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Historically, people measured time with the help of naturally recurring phenomena (say, a day). Then a day was split into smaller chunks (an hour, a minute, a second). Suppose we define an hour as 1/24th of a day. My questions is, how would we split a day into 24 equal parts? How can we be sure that they last the same amount?

Take the length for example. We may take anything as our 'length standard' and then directly compare its length to whatever object's size we're trying to measure. We may also split this 'unit lenght' into smaller divisions that will be more or less equal (again, because we are able to compare things with our own eyes).

With time, I can't think of any obvoius way to assess whether there is a substantial difference between two time intervals, especially if they are relatively big. So what (not overly fancy) experiment can we use to determine how long an hour (1/24th of a day) is? The same goes for minutes and seconds.

Qmechanic
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palkovna
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    We use a fancy technological gadget invented just for this purpose, called a 'clock'. – Emilio Pisanty Jul 06 '20 at 10:38
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    People have been using hours since ancient times, but they often used systems with variable length hours. Fixed length hours are a relatively modern invention. https://en.wikipedia.org/wiki/Hour has some info on this. – PM 2Ring Jul 06 '20 at 10:44
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    @EmilioPisanty I'm pretty sure hours were introduced before the invention of the said technological gadget. – palkovna Jul 06 '20 at 11:38
  • I think what emilio meant is you use some kind of pendulum/hourglass (i.e. a primitive clock) to measure one day, and then you can divide by twenty four. You can also make some simplifying assumptions, like measure 1/12 of the day (when the sun is up) or even 1/6 (from sunrise to the apex of the sun). – Frotaur Jul 06 '20 at 13:00
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    The title asks "How do we introduce an hour as a time unit?" That's trivial (well, almost trivial): An hour is 3600 seconds long. I wrote almost trivial is because a few hours have been 3601 seconds long. There have been 27 of these odd length hours since 1 Jan 1982. If on the other hand you meant to ask "How did we introduce an hour as a time unit" -- i.e., how did the concept of an hour arise millennia ago -- that question is perhaps better suited to the History of Science and Mathematics sister site. – David Hammen Jul 06 '20 at 13:47

6 Answers6

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Short:
Use a pendulum.
Better still, take advantage of the self timing aspects of Foucalt's pendulum.

Detail:

A "Fuocault's Pendulum" consisting of a suitably massive, suitably dense weight suspended on a suitably long, suitably thin wire will serve as a pendulum with adequately constant period of oscillation and with a duration of operation in excess of a day. Counting cycles will then allow division as desired up to at least as small as a half cycle of oscillation.

IF you have an accurate 24 hour period available the suitably compelled can count pendulum cycles over this period and then subdivide as desired. However, as a bonus, the line of swing of the pendulum precesses with time with a rate related to the latitude of the site - no precession occurs at the equator. If latitude is known then the period of one full rotation of the line of swing is able to be calculated - so the time between any number of of swings can be calculated.

See Physics and maths explained,
General overview - Brittanica - Foucault's pendulum and
Wikipedia - many

Values for "suitably" are 'to be established' but I have seen a steel mass of a few 10's of kg, swinging on a piano wire maybe 15 metres long with a duration of operation of many days. (In a stairwell of the Physics building At Auckland University in New Zealand - probably in 1969! :-) ).

Period of oscillation is $2\pi\sqrt{(l/g)}$ - so for a 15m wire, about 7.695 second.
To obtain a desired period, rearranging gives
$L = (t/(2\pi))^2×g$ eg For a 6 second period (1/600 of an hour) $L \approx 8. 937$ metre.

Russell McMahon
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There's a many ways to re-define 1 hour. If you can deduce Earth rotation angle by looking at the stars/sun movement in the sky, and their respective inclination angles, you can say that 1 hour is $15 {}^\circ$ of Earth angular rotation.

Or you can measure time by distance needed to walk by foots for reaching some target place. For example, approximately 1 hour will pass while you will walk $5~km$ distance.

