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A term that designates four different concepts: (1) objective pattern (or natural regularity), (2) formula purporting to represent an objective pattern, (3) law-based rule (or uniform procedure), and (4) principle concerning any of the preceding.
For example, Newton's second law of motion, ma = F, is a law of type 2. It represents, to a good approximation, the actual behavior (law of type 1) of medium-size particles moving slowly relative to the speed of light. Alternative laws of motion, such as the relativistic and quantum-mechanical ones, are different laws of type 2 representing the same objective pattern or law of type 1 to even better approximations. One of the rules (laws of type 3) associated with Newton's second law of motion is: In order to set in motion a stationary particle, exert a force on it. Another is: In order to stop a moving particle, exert on it a force in the opposite direction. An example of a law of type 4 is: Newton's laws of motion are invariant under a Galileo transformation. See Newton's laws of motion
A physical law of type 1, or objective pattern, is a constant relation among two or more properties of a physical entity. In principle, any such pattern can be conceptualized in different ways, that is, as alternative laws of type 2. The history of theoretical physics is to a large extent a sequence of laws of type 2. Every one of these is hoped to constitute a more accurate representation of the corresponding objective pattern or law of type 1, which is assumed to be constant and, in particular, untouched by human efforts to grasp it. Likewise, the history of engineering is to some extent a sequence of laws of type 3, or law-based rules of action, of which there are least two for every law of type 2. As for the laws of type 4, or laws of laws, they are of two kinds: scientific and philosophical. The general covariance principle is of the first kind, whereas the hypothesis that all events are lawful is a philosophical thesis. Unlike the former, whose truth can be checked, the principle of lawfulness is irrefutable. See Theoretical physics
Not all formulas are called physical laws. For example, the regularities found by curve fitting are called empirical formulas. In physics a formula is called a law if and only if it meets the following conditions: it is part of a theory, and it has been satisfactorily confirmed by measurement or experiment at least within a certain domain (for example, for small mass densities or high field intensities). Thus, the basic assumptions of all the standard physical theories are laws, and so are their logical consequences. In particular, the usual variational principles, such as Hamilton's, are basic laws. However, the equations of motion and field equations entailed by such principles are derived laws (theorems); so are the conservation laws entailed by the equations of motion and field equations. However, the distinction between basic and derived laws is contextual: what is a principle in one theory may be a theorem in another. For example, Newton's second law of motion is a theorem in analytical dynamics, and the first principle of thermodynamics is a theorem of statistical mechanics. See Conservation laws (physics), Hamilton's principle, Physical theory, Statistical mechanics, Thermodynamic principles, Variational methods (physics)