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According to Wikipedia, concepts superficially similar to the modern system of hours have been around since at least ancient Egypt c. 2800 BC. But their system divided "daytime" (after dawn and before sunset) and "nighttime" (after sunset and before dawn) into 12 hours each, whose length would of course vary at different times of the year.

At some point in the intervening ~5000 years, we moved to a system of a day being composed of 24 equal hours that daytime or nighttime could take up a varying quantity of at different times during the year. But I'm having trouble determining at what point this concept first took hold.

There's a related question on here that was closed for being confusing and unclear what exactly was being asked, so to avoid the same fate, here's exactly what I'm asking: when (and by who) was the system established in which each day has 24 hours, each of which are supposed to be of identical length rather than being dependent on varying values such as the length of time that the sun is in the sky?

From Scientific American:

Hipparchus, whose work primarily took place between 147 and 127 B.C.,
proposed dividing the day into 24 equinoctial hours, based on the 12
hours of daylight and 12 hours of darkness observed on equinox days.
Despite this suggestion, laypeople continued to use seasonally varying
hours for many centuries.

In terms of when the 24 hour day began to be relevant to ordinary people in their daily lives, my impression is that this would have come with advancements in mechanical clocks over the course of the Middle Ages and early modern period. See the history of timekeeping devices on Wikipedia, which states:

The appearance of clocks in writings of the 11th century implies that
they were well known in Europe in that period. In the early
14th-century, the Florentine poet Dante Alighieri referred to a clock
in his Paradiso; the first known literary reference to a clock that
struck the hours.

However that article also points out with specific reference to sundials: "The idea of using hours of equal length throughout the year was the innovation of Abu'l-Hasan Ibn al-Shatir in 1371."