Light travels a certain distance in, say, 20,000 years. How is it possible that an astronaut, traveling slower than light, could go as far in 20 years of her life as light travels in 20,000 years?
Solution 19E It’s possible because time is not an absolute entity as Galileo had taught us, but it’s relative. Time flows with different speeds depending upon how fast you are moving and the gravitational field you are in. but all these things are relative. In your rest frame time moves as usually. It’s the different frame of references for which your time varies. So, if light take 20000 years to travel a distance you too can travel that distance in 20 years. But those 20 years should be counted in your rest frame, not according to any frame situated in earth. As you move with an enormous speed, the people on earth will observe that your clock ticks extremely slower than their clock. But you won’t feel any such thing as in your rest frame the time behaves normally. This is called the proper time. When we say light travelled the distance in 20000 years, the 20000 year we have measured in our frame of reference. In it’s rest frame time has a very complicated form. So if you sit on a photon and travel around the universe, you will not have a definition of time. Time gets infinite for the photon in it’s rest frame. So, in your rest frame you can reach that distance in 20 years.