### Scientific laws

This article discusses the philosophy of scientific laws. For the scientific and mathematical details, see laws of science.

A scientific law is a statement based on repeated experimental observations that describes some aspect of the world. A scientific law always applies under the same conditions, and implies that there is a causal relationship involving its elements. Factual and well-confirmed statements like "Mercury is liquid at standard temperature and pressure" are considered too specific to qualify as scientific laws. A central problem in the philosophy of science, going back to David Hume, is that of distinguishing causal relationships (such as those implied by laws) from principles that arise due to constant conjunction.

Laws differ from scientific theories in that they do not posit a mechanism or explanation of phenomena: they are merely distillations of the results of repeated observation. As such, a law is limited in applicability to circumstances resembling those already observed, and may be found false when extrapolated. Ohm's law only applies to linear networks, Newton's law of universal gravitation only applies in weak gravitational fields, the early laws of aerodynamics such as Bernoulli's principle do not apply in case of compressible flow such as occurs in transonic and supersonic flight, Hooke's law only applies to strain below the elastic limit, etc. These laws remain useful, but only under the conditions where they apply.

Many laws take mathematical forms, and thus can be stated as an equation; for example, the Law of Conservation of Energy can be written as $\Delta E = 0$, where E is the total amount of energy in the universe. Similarly, the First Law of Thermodynamics can be written as $\mathrm\left\{d\right\}U=\delta Q-\delta W\,$.

The term "scientific law" is traditionally associated with the natural sciences, though the social sciences also contain laws. An example of a scientific law in social sciences is Zipf's law.

Like theories and hypotheses, laws make predictions (specifically, they predict that new observations will conform to the law), and can be falsified if they are found in contradiction with new data.

## Introduction

A scientific law or scientific principle is a concise verbal or mathematical statement of a relation that expresses a fundamental principle of science, like Newton's law of universal gravitation. A scientific law must always apply under the same conditions, and implies a causal relationship between its elements. The law must be confirmed and broadly agreed upon through the process of inductive reasoning. As well, factual and well-confirmed statements like "Mercury is liquid at standard temperature and pressure" are considered too specific to qualify as scientific laws. A central problem in the philosophy of science, going back to David Hume, is that of distinguishing scientific laws from principles that arise merely accidentally because of the constant conjunction of one thing and another.

A law differs from a scientific theory in that it does not posit a mechanism or explanation of phenomena: it is merely a distillation of the results of repeated observation. As such, a law is limited in applicability to circumstances resembling those already observed, and is often found false when extrapolated. Ohm's law only applies to constant currents, Newton's law of universal gravitation only applies in weak gravitational fields, the early laws of aerodynamics such as Bernoulli's principle do not apply in case of compressible flow such as occurs in transonic and supersonic flight, Hooke's law only applies to strain below the elastic limit, etc.