Definitions

# Physical law

A physical law or scientific law is a scientific generalization based on empirical observations of physical behavior (i.e. the law of nature ). Laws of nature are observable. Scientific laws are empirical, describing the observable laws. Empirical laws are typically conclusions based on repeated scientific experiments and simple observations, over many years, and which have become accepted universally within the scientific community. The production of a summary description of our environment in the form of such laws is a fundamental aim of science.

Laws of nature are distinct from religious and civil law, and should not be confused with the concept of natural law. Nor should 'physical law' be confused with 'law of physics' - the term 'physical law' usually covers laws in other sciences (e.g. biology) as well.

## Description

Several general properties of physical laws have been identified (see Davies (1992) and Feynman (1965) as noted, although each of the characterizations are not necessarily original to them. Physical laws are:

• True, at least within their regime of validity. By definition, there have never been repeatable contradicting observations.
• Universal. They appear to apply everywhere in the universe. (Davies, 1992:82)
• Simple. They are typically expressed in terms of a single mathematical equation. (Davies)
• Absolute. Nothing in the universe appears to affect them. (Davies, 1992:82)
• Stable. Unchanged since first discovered (although they may have been shown to be approximations of more accurate laws—see "Laws as approximations" below),
• Omnipotent. Everything in the universe apparently must comply with them (according to observations). (Davies, 1992:83)
• Generally conservative of quantity. (Feynman, 1965:59)
• 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 Philosophiae Naturalis Principia Mathematica, and in 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 definitions

Those laws which are just mathematical definitions