Physics · Ch 1 — Physical World and Measurement

The Need for Measurement

1.4

Physics differentiates itself from purely descriptive or philosophical accounts of nature by

insisting that every claim be checked against a number — obtained by comparing an unknown

quantity with a fixed, agreed reference amount of the same kind. This comparison process is

called measurement, and the reference amount used for comparison is called a unit.

Formally, any measurement of a physical quantity $Q$ is expressed as:

Q = n \times u

where $n$ is a pure (numerical) magnitude and $u$ is the unit used. For example, saying a rod

is " $4.7$ " long is meaningless — saying it is " $4.7$ cm" long is a complete statement, because

it names both the number and the unit of comparison.

Testing a law. A law such as $F = ma$ is only useful if force, mass and acceleration can each be independently measured and the equation checked against real numbers.
Communicating results. A measurement recorded with its unit can be reproduced by any other observer, anywhere, using the same standard — this is what allows results from different laboratories (and different countries) to be compared directly.
Engineering and technology. Every device built from a physical law — a bridge, a satellite, a microchip — depends on components manufactured to a measured tolerance; without reliable measurement, the underlying physics could never be turned into a working technology.

For a measurement to be trustworthy and comparable across the world, the unit it is expressed

in must be:

Well-defined — unambiguous, so that two people applying the definition independently get the same result. …