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 or to the left 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. You must also stop the acceleration before reversing it. 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.
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, it 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 that time.
In this new 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. 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 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 photon in slow motion, it 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 pixel at a time, but those steps are instantaneous, so if you want to see the action, just 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 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 step almost at the same time while the photon travels only half the initial distance, so the speed of the system is almost c. Notice also that the time of the system contracts while its speed increases. At c, the time gets to .5 times the initial time.
Before I reverse the acceleration in that simulation to see how it works, 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 but towards the left, and the system would begin moving to the left. No length contraction that doesn't reverse this time, everything seems to work fine. 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 synchronyzed during their acceleration. If they do, that simple mechanism will explain the null result of the MM experiment without any need for the ad hoc relativistic length contraction.