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Albert Einstein didn't think so. His idea was that, theoretically, the closer we come to traveling at the speed of light (186,000 miles per second), the more time would appear to slow down for us from the perspective of someone who, in relation to us, was not moving. He called the slowing of time due to motion time dilation.
What happened when the clock flown around the world returned to the spot where the other clock was? As Einstein had predicted in a general way, the clocks no longer showed the same time—the clock on the jet was behind by a few billionths of a second. Why such a small difference? Well, 600 mph is fast but still just the tiniest fraction of the speed of light. To see any significant differences in time, you'd have to be traveling many millions of miles an hour faster. 
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