I'm not studied in physics to the extent where I could have a detailed
discussion with you, but it would seem that you have the same problem
when objects approach each other. Something even as simple as light
traveling towards a planet. Since time is relevant to the observer
and speed is based on distance over time, time must speed up as the
objects approach each other in order to maintain the speed of light
maximum. They should be able to study this in the colliders I would
think.