Date, time and timezones

This is a collection of notes about time and related concepts. A future post will talk about the problems of representing time in computer systems, especially distributed systems. These notes will be occasionally updated.

Introduction

Time is taken to be a primitive concept that cannot be defined in terms of other phenomena, but can be characterised as a parameter of a system that allows the system to change.

In closed systems, time is measured relative to some event within that system, such as the time elapsed since the start of an experiment. In such systems, time can be unambiguously specified as a single real number (or sometimes an integer, in discrete-time models).

Things are more complicated when it is necessary to describe times "in the real world", where there are a number of closely related but confusing concepts.

Under a non-relativistic model of physics, all observers have a common notion of time: in particular, instantaneous events may be totally ordered along a timeline, and all observers can agree whether event A happened before, after or simultaneously with event B. However, observers might report different numerical values of a time, depending on how they measure it: in particular, depending on their timezone and the accuracy of their clocks. The synchronisation of different clocks is a difficult but important problem in distributed systems.

Absolute time, relative time, and time of day

The English word time may refer to:

• an absolute position on the timeline ("when did something happen?"),
• the interval (or timedelta) between two positions on the timeline ("how much time passed?"), or
• the time of day, or the interval relative to the local midnight ("what is the time?").

Intervals of time are measured in units such as seconds (see below).

One may convert between absolute times and timedeltas by specifying a position on the timeline as an epoch, relative to which all other times are measured. The epoch may be chosen to be the time of a significant event, or an arbitrary point.

Since local midnight depends on the locale of the observer, a "time" in the third sense can be converted into an absolute time only by additionally specifying a date as well as a timezone - often implicitly.

Units of timedeltas

The basic unit of a timedelta is the second, also the millisecond, microsecond, etc., defined in terms of the (constant) frequency of a certain atomic oscillator. The minute, the hour and the day) are defined as 60 seconds, 60 minutes (3,600 seconds) and 24 hours (86,400 seconds) respectively.

The month and the year are not precise units of timedeltas, since they vary in length. They are however used informally.

Astronomical days

Although the day is based on the rotation of the Earth and the relative position of the Sun, the 24-hour day is distinguished from:

• the solar day, the time between two successive maxima of the Sun's position in the sky, and
• the sidereal day, the time taken for the earth to complete a rotation on its axis.

The solar day is longer than 24 hours by a few seconds. The sidereal day is about 4 minutes shorter than 24 hours; this difference is due to the orbit of the Earth around the Sun.

The rotation of the earth is gradually slowing down. Over the course of millennia, the 24-hour day will diverge from these astronomical definitions.

The time of day: solar time, civil time and timezones

Traditional measurements of time are based on the position of the Sun and the other stars in the sky. These are the solar time and sidereal time respectively. For example, noon is defined to be the time at which the Sun is at its highest position, and midnight is defined to be twelve hours after that.

Since the position of the Sun in the sky depends on geographical location as well as the time of year, solar time is an impractical measurement of time. Thus the development of civil time and of timezones: that in a given region (such as a country or province), all clocks should report the same value of time. The development of timezones is based on political considerations rather than reflecting astronomical phenomena: for example, the People's Republic of China uses a single timezone despite its geographical span; and most Western European countries use the same timezone.

All timezones are specified relative to Coordinated Universal Time (or UTC), which is based on the time at Greenwich, London.

Computers and distributed systems

Future post...