Even with purely Newtonian mechanics (i.e., infinite speed of transmission of electrostatic forces) your model should obey conservation of energy. I suspect a simulation artifact -- did you try working out the differential equations symbolically?

I don't say my model does not obey conservation of energy. If you believe it does not, please provide a description of what should really happen between repulsive particles first.

One thing for sure, in an ideal spatial setting, particles will not slow down. Since electromagnetic force has an infinite range (but a finite speed of propagation), I don't see why particles should not accelerate until their relative speed exceeds C, since they do accelerate as soon as they are not restrained anymore. You don't seem to understand the setting.

They will both reach almost c not c/2 (if they a brought together close enough initially)

Can you write down the eom you are using?

Just energy conservation. Potential energy will be transformed to kinetic energy (since potential energy is zero at infinity). Even if thd force would be shortt ranged it would happen like this.

@lalala: essentially, I add to the current velocity of a particle a value that is inversely proportional to the square of the distance of particles. So the acceleration decreases with the distance. Yet the velocity never stops accumulating the acceleration boosts, obviously. I assumed identical mass for all particles.

@lalala: I think my surprise comes from the fact the electric charge could accelerate particles to extremely high energies that did not seem to be taken from the sources.

Don't forget about the huge amount of work you have to do to create the initial configuration. It's not easy to push 2 electrons very close to each other.

BTW, if 2 bodies travel at .5c away from each other in the lab frame, then their relative speed is .8c, not c.

"I cannot see how such energetic particles could emerge from a simple initial containment and still respect energy conservation." Where does this statement come from? The correct and lazy way to calculate this is to calculate the energy you'd need to bring the particles together from infinity (i.e., the potential energy already mentioned), then calculate the speed they'd be going if all of that energy were kinetic -- but that just uses energy conservation, which you seem to want to avoid. There are correct ways to do this that don't involve energy conservation, but they're harder.

@TimWescott: I don't want to avoid anything, actually, I am just trying to get things straight. I suppose phenomena here are reversible and integrating acceleration of particles moving apart correspond to what is needed to contain them in the first place, as PM 2Ring points out. But while it seems intuitive that forcing electrons very close to each other requires a lot of energy, I observe the same, although slower to build up velocity accumulation whatever the initial distance of particles. That is, it is as if in our universe electrons had to be contained in the same volume.(continued)

Gravity, orbitals, probably explain why electrons can be found near each other. Yet, I believe I cannot figure how this potential energy was accumulated in the first place, just like I would not understand why springs would be compressed and not relaxed in their initial state.

@PM 2Ring: thanks for the relativistic correction.

No worries. In atoms, you have a positive nucleus attracting electrons. And in the nucleus itself you have the (residual) strong force (mostly) overcoming the Coulomb repulsion between protons. You can mostly ignore gravity here: the gravitational force between 2 electrons is like 40 orders of magnitude smaller than the electrostatic force, IIRC.

@PM 2Ring: Is it assumed that in the early days of the universe positive nuclei and negative electrons already plugged into each other? Or is it possible a lot of electrons exploded (as a population) to never be found again?

I'm tempted to vote to close because this does not look like mainstream physics.

@allure: you clearly have a problem understanding what Coulomb interaction is. You seem to believe it acts instantaneously.

No comment, and voting to close.

I am flagging your comment, as it does not add anything new.

Great. The only interesting answers are now moved to the junkyard.