Understanding how the rate of time changes The rate at which time passes is relative depending on speed and the gravity as predicted in general relativity. This theory has been tested by scientists by comparing two identical atomic clocks, one on Earth the other on a rocket speeding at escape velocity. The initially synchronised clocks measured different amounts of time when the rocket returned. 
Given the current scientific definition of time rate, 
"The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom",
does this mean that 1) the above definition is only true on the surface of an object with Earths mass and 2) the fundamental properties of sub-atomic particles change on the speeding rocket so the rate at which electrons of the caesium 133 atom oscillate between the two energy levels is different?
 A: The definition is true everywhere, but only as long as you and the caesium atom are in the same place and moving at the same rate.
Suppose two scentists calibrate their clocks on Earth to make sure they measure time at the same rate, then one scientist stays on Earth while the other scientist flies off in a rocket travelling near the speed of light. If the scientists count the number of oscillations of their caesium atom in one second they'll both count 9,192,631,770 (give or take experimental error). However if they count the oscillations of the other caesium atom they will both count less than 9,192,631,770 because they will see time running slowly for the other scientist.
Re your Q2, I wouldn't say:

the fundamental properties of sub-atomic particles change

Firstly the scientist on the rocket would deny there was any change (though they would claim the earth's time had changed). Secondly though the Earth scientist would claim time has changed on the rocket, this change affects everything on the rocket not just the fundamental properties of sub-atomic particles.
