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Time is math I think
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this post was submitted on 23 Mar 2025
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the most impressive thing to me is that people managed to standardize and zero in a precise "second" especially back when seconds were kept by mechanical means. I wonder how they went about ensuring it.
A 1m pendulum has a 1 second half-period.
is it not dependent on mass at all? It's possible given that this is the metric system that this is actually just a convenient retroactive truth about meters. I suppose it wouldn't necessarily be, but then you're accounting for gravity as well, which means you're going to need a pretty effective approximation there. As well as a way to account for any mechanical losses as well.
I'm not sure the metric system even existed when we developed the first mechanical time keeping devices.
So I did some digging and the use of 1-second pendulum as a unit of length predates the metre by about a century. It's very possible it informed the choice of ratio to use when defining it properly, like we did with the recent definition change.
It's all on Wikipedia if you want to dive in yourself.
that sounds about right. About what i expected, i'll have to do some reading sometime i suppose.
The mass cancels out.
I don't know if it's purely a coincidence. The meter comes from the Earth's circumference (1/10 000 000 of the pole-equator distance) and I believe the second is much older, which points to a coincidence.
it makes sense that the mass does cancel out, it is a change of potential and kinetic energy at all, i suppose i'm just conflating more complicated things with it lol.
it's pretty likely to be a coincidence, but if i had to guess it's a "lucky coincidence" one that was intentionally chosen because of it's convenience. Rather than by pure happenstance. There's not a particularly good reason 1 meter needs to be 1/10000000 the pole equator distance for example. So that would be pretty easy to reverse fudge nicely.
At least that's an useful approximation, but too inprecise for accurate measurements over an entire day.
It's only 0.3% off. You probably have more uncertainty on the length of the pendulum.
0.3 % would correspond to 3 mm difference in length of the pendulum.
After an hour, the difference between real and measured time would already be 10.9 s, and over an entire day, it would accumulate to 261.3 s, way too much for useful long term measurements.
Yet, it is an useful approximation for qualitative measurements, e.g. when Galileo Galilei did his fall experiments, he might have used a prendulum instead of his pulse for measuring.
I'm not hauling this as the ultimate time keeping method. Friction in the system will mean you need to readjust it anyways. It's just a neat fact that pi^2 ~= g
Atomic measurments, it's why atomic clocks are the most accurate.
that's a recent invention though, the first mechanical time keeping devices are what's interesting to me.
The atoms are the powerhouse of the clock.