. . .
Red's location =
Blue's location =
Speed of red particle =
Speed of blue particle =
Length contraction ratio =
Time contraction ratio =
This simulation shows two bonded particles being accelerated to the right or to the left. For slow motion, hold the "Enter" key down after having hit the "One Step" button. You must also stop the acceleration before reversing it. If you want to know how the program works, right click on the screen and select "Source code".
This time I was surprized: I thought that accelerating a system of two particles alternatively in opposite directions might reverse the contraction and it doesn't. The system goes on contracting whatever the direction of the acceleration. Of course, again, the particles' components must contract at the same rate if their own bonds depend on the speed of light, so such a system could go on contracting forever without an inside observer being able to notice it. But to contract, it needs to be accelerated, and bodies do not accelerate all the time. They do only when they suffer an external collision or an internal explosion. In a gaz for example, molecules meet quite often, but the atoms that are part of those molecules vibrate even more often, and as my simulation shows when we stop the acceleration, they go on executing small steps to move at constant speed, and those steps are made of accelerations followed by decelerations. So even if at our scale, bodies may not seem to be accelerating to move at constant speed, their atoms might be, and as my simulation shows, they might be contracting if the information that holds them together has a limited speed.
When I imagined that synchronization might be a cause for motion and mass a few years ago, I began to think that gravitation was also a synchronization issue, so I started looking for a mechanism. I suspected that constant motion could cause a time shift between scales, so that a body's particles would have to move to stay on sync with another body's particles, but I didn't suspect acceleration to cause contraction because I didn't know how to simulate my small steps to begin with. Now that I can rely on such an effect, gravitation looks easier to explain. If the universe seems to be expanding for instance, it may be because matter is contracting, and if particles have to stay synchronized despite that contraction, they may have to move towards one another even from a large distance, because then, they would be compensating for the redshift produced by the contraction.
I said previously that such a contraction could be unobservable for an inside observer, but we know that expansion produces redshift, so if we invert the process, if we imagine that matter is contracting instead of the galaxies being expanding, we also get a redshift when we observe the galaxies if they are not moving towards one another at the same rate they are contracting. I don't even have to make another simulation to show that contraction may cause gravitation, just to observe the way my four particles' simulation behaves: the two upper particles and the two lower ones represent two horizontal light clocks accelerating side by side, what forces them to move towards one another for their horizontal photon to stay on sync with the vertical photon traveling between them. If we would put those two light clocks away from one another, we would get the same effect: the two clocks would have to move towards one another to stay on sync, which means that if they were held at a constant distance, they would both observe the other clock as red shifted, except maybe if they were orbiting around one another, because then, they would be executing some steps towards one another to compensate for the centrifugal effect the same way they do in the simulation.
The contraction rate that we get from the simulation may be different without the principle being affected though. The two particles' components may be contracting while the distance between the particles contracts for instance, so that for an inside observer, no contraction would be observable, but light would still take less and less time to make its roundtrip, and an outside observer looking at that clock could measure that his clock runs faster. That's quite different from SR though, time dilation becomes time contraction, so the predictions are not the same. The traveling twin would get contracted while he accelerates, and he accelerates both ways, so he would still be contracted at the end, and that looks weird, so something might be wrong with the logic, but not necessarilly. We got used to the weirdness of time dilation, but it is as weird as length contraction, and I still think that Einstein should have rejected it. I will try to make a simulation that accounts for what is going on with light between the particles' components while the particles themselves are accelerated.
Doing that, I must keep in mind that the steps executed by the particles to simply move at constant speed should also produce contraction, because they are made of accelerations followed by decelerations, and that there should not be any lack of synchronism there otherwise constant motion would not be constant, so that there might not be any contraction either. On the other hand, bodies have to accelerate all the time to account for gravitation, and we know that they can't stay synchronised during that time even if that's what they are trying to do otherwise we wouldn't feel a force while standing on a planet (In my simulations, resistance to acceleration manifests itself only when particles get out of sync). Again, it is completely circular to consider that gravitation produces gravitation, but it is no more circular than constant motion producing constant motion, and it is exactly what my small steps do, so let's simulate it and observe the result.