# Big Idea Physics/Units
## Measurement

The need for measuring and comparing things is a very important part of physics. As measurements are important, rules are set in place to ensure that measuring is consistent. Measurement is not arbitrary however: it is based on units. Scientists measure and create things to meet standards and measurements to extreme accuracy so that measurements can be found out precisely. Measurements are an important part of comparing things, as they provide the basis on comparing objects to other objects. Measurements allow us to recognize three hours and see how it's shorter than five hours, without having to observe the hours passing by themselves.
The rules that are set in place are called standards. Things are measured based on comparison to standards. A unit is the standard chosen to which other things are compared to. An example is the meter for measuring length.
People have agreed to define standard units to allow consistency. For example, physicists have defined the meter as the distance travelled by light in a certain fraction of a second. An important part of defining standards is invariability. If instead we measured distance based on how long a person's foot was, it would be convenient, but it wouldn't be consistent. People have different lengths of feet, so what would be one foot for one person would not be one foot for another person.
But why is invariability important? Invariability is important because it allows for universal communication: what is three meters here will be three meters there, and thus anyone from any place can read about three meters and know how long it is. It also means that if something is three meters today, it would be three meters after ten years if nothing has changed about it.
Having a standard is not the end itself however. There needs to be ways of measuring based on the standard. If we have the standard for mass, we would need to work out a way to find out how heavy something is based on that standard. Whether it be a hydrogen atom or an apple or the sun, there needs to be ways to measure their mass based on that standard. An example for this is the weighing scale: it approximates the standard for mass. Other ways need to be devised if you want to measure the mass of the sun, for example, through indirect measurement.

## The SI

Of course, the world didn't start out using standards. Things were initially measured arbitrarily. "It's about as long as my foot." "It's as heavy as a watermelon." Back then, without the need for precision, these measurements were acceptable. However, scientists recognized the value of standards. And so, out of the French Revolution, the International System of Units was born.
The International System of Units, popularly known as the metric system, had its roots in the French Revolution with only two standards: the meter and the kilogram for length and mass. After multiple treaties and multiple conventions, the 11th General Conference on Weight and Measures held on 1960 gave way for the International System of Units, abbreviated SI for its French name (Le Système International d'Unités).
The SI was made to establish an international standard, applicable anywhere. It is based on seven base units, the set on which all other SI units are derived from.

### Base Units

Base units are the basis for all other SI units. All other units can be measured in terms of the product, power or quotient of these units. Gauss laid the foundations for length, mass and time. The need for an electrical base unit was identified by Giorgi, and noted by the 8th General Conference on Weights and Measures. Three more base units were added, the last being the mole by the 14th General Conference on Weights and Measures. These base units are shown in the table below, taken from the Wikipedia page on w:SI base unit.
SI base units :
| Name | Symbol | Measure | Current (2005) formal definition | Historical origin / justification | Dimension symbol |
| metre | m | length | "The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second." 17th CGPM (1983, Resolution 1, CR, 97) | 1/10,000,000 of the distance from the Earth's equator to the North Pole measured on the circumference through Paris. | L |
| kilogram | kg | mass | "The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram." 3rd CGPM (1901, CR, 70) | The mass of one litre of water. A litre is one thousandth of a cubic metre. | M |
| second | s | time | "The second is 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." 13th CGPM (1967/68, Resolution 1; CR, 103) "This definition refers to a caesium atom at rest at a temperature of 0 K." (Added by CIPM in 1997) | The day is divided in 24 hours, each hour divided in 60 minutes, each minute divided in 60 seconds. A second is 1/(24 × 60 × 60) of the day | T |
| ampere | A | electric current | "The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10$^{−7}$ newton per metre of length." 9th CGPM (1948) | The original "International Ampere" was defined electrochemically as the current required to deposit 1.118 milligrams of silver per second from a solution of silver nitrate. Compared to the SI ampere, the difference is 0.015%. | I |
| kelvin | K | thermodynamic temperature | "The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water." 13th CGPM (1967/68, Resolution 4; CR, 104) "This definition refers to water having the isotopic composition defined exactly by the following amount of substance ratios: 0.000 155 76 mole of $^2$H per mole of $^1$H, 0.000 379 9 mole of $^{17}$O per mole of $^{16}$O, and 0.002 005 2 mole of $^{18}$O per mole of $^{16}$O." (Added by CIPM in 2005) | The Celsius scale: the Kelvin scale uses the degree Celsius for its unit increment, but is a thermodynamic scale (0 K is absolute zero). | Θ |
| mole | mol | amount of substance | "1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is 'mol.' 2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles." 14th CGPM (1971, Resolution 3; CR, 78) "In this definition, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to." (Added by CIPM in 1980) | Atomic weight or molecular weight divided by the molar mass constant, 1 g/mol. | N |
| candela | cd | luminous intensity | "The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×10$^{12}$ hertz and that has a radiant intensity in that direction of 1/683 watt per steradian." 16th CGPM (1979, Resolution 3; CR, 100) | The candlepower, which is based on the light emitted from a burning candle of standard properties. | J |

