Quote:
special relativity has nothing to do with the outcome of the experiment.


Are you joking , I suppose ?
The relativism of time and space has been introduced with the special relativity
The super famous equation :

dT = dT'/SQRT( 1- (v/c)^2))

It has been announced in the year 1905
The general relativity 1915 further expanded the principle of equivalence
assimilating inertial and gravitational forces

The surrounding mass / energy further curve the space /time but the relativism of time / space by itself does not depend only on the presence of mass / energy

"You must study a little bit more , young lad "

Albert(o) Einstein