i think you should post the math
happyjack , whats the furthest apart the two slits have been and the interference pattern still occurs , does the singularity cause a shockwave or resonance in the em field?
I'll do the easier one!
A is stationary twin, B is twin who travels as speed v (relative to A) to alpha centauri and then at speed v back. Suppose B clock shows elapsed time T during journey from earth to alpha centauri.
LT transforms between A and B clocks.
Since A frame stays constant (fixed newtonian frame) we can use A's transformation of B clock consistenctly through journey to compare times.
Note we can't do the reverse so simply since B's frame changes, which means a correction must be made at the frame change to B's transformation of A's clock.
we know that A clock changes by T/gamma during outward journey as B clock changes by T (the subjective journey time).
gamma = 1/(sqrt(1-v^2/c^2).
Similarly on the return journey. Although the speed and therefore LT is different, the coefficient between A and B times is the same , and there is no change in the B clock time as transformed into A frame during the turnaround.
Therefore total elapsed time on clocks when they meet is:
A: 2T/gamma > 2T
Note I'm assuming here that v is high enough for this effect to be much larger than any GR effects due to gravity well (which would make A clock read slightly slower than B clock).
This proves my statement about proper time of "bent" path being less than proper time of stright path between same two points with timelike separation. (the points here are the B leaving A and B returning to A events).
Best wishes, Tom