This is mainly for my own reference and is a summary of the information on the USNO website. See here for a more detailed explanation.
| Time definition | Leap Seconds? | Notes |
|---|---|---|
| Ephemeris Second | --- | 1/86,400 mean solar day^ |
| Atomic Second | --- | 9,192,631,770 periods of Cesium 133 atom |
| UT1 | No | The non-uniform time based on the Earth's rotation |
| TAI (International Atomic Time) | No | Statistical atomic time based on many atomic clocks |
| UTC (Coordinated Universal Time) | Yes | Atomic time. UTC = TAI - dAT^^ |
| GPS (Global Positioning System) | No | Synchronised to UTC, but no leap seconds |
| TT (Terestrial Time)^^^ | No | The time maintained by an atomic clock on the geoid |
^ Note, the exact definition in the paragraph below ^^ dAT, the algebraic sum of leap seconds ^^^ Superseded UT, then ET. Formerly TDT.
The historical definition of the ephemeris second was defined as 1/86,400 of the mean Solar day (the exact definition of the ephemeris second is the fraction 1/31,556,925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time).
Researchers in the 60s found relationship between the frequency of the cesium atom (the standard of time) and the ephemeris second and defined 1 second of atomic time as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom (in zero magnetic field).
The Earth's rotation is decelerating on average at 1.4 ms/day/century due to tidal dissipation, so the time based on the Earth's rotation and atomic time slowly drift apart. Modern studies have indicated that the epoch at which the mean solar day was exactly 86,400 SI seconds was approximately 1820.
Today the mean solar day is 2.772 ms longer than in 1820 ((2018-1820)/100)*1.4 = 2.772 ms
International Atomic Time (TAI) is a statistical atomic time where the time comes from a large population of atomic clocks. The unit is 1 SI second at sea level. The reference frame for TAI is UT1 - TAI ~ 0 on Jan 1st 1958. TAI is NOT adjusted for leap seconds.
Coordinated Universal Time (UTC) IS adjusted by leap seconds such that UT1 - UTC < 0.9 s. Leap seconds tend to be positive and account for the general slowing of the Earth's rotation. TAI above is expressed in terms of UTC as TAI = UTC + dAT.
Global Positioning System (GPS) has an epoch of Jan 6, 1980 and is synchronised to UTC, but WITHOUT the leap second correction.
Terestrial Time (TT) replaced Universal Time (UT) and Ephemeris Time (ET), which were then superseded by Terestrial Dynamic Time (TDT). TDT was then shortened to TT. TT and Barycentric Dynamical Time (TDB) account for relativistic effects. In general relativistic terms TT is a proper time, while TDB is a time coordinate. See here for more details.
TT is a uniform atomic time scale, with units of SI seconds. It is the time maintained by an atomic clock on the geoid. To convert TT to UT1 we must know dT = TT - UT1. dT~32.184 at the origin on TAI, hence we can say TT = TAI + 32.184, in practice we would like this in terms of UTC (instead of TAI), so TT = UTC + dAT + 32.184, where dAT is the algebraic sum of leap seconds, as before.
Given the above, it is CRITICAL to know the types of time being quoted when comparing timestamps and requiring even basic timing precision (e.g. at the 1 s level). For example, if you have a datetime object given as TT and compare it to another time given in UTC, the comparision could be wrong by 10's of seconds if the timescales are not normalised before comparison.