Besides Mr Thorpe(Thanks David) I haven’t received any other input. For me this is quite obvious. But before you jump on me please understand that I am only stating that relativistic mass plays a role in limiting “acceleration” in dependent frames. To be dependent some amount of energy has to be exerted over a period of time between the two frames making them dependent and causing an effect of acceleration. And to use it to place a speed limit on the velocity(defined as the delta of distance per time interval) of mass is wrong.
There is nothing wrong with newton’s theory, except at high speeds and masses.
It is measurably wrong by experiments on earth.In this example you are mixing your reference frames, first you are suggesting that the difference between them from a stationary, relative to both, observer. Then you proceed to move the observe from his relatively stationary position to the reference frame of A.the measurements made will be unique to each observer (at different positions and velocities)from the centre of the two particles and stationary to both, the distance each would appear to move would be indeed nearly two times the distance light can travel in one second apart from each other. But light will always be travelling (arbitrarily) left faster than the particle moving left (arbitrarily B) and moving right faster than the particle moving right (particle A). light from particle A would be severely redshifted when it reaches particles B and vice versa. Light is always constant velocity to every observer no matter the velocity of what emits it velocity.in the second case where you shifted from the centre to particle A’s reference frame, you would do the equation i did earlier using the lorentz transform to find out their velocities relative to each other.
giving you a value of 0.9999494975c meaning again, for light to reach one particle from the other, light speed does not need to be broken. The light will merely be redshifted.