### Derived Units

From the seven SI base units, many other units can be derived. Derived units are formed by powers, products or quotients of the base units. Derived units are based on derived quantities. Take for example velocity, derived from length over time. Its unit is the meter per second, derived from the meter and the second. The following table shows some derived units, based on a table on the Wikipedia page for w:International System of Units.
Some named units derived from SI base units :
| Name | Symbol | Quantity | Expressed in terms of other SI units | Expressed in terms of SI base units |
| radian | rad | angle | | m⋅m$^{−1}$ |
| hertz | Hz | frequency | | s$^{−1}$ |
| newton | N | force, weight | | kg⋅m⋅s$^{−2}$ |
| pascal | Pa | pressure, stress | N/m$^2$ | kg⋅m$^{−1}$⋅s$^{−2}$ |
| joule | J | energy, work, heat | N⋅m | kg⋅m$^2$⋅s$^{−2}$ |
| watt | W | power, radiant flux | J/s | kg⋅m$^2$⋅s$^{−3}$ |
| coulomb | C | electric charge or quantity of electricity | | s⋅A |
| volt | V | voltage (electrical potential difference), electromotive force | W/A | kg⋅m$^2$⋅s$^{−3}$⋅A$^{−1}$ |
| farad | F | electric capacitance | C/V | kg$^{−1}$⋅m$^{−2}$⋅s$^4$⋅A$^2$ |
| ohm | Ω | electric resistance, impedance, reactance | V/A | kg⋅m$^2$⋅s$^{−3}$⋅A$^{−2}$ |

### Prefixes

The SI also has a set of prefixes that multiply a value by a power of 10. These are made for convenience when expressing very large or very small values. As an example, adding the prefix kilo to the unit meter gives kilometer, a thousand times longer than a meter. They are shown in the table below, adapted from the Wikipedia page on w:Metric prefix.
Metric prefixes :
| Prefix | Symbol | 1000$^m$ | 10$^n$ | Decimal |
| yotta | Y | 1000$^8$ | 10$^{24}$ | 1 000 000 000 000 000 000 000 000 |
| zetta | Z | 1000$^7$ | 10$^{21}$ | 1 000 000 000 000 000 000 000 |
| exa | E | 1000$^6$ | 10$^{18}$ | 1 000 000 000 000 000 000 |
| peta | P | 1000$^5$ | 10$^{15}$ | 1 000 000 000 000 000 |
| tera | T | 1000$^4$ | 10$^{12}$ | 1 000 000 000 000 |
| giga | G | 1000$^3$ | 10$^9$ | 1 000 000 000 |
| mega | M | 1000$^2$ | 10$^6$ | 1 000 000 |
| kilo | k | 1000$^1$ | 10$^3$ | 1 000 |
| hecto | h | 1000$^{2/3}$ | 10$^2$ | 100 |
| deca | da | 1000$^{1/3}$ | 10$^1$ | 10 |
| | | 1000$^0$ | 10$^0$ | 1 |
| deci | d | 1000$^{−1/3}$ | 10$^{−1}$ | 0.1 |
| centi | c | 1000$^{−2/3}$ | 10$^{−2}$ | 0.01 |
| milli | m | 1000$^{−1}$ | 10$^{−3}$ | 0.001 |
| micro | μ | 1000$^{−2}$ | 10$^{−6}$ | 0.000 001 |
| nano | n | 1000$^{−3}$ | 10$^{−9}$ | 0.000 000 001 |
| pico | p | 1000$^{−4}$ | 10$^{−12}$ | 0.000 000 000 001 |
| femto | f | 1000$^{−5}$ | 10$^{−15}$ | 0.000 000 000 000 001 |
| atto | a | 1000$^{−6}$ | 10$^{−18}$ | 0.000 000 000 000 000 001 |
| zepto | z | 1000$^{−7}$ | 10$^{−21}$ | 0.000 000 000 000 000 000 001 |
| yocto | y | 1000$^{−8}$ | 10$^{−24}$ | 0.000 000 000 000 000 000 000 001 |