. . . . . . . . . . . . . .Vertical step's length of red particles
Horizontal step's length of red particles
Horizontal step's length of blue particles
Speed of the system
Time contraction ratio
This simulation shows four 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. 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.
This time, the issue was to compute the vertical photon's motion and to move the particles vertically so that the two photons keep on hitting the upper red particle on sync at the end of its step. If the horizontal photon hits first, the distance between the red particles contracts a bit until the two photons hit on sync again, but since the particles must detect the photons, it is impossible to synchronize them pefectly, they are always late, so the simulation must compensate for that otherwise the vertical photon wouldn't head directly on the red particle, but even when it does, the simulation stays qualitative due to the lack of precision. To avoid programming the whole motion of the particles, the vertical photon is programmed to change its direction when it hits the vertical component of the bottom red particle, as if the particle was there. This way, the particles still make instantaneous steps and the photons still appear to lag behind, a feature that allows us to better observe the steps. As we can see, the particles succeed to keep the two photons on sync, which shows again that when bonded particles are free to move to stay on sync with the information they exchange, they can adjust to any kind of motion, so even if those particular steps are wrong, I think that the principle stays right.
Now, how would those steps at the particles'scale influence the MM experiment at our scale? Before simulating it, let's first try to imagine the interferometer with its atoms moving by steps: as the present simulation shows, at their scale, there would be time contraction on the two axis and length contraction on the vertical one, while at our scale, there would still be time dilation on the two axis and length contraction on the horizontal one, so it seems that such a simulation wouldn't give a null result, but let's look at it more closely. The reading we get with an interferometer is a phase shift, which is a difference in the timing of only one photon, and it is precisely what my simulations with particles are about. In a simulation showing the two scales for instance, while the photons would be traveling between the mirrors, they would not change phases, and they would constantly stay on sync with the steps of the mirrors' atoms, so there would be no phase shift at the detector, and there would be no need for the contraction of the horizontal arm to explain the null result. At first sight, that kind of steps seems to work fine, but the devil is in the details, so if you see a mistake somewhere, don't hesitate to tell me. Meanwhile, I'll try to simulate two bonded particles on circular motion with it. My discussion with David Cooper on this idea is here, and if you have any comment or any idea about it, don't hesitate to participate.