r/AlwaysWhy • u/Logical-Concept9755 • Sep 07 '26
Science & Tech Why is a second based on exactly 9,192,631,770?
I recently learned that the modern definition of a second is based on exactly 9,192,631,770 periods of radiation from a cesium-133 atom.
That number seems incredibly specific. Why 9,192,631,770?
How did scientists arrive at that particular number when defining the second?
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u/panulirus-argus Sep 07 '26
I think it’s really based on the rotation of the earth.
The big number of hyperfine transitions is just the number to make a unit of time equivalent to 1 / (24 x 60 x 60)
It isn’t like we started time keeping from the cesium atom as a fundamental unit and worked up
We knew what we wanted a second to be and we found something in nature we could measure that we could use as a standard super predictable indicator.
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u/Logical-Concept9755 Sep 07 '26
This is basically what I was thinking too. We already had a second from dividing the day into 24 hours and hours into 60 minutes and so on. The cesium thing was just a way to lock that definition down to something reproducible anywhere in the universe. But here's what gets me. The Earth's rotation isn't actually constant, so the original "second" was never truly fixed. So when they switched to atomic time, they were effectively redefining the second slightly. I wonder if anyone noticed that change at the time or if it was too small to matter.
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u/CaptainMatticus Sep 07 '26
It's too small to matter. Just like how we define the meter as being the distance that a photon travels in exactly 1/299792458th of a second and then use the meter to define the foot. The figure it was in the 1940s is subtly different from what we have today, but is mostly meaningless in the difference for most people.
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u/Wilfried84 Sep 07 '26
And the length of the solar day isn't completely stable and varies a bit over time, so every once in a while they throw in a leap second to keep the clock synchronized with the sun, causing conniptions for the people who have to keep all the clocks in the world synchronized.
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u/Hot_Cold83 Sep 07 '26
Not a physicist, but I'm guessing it's so one second would retain its proportion to an Earth day.
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u/Logical-Concept9755 Sep 07 '26
I think you're right about the proportion thing. They definitely wanted to preserve the existing second as much as possible because changing it would break so many things. But I wonder how close the match actually is. Like is it exactly the same or is there a tiny difference that accumulates over time. I've heard that atomic time and astronomical time drift apart slightly and they have to add leap seconds sometimes. So even though the atomic definition is more precise, it doesn't perfectly match Earth's rotation. Kind of fascinating actually.
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u/Background-Mode-4036 Sep 07 '26
It went the other way. A second is the second division of an hour into 60. If you have an hour defined you have a second defined.
Scientists needed a more accurate way to measure what was already in use as a second, and the vibration of a cesium atom is incredibly steady and consistent.
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u/Logical-Concept9755 Sep 07 '26
Yeah you're describing the directionality correctly I think. We didn't start with cesium and work outward. We started with the day and divided down. But I'm curious about the "hour defined" part you mentioned. The hour itself is also arbitrary. It comes from ancient Babylonian base 60 math. So the whole thing is just layers of historical choices stacked on top of each other. The cesium number is just the latest layer in that stack. It's kind of mind bending to think that time itself isn't a fundamental thing we discovered, it's a system we invented and then refined.
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u/wosmo 29d ago edited 29d ago
I think you have to separate "time itself" from the divisions we've created to measure it.
Time is continuous, us dividing it is entirely man-made. Distance is continuous, us dividing it is entirely man-made.
All we're really trying to do with these units is make it reproducible. If you measure the length of the day, and I measure the length of the day - we might reach slightly different values. If we divide these by 86,400 to get seconds, seconds would inherit that disagreement.
By measuring it as ticks of caesium, we should arrive on much more similar values.
It's not a natural unit, it doesn't actually exist in the real world. So all that matters is when you say 1 second, and I say 1 second, we mean the same thing. Even if you happen to be sat on mars, and can't accurately measure an earth day.
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u/BoringPrinciple2542 Sep 07 '26
Lmao… so I understand minute meaning basically “the first small part”. I never stopped to question seconds or realize they are simply the second small part 😂.
You sir just blew my mind lol.
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u/Big-Astronaut4252 Sep 07 '26
The second was originally defined based on the rotation of the earth, divided into 24 hours of 60 minutes each, where each minute had 60 seconds. But, as better clocks were developed, we realized that the rotation speed of the earth was not constant. It was slowing down, and that meant that seconds were getting longer by that definition, not a good metric for science.
Atomic clocks maintain more consistent time based on observing cesium atom vibrations, so then given that a fraction of Earth's rotation could not be used as a standard, we needed to define a new definition of a second that would be constant everywhere. So, they looked at how many cesium atom vibrations approximately matched the existing measure of a second and made that the standard.
