I used to have a similar stumbling block to relativity and time. Surely, they must be referring to our experience of time..how could time itself actually pass differently or not be concordant in different frames of reference?
Quote:Since one can not travel faster than light, one might conclude that a human can never travel farther from Earth than 40 light years if the traveller is active between the ages of 20 and 60. One would easily think that a traveller would never be able to reach more than the very few solar systems which exist within the limit of 20–40 light years from the earth. But that would be a mistaken conclusion. Because of time dilation, a hypothetical spaceship can travel thousands of light years during the pilot's 40 active years. If a spaceship could be built that accelerates at a constant 1 , it will, after a little less than a year, be travelling at almost the speed of light as seen from Earth. This is described by:https://en.wikipedia.org/wiki/Special_relativity
where v(t) is the velocity at a time, t, a is the acceleration of 1g and t is the time as measured by people on Earth.[40] Therefore, after 1 year of accelerating at 9.81 m/s2, the spaceship will be travelling at v = 0.77c relative to Earth. Time dilation will increase the travellers life span as seen from the reference frame of the Earth to 2.7 years, but his lifespan measured by a clock travelling with him will not change. During his journey, people on Earth will experience more time than he does. A 5-year round trip for him will take 6½ Earth years and cover a distance of over 6 light-years. A 20-year round trip for him (5 years accelerating, 5 decelerating, twice each) will land him back on Earth having travelled for 335 Earth years and a distance of 331 light years.[41] A full 40-year trip at 1 g will appear on Earth to last 58,000 years and cover a distance of 55,000 light years. A 40-year trip at 1.1 g will take 148,000 Earth years and cover about 140,000 light years. A one-way 28 year (14 years accelerating, 14 decelerating as measured with the astronaut's clock) trip at 1 g acceleration could reach 2,000,000 light-years to the Andromeda Galaxy.[41] This same time dilation is why a muon travelling close to c is observed to travel much further than c times its half-life (when at rest).[42]
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