email protected]> To: vortex-l <[email protected]> Sent: Fri, Feb 21, 2014 2:05 pm Subject: Re: [Vo]:Time Dilation impossibility On Wed, Feb 19, 2014 at 9:50 PM, Eric Walker <[email protected]> wrote: On Wed, Feb 19, 2014 at 3:25 PM, H Veeder <[email protected]> wrote: Imagine two friends with synchronized watches. One friend boards a train and zips away for a time at near c and then gets off and walks back to his friend so that they can compare the time on their watches. Which watch is ahead? Using the principles of SR I can come up with contradictory answers. I'm curious what the two scenarios are. Eric Each friend should see the other's watch tick more slowly according to special relativity. Therefore when they meet up again, both watches should record the same elapsed time, but what happened to the time-dilation effect on the passage time? SR ends in contradiction when watches are compared after the travelling. Dave mentions that acceleration might play role in resolving the contradiction. I have heard that reason too, but it strikes me as hand waving. Even if acceleration has to be factored in, the ratio of time spent accelerating to the time spent travelling at uniform speed near c can be assumed to be arbrarily small so that the acceleration becomes irrelevant. Harry
