The speed of light is absolutely constant. In effect time will "change" in order to accomodate this.
You start off driving down a raod at 10mph. You look out the window, and see the scenery flying by. To you, you could imagine that YOU are infact stationary, and that it is everything else, which is moving at 10mph.
Now a second car, coming up behind you is travelling at 30mph. You watch it as it passes you. From your perspective, the car appears to pass you at 20mph. This is relative velocity.
Now repeat the experiment. This time in space. Two space ships are side by side. Space ship A takes off at a quarter the speed of light. Very fast indeed! After a very brief pause, Spaceship B switches on his headllamps. The beams off light shoot off after Spaceship A at the speed of light, and eventually catch up and overtake spaceship A.
Now suppose you are in Spaceship A, lookign out your window. At what speed will the light APEAR to pass you at? Well, appling classical mechanics, it would appear that you would see the light pass you at 3/4 the speed of light. Right?
Wrong! Like I said, the speed of light is absolutely constant. You will see the light beam pass you at the full speed of light. How is this possible?
Well, you are looking out your window at or world speeded up. Or, put another way, in your spaceship, time is running slower than for the rest of the world! You could, in a way, travel into the future! Since you are seeing the outside world age more quickly, if you timed yourself and waited say a year, and returned to earth, you would find that you had been gone for longer than a year! Travelled into the future!
This traveling into the future IS NOT just some mathematical conjecture. It is an observable fact! Indeed we have time travellers living among us today! No I'm not from some weird cult: Many astronaughts are fractions of a second younger than they should be!
Also artificial satelites of earth must have their clocks periodically re-callibrated, as the accuracy of their measurements requires extrememly accurate time measurements... this is componded by the fact that they lose minute fractions of a second every year through "time travel".
Now go back to our spaceships experiment. As you move faster and faster, you experience time slower and slower. If you were to extrapoate these results, you could come to some interesting conclusions.
At the speed of light, your experience of time would stop! Time would pass at a rate of...0!
Looking out your window you would see everything happen at once! From your position, there is no time!
Now what would happen if we were to go even faster than the speed of light? Well, again extrapolating our results we would find that our experience of time would become negative. We would travel BACKWARDS in time!
As you can see, these results show why it would be impossible for us to accelerate to the speed of light.
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