What's the significance of date 0000? Why was this day chosen to be the start of the calendar?
What comes before 0000? I know they say 1BC. But then shouldn't current time be called AD?
Don't know if 0000 is termed as Year Zero
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In the common counting (in history) there is no year zero. Our common calendar begins with year 1 AD preceded by year 1 BC. See https://en.wikipedia.org/wiki/Calendar_era, chapter Dionysian Common Era.
Of course this is inconvenient for astronomy. So astronomers sometimes use year 0, which is the same as 1 BC in the common system, and then use negative numbers for the preceding years. See the same article, chapter Dionysian derived. For other, more convenient systems used in astronomy, see the same article, and the article "Julian Day" in Wikipedia, they place year 0 further in the past, so that all events in the recorded history have positive year numbers.
I suspect that your notation 000 misses one extra zero and what you have in mind is the ISO 8601 calendar. This calendar does have the year 0000 (which corresponds to 1BC), dates prior to that have negative value (say, 2BC = -0001, etc). The date 0000 has no particular significance, according to Christian traditions, this is within a couple of years from the birth of Jesus. From the modern physics viewpoint, a more reasonable choice for "year zero" would be the time of the "big bang". More information you can easily find by googling.