Physical law

A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. They are typically conclusions based on repeated scientific experiments over many years, and which have become accepted universally within the scientific community.

The production of a summary description of nature in the form of such laws is the fundamental aim of science. Laws of nature are distinct from the law, either religious or civil, and should not be confused with the concept of natural law.

Description
Several general properties of physical laws have been identified (see Davies (1992) and Feynman (1965) as noted, although each of the characterizations is not necessarily original to them). Physical laws are:
 * True (a.k.a. valid). By definition, there have never been repeatable contradicting observations.
 * Universal. They appear to apply everywhere in the universe. (Davies)
 * Simple. They are typically expressed in terms of a single mathematical equation. (Davies)
 * Absolute. Nothing in the universe appears to affect them. (Davies)
 * Stable. Unchanged since first discovered (although they may have been shown to be approximations of more accurate laws&mdash;see "Laws as approximations" below),
 * Eternal. they appear unchanged since the beginning of the universe (according to observations). It is thus presumed that they will remain unchanged in the future. (Davies)
 * Omnipotent. Everything in the universe apparently must comply with them (according to observations). (Davies)
 * Generally conservative of quantity. (Feynman)
 * Often expressions of existing homogeneities (symmetries) of space and time. (Feynman)
 * Typically theoretically reversible in time (if non-quantum), although time itself is irreversible. (Feynman)

Often, those who understand the mathematics and concepts well enough to understand the essence of the physical laws also feel that they possess an inherent intellectual beauty. Many scientists state that they use intuition as a guide in developing hypotheses, since laws are reflection of symmetries and there is a connection between beauty and symmetry. However, this has not always been the case; Newton himself justified his belief in the asymmetry of the universe because his laws appeared to imply it.

Physical laws are distinguished from scientific theories by their simplicity. Scientific theories are generally more complex than laws; they have many component parts, and are more likely to be changed as the body of available experimental data and analysis develops. This is because a physical law is a summary observation of strictly empirical matters, whereas a theory is a model that accounts for the observation, explains it, relates it to other observations, and makes testable predictions based upon it. Simply stated, while a law notes that something happens, a theory explains why and how something happens.

Examples
Main article: List of laws in science. See also: scientific laws named after people

Some of the more famous laws of nature are found in Isaac Newton's theories of (now) classical mechanics, presented in his Principia Mathematica, and Albert Einstein's theory of relativity. Other examples of laws of nature include Boyle's law of gases, conservation laws, the four laws of thermodynamics, etc.

Laws as approximations
Some laws are low (or high) limits of others, more general laws (or as scientists say, of more fundamental laws). For example, Newtonian dynamics (which is based on Galilean transformations) is simply the low speed limit of laws of special relativity (simply because Galilean transformation follow from Lorentz transformation at the limit of low speed). Similar, the Newtonian gravitation law follows from general realtivity at the limit of low gravitational potential (compared to square of speed of light), and Coulomb's law follows from QED at large (compared to range of weak interactions) distances. In such cases we understandably use more simple laws-approximations instead of more accurate fundamental laws.

Those laws which are just mathematical definitions (say, fundamental law of mechanics - second Newton's law $$ F = \frac{dp}{dt}$$), or uncertainty principle, or least action principle - are absolutely correct (simply by definition). Others which reflect symmetries found in Nature (say, identity of electrons or homogenuity of space and time) are constantly being checked experimentally to higher and higher degree of accuracy. The fact that they have never been seen repeatably violated does not preclude testing them at increased accuracy, which is one of main goals of science. It is always possible for them to be invalidated by repeatable, contradictory experimental evidence, should any be seen. However, fundamental changes to the laws are unlikely in the extreme, since this would imply a change to experimental facts they were derived from in the first place.

Well-established laws have indeed been invalidated in some special cases, but the new formulations created to explain the discrepancies can be said to generalize upon, rather than overthrow, the originals. That is, the invalidated laws have been found to be only close approximations (see above examples), 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. Thus, rather than unchanging knowledge, physical laws are actually better viewed as a series of improving and more precise generalisations.

