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 SI base unit.

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 International System of Units.

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 Metric prefix.