Most physical laws express numerical relations between quantities which can be independently measured, such as the mass of a body, its acceleration and the force which is applied to it. Ultimately, they are established or refuted by experiment. The range of their validity is determined by the range of practicable experiments. Their generality is always in question, and physicists continually seek new insights in the breakdown of old theories.

It is important therefore to distinguish between physical laws, which are provisional and approximate (since, in principle, we expect to find circumstances in which they do not apply), and other mathematical relationships which are merely conventional definitions, such as ‘momentum equals mass times velocity’. These cannot be overturned, although there may be a time or a place in which they are not useful.

Given a problem to solve, we make the transition to mathematics by choosing appropriate physical laws and definitions. For the purposes of mathematical manipulation we may provisionally regard this formulation as exact, but in practice we will soon encounter uncertainties of two kinds.

First, if we wish to use experimentally measured quantities as numerical input to our calculations, as must ultimately be the case, we should recognise that every measurement involves some degree of uncertainty. The word ‘error’ is commonly used for this, which is unfortunate, because it need not be the result of any mistake or misjudgement, but may simply follow from the limited accuracy of the available measuring apparatus.