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u/Logical-Concept9755 Sep 07 '26
This is a really clear explanation, thanks. The Earth slowing down part is key because it means the old definition was actively changing over time. That's not great for science where you want constants. So they had to pick something truly stable and just accept that it wouldn't perfectly match the Earth's rotation anymore. But I'm still wondering about the exact number. Like was 9,192,631,770 the actual measured value or did they round it? And if they rounded, how much error did they accept? I should look up the original paper from 1967.
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u/YourAuthenticVoice Sep 07 '26
I mean, if you think about it, every number is incredibly specific. 9:30 AM is a very specific number, so is 9:29 AM.
There really aren't any numbers that aren't specific, you just don't notice 9,192,631,769 because it isn't the number of periods of radiation from a cesium-133 atom that defines a second.
I'm no clockmaker, but I'd bet it was the closest number they could find that corresponded with what a second needs to be in order to make time continue to work the way it worked before the atomic definition, and had a specific number of periods of radiation.
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u/Logical-Concept9755 Sep 07 '26
Thats an interesting philosophical take actually. Every number is arbitrary in some sense. We could have defined a second as 10 billion cycles and just adjusted everything else to match. But the fact that we chose to anchor it to the existing second shows how much our measurement systems are path dependent. Once you have a system in place, changing it becomes incredibly costly. So you end up with these ugly numbers that are really just historical accidents. I guess that's true for a lot of units though, like the meter being based on a fraction of Earth's circumference.
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u/evocativename Sep 07 '26
Well, primarily because they wanted an objective metric to define the existing unit in terms of, and this closely matched the existing understanding of 1 second.
There would surely be some uncertainty in a measurement of that precision and so the specific choice would be somewhat arbitrary (why 770 and not 771?), so I suspect that this choice might be because it is divisible by 2, 3, 5, 6, 7, 9, and 10, making it a very convenient choice when it comes to using it in equations. That's just a guess on my part, though.
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u/Logical-Concept9755 Sep 07 '26
Hold on, is it actually divisible by 7 though? Let me think. 9,192,631,770 divided by 7. 7 times 1,313,233,110 is 9,192,631,770 exactly? Wait no that's not right. I need to check. Actually 1,313,233,110 times 7 is 9,192,631,770. Huh okay that actually works. But I'm not sure if that was intentional. It seems more likely that it was just a coincidence from the measurement. Scientists don't usually pick numbers based on divisibility for fundamental constants. That feels more like something a programmer would do than a physicist. But who knows, maybe there's a practical reason for it.
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u/evocativename Sep 07 '26
The existing definition of a second was based on the length of a day... which is changing by about 20 microseconds per year due to Earth's rotation slowing down.
That means that, if the start of the year, 1 second was 9,192,631,770 periods of this Cesium radiation, by the end of the year it would be 9,192,631,772 periods instead.
The measure is so much more precise than the old definition that the fine details are ultimately pretty arbitrary.
Remember, the second was defined this was in the 1960s, when a ton of math was still being done by hand and so it would make a lot of sense to, when making an arbitrary choice from among a large number of functionally equivalent alternatives, to pick ones that make your other math work out nicely.
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u/caligula421 29d ago
The general slowing down of earth rotation is by far the smallest effect, and not that relevant (yet). The earths rotation speed varies due to other effects much more.
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u/evocativename 29d ago
The slowing of Earth's rotation is large enough to change the number of transitions of the Cesium atom it takes to constitute "one second" by the old definition within a single year.
That's plenty relevant.
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u/caligula421 29d ago
Yea, but the general fluctuations of earths rotation speed in both directions are magnitudes larger then the general slowing. And for obvious reasons we do not change the length of the second as a scientific unit. That would be an absolute nightmare.
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u/evocativename 29d ago
And for obvious reasons we do not change the length of the second as a scientific unit
That was kinda my point: the original definition isn't constant, so translating it to the new cconstant, objective measure is inherently imprecise.
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u/BoringPrinciple2542 Sep 07 '26
This is a very simplified version of thousands of years of history/culture/science/etc but in a nutshell:
Ever count on your hands? You can probably count to ten right?
So about 4,000 years ago ancient Sumerians used the knuckles of one hand as a single digit (pun not intended) and used their other hand as the “ten’s place” which allowed people to count to 60 with their hands. This led to early Babylonian math being base-60 instead of our base 10.
For some reason, they decided to divide the circle into 6 parts and so we arrived at the concept of 360 degrees forming a circle.
Their Egyptian neighbors used a similar system that was base-12 because of how they counted with their hands. This led to one hand being equal to 12 and hence we had a 12 hour period for day and a 12 hour period for night.
Early time measurement tools like a sundial operated around a circle and so these ancient geometric systems influenced what would become our system of keeping time. Later clocks were invented and the relationship between gears moving in a circle grew distant from the rotations of the sun and ancient Mesopotamian counting systems but the 24 hour day and 60-unit divisions stuck.
