# How is a second measured? And why is it measured that way?

The earth's rotation around the sun isn't exactly 24 hours. It off by some seconds which becomes somewhere around 6 hours per year and 1 day in 4 years(leap year), which brings the question why didn't we modify the measurement of 1 second ever so slightly so as to avoid leap years altogether.

Well how is 1 second measured exactly? Wikipedia says

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 caesium 133 atom. [1]

Well, why is it measured that way? Is there any technical reason like it is easy to measure and can be standardized easily? Or is it really possible to modify the measurement of time?

• Caesium – Abhimanyu Pallavi Sudhir Aug 10 '13 at 17:44
• Just a side comment, not an answer (there are plenty of good answers already). Leap years have nothing to do with "seconds". Leap years exist because the number of days in a year is not an integer. A year is close to 365.25 days long (resulting in a leap year every four years), closer yet to 365.2425 days (the Gregorian calendar). Leap seconds exist because the number of seconds in a day is no longer an integer (specifically, not exactly 86400). Leap years and leap seconds are very distinct concepts. – David Hammen Apr 27 '15 at 15:41
• You appear to be confusing seconds, days and years. The earth's rotation around the sun is rather a lot more than 24 hours. – OrangeDog Mar 14 '16 at 15:24
• Hrm, none of the answers here really talk about why 9,192,631,770 was chosen. There's a whole story behind it. scientificamerican.com/article/how-does-one-arrive-at-th has a good summary and quora.com/… has good detail with links. – Jason C Sep 9 '16 at 16:30

why didn't we modify the measurement of 1 second ever so slightly so as to avoid leap years altogether.

The rotation of earth and the revolution of earth around the sun is not at all synchronized. The Earth really rotates 365.24219647 times during each revolution (at 1992, this ratio changes slightly every year, the tropical year gets roughly a half second shorter each century); so even if we fixed the definition of time to the revolution of earth around sun, we will still need a leap year every 4 years (what we wouldn't need would be leap seconds).

Another reason is because precise time measurement would become incomparable. Since the period of rotation of earth (i.e. tropical year) isn't constant, if we used the definition of second to exactly match the period of revolution, then whenever you want to specify a precise duration of time, you'll also have to specify which year that definition of second is taken from, and you'll need a table that records the length of second of each year.

Is there any technical reason ... ?

Yes, because with the proper equipments anyone, anytime can take a caessium-133 atom, put it under the specified condition and measure the same second, and it won't have yearly change like second from earth rotation/revolution would. As far as we know, the frequency of caessium-133 in the 1978 should be the same as the frequency of another caessium-133 in 2049.

Yes, there is a very good reason why one second, our main unit of time, is defined in this way: precision. The most accurate device we have (or we had) to measure time are atomic clocks; if one second were defined as 0.7 of a heartbeat, the precision and constancy of this "one second" would clearly be poorer. Some of the most accurate and available atomic clocks have been based exactly on this transition of caesium. When an atom emits a photon while dropping to a lower energy level, the frequency of the light is always the same.

In these laser-based clocks, one has a beam that periodically oscillates and the oscillations are truly coherent and accurate and one may literally count the periods. The precise number around 9.19 billion was chosen to agree – within the available accuracy – with the previous definitions of one second that was originally defined as 1/86,400 of an average solar day. These days, our clocks – atomic clocks – are able to measure time more accurately and detect irregularities in the motion of the Earth, too. That's why we sometimes have to insert leap seconds etc., too.

If and when more accurate types of clocks are constructed, the definitions will be updated according to these new clocks.

For everyday purposes, there are exactly 86,400 seconds in a day (midnight to midnight). But, the rotation of the Earth about its axis and the path of the Earth around the Sun aren't exactly either uniform or stable. The rotation of the Earth is very gradually slowing, and there are a number of factors which make "midday" by solar observation sometimes more, sometimes less than 86,400 seconds from the preceding solar "midday". If you average over a solar year, sure, you'll get very close, but over a number of years, you'll see variation.

For scientific and engineering purposes, the fundamental unit for the measurement of time (the second) must have a fixed definition, not one that gets updated every few years just to keep in step with the occurence of solar midday. So, atomic clocks were developed to provide a stable reference against which the second can be defined once and for all (until or unless it is found that current atomic clocks are not a stable enough reference and there is some other measureable phenomenon which is even more stable).

## protected by Qmechanic♦Sep 7 '14 at 17:20

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