HereToLearn
Temporal Novice
What does this have to do with time travel? Imagine an imaginary journey to Andromeda, some 2.2 million light years away. For the time being ignore the problems of propulsion (like they do in all Sci-Fi films!). Firstly, lets assume a Newtonian Universe and we'll ignore the effects of gravity and friction (not much of this in space anyway). The first problem: how fast do we accelerate? Well, if we could accelerate at an infinite rate we could reach an infinite speed instantly and reach our destination in no time at all! Unfortunately, if we were to do so we would experience infinite acceleration forces and be crushed to an infinitesimally thin film instantly. Not much use. The gravitational field of the Earth of 1g (9.81 m/s per second) is however a comfortable acceleration to subject us to, so lets assume the acceleration of our spaceship will be 1g.
So how long to Andromeda at 1g using Newton's theory? We will add the condition that we wish to stop when we get there, if only to turn around and come back. The best time we can make is achieved by accelerating for the first half of the journey and decelerating for the second. The total time for the trip can be calculated to be some 2,065 years. Rather a long time really. Consider the same journey in an Einsteinian Universe. We now have a limited maximum speed (the speed of light), which at 1g is reached in 30,000,000 seconds, or a little under 354 days. After we reach this speed, how much longer will it take to reach Andromeda? The answer is no time at all! For the distance to Andromeda will have shrunk to zero for the spacecraft. However to the people back on Earth a considerable length of time would pass: some 2.2 million years.
So how long to Andromeda at 1g using Newton's theory? We will add the condition that we wish to stop when we get there, if only to turn around and come back. The best time we can make is achieved by accelerating for the first half of the journey and decelerating for the second. The total time for the trip can be calculated to be some 2,065 years. Rather a long time really. Consider the same journey in an Einsteinian Universe. We now have a limited maximum speed (the speed of light), which at 1g is reached in 30,000,000 seconds, or a little under 354 days. After we reach this speed, how much longer will it take to reach Andromeda? The answer is no time at all! For the distance to Andromeda will have shrunk to zero for the spacecraft. However to the people back on Earth a considerable length of time would pass: some 2.2 million years.