Whose clock measures the interval?

Inertial frames move at constant velocity relative to one another. Special relativity assumes the same laws of physics in all inertial frames and the same vacuum light speed for every inertial observer, independent of source motion. These replace the idea of universal simultaneity.

Proper time is measured by a clock present at both events, so the events occur at one location in that clock’s rest frame. A frame in which that clock moves measures a longer interval. Muons reaching Earth provide evidence: their laboratory-frame lifetime exceeds their rest-frame lifetime.