Nature of Physical Law

What Do We Mean by a "Physical Law"?

A physical law is a concise statement, usually written as a mathematical relation, that

describes a pattern observed to hold in nature under a given set of conditions. What

distinguishes a physical law from a casual observation is that a law is expected to be:

• Universal — it holds at every place in the universe, not just where it was first measured.
• Time-invariant — it holds at every instant of time; the constants that appear in it (such as the gravitational constant $G$) do not drift with the calendar.
• Observer-independent (within the appropriate frame) — different observers, correctly accounting for their own motion, measure results consistent with the same law.

Two Illustrations

Mechanics — Newton's law of gravitation. The same inverse-square law,

$F = G\dfrac{m_1 m_2}{r^2}$, that predicts how a stone falls to the ground in a classroom

also predicts the orbit of the Moon around the Earth and the orbits of exoplanets around

distant stars thousands of light-years away. Nothing about the law changes with location.

Electromagnetism — Coulomb's law. The force between two point charges,

$F = k\dfrac{q_1 q_2}{r^2}$, has exactly the same mathematical form as gravitation (an

inverse-square law) and is found to hold with the same constant $k$ whether the charges are

sitting on a laboratory bench or embedded in the interstellar medium.

Conservation Laws — A Special Kind of Physical Law

Some of the deepest physical laws are conservation laws — statements that a particular …