A time of rotation, not a time of the atom

Why a Jewish time server, and why it resembles no other calendar tool.

Two times exist today

For almost all of human history the second was a fraction of the day: 1/86,400 of the mean solar day. Time was the Earth turning. By the middle of the twentieth century astronomers already knew that this rotation is irregular: the Earth slows under the pull of the tides and fluctuates with the seasons, the winds, the motions of the core. In 1960 the 11th General Conference on Weights and Measures (CGPM) replaced rotation with orbit and defined the “ephemeris second”, a fraction of the tropical year 1900¹. That interlude lasted seven years. In 1967 the 13th CGPM redefined the second as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom². Since then the second has depended on no celestial motion at all.

Civil time, however, could not break away from the sun all at once. So UTC, Coordinated Universal Time, was built: an atomic time, advancing by caesium seconds, but tied back to the Earth’s rotation — to UT1, the scale defined by the Earth’s rotation angle — by inserting a leap second whenever the difference UT1−UTC threatens to exceed 0.9 s. Since 1972, twenty-seven leap seconds have been inserted³. Each is a rare event, announced only six months ahead, and one that computer systems handle badly: the leap second of 30 June 2012 brought down Linux servers and whole services⁴; the one of 31 December 2016 took out part of Cloudflare’s DNS because a duration came out negative⁵.

In November 2022 the 27th CGPM adopted its Resolution 4⁶. It deserves a precise statement, because it is often summarised as “the end of leap seconds”, which it is not, literally. The resolution decides that the maximum value of the difference UT1−UTC will be increased in, or before, 2035, and requests that the International Committee for Weights and Measures propose a new maximum value that ensures the continuity of UTC for at least a century. It is therefore not an abolition: it is a widening of the tolerance, so wide that no correction will be needed in our lifetime, nor in our grandchildren’s.

The consequence is simple to state and long to think about: from 2035 on, the time of clocks and the time of the sky will be two independent things. The gap, today under a second, will grow freely — a few tens of seconds in a century, perhaps a minute. It is not much. But it is the first time in history that we accept, by decision, that noon will no longer be, even approximately, the moment the sun crosses the meridian. Every civilisation until now took the sky as the reference and the clock as the approximation. We are reversing the order.

Jewish time is a time of rotation

Jewish time has never been a time of durations. It is made of proportions of celestial phenomena.

The day begins at sunset: “there was evening, there was morning” (Genesis 1:5). The halachic hour, the שעה זמנית, is one twelfth of the day, from sunrise to sunset — or from dawn to nightfall, according to the opinions — and one twelfth of the night; in Jerusalem a daytime hour exceeds 70 minutes in summer and falls short of 50 in winter. The month begins at the new moon, the מולד. The year is realigned with the sun by adding a thirteenth month. At no level does the system posit an absolute duration and measure the rest against it: it posits a phenomenon — rotation, lunation, the year — and divides it.

The fixed calendar, which replaced observation from the exile onward, kept this logic down to its smallest units. The hour is divided into 1,080 חלקים (Rambam, Hilkhot Kiddush ha-Chodesh 6:2)⁷, a number chosen for its abundance of divisors, which lets the mean lunation — 29 days, 12 hours and 793 chalakim — be written without a fraction. The chelek is itself divided into 76 רגעים (ibid. 10:1)⁸. A day therefore has 24 × 1,080 = 25,920 chalakim, and 25,920 × 76 = 1,969,920 rega’im. By definition. Always.

But the day itself has no fixed duration. The Earth’s rotation slows by about two milliseconds per century on average and fluctuates by several milliseconds from one season to the next. When the day lengthens, the chelek and the rega lengthen with it, by a minute but real amount: the rega is a proportion of the day — one 1,969,920th — and not a duration. This is exactly the reverse of the second of 1967. There, the second is fixed and the day contains a variable number of seconds; here, the day is the unit and the rega is an invariable fraction of it.

A word of honesty about the rega. The Talmud (Berakhot 7a)⁹ gives another definition: 1/58,888 of an hour, the span of divine anger, “the time it takes to say רגע”. That value does not divide the chelek into a whole number and was not conceived as a unit of calculation. We keep the Rambam’s because it subdivides the chelek exactly, which makes the counter an integer and the arithmetic free of remainders. It is not a theological preference; it is an engineering choice, and we call it that.

What this server does

This server exposes a single number: an integer, the number of rega’im elapsed since the beginning of the week of creation — precisely, since the Saturday evening, 18:00 Jerusalem mean time, that precedes the molad ב״ד ר״ד, the “molad Tohu”, which the Rambam places on day 2, 5 hours and 204 chalakim (Hilkhot Kiddush ha-Chodesh 6:8)¹⁰. This molad is the origin of the entire fixed calendar: every later molad is derived from it by adding mean lunations.

From that integer, by pure arithmetic, everything else follows: the day, by division by 1,969,920; the hour, the chelek, the rega; then, by the rules of the fixed calendar — months of 29 and 30 days, the nineteen-year cycle, the four דחיות — the year, the month, the day of the month, the day of the week. Nothing is looked up in a table, nothing is translated from another calendar.