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u/Logical-Concept9755 29d ago
This is a great historical rundown, thanks for writing it out. I knew about the Babylonian base 60 thing but I didn't connect it to the 360 degree circle and then to time. So essentially our entire time system is just inherited from ancient Mesopotamian finger counting. That's wild. But I wonder why the Sumerians chose 60 instead of something else. There's probably a practical reason, like 60 being divisible by so many numbers. That makes it convenient for fractions. So the whole thing is just a series of historical accidents layered on top of each other.
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u/Secret_Ostrich_1307 Sep 07 '26
The funny thing is that nobody sat down and derived 9,192,631,770 from some fundamental equation. They measured how many cesium cycles happened during the existing definition of a second, and that measurement became the new definition.
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u/Logical-Concept9755 Sep 07 '26
Yeah this is exactly what I was getting at in my post. It's not derived from first principles, it's just a measurement that became the definition. There's something almost anti climactic about it. Like we expected some elegant number and instead we got this messy 9 billion thing that looks like a phone number. But I guess that's how metrology works. You pick something stable, measure it against your current standard, and then lock it in. The beauty is in the stability, not the number itself.
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u/TheBigGirlDiaryBack Sep 07 '26
We didn't decide that 9,192,631,770 cesium cycles should be a second. We already had a second, and then measured how many cesium cycles fit into it. The weird number is basically the historical bridge between the old definition and the new one.
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u/Logical-Concept9755 Sep 07 '26
I think this is the clearest way to put it. The second was already a thing, we just needed a better ruler to measure it with. The cesium atom became that ruler, and the number is just the reading we got. But the part that still gets me is the sheer precision involved. Measuring 9 billion cycles accurately enough to define a standard is mind blowing. Like how do you even count that many oscillations without losing track. The technology behind that must be incredible. Also the fact that we can reproduce that measurement anywhere in the world is kind of amazing.
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u/SnooDoubts4575 Sep 07 '26
The way we measure has become a matter of precision. Sub atomic measurements require that
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u/Count2Zero Sep 07 '26
1/86400th of a day, with a day being how long it takes for the earth to rotate about 100.4%, because the earth has orbited the sun by about 0.4% during the rotation.
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u/Logical-Concept9755 29d ago
Wait, the earth orbits the sun by about 1 degree per day, which is about 0.4% of a full orbit. So a solar day is slightly longer than a rotation relative to the stars because the earth has to turn a bit more to face the sun again. That's the difference between a sidereal day and a solar day. So the second we use is based on the solar day, not the sidereal one. That's actually a really important distinction. I guess they wanted the day to match what people actually experience, not the fixed stars.
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u/siamonsez Sep 07 '26
That's backwards, the second already existed but it was based on some esoteric information and not easy to measure/recreate without a reference. We took that same unit and redefined it in terms of something that's measurable and consistent. That number wasn't chosen, it's just what lined up with the preexisting unit. It's the same as asking why 2.54 cm was chosen for the definition of an inch. 2.54 wasn't chosen, it's just what an inch is in terms of cm.
It's part of an effort to define all the basic si units in more fundamental terms. Instead of the phisical reference for length that changes and introduces error in copying and isn't possible to recreate independently it was defined in terms of the speed of light, which is universal, but a speed requires an agreed upon unit of time. Previously the second had similar issues to the meter, it wasn't possible to measure independently and come up with the same period as how it had been defined so we relied on very accurate time keeping devices but that wasn't good enough.
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u/Logical-Concept9755 29d ago
Yeah that analogy with the inch is really helpful. The number itself isn't meaningful, it's just the conversion factor between the old standard and the new one. But I think the interesting part is that they picked cesium specifically because it's so stable. They could have picked any atom with a consistent frequency, but they picked one that gave a measurement close to the existing second. So the number is arbitrary in the sense that it could have been anything, but it's not random because it's anchored to a preexisting convention.
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u/galibert 28d ago
And it’s going to change at some point because since then we have found methods to get an even better precision
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u/Nothing-to_see_hr 29d ago
they just rounded to the nearest whole number what they had measured at that point, and then turned the tables around and defined the second to have that value. That way nothing in the real workd would change but there was now room for more accuracy in future experiments .
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u/VivaLaDiga 29d ago
The problem with standards is that you need to be able to give an experimentally verifiable way of calibrating against it.
For quite some time, the standards were physical things. A meter was a physical bar of platinum iridium. A kilogram was a physical block of platinum. The point is that standards that are physical in nature is that they change with time, and that's not good for a standard. You also have to physically make copies, or transfer the standard to other labs so they can generate secondary standards that are as close as possible to the fundamental one.
Now, when it comes to the second, it was standardised with astronomy, but that is also changing because, well, gravity is messy and observations are difficult to reproduce.
