Acceleration by steps

. . .

Red particle's location =
Green particle's location =

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

Mean distance between the particles =
Elapsed time between the particles =

(For slow motion, hold the "Enter" key down after having hit the "One step" button.)

To observe the way the acceleration between the components would affect the acceleration between the particles, I added that feature to my first simulation on acceleration between two particles. As expected, the rate of contraction due to a particle accelerating before the other began to decrease, but after a while, the distance stopped contracting and began stretching instead. In that simulation, the contraction produced at one scale was used to decrease the one produced at the other scale and vice-versa, so that when contraction switched to stretching at both scales, stretching was all of a sudden used to increase stretching. I wished that the rate of contraction would only have gotten smaller and smaller with time, thus getting closer and closer to 1, because this way, reversing the acceleration wouldn't have changed anything, but it didn't, and I didn't find how it could naturally do that, so I decided to switch to another idea I had during the time I was trying this out.

This time, 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. 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. They make an instant step on the screen because it is easier to program, but in reality, they should move at constant speed until the photon strikes them. That's why, if we observe the action in slow motion, the photon seems to be left behind by the red particle, and why it seems to leave the green one before it has made its step. 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 motion, I chose to increase the length of the particles' steps by the same amount the photon is moving, which is one picometer, so if you want to slow the motion, just hit the "enter" key after having hit the "one step" button. The new display shows the total length of the steps, the mean distance between the particles, and the roundtrip time the photon takes between them. Notice that the mean distance and the roundtrip time contract exactly at the same rate, so that the speed at which the system is moving coincides to twice the mean distance between the particles. If we let the simulation run until the two particles almost collide for instance, the contraction gets to .5, so the speed of the system is c. For the two particle to each have the time to make one step forward, thus for two steps, a step that is then almost equal to the distance between them, the photon has to make two roundtrips, a roundtrip that is also almost equal to the distance between the particles.

Before I reverse the acceleration in that simulation to see if contraction will reverse, let's try to imagine it. First, we would have to wait till the green particle begins to make its step away from the red one to shorten it, then the photon would carry that information back to the red one, which would also shorten its step, and so on until the motion would stop on the screen, after what the steps would start to lengthen again and the system would begin moving to the left. This way, any time or length contraction happening to the famous traveling twin would be unobservable once the two twins would be reunited, and they would also be unobservable from a distance the same way they already are with SR. This is exactly what I was expecting when I started making those simulations, but before yelling eureka, I need to apply that mechanism to my simulation with four particles to check if the two orthogonal clocks will still be able to stay synchronized during their acceleration. If they do and if contraction reverses, that simple mechanism will explain the null result of the MM experiment without any need for the ad hoc relativistic length contraction.