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As many of you know, the second is defined 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 caesium-133 atom

This decision was adopted in 1967 by International Committee of Weights and Measures. In that time, computers were in a very low stage, not being able to do much things.

Nowadays, with such technology that we own it's quite easy and very precised to measure those periods of radiations of an atom.

My question is, how they were able to measure those 9,192,631,770 oscillations with a low amount of technology and how they did it? Which processes they've been using?

if someone consider that is not the right Stack Exchange community to post on, tell me please.

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The principle of the cesium beam tube hasn't changed substantially between the 1950s and today. The idea that there was a "low amount of technology" in 1967 isn't true. A good summary of the operation of such a device can be found in the manual of the HP 5062C, published in 1974. In short, a beam of cesium ions is split using a magnet to select only the ones with a certain hyperfine state, then bombarded with microwave energy, then passed through another selector after which the ions hit a detector. The number of ions that pass through the second selector and reach the detector depends on whether or not the microwave frequency corresponds to the energy difference between the relevant hyperfine states, so a simple analog servo is able to maintain the RF frequency equal to the cesium frequency.

From there, measurement is a relatively simple (if tedious) matter of operating the experiment for a long enough period of time, integrating the frequency, and comparing it to the best available pre-atomic standards of time (which were derived from astronomical observations). The only computing power necessary is the ability to add and divide numbers, which would not be a problem for a national standards organization at a time when computers capable of 3D vector coordinate transforms were already flying in outer space.

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What was done is to excite the resonance of that transition, and lock a crystal oscillator to that resonance. Fortunately for 1960's physics, this frequency is right smack in the radio band, so engineers knew how to work with it quite well.

Once you have that, it is a matter of counting oscillations. This needs a scaler (a device that counts oscillations), not a computer. Then the tough part was to count the oscillations over many multiples of what was then the standard second.

The number of oscillations quoted represents about ten times the precision the scientists were able to achieve at that time. This was OK, since the standard second specification before then was a lot less accurate. The point is, if you take your best number and declare the nearest integer to be the definition of the second, then future scientists can (and have) used that definition even after their capabilities exceeded the implied precision.

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