The beauty in the theory of special relativity is that it gives us laws from which we can unite space and time and also energy and mass.
We measure the passage of time in seconds, minutes, hours and years, but this doesn't mean time flows at a constant rate. Just as the water in a river rushes or slows depending on the size of the channel, time flows at different rates in different places. In other words, time is relative.
Time can't exist without space, and space can't exist without time. The two exist as one: the space-time continuum. Any event that occurs in the universe has to involve both space and time.
Time dilation explains why two working clocks will report different times after different accelerations. For example, at the ISS time goes slower, lagging 0.007 seconds behind for every six months. For GPS satellites to work, they must adjust for similar bending of spacetime to coordinate with systems on Earth.
In order to attempt to prove this theory of time dilation, two very accurate atomic clocks were synchronized and one was taken on a high-speed trip on an airplane. When the plane returned, the clock that took the plane ride was slower by exactly the amount Einstein's equations predicted. Thus, a moving clock runs more slowly when viewed by a frame of reference that is not in motion with it. Keep in mind that when the clock returned, it had recorded less time than the ground clock. Once re-united with the ground clock, the slow clock will again record time at the same rate as the ground clock (obviously, it will remain behind by the amount of time it slowed on the trip unless re-synchronized)
Time slows down as you approach the speed of light, if you could find a way to travel faster than the speed of light, could you travel back in time?
In order to travel faster than the speed of light, I assume that you would at some point have to travel at exactly the speed of light. For example, you can not travel 51 miles/hour without having traveled 50 miles/hour at some point, of course, this is providing that you were traveling 50 miles/hour or less to begin with.
Now Special Relativity tells us that at the speed of light, time stops, your length contracts to nothing, and your resistance to acceleration becomes infinite requiring infinite energy (as observed by a frame of reference that is not in motion with the system). These conditions do not sound very conducive to life. We can conclude that time travel into the past, using the concepts of Special Relativity is possible but it also has some severe issues to overcome.
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