Fly near light speed for a year. Come back. Everyone you knew is old or gone. How much younger are you?
Einstein's special relativity says the faster you move through space, the slower you move through time. The time dilation factor is gamma = 1 / sqrt(1 - v²/c²). At 90% the speed of light, one year on your spaceship equals 2.29 years on Earth. At 99.9%, one ship year equals 22 Earth years.
This isn't science fiction. GPS satellites have to correct for relativistic time dilation every single day, or your navigation would be off by kilometers within hours. The satellites' atomic clocks run slightly faster because they're farther from Earth's gravity well, and slightly slower because they're moving fast. The two effects partially cancel, but not completely.
Astronauts on the ISS age about 0.005 seconds less per year than people on Earth. After six months in orbit, they're technically 0.0025 seconds younger. Not enough to notice, but enough to prove Einstein right.
Moving clocks run slow. At 99% the speed of light, 1 year on the ship = ~7 years on Earth. This is real and measured daily on GPS satellites.
Yes — the twin paradox. Travel at near-light speed for a year, return, and decades have passed on Earth. It's one-way travel.
At everyday speeds (1000 km/h), the effect is nanoseconds. You need a significant fraction of light speed to feel it.