. . .
Red's location =
Green's location =
Speed of red particle =
Speed of green particle =
Length contraction ratio =
Time contraction ratio =
This simulation shows two bonded particles being accelerated to the right. For slow motion, hold the "Enter" key down after having hit the "One Step" button. If you want to know how the program works, right click on the screen and select "Source code".
To simulate acceleration, I had to restrict the way the steps made by the red particle towards the blue one during its acceleration were executed: they can only take certain values, as if they were quantized, and the red particle has to wait till the blue one has made its step away from it to increase its speed. To be able to see the progression, I chose .01c steps, which is an important acceleration. The red particle has to be forced to move towards the blue one all the time during acceleration, in such a way that if we would stop forcing it before it is informed that the blue one has moved away, it would immediately get back to its original location. For the system to accelerate, we actually have to be exerting a force on the red particle at the moment the light from the acceleration of the blue particle is back, which is why, when we accelerate it once more after having stopped the acceleration, it waits for the photon to come in before increasing its speed. When acceleration stops, it is the energy of the photons sent by the red particle moving at constant speed that produces the constant speed of the blue particle and vice-versa, in such a way that if light would suddenly shut off, the particles would stop moving. In that world, motion is caused by light and vice-versa.
I'm looking for a mechanism to explain the relativistic contraction, and as we can see, the acceleration of red particle effectively contracts the distance between the two particles. The faster the particles travel, the bigger the contraction and the faster the roundtrip, but with such a contraction rate, time would be contracted instead of dilated. In fact, there is always a distance and a speed for a light clock to display the same round-trip elapsed time than at rest, and we can find it by running the Twins paradox simulation while progressively adjusting the speed in the program until the two clocks show the same elapsed time: it took a while because I had to run the simulation each time I changed the speed, but I could nevertheless get as precise as I wanted. Here is an example for v=.7027c and d'=.5d: Twins even
I made a graph for four specific distances (.125/.25/.5/.8) and the four respective speeds provided by the simulation(.917/.854/.703/.477), and I got what looks like a sinusoidal curve. It is interesting to see that such a possibility exists, because until we find a mechanism for the relativistic contraction, it stays an ad-hoc assumption. If we considered that the vertical arm of the Michelson/Morley interferometer was also contracted for example, we could adjust the two contractions so that the light takes the same time to make the roundtrip in both arms, and we wouldn't need time dilation to explain the null result. That's what the following four particles simulation shows when we stop the acceleration. The two yellow photons moving at 90 degree from one another when the particles are at rest keep on hitting the top-left red particle at the same time when the system is moving: Acceleration with four particles