Defining the second by an alien civilization

Question

(The above question could be phrased better, so feel free to suggest.)

Like many, I was imprecisely told that the second is 9192631770 oscillations of caesium valence electron (or smth along those lines). I was under the impression that the electron makes that many transitions in a second, meaning that many pulses of light are shot out every second... which turns out to be wrong(?).

I recently got to know that the number is actually the frequency of EM wave that the caesium atom emits as the electron transitions back down. In that case, would I be correct to infer that a single pulse is read by our detector and the frequency is used in the $f=n/t$ formula to get 1 second? Or is there something else?

My confusion arises from the fact that this frequency just 'happened' to be precisely the same as our previous definition/precision of the second (quartz frequency, right?) and if applied to a extraterrestrial civilizations, would be unusable... right?

For instance, let's say some alien civilization (similar to us) went through the evolution of timekeeping from sundials, to pendulum clocks, mechanical clocks, quartz clocks and finally atomic clocks. And their planetary day is, like, 10% slower than us. If one uses the definition "1 second is 1/(24*3600)th of the average length of a day" their 1 second is actually 1/0.9 of our 1 second (But of course 'they' wouldn't know that).

When it comes to reaching the precision of quartz, it's relatively easy to calibrate the crystal with gold bits to arrive at 32768 osc per alien-second. Even though the number is same as ours, it's just that the calibration has made the oscillations 'slower'.

From my initial misconception, I was under the impression that if this civilization were to develop atomic clocks, all they would have to do is read the number of pulses given off by caesium within the time for 1 a-second from their quartz, and easily arrive at the value of 10,214,035,300 (pulses per a-second). But now with my new inference, that doesn't seem possible at all.

How would such a civilization deal with not being able to use (this transition frequency of) caesium? Simplest answer sounds like using a different material, but how many materials even are there that satisfies all the conditions that caesium does?

On the flip side, if my current inference is wrong, can someone give me a step by step breakdown of how the atomic clocks work? (I know as much as the video by Dom Burgess has shown)

Answer 1

First, neither of your guesses about what is read by a cesium fountain clock are correct. The second guess is much closer though.

The cesium (I'm American, hence American English) fountain clock essentially has a microwave generator that is always outputting a frequency of $9,192,631,770\text{ Hz}$. This frequency is the optimal frequency for exciting a transition from one quantum energy level to another in cesium. Therefore, to prevent the microwave generator from drifting (let's say the temperature of the electronics increases slightly in the day and the frequency changes slightly), the clock routinely checks that the microwaves can excite the quantum state change in cesium. If the frequency of the microwaves drifts slightly, we will observe a change in the number of cesium atoms that we excite, and we will know to adjust the frequency back up or down.

[I'm ignoring the expert-level discussion about how the clock actually uses Ramsay interferometry. But if you want a fuller understanding of the process, read that Wikipedia page]

(1) We don't use the frequency with which excited Cesium atoms emit photons because this is very rare. Much, much slower than $9\text{ GHz}$. Spontaneous emission of photons, first of all, only comes from atoms that were previously excited; its not like all atoms are constantly emitting light. And also this phenomenon becomes slower with lower frequencies. It's much more of a concern with optical or ultraviolet frequencies of light, while the cesium frequency is relatively low.

(2) We don't use the frequency of photons that cesium emits for several reasons. First, as mentioned before it's actually very uncommon for Cesium atoms to emit photons in the Cesium fountain clock. The photons would also be very hard to detect, and it would be even harder to measure their energy/frequency. Second, a single photon, unlike a continuous microwave signal, actually doesn't have a well-defined frequency. It has a range of frequencies which is limited by quantum mechanics. We have the photon-frequency-uncertainty relation $\Delta t\Delta f\geq 2\pi$ (meaning the uncertainty in the emission time, given by the decay rate of the excited state, times the uncertainty in the frequency, is greater than $2\pi$). We can't abide having a fundamental limit to the precision of our clock.

No, this frequency didn't just happen to obey our previous definition of the second. The arbitrary-looking number $9,192,631,770$ was chosen so that the new definition of the second was as close as possible to the old definition (based on the Earth's orbit), to within how accurately the old definition could be measured. The whole point of changing the definition was that the cesium transition frequency could be measured a lot more precisely. If the original definition of the second had been... let's say $1/100000$ of a day instead of $1/86400$ of a day, we easily could have made the new definition of the second $7,942,433,385$ divided by the frequency that excites cesium atoms, and the transition frequency would be called $7,942,433,385\text{ Hz}$ instead of $9,192,631,770\text{ Hz}$.

Answer 2

In the SI system, frequency is measured in Hz. Radiation produced by the transition between the two hyperfine ground states of cesium has a frequency of 9192631770 Hz, by definition. This number was chosen to correspond to the previous meaning of "second", since Hz in the inverse of second.

In other words, if you want to define a different time unit, you can simply count the number of wavelengths that pass by a point in that time and define a new unit of frequency accordingly. In your example, if radiation from cesium is simply defined to have a frequency of 0.9 X 9192631770 Alien-Hertz, then an Alien-second would be equivalent to 0.9 seconds.

Answer 3

An alien civilisation would not define the second

All units are totally arbitrary and exist for historical reasons. That is, they are what they are because they are what they are - not due to any fundamental properties of the universe.

There have only ever been three definitions of the second: as a fraction of the day, as a fraction of an extrapolated year, and as the microwave frequency of a caesium atomic clock, which have each realized a sexagesimal division of the day from ancient astronomical calendars.

Until mechanical clocks were developed in the 14th century, there was no practical time period shorter than the hour. And the hour was not a fixed length but varied from day to day since it was 1/12th of the period between sunrise and sunset. It was the mechanisation that forced the hour to become a fixed period of time, rather than one that varied with the seasons.

Th earliest clocks displaying seconds date from the second half of the 16th century and they were pretty good by the standards of the day - meaning they were absolutely abysmal by modern standards - a half-decent musician could keep better time.

So, an alien civilisation with a different history would come up with a completely different time period. Initially the definition would be fuzzy, just like the second was, but as their civilisation advanced they might come up with the idea of an atomic clock based on caesium but given a completely different technologically history, the odds are they would come up with something different.

Whatever they came up with would be convertible to seconds in the same way that pounds are convertible to kilograms or furlongs per fortnight are convertible to metres per second.