The reference clock is UT1, the actual rotation of the Earth as measured by the International Earth Rotation and Reference Systems Service (IERS)¹¹, not UTC. Concretely, the server reads the machine clock, adds the UT1−UTC difference published in the IERS Bulletin A¹², shifts to Jerusalem mean time, and converts the time elapsed since the epoch into rega’im. That is the only place in the program where the SI second and the Gregorian calendar exist: one package, isolated, replaceable. The public API never returns a Gregorian date, never a UTC time, never a Unix timestamp, never a second. An automated test checks this on every build.

The result: a day always has exactly 25,920 chalakim, and the Earth decides how long it lasts. There will never be a leap second here, because there is nothing to realign. The counter does not drift from the sky; it is the sky, cut into parts.

The limitation must be stated just as plainly. This server does not measure the Earth’s rotation itself. It uses the IERS measurements, obtained by very long baseline interferometry (VLBI) on quasars billions of light-years away, supplemented by GNSS constellations and laser ranging, published a few days late and extended by predictions. The server displays the age of the data and says when it is running on a prediction. For now, then, it depends on an institution — learned and reliable, but external. The next step is a local sensor: a gnomon filmed by a camera by day, an astrometric solution of the sky (plate-solving) by night, to obtain the Earth’s rotation angle directly, with no intermediary. The Clock interface in the code is designed for that: one method, “now, in rega’im”, which any source can implement, and nothing in the API depends on the IERS.

How this differs from hebcal, KosherJava and the others

Excellent Jewish calendar tools exist, and this project does not claim to replace any of them.

Hebcal has been the reference service since the 1990s: conversion between Gregorian and Hebrew dates, holidays and fasts, Torah readings, Shabbat times and zmanim by location, yahrzeits and anniversaries, all through a free, keyless, documented REST API whose data is licensed CC BY 4.0. Its Go library, hebcal-go, reimplements the core of the calendar with the same care. KosherJava, by Eliyahu Hershfeld, is the reference for astronomical zmanim calculations: sunrise and sunset, dawn and dusk according to dozens of opinions, halachic hours, molad, tekufot, Daf Yomi; the library has been ported to more than fifteen languages, under the LGPL. These tools are complete, exact, and maintained for decades. If you want to know when to light candles in Lyon next Friday, that is where to go.

But they all share an architecture: they take a Gregorian date as input — a Java Date, a Go time.Time, an ISO string — and a UTC time as their base, and then they translate. Jewish time there is a function of the time of the nations: correct, but derived. That is natural, since it is how machines count.

Here there is nothing to translate. The counter is native: the epoch is Jewish, the unit is the rega, the clock is the Earth. One does not ask “what is today’s Hebrew date”; one asks “how many rega’im have elapsed”, and the date follows. That is the only thing this server does, and to our knowledge no one else does it: an autonomous Jewish timestamp, with no reference to the Gregorian calendar or to the atom. It does no holidays, no zmanim by location, no readings. It produces a number.

Time entrusted

Three ideas, drawn from the sources, say why this way of counting is not a technical eccentricity but a fidelity.

The first mitzvah given to Israel as a people is neither Shabbat nor Passover: it is the month. הַחֹדֶשׁ הַזֶּה לָכֶם, “this month shall be for you the beginning of months” (Exodus 12:2)¹³. Rashi on this verse reports that Moses struggled to grasp the exact moment of the moon’s renewal, and that God showed it to him in the sky: “like this you shall see, and sanctify”¹⁴. The Gemara reads in “for you” the handing over of testimony to human beings: “this testimony is entrusted to you” (Rosh Hashanah 22a)¹⁵. And Rashi, opening his commentary on Genesis, quotes Rabbi Yitzchak: the Torah should have begun with this verse, since it is the first mitzvah¹⁶. Time, in this tradition, is not received ready-made; it is entrusted. One watches it, declares it, answers for it.

The second idea sharpens the relation between measurement and declaration. On Leviticus 23:4, “these are the appointed times of the Lord, which you shall proclaim in their season”, the Gemara (Rosh Hashanah 25a)¹⁷ reads אֹתָם, “them”, as אַתֶּם, “you”: אתם אפילו שוגגין, אתם אפילו מזידין, אתם אפילו מוטעין — you, even in error; you, even deliberately; you, even misled. The date declared by the court stands, even if it is astronomically wrong. That is what is at stake in the episode of Rabban Gamliel and Rabbi Yehoshua, who had to come with his staff and his purse on the day that he, for his part, held to be Yom Kippur. Jewish time is a declared time, not merely a measured one. Perfection of measurement was never the criterion; honesty of declaration was. That is why this server displays the quality of its data — measured or predicted, and how old — rather than claiming an exactness it does not have.

The third idea concerns the fixed calendar itself. The Rambam (Hilkhot Kiddush ha-Chodesh 5:1–3)¹⁸ teaches that the calculation which now fixes the months is not the primary rule. The rule is observation and sanctification by the court; the calculation holds as long as there is no Sanhedrin in the Land of Israel. The calendar attributed to Hillel II is a regime of exile. What is fixed is provisional by nature; when one can observe again, one observes. This server leans that way, modestly: between the real rotation of the Earth and a calculation frozen on an atomic second, it chooses rotation, and it is built to end up looking at the sky itself.

In 2035 civil time will stop following the sun. It will be a reasonable decision, taken by competent people, for good engineering reasons. Jewish time cannot stop following it, because it is not a clock that one realigns with the sky: it is the sun and the moon, cut into parts. It just needs someone to keep it.