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In the scenario that I am interested in, and which I have analyzed, the two rockets (immediately after they are ignited) always have the same constant acceleration, as reported by accelerometers attached to the two rockets.
In 1907, Einstein derived the gravitational time dilation equation (GTD), which says that if two clocks are separated by a fixed distance "L", in a constant gravitational field (with the separation along the direction of the field)
Note that all the new ships actually, which accelerating forward at first, move backwards initially.
That chart is wrong, because the famous length contraction equation (LCE) of special relativity says that an inertial observer (stationary with the two spaceships immediately before their rockets are fired) will conclude that the spaceships get closer together as their speed increases
Quote from: MikeFontenot on 04/07/2023 17:47:16To get a chart that shows the conclusions of INERTIAL OBSERVERS who are stationary wrt the spaceships immediately before the rockets are ignited:I have no beef with the chart in post 6 that shows this. It seems totally accurate.
To get a chart that shows the conclusions of INERTIAL OBSERVERS who are stationary wrt the spaceships immediately before the rockets are ignited:
Your chart says at t=1, d1 is 0.4338, v=.7616, gamma=1.543If you take D at 2 (the top line of the edited picture I posted), it starts at x=2 at time 0.2/gamma is 1.2962 which we add to d1 0.4338 to get 1.73 which is exactly where I drew the data point.
I found your post extremely hard to follow. But I THINK I see a (really bizarre) mistake you're making here:Quote from: Halc on 06/07/2023 23:30:09Your chart says at t=1, d1 is 0.4338, v=.7616, gamma=1.543If you take D at 2 (the top line of the edited picture I posted), it starts at x=2 at time 0.2/gamma is 1.2962 which we add to d1 0.4338 to get 1.73 which is exactly where I drew the data point.In the above, you use the value of gamma at t = 1 to divide the distance between the curves at t = 0 to get the new curve at t = 1. That's completely incoherent!I think any further discourse would waste both our times.