Origin of laws of nature
Some extremely important laws are simply definitions. For example, central law of mechanics F = dp/dt (Newton's second "law" of mechanics) is not a law at all but is a mathematical definition of force (introduced first by Newton himself). The principle of least action (or principle of stationary action),Schroedinger equation, Heisenberg uncertainty principle, and a few other laws fall into this category.

Most of the other laws are mathematical consequences of various mathematical symmetries (see Emmy Noether theorem as a proof of this). For example, conservation of energy is a consequence of the shift symmetry of time (no time moment is different from any other), while conservation of momentum is a consequence of the symmetry (homogeneity) of space (no place in space is different from any other). Indistinguishability of similar particles (say, electrons, or photons) results in the Dirac and Bose statistics which in turn results in the Pauli exclusion principle for fermions and in Bose condensation for bosons. Symmetry between time and space coordinate axis results in Lorentz transformations which in turn results in special relativity theory. Symmetry between inertial and gravitational mass results in general relativity, and so on.

Inverse square law of interactions mediated by massless bosons is the mathematical consequence of 3-dimensionality of space.

So to large extent laws of nature are not laws of nature per se, but mathematical expressions of certain simplicities (symmetries) of space, time, etc.

The application of these laws to our needs has resulted in spectacular efficacy of science – its power to solve otherwise intractable problems, and made increasingly accurate predictions. This in turn resulted in design and implementation of variety of reliable transportation and communication means, in building more quality and affordable shelters, in creating variety of drugs, in finding new energy sources, in developing variety of entertainments, etc.

History, and religious influence
Compared to pre-modern accounts of causality, laws of nature fill the role played by divine causality on the one hand, and accounts such as Plato's theory of forms on the other.

In all accounts of causality, the idea that there are underlying regularities in nature dates to prehistoric times, since even the recognition of cause-and-effect relationships is an implicit recognition that there are laws of nature.

Progress in identifying laws per se, though, seems to have been hampered by belief in animism, and by the attribution of many effects that do not have readily identifiable causes&mdash;such as meteorological and astronomical phenomena&mdash; to the actions of various gods,spirits, supernatural beings, etc. Early attempts to formulate laws in material terms were made by ancient philosophers, including Aristotle, but suffered from lack of definitions, lack of experimenting, and hence had various misconceptions - such as the assumption that observed effects were due to intrinsic properties of objects, e.g. "heaviness", "lightness", "wetness", etc - which were results lacking accurate supporting experimental data.

The formal and precise formulation of what are today recognized as correct statements of the laws of nature did not begin until the 17th century in Europe, with the beginning of accurate experimentation and development of advanced form of mathematics (see scientific method).

Despite lay belief that laws of nature are somehow God(s) given), there is no scientific evidence of that - because most laws are either simply definitions or statements of identity (or symmetry), irrespective of its causes.

In essence, modern science aims at minimal speculation about metaphysics, and laws of nature are the result. The case for this method was perhaps most crucially made in the works of Francis Bacon.

Significance, and renown of discoverers
Because of the understanding they permit regarding the nature of our existence, and because of their above-mentioned power for problem-solving and prediction, the discoveries or defining (creation) of the new laws of nature are considered among the greatest intellectual achievements of humanity. Due to their subtlety, their discovery has typically required extraordinary powers of observation and insight, and their discoverers are typically considered among the best and brightest by others in their fields, and, notably in the cases of Newton, Einstein, Emmy Noether, in the general populace as well.

Currently search for most fundamental law(s) and most fundamental object(s) of nature is synonimus to search of most general mathematical symmetry group.

Other fields
Some mathematical theorems and axioms are referred to as laws because they provide logical foundation to empirical laws.

Examples of other observed phenomena often described as laws include the Titius-Bode law of planetary positions, Zipf's law of linguistics, Moore's law of technological growth. Many of these laws fall within the scope of uncomfortable science. Other laws are pragmatic and observational, such as the law of unintended consequences. By analogy, principles in other fields of study are sometimes loosely referred to as "laws". These include Occam's razor as a principle of philosophy and the Pareto principle of economics.