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Tomorrow time will stop, but don't worry: It will only be for a second. Researchers will add a sliver of time - a leap second - to the world's clocks. Just as leap years keep our calendars lined up with Earth's revolution around the sun, leap seconds adjust for Earth's rotation.
Most of us won't notice the addition. Unless we deal in timescales shorter than a second, or if we use a computer program that crashes because it can't handle the leap second. It's happened before: The 2012 leap second brought down Reddit, Gawker Media, and Mozilla.