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What's the Unix Time for the UTC second 1985-06-30 23:59:60? My understanding is this physical second is not representable in unix time. How about the UTC seconds before and after that one, 1985-06-30 23:59:59 and 1985-07-01 00:00:00? My understanding is that the first is 489023999, and the second is 489024000. There is one unix second, but two physical seconds between the start of the two times.
> What's the Unix Time for the UTC second 1985-06-30 23:59:60? My understanding is this physical second That's not a physical second, it's a calendar second.
On most days, every unix second corresponds with exactly one UTC second and they all correspond with exactly one physical second, and each one could be measured as the number of vibrations of some particular atom.
On a day with a positive UTC leap second, it's different. At 12:00:00 UTC, it's 12:00:00 unix time, the next day at 12:00:00 UTC, it's also 12:00:00 unix time; 86401 physical seconds have passed, and UTC has counted 86400 calendar seconds, one of which was a leap second, but unix has only counted 86400 seconds.
If you're running leap smearing, all of the unix seconds in that day are a little bit longer than the physical seconds (the exact details depending on your smear technique). If you're using classical techniques, 23:59:59 will be two physical seconds long, and the fractional second will reset to zero as the second physical second starts and count up again.
In contrast to UTC, and Unix Time, TAI always has exactly 86400 physical seconds per day, but after a UTC leap second, both UTC and Unix Time will be offset from TAI by an additional second.