Unix time and leap seconds

The number of seconds per day are fixed with Unix timestamps.

The Unix time number is zero at the Unix epoch, and increases by exactly 86400 per day since the epoch.

So it cannot represent leap seconds. The OS will slow down the clock to accommodate for this. The leap seconds is simply not existent as far a Unix timestamps are concerned.

Unix time is easy to work with, but some timestamps are not real times, and some timestamps are not unique times.

That is, there are some duplicate timestamps representing two different seconds in time, because in unix time the sixtieth second might have to repeat itself (as there can't be a sixty-first second). Theoretically, they could also be gaps in the future because the sixtieth second doesn't have to exist, although no skipping leap seconds have been issued so far.

Rationale for unix time: it's defined so that it's easy to work with. Adding support for leap seconds to the standard libraries is very tricky. For example, you want to represent 1 Jan 2050 in a database. No-one on earth knows how many seconds away that date is in UTC! The date can't be stored as a UTC timestamp, because the IAU doesn't know how many leap seconds we'll have to add in the next decades (they're as good as random). So how can a programmer do date arithmetic when the length of time which will elapse between any two dates in the future isn't know until a year or two before? Unix time is simple: we know the timestamp of 1 Jan 2050 already (namely, 80 years * #of seconds in a year). UTC is extremely hard to work with all year round, whereas unix time is only hard to work with in the instant a leap second occurs.

For what it's worth, I've never met a programmer who agrees with leap seconds. They should clearly be abolished.

There is a lot of discussion here and elsewhere about leap seconds, but it isn't a complicated issue, because it doesn't have anything to do with UTC, or GMT, or UT1, or TAI, or any other time standard. POSIX (Unix) time is, by definition, that which is specified by the IEEE Std 1003.1 "POSIX" standard, available here.

The standard is unambiguous: POSIX time does not include leap seconds.

Coordinated Universal Time (UTC) includes leap seconds. However, in POSIX time (seconds since the Epoch), leap seconds are ignored (not applied) to provide an easy and compatible method of computing time differences. Broken-down POSIX time is therefore not necessarily UTC, despite its appearance.

The standard goes into significant detail unambiguously stating that POSIX time does not include leap seconds, in particular:

It is a practical impossibility to mandate that a conforming implementation must have a fixed relationship to any particular official clock (consider isolated systems, or systems performing "reruns" by setting the clock to some arbitrary time).

Since leap seconds are decided by committee, it is not just a "bad idea" to include leap seconds in POSIX time, it is impossible given that the standard allows for conforming implementations which do not have network access.

Elsewhere in this question @Pacerier has said that POSIX time does include leap seconds, and that each POSIX time may correspond to more than one UTC time. While this is certainly one possible interpretation of a POSIX timestamp, this is by no means specified by the standard. His arguments largely amount to weasel words that do not apply to the standard, which defines POSIX time.

Now, things get complicated. As specified by the standard, POSIX time may not be equivalent to UTC time:

Broken-down POSIX time is therefore not necessarily UTC, despite its appearance.

However, in practice, it is. In order to understand the issue, you have to understand time standards. GMT and UT1 are based on the astronomical position of the Earth in the universe. TAI is based on the actual amount of time that passes in the universe as measured by physical (atomic) reactions. In TAI, each second is an "SI second," which are all exactly the same length. In UTC, each second is an SI second, but leap seconds are added as necessary to readjust the clock back to within .9 seconds of GMT/UT1. The GMT and UT1 time standards are defined by empirical measurements of the Earth's position and movement in the universe, and these empirical measurements cannot through any means (neither scientific theory nor approximation) be predicted. As such, leap seconds are also unpredictable.

Now, the POSIX standard also specifies that the intention is for all POSIX timestamps to be interoperable (mean the same thing) in different implementations. One solution is for everyone to agree that each POSIX second is one SI second, in which case POSIX time is equivalent to TAI (with the specified epoch), and nobody need contact anyone except for their atomic clock. We didn't do that, however, probably because we wanted POSIX timestamps to be UTC timestamps.

Using an apparent loophole in the POSIX standard, implementations intentionally slow down or speed up seconds -- so that POSIX time no longer uses SI seconds -- in order to remain in sync with UTC time. Reading the standard it is clear this was not what was intended, because this cannot be done with isolated systems, which therefore cannot interoperate with other machines (their timestamps, without leap seconds, mean something different for other machines, with leap seconds). Read:

[...] it is important that the interpretation of time names and seconds since the Epoch values be consistent across conforming systems; that is, it is important that all conforming systems interpret "536457599 seconds since the Epoch" as 59 seconds, 59 minutes, 23 hours 31 December 1986, regardless of the accuracy of the system's idea of the current time. The expression is given to ensure a consistent interpretation, not to attempt to specify the calendar. [...] This unspecified second is nominally equal to an International System (SI) second in duration.

The "loophole" allowing this behavior:

Note that as a practical consequence of this, the length of a second as measured by some external standard is not specified.

So, implementations abuse this freedom by intentionally changing it to something which cannot, by definition, be interoperable among isolated or nonparticipating systems. Alternatively, the implementation may simply repeat POSIX times as if no time had passed. See this Unix StackExchange answer for details on all modern implementations.

Phew, that was confusing alright... A real brain teaser!