Q: If time slows down when you travel at high speeds, then couldn’t you travel across the galaxy within your lifetime by just accelerating continuously?
The far side of the galaxy is about 100,000 lightyears away, so it will always take at least 100,000 years to get there. Leaving a rocket on until it’s moving near the speed of light is totally infeasible. A rocket capable of 1g of acceleration for years is a rocket that can hover just above the ground for years. According to every one else in the galaxy, you’d have been cruising at nearly light speed for the full 100,000 years. The stars pass by slower than light speed, but they’re closer together (in the direction of travel).