Is this a truth and its evidence?

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HuaMin
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Hi,
I remember that long long time ago, I got that the time will slow down when one object does accelerate to be in light speed. What is the evidence to prove this?

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Sounds like the theory of relativity, there is a lot of evidence for this. Here is a list of some experimental evidence:

http://en.wikipedia.org/wiki/Tests_of_special_relativity

The phenomenon isn't exactly as you describe, but it sounds like time dilation, where an observer moving relative to a clock will see that the clock ticks slower than an observer at rest relative to the clock. This disagreement between two observers is strange, but it is not a paradox.