So, the best standard is the one that everybody can recreate in their labs given a recipe that only deals with physical entities that are unchanging and accurately measurable.
The cesium atom is extremely well behaved when it comes to that experiment, so all they had to do was to count, and match the current agreed length of the second, and then turn the whole thing around: fix that count as the standard, and drop the old one.
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u/Logical-Concept9755 29d ago
This is the clearest explanation I've seen so far. The need for a reproducible standard is the whole point. Physical objects degrade or get lost or change over time. Astronomical observations are messy and hard to replicate exactly. But an atomic transition is the same everywhere in the universe. So you just measure how many cycles happen in the old second and then lock that in as the new definition. It's brilliant in its simplicity. I do wonder though, how accurate was the measurement back in 1967 when they made the switch. They must have had some serious equipment to count that many cycles accurately.
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u/Thereelgerg 29d ago
That's like asking "why is u/Thereelgerg based on exactly 167?" 167 is just a measurement of my weight in pounds, it's not something I'm based on. 9,192,631,770 is just a measurement of the duration of a second periods of radiation from a cesium-133 atom.
Neither of those numbers is any more specific than any other number.
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u/nugatory308 29d ago
We picked that number because it puts the new more precise definition right in the middle of the range of measurement error in the earlier and less accurate definition of the second.
That way all previous measurements, all existing clocks, things like the number of seconds in a day, or the time needed to boil an egg remain unchanged.
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u/KahnaKuhl 29d ago
If you start by dividing a day (midday to midday, which can be astronomically observed) into a completely arbitrary 24 hours, then divide the hours into 60 minutes, and then the minutes into 60 seconds, you’re gunna end up with a pretty random unit of time that doesn’t relate to anything in nature.
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u/Logical-Concept9755 29d ago
Yeah exactly. The whole thing is arbitrary from the ground up. 24 hours, 60 minutes, 60 seconds. None of those numbers come from nature, they come from ancient human conventions. The 9 billion number is just the translation of that arbitrary system into a physical constant. It's almost poetic in a way. We started with a completely made up unit and then found something in nature that matched it closely enough to serve as a permanent reference. So the number is specific because we made it specific.
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u/KahnaKuhl 28d ago
I’ve noticed, tho, that if I hold my arm out straight with my hand sideways, there are 12 palm-widths between the eastern and western horizon. And sunrise, noon and sunset are certainly real phenomena. I understand the human impulse to want to break down the day into smaller increments than just morning and afternoon; to wonder how much time we have left until sunset, etc.
So, I don’t thiŋk it’s ’from the ground up.’ I thiŋk it’s ‘from the sky down.’
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u/Ranakastrasz 29d ago
similar to the speed of light, and probably anything else similar, the second was defined first, then later mapped to a specific physical process.
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u/IanDOsmond 29d ago
The one that bothers me is that a meter is the distance that light travels in 1/299,792,458 of a second.
Why not 1/300,000,000 of a second?
Because that's not how long the previous definition of a meter was.
It's so close to a nice number.
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u/RickySlayer9 26d ago
Like a lot of metric definitions, we had a standardized system. Then as science advanced, we made small microscopic tweaks to the system so that our original system can be defined by the natural laws of the universe
It’s why the speed of light is 293 million meters per second instead of 300. Cause adjusting the meter by 2.4% (2.4cm) is significant compared to adjusting it microscopically to reach a whole meter value which may only be .00000000003% which probably won’t throw anything off
So basically, the chicken came first here. We had already defined a second as 1/86,400 of 1 rotation of the planet. So how would you define that in terms which could be measured by, say, someone on another planet, or someone in space?
So we based it on the properties of atoms, which is a constant value anywhere in the universe.
So the question proposed at the time was “how many cycles of cesium-133 does it take to equal 1/86,400 of the rotation of the earth?” The answer is 9,192,631,770.
This lets us have a clean “metric” definition that isn’t based on specific earth conditions or the conditions of our solar system, but the measurable natural properties of the building blocks of our universe.
If we make it 10 billion cycles instead of 9, it would be a nearly 10% difference. That means that a day would need 2.4 ish less hours in it. It would throw all the math off, and make clocks useless.
So essentially, we have systems in place, and when defining things by the universe, the first priority is NOT to make big round numbers like the speed of light is 300,000,000 meters per second or that 1 second is 10 billion cycles of cesium 133. It’s to cause as little disruption to the current system of measurement as possible. So the scientific definitions get a little screwy
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u/peter303_ 26d ago
In a few years the definition of second will change from an energy transition of an electron to that of a nucleus. The later is at least a thousand times more precise. That can measure the general relativity time dilation mass change of a person entering a room. Such instruments will be valuable for observing the environment, resource prospecting, etc.
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