I guess it is that counter-interintuitive loss which is disturbing with the theories of relativity. I felt this disturbance, too.
Thank you Martin, yes that gets to the heart of my objection.
Allow me to press a little farther: I wonder if the calculations for relativity fit together because they are self-referential and constructed with their own set of rules.
For example: it is my understanding that the speed of light has not been measured -- even if we grant that round-trips have been calculated -- the idea that light moves at a consistent speed is only a convention, is this correct?
Yet the assumption of this constancy of the speed of light is at the basis of his subsequent propositions.