Editing Scientific law (section)

== Overview ==
A scientific law always applies to a [[physical system]] under repeated conditions, and it implies that there is a causal relationship involving the elements of the system. [[Scientific fact|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]].<ref>
{{citation
  | contribution = Laws, natural or scientific
  | editor-last = Honderich
  | editor-first = Bike
  | title = Oxford Companion to Philosophy
  | pages = [https://archive.org/details/oxfordcompaniont00hond/page/474 474–476]
  | publisher = Oxford University Press
  | place = Oxford
  | year = 1995
  | isbn = 0-19-866132-0
  | url = https://archive.org/details/oxfordcompaniont00hond/page/474
}}</ref>

Laws differ from [[scientific theory|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, the applicability of a law is limited to circumstances resembling those already observed, and the law may be found to be 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 the case of [[compressible flow]] such as occurs in [[transonic]] and [[supersonic]] flight; [[Hooke's law]] only applies to [[strain (physics)|strain]] below the [[elastic limit]]; [[Boyle's law]] applies with perfect accuracy only to the ideal gas, etc. These laws remain useful, but only under the specified conditions where they apply.

Many laws take [[mathematics|mathematical]] forms, and thus can be stated as an equation; for example, the [[law of conservation of energy]] can be written as <math>\Delta E = 0</math>, where <math>E</math> is the total amount of energy in the universe. Similarly, the [[first law of thermodynamics]] can be written as <math>\mathrm{d}U=\delta Q-\delta W\,</math>, and [[Newton's laws of motion#Newton's second law|Newton's second law]] can be written as <math>\textstyle F = \frac{dp}{dt}.</math> While these scientific laws explain what our senses perceive, they are still empirical (acquired by observation or scientific experiment) and so are not like mathematical theorems which can be proved purely by mathematics.

Like theories and hypotheses, laws make predictions; specifically, they predict that new observations will conform to the given law. Laws can be [[Falsifiability|falsified]] if they are found in contradiction with new data.

Some laws are only approximations of other more general laws, and are good approximations with a restricted domain of applicability. For example, [[Newtonian dynamics]] (which is based on Galilean transformations) is the low-speed limit of special relativity (since the Galilean transformation is the low-speed approximation to the Lorentz transformation). Similarly, the [[Newton's law of universal gravitation|Newtonian gravitation law]] is a low-mass approximation of general relativity, and [[Coulomb's law]] is an approximation to quantum electrodynamics at large distances (compared to the range of weak interactions). In such cases it is common to use the simpler, approximate versions of the laws, instead of the more accurate general laws.

Laws are constantly being tested experimentally to increasing degrees of precision, which is one of the main goals of science. The fact that laws have never been observed to be violated does not preclude testing them at increased accuracy or in new kinds of conditions to confirm whether they continue to hold, or whether they break, and what can be discovered in the process. It is always possible for laws to be invalidated or proven to have limitations, by repeatable experimental evidence, should any be observed. Well-established laws have indeed been invalidated in some special cases, but the new formulations created to explain the discrepancies generalize upon, rather than overthrow, the originals. That is, the invalidated laws have been found to be only close approximations, to which other terms or factors must be added to cover previously unaccounted-for conditions, e.g. very large or very small scales of time or space, enormous speeds or masses, etc. This, rather than unchanging knowledge, physical laws are better viewed as a series of improving and more precise generalizations.