How long is a second ?

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How long is a second ?

Post by JohnM »

During last nights PopAstro Live I commented about the difference between UTC and GMT seconds.

The following is a brief explanation I wrote last year about the differences that may help clarify the difference. The article approaches the question from the difference between GMT & UTC but explains the difference.

In is frequently stated that Universal Time (UTC) is the same as GMT including many places on the internet . As any Time Lord will tell you there is in fact a subtle difference. The GMT second is derived from the average of the Earth’s rotation over a year hence there are 365 x 24 X 60 x 60 = 31,536,000 GMT seconds in a year (a leap year has an extra 86,400 GMT seconds). As the Earth does not rotate at a constant rate and is slowing down due to friction from the tides amongst other things the GMT second has to get longer to meet the fixed number in a year.
Before we describe UTC we need to understand that atomic clocks are more stable than the Earth’s rotation and as a result the changes in the Earth’s rotation could be measured. As time is fundamental to a lot of physics measurements the variable GMT second was replaced by the TAI (International Atomic Time) second derived from a worldwide network of atomic clocks. This ensures that for instance the speed of light does not change as the GMT second changes. However living on the surface of the Earth we see astronomical phenomena such as sunrise, sunset and transits which depend on the rotation of the Earth and are thus related to GMT.

Since GMT is slowly drifting away from TAI time it would be awkward to use TAI for astronomical use as corrections would need to be added for the times of all astronomical phenomena. As a compromise UTC was created which is kept within 0.9 seconds of GMT. As described above there are a fixed number of variable length GMT seconds in a year so to allow UTC to keep within 0.9 seconds it has a variable number of fixed length seconds in a year. To achieve this one or two leap seconds are added to the last minute of June and or December when required though the definition of UTC allows them to be added to the end of other months if required. Provision is also made for the last minute to have one or two seconds less in the event this is required. Thus the last minute of the UTC month may have 58, 59, 60, 61 or 62 seconds depending on the Earth’s rotation speed.

The requirement for adding or removing seconds at the end of the month is determined by the The International Earth Rotation and Reference System Service (IERS), their web pages at has a lot of interesting information including when the next leap seconds will be added. Leap seconds are normally added at the end of December or June as required. So far only single positive leap seconds have been added. The document ‘Bulletin C’ contains announcements about UTC seconds and also shows that UTC is currently 37 seconds behind TAI. GMT is not defined on this site as its use is deprecated due to poor definition and also it alters depending on where on the Earth it is observed from due to polar wobble. A better defined time similar to GMT is known as UT1 and it is this time difference that is kept to within 0.9 seconds. The data page at ... /eop.html shows the current difference between UT1 & UTC and thus shows the changes in the Earth rotation. The current version is reproduced below. The vertical steps are due to the introduction of leap seconds. Kinks can be seen in the curve particularly around the year 2000, these are annual variations largely due to the freezing and melting of water at the poles. It is unclear why the rate of slowing change around 2000 as evidenced by the change in the slope of the diagonal lines. The part of the graph before 1971 should be ignored as more frequent fractional leap seconds were used.
EOPC04_14_62-NOW_IAU2000A-UT1-UTC.png (22.81 KiB) Viewed 282 times
Computer and other electronic system clocks have problems when leap seconds occur mostly due to lazy programming and a lack of a specified way to allow for leap seconds. As a result when a leap second occurs a lot of computer times will be in error by one second and most will take some time to correct this. Some systems such as Amazon are known to start the correction before the leap second happens and others adjust after the event. You may not think a second difference is important but in high speed automatic trading in international currency exchanges an error in the time can cost billions of pounds. As a panacea to this the International Telecommunications Union who regulate such things are considering a proposal to stop the use of leap seconds. This would solve the problem for some but would in the long term result in UTC and GMT diverging due to the lack of leap seconds. This would then result in interesting challenges to other users. Do you follow UTC which will be shown on your computer and other systems and ignore the fact that that eventually UTC will have diverged from GMT enough that we may be getting up and working at night ? Astronomers including amateur astronomers who need to use GMT or UTC1 to point automated telescopes will need to allow for the difference between UTC & UT1 when setting their telescope time.
To keep this article to a sensible length this is a simplified version of the difference – in reality there are other things that need to be considered such as the changes in TAI due to the impact of gravity and moving clocks as described in Einstein’s theories of relativity. If you want more information contact your local Time Lord !

To check your understanding here are some quiz questions:
1. which year(s) since UTC was introduced in 1971 had the most (UTC) seconds ?
2. how many (UTC) seconds were there in that year ?
3. Which year(s) had the most GMT seconds ?
4. How many (GMT) seconds were there in this/these year(s) ?

A couple of updates since I wrote this article:

1: Something unusual started happening to the Earths Rotational period in mid 2019 - the Earth has started speeding up rather than slowing down. As a result there have been no leap seconds since 2017. If the current increase in speed continues it is possible that a negative leap second will have to be introduced in a few years time. If this happens this will be the first one ever and one can predict that computer systems will have a problem coping with this.

2: I have not covered where the time is measured - with more amateur astronomers carrying out measurements of critically timed events such as exoplanet transits the time that light takes to travel across the solar system - about 16 minutes worst case needs to be taken into account. To do this the observation times are reduced to a fixed point in the centre of mass of the solar system known as the Barycentre.

3: The legal time in the UK is Greenwich Mean Time and in the Summer GMT + 1 defined by the Greenwich Mean Time Act and the Summer Time regulations. What is interesting is that the Act does not define what Greenwich Mean Time is or how it is calculated. As implied above no one keeps GMT any more an approximate equivalent may be UT1 but since there appears to be no legal definition of GMT is is difficult to know.

4: The situation with the proposal to abandon leap seconds is still unclear - there have been other proposals to have a 'leap hour' which moves the problem far enough into the future to make it someone else's problem for computer & telecoms engineers but will become a now problem for both amateur & professional astronomers.

There is more about time conversions in the Astropy time module manual available on line and if you really want to go into details the supplement to the Astronomical Almanac is a good if pricey place to start

John Murrell (Apprentice Time Lord)
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Re: How long is a second ?

Post by Lariliss »

Dear JohnM,

Your facts and data presented is correct and those would be up to the system (humans, populations, operational systems, etc.) whatever they accept.
And it should be adjusted all the time (as you are well spotlighting, that even Earth itself started to spin faster.
As long as we know, that time itself is relational to the observer.
The best precision that we have is atomic clock. GPS system gets aligned with it all the time, otherwise the given data from the GPS will be wrong (due to the satellites are far enough from the Earth to have relativity effect of different time perception).
4G mobile networks are relied on GPS, for instance, when in some areas there is no better way to synchronize the base stations with less than 1 ms precision.

In any system time should be continuously aligned (as regular as it requires).

How long is the second: the best way is to measure by atomic clock.
Number, Letter, Note: Know, Think, Dream.
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