Acceleration by steps

Red particle's location
Green particle's location

Step's length of red particle
Step's length of green particle

Speed of the system
Elapsed time between the particles

. . .

This simulation shows two bonded particles moving by offset steps to the right while the information about their location takes time to reach them. For extra-slow motion, hold the "Enter" key down after having hit the "One Step" button. To know how the program works, right click on the screen and select "Source code". I took care to describe each code line so that anybody can easily follow the logic.

In this simulation, the distance between the particles doesn't contract because the first particle accelerates before the second one, but only because it makes its step before the second one, so it is not really a contraction. As usual, the red particle resists to get accelerated until it is informed that the blue one has moved away from it, which explains its mass. As usual, the particles make a step when the photon strikes them, then wait until it is back before making another one. If acceleration is on, the length of the step increases, otherwise it stays the same. If we observe the photon in slow motion, it seems to be left behind by the red particle, and to leave the green one before it has made its step. It is so because I programmed the particles to make instant steps, and I did so because it is easier to program, but in reality, a photon starts to be emitted when an incoming one strikes a particle, and it is being emitted all along the step the particle makes. It is thus shortened by the motion of the red particle towards the green one, and stretched by the motion of the green particle away from the red one. I will try to simulate the whole photon later on, but meanwhile, we may consider that the yellow dot is only its front end.

This time, to accelerate the display, I chose to increase the length of the particles' steps by the same amount the photon is moving, which is one pixel at a time, a huge amount, but those steps are instantaneous, so if you want to see the action, you still need to hit the "enter key" after having hit the "one step" button. The new display shows the total length of the steps for both particles, the speed of the system, and the roundtrip time the photon takes between them. Notice that the speed of the system is equal to the length of the two steps the particles make by the time the photon makes a roundtrip. If we let the simulation run until the two particles almost collide for instance, they make their two steps almost at the same time while the photon is running behind them, so the speed of the system is almost c. Notice also that the internal time of the system contracts while its speed increases. At c, the time gets down to .5 times the rest time.

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