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A thought occurred reflecting upon SI and its system of units.

The definition of the unit meter (the distance a light beam in a vacuum travels in 1/299,792,458 of a second) is a perfect definition of length, because the speed of light is invariant throughout the universe. But it is contingent on the definition of a second.

The unit second has a more curious definition. It is defined as the duration such that the ground-state hyperfine transition of the Cs_133 atom works out to 9,192,631,770 Hz.

But this raises the question: is it possible to get a precise definition of time in a hylemorphic universe? That is, does the concept of time inherently presuppose an atomic theory of matter?

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    Please define what you understand by a hylemorphic universe. The term as a long tradition, but is not generally known. - Time was defined already before referring to atomic phenomena. The astronomical definition refers to the daily rotation of the earth or the circular movement of the earth around the sun defining the time of one year.
    – Jo Wehler
    Feb 17 at 5:09
  • Hylemorphic in this context means "universe where matter is continuous and not finite". And traditional definitions of time (the ones you cited) suffer from the problem of being analog definitions, and analog definitions cannot be perfect (there's always slight disagreements or errors in measurement).
    – Fomalhaut
    Feb 17 at 5:11
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    You do know that pendulums have periods and waves have frequencies whether they are made of atoms or not? You can get precise measurement standard (not "definition") of time in any universe with recurring processes. Regardless of what they are made of, atoms or form and matter.
    – Conifold
    Feb 17 at 5:16
  • Duplicate of this question from Physics SE. physics.stackexchange.com/questions/675075/…
    – g s
    Feb 17 at 8:35
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    Is it possible to get a precise definition of anything in any universe? Just define 'precise' appropriately. "Measure with a micrometer. Mark with chalk. Cut with an axe." No matter how you measure time, there never seems to be enough of it. At least the days expand with the heat of summer, that's something...
    – Scott Rowe
    Feb 17 at 12:56

2 Answers 2

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A few observations...

A second is a unit of time, not time, so the definition of a second is not a definition of time any more than a kilogram is a definition of mass.

The advantage of using atomic transitions, aside from the fact that the seem reliably periodic, is that they are very short in duration, so you can use them to measure short intervals of time and they allow a high degree of precision.

Without atomic transitions we would have to fall back on some other reliably periodic phenomenon. The metre used to be defined as the length of a standard rod kept in Paris, so there could be a standard clock that everyone used as their point of reference.

In your comments you suggest that other measures of time are 'analogue' and consequently error-prone. The distinction between an analogue and digital clock is perhaps not as clear cut as you think. The underlying periodic phenomenon within an atomic clock would also count as 'analogue' in the sense you have used it- the digital aspects are to do with the electronics that keep count of the periods etc. I could easily create a digital pendulum clock with some electronics that tracked the sweep of the pendulum past the mid-point of its arc. Properly constructed pendulum clocks can be surprisingly accurate!

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    I have a digital clock (it actually displays in binary) which counts seconds by the zero-crossings of the 60 Hertz AC power. Power is produced as a sine wave by giant spinning alternators, an analog process if there ever was one. These alternators have a consistent speed which is closely regulated. In fact, all AC powered clocks used synchronous motors, some still do, and it was sufficient to keep the traffic signals in large cities synchronized together, and everyone out of bed to catch the bus on time, month after month. Those old guys a hundred years ago knew what they were doing.
    – Scott Rowe
    Feb 17 at 12:35
  • Binary Clock Kit a bit pricey, but interesting. I've had it for over 10 years, so it is not junk. Oh, I see that it is currently not being sold, but just nag them.
    – Scott Rowe
    Feb 17 at 12:42
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    @ScottRowe I remember when I was being taught physics at school (a long time ago!) being impressed when my physics teacher told me that the power generation companies in the UK were under a regulatory obligation to maintain a consistent AC frequency for time-keeping purposes. We had a mains electric clock in our kitchen that always kept great time. The odd thing was the if there was a power cut, when the power returned the clock would sometimes run backwards! Feb 17 at 13:41
  • @MarcoOcram, that's because the clock uses a single-phase synchronous motor. The motor windings only determine how fast it rotates and the direction is determined effectively randomly: by alignment of the magnet in the rotor with the magnetic field generated by the coils at the point of time when it starts. Many microwave ovens use such motor (with appropriate gearing) to rotate the plate. Try writing down the direction of plate every time when you start it – it should be random. Some larger sync. motor-powered clocks even used a spring mechanism to „kick“ the motor to the correct direction.
    – jiwopene
    Feb 18 at 13:19
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People have had measures of time long before we knew about atoms.

Atomic theory came about around the 18th century, but sundials date back to 1500 BCE, and we were able to roughly determine time of day and measure the passage of days much earlier than that. So no, the concept of time definitely doesn't presuppose atomic theory.

As for more precise measurements, there are things with very reliable regularity that could be measured quite precisely. Clocks can work in different ways, only 1 of which directly involves atoms (and you could potentially calibrate clocks with sundials or the passage of days, if nothing else).

As for atomic-level precision, a big part of the problem in asking the question would be that this would involve the behaviour of atomic-level matter, but without atoms - you'd need to explain what exactly the universe looks like at that level. Although if it's continuity all the way down, we could probably build a clock measuring a portion of a day, and the build a clock measuring a portion of the time that clock measures, and a clock measuring a portion of the time that clock measures, and so forth, down to whatever precision we want (and that we're able to construct and observe).

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  • Same for a ruler, just subdivide from that platinum stick in Paris. Atoms are overrated. I mean what else comes with 88 of something? A piano, right. "Too many notes..."
    – Scott Rowe
    Feb 17 at 12:49

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