Author: Dave Smith
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Package: PHP Time Dilation
Einsteins theory of Special Relativity is about the relationship between space and time. Time is not the constant it appears to be and is different for the same event depending on how it is observed. This is time dilation.
Lets start out by getting an understanding of observers. I am standing on a road and you are in a car traveling toward me at 50 miles per hour. You pick up a ball getting ready to throw it to me. At this point, I know the ball is already traveling 50 mile per hour because it is in the car with you, however you are still holding the ball, so from your perspective the ball is not moving at all. You have an okay throwing arm, and on average can get a ball moving around 60 miles per hour, which is how fast you now throw this ball. Measured from you perspective, it is traveling at 60 miles per hour, however from my perspective it is coming toward me at 110 miles per hour, the speed it was already traveling plus the speed it was thrown. This is how time (hour) and space (mile) are different depending on who is observing them. In this example, I am the stationary object and you are the moving object and we can see how space and time are relative to the observers frame.
Special relativity also states that light in a vacuum moves at a constant speed, so it never moves faster or slower. Using our previous example, it is now the middle of the night and you are driving your car toward me at 50 miles per hour with the lights off. Suddenly you turn on your headlights and from your perspective the light is traveling away at the speed of light. You would reason that, from my perspective, the light must be traveling toward me at the speed of light plus the speed of the vehicle, however this can not be possible since the speed of light is a constant and can never travel faster. This means that the light is traveling toward me at the speed of light, the same exact speed as you are observing it, so is anything different between our frames of observation? Yes, time changes.
To illustrate this, imagine you have two mirrors facing each other and a light particle is bouncing back and forth between them. The space between the mirrors determines how long it takes the light to get from one surface to the next. Currently you and I are both in the same frame, observing the light bouncing back and forth between the mirrors, straight up and down. Suddenly you start moving while I remain standing still, we are now in two different frames. The mirrors are moving with you, so you continue to observe the light bouncing up and down across the same distance as you did before. I observe the mirrors moving and from my point of view the light bounces off of one and the other has moved so the light has to travel a little bit further to get to it. The faster you and the mirrors are moving, from my frame of observation, the further the light has to travel from one mirror to the next because the one it is bounding to has moved that greater a distance.
This is time dilation and how time can pass normally for you and anyone else observing it from the same frame while passing at a different rate for those observing it from a different frame. The time dilation between you an someone walking away from you is so small that it can hardly be measured, however the faster they move the greater dilation. If they start moving away near the speed of light, the dilation is immediately noticeable and they will observe years starting to pass for you while only minutes have passed for them.
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