Short answers, pulled from the story.
Time dilation is the measured difference in elapsed time shown by two clocks that have moved relative to each other or experienced different gravitational environments. A clock moving at high speed ticks more slowly than a stationary clock, and a clock deeper in a gravitational field runs more slowly than one at higher altitude. These are predictions of Einstein's relativity, confirmed repeatedly by experiment.
Yes. In 1941, Rossi and Hall confirmed time dilation by comparing cosmic-ray muon counts at mountaintop and sea-level detectors. In 1971, Hafele and Keating flew caesium atomic clocks around the Earth and measured nanosecond discrepancies matching relativistic predictions. At CERN, muons stored in a ring with a Lorentz factor of 29.327 showed a dilated lifetime of 64.378 microseconds, agreeing with theory to 0.9 plus or minus 0.4 parts per thousand.
The clocks aboard GPS satellites are corrected for both velocity-related and gravitational time dilation so they stay synchronized with clocks on Earth's surface. Without these relativistic corrections, the system's position readings would accumulate errors and drift by kilometres within a single day.
The twin paradox involves one twin staying on Earth while the other travels at high speed on a round trip. Although reciprocity in special relativity might suggest both should age equally, the traveling twin returns younger. The asymmetry arises because the traveler switches between two different inertial frames on the outbound and return legs, while the Earth-bound twin remains in a single inertial frame throughout.
Yes. Clocks at lower altitude, deeper in a gravitational field, run more slowly than clocks at higher altitude. Both observers agree on which clock is slower, making gravitational time dilation non-reciprocal. Richard Feynman calculated that Earth's core is about 2.5 years younger than the crust because of this effect, out of a total planetary age of 4.5 billion years.
Joseph Larmor noted a time-shortening effect for electrons in 1897, and Emil Cohn explicitly related the formula to clock rates in 1904. Albert Einstein showed in 1905 that the effect concerns the nature of time itself and was the first to identify its reciprocity. Hermann Minkowski introduced the concept of proper time in 1907, providing a precise framework for the phenomenon.