Yet another way is to use thermodynamic properties of matter. You can define 1 hour as time needed to melt ice cube of $m$ mass completely under direct sunlight in summer, as per $$ 1~\text{hour} = m_{ice}\times H_{fus} \times P^{-1},$$

now solve equation for $m_{ice}$, substituting water's $H_{fus} = 333~J/g$, and solar irradiance power $P$ based on your location, time of day/year and cube irradiated area. (On winter you can employ a reverse process,- mass of liquid water $m$ needed to freeze it into ice completely in the duration of 1 hour.)

In general,- any process fits for describing 1 hour as long as you can map process with duration and have abilities to measure progress.

Agnius Vasiliauskas
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I believe if you know the start and end of your day, you can just start walking on a plane surface try to keep the same speed $v_h$. At the end of the day count the km you walked. Say it's 120 km, then you know that 1 hour is exactly you walking 5 km with a speed $v_h$.

You can also, instead, use earth's rotation. You know well that the earth needs 24 hours to make a full rotation on it self. While it maintains the same speed, and knowing the distance between the earth and the sun $=d$, you can measure the sun's displacement needed for one hour, i.e. $$D_{\text{1hour}}=\frac{2\pi d}{24}$$ Whenever the sun moved by a distance $D_{\text{1hour}}$ then you know an hour has passed.

The earth's surface speed is $$v_\oplus=\frac{2\pi R_\oplus}{24\text{h}}$$ and so the hour is defined as \begin{align} \text{1 hour} &= \frac{D_\text{1hour}}{v_\oplus}\\ \end{align}

devCharaf
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  • Sorry but I think the OP meant how did they do it historically. I believe that if people know the distance to the sun, they have already figured out how to build a clock. – Frotaur Jul 06 '20 at 12:51
  • The distance to the sun can be approximated easily using some geometry tricks. When you put your thumb in the direction of the sun, your thumb and the sun kind of have the same apparent size. Knowing the length of your arm ($\approx 1$m), the size of your thumb ($\approx 3$cm) and the sun's diameter ($\approx 1.4\cdot 10^6$km), you can find the distance Earth-Sun. About the sun's diameter, I think there is another trick but I am only familiar with the one that estimates the earth's diameter. Still if it's history the OP is asking for, I have no idea. – devCharaf Jul 06 '20 at 13:36
  • Yeah, with the sun diameter you are just trading an unknown for another. I think it is rather the opposite, from the knowledge of the distance to the sun using Newtonian Gravity, we infer its diameter. – Frotaur Jul 07 '20 at 11:53
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It is possible to define a time unit absolutely, in terms of frequency for instance. (Of course understanding that this is the duration of a second in the inertial frame of reference - other frames of reference can experience a different duration between the start and end events of that same second.)

"The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency ∆νCs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be 9192631770 when expressed in the unit Hz, which is equal to s−1."

https://en.wikipedia.org/wiki/SI_base_unit

For lengths, typically time is then used to define a length:

"The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299792458 when expressed in the unit m s−1, where the second is defined in terms of ∆νCs."

Now you may wonder, meters are defined using seconds? Doesn't this create a loophole?

Why is the meter considered a basic SI unit if its definition depends on the second?

buddhabrot
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Build a device an adjustable oscillator which oscillates roughly 24 times per day. Over the course of weeks or months adjust the oscillator faster or slower if you find it is ticking a little too slow or a little too fast. If you get it just right then you can leave it at that frequency. But you'll likely find that over time the hour ticker gets out of sync with days. So you can continuously adjust the hour ticker so that it ticks 24 times per day.

This is a rudimentary phase locked loop with a frequency divider.

Jagerber48
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Use a water clock, where time is measured by the water collected in a transparent container.

Edit: if the water flow (e.g. as drop by drop) is constant, the water height on the glass container can be divided into 24 parts with a ruler.

KlausK
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  • The question is what kind of device could determine how long 1/24th of a day is, which is not addressed in this answer as currently written. It could, however, likely be expanded to answer the question, – David Bailey Jan 23 '23 at 07:22