In my infamous simulation of the twin paradox, i assume a near instantaneous acceleration, with the results being almost identical with the "real" thing sub some extremely small values which you could not see with the naked eye anyway.(adsbygoogle = window.adsbygoogle || []).push({});

But i might want to take the simulation a step further, to give the exact value for slower accelerations.

For the near instantaneous case, as an example.

When two observers A and B are e local to each other, and B accelerates to 0.6c near instantaneously, then an event which B measured to be at x=1ls, t=0s pre-acceleration, post acceleration he will measure to be almost exactly at.

x' = γ(x-vt) = 1.25ls

t' = γ(t-vx/c^{2}) = - 0.75s

Increasing the acceleration, we would get arbitrary close to those two values.

Now i could of course do the acceleration in small steps, accelerating to a given v, then let some time pass. The more steps, the closer i would get to the real value. But that would be too intensive computational and would not really be "perfect". Again i would have to work with just an approximation.

Is there any way to get the exact values for x' and t' for let's say the case of the accelerating observer B measuring the acceleration towards 0.6c to be taking 1 second on his clock?

Is it calculable without having to do it in "steps" where you could get arbitrary close to the results, but never get the exact results?

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# B Need help with the math for a more advanced Simulation

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