Definition:Time
Contents
Definition
A true definition of what time actually is has baffled philosophers from the dawn of, er, time.
Therefore it will be left as an exercise for the reader.
It is usually treated as a scalar quantity.
Dimension
Time is one of the fundamental dimensions of physics.
In dimensional analysis it is assigned the symbol $T$ or $\mathbf T$.
It is a scalar quantity which can be mapped directly to the real number line.
Unit Time
The usual units of time are seconds, and compound units consisting of multiples of seconds.
However, when discussing a general physical process it is convenient to discuss the general situation, in which case the term unit time is used.
Thus the specific units are not mentioned.
Time Unit
The units of measurement of time are universal in all systems of measurement.
Second
The second is the SI base unit of time, and also therefore of the MKS system.
It is also the base unit of time for the FPS and CGS systems.
The second is defined 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 $133$ atom at rest at $0 \ \mathrm K$.
Derived units of time include:
Minute
The minute is a derived unit of time.
- $1$ minute $= 60$ seconds.
Hour
\(\displaystyle \) | \(\) | \(\displaystyle 1\) | hour | ||||||||||
\(\displaystyle \) | \(=\) | \(\displaystyle 60\) | minutes | ||||||||||
\(\displaystyle \) | \(=\) | \(\displaystyle 60 \times 60\) | \(\displaystyle = 3600\) | seconds |
Day
\(\displaystyle \) | \(\) | \(\displaystyle 1\) | day | ||||||||||
\(\displaystyle \) | \(=\) | \(\displaystyle 24\) | hours | ||||||||||
\(\displaystyle \) | \(=\) | \(\displaystyle 60 \times 24\) | \(\displaystyle = 1440\) | minutes | |||||||||
\(\displaystyle \) | \(=\) | \(\displaystyle 60 \times 60 \times 24\) | \(\displaystyle = 86\, 400\) | seconds |
There are longer time periods, all of which are more or less approximate:
Week
- $1$ week $=7$ days.
Fortnight
Month
The month is measured only approximately in duration, and is not used as a scientific measure.
- $1$ month is between $28$ and $31$ days, depending on which month it is.
Lunar Month
The lunar month is defined as the length of time between $2$ new moons.
- $1$ lunar month $\approx 29 \cdotp 530588$ days
or:
Season
The season is measured only approximately in duration, and is not used as a scientific measure.
- $1$ season $= 3$ months, although exactly which months fall into which season depends on the locale and the culture.
Quarter-Year
The quarter-year is defined as:
- $91$ days
or
Year
\(\displaystyle \) | \(\) | \(\displaystyle 1\) | year | ||||||||||
\(\displaystyle \) | \(\approx\) | \(\displaystyle 365 \cdotp 24219 \, 878\) | days | ||||||||||
\(\displaystyle \) | \(\approx\) | \(\displaystyle 365 \cdotp 24219 \, 878 \times 24 \times 60 \times 60\) | seconds |
That is:
\(\displaystyle \) | \(\) | \(\displaystyle 1\) | year | ||||||||||
\(\displaystyle \) | \(\approx\) | \(\displaystyle 365\) | days, | ||||||||||
\(\displaystyle \) | \(\) | \(\displaystyle 5\) | hours, | ||||||||||
\(\displaystyle \) | \(\) | \(\displaystyle 48\) | minutes, and | ||||||||||
\(\displaystyle \) | \(\) | \(\displaystyle 45 \cdotp 9747\) | seconds |
It is defined to be equal to the orbital period of Earth round the sun.
Decade
- $1$ decade $=10$ years.
Century
- $1$ century $=100$ years.
Millennium
- $1$ millennium $=1000$ years.
Great Year of Plato
\(\displaystyle \) | \(\) | \(\displaystyle 1\) | great year of Plato | ||||||||||
\(\displaystyle \) | \(=\) | \(\displaystyle 12 \, 960 \, 000\) | days | ||||||||||
\(\displaystyle \) | \(\approx\) | \(\displaystyle 36 \, 000\) | years (of $360$ days) |
Length of Time
A quantity of time is usually referred to in natural language in the same terms as linear measure.
Thus it is usual to refer to a length of time of an elapsed quantity of time.
Fourth Dimension
In the Theory of Relativity, it is convenient to consider time as another dimension in addition to, and treated similarly to, the $3$ dimensions of ordinary space.
Sources
- 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{VI}$: On the Seashore
- 1964: D.E. Rutherford: Classical Mechanics (3rd ed.) ... (previous) ... (next): Chapter $\text I$: Kinematics: $1$. Space and Time
- 1970: George Arfken: Mathematical Methods for Physicists (2nd ed.) ... (previous) ... (next): Chapter $1$ Vector Analysis $1.1$ Definitions, Elementary Approach
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: time