Relativistic acceleration

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Red's location =
Green's location =

Speed of red particle =
Speed of green particle =

Length contraction ratio =
Time dilation ratio =

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This simulation is the same as the previous one, but it accounts for the relativistic phenomenon happening at the components' scale, which is happening at the same time it happens at the particles' one. I first figured that the wrong contraction rate of the first simulation was due ccto not accounting for that scale, and then I looked for a way to slow it down. I tried different things before I realized that I just had to add a delay to the acceleration of the red particle while the photon that is triggering that acceleration is already moving away. This way, the red particle is traveling less distance towards the blue one before it starts accelerating away from it, thus producing less contraction between them. I knew I had to use the relativistic equation in the process, but it took a while before I found the right way. I finally realized that I only had to compare the contraction data the first simulation was producing at the speed the particles were traveling to the data issued from the relativistic equation for the same speed, and to start accelerating the red particle only when the two data were the same. This way, the simulation produces the right length contraction and time dilation rates. The right way to do this would be to simulate acceleration at the components' scale and move the particles accordingly, but those components accelerate millions of times during only one acceleration at the particles scale, so it would slow down the simulation too much. I'm usually reluctant to use an equation instead of simulating the whole process, but this time, I didn't really have the choice. This simulation is meant to show that time dilation and relativistic contration can really happen during acceleration, and that contraction can really be due to the distance the accelerated particle travels towards the other one before that other one accelerates away. If you don't think it is right or if you think you can improve it, please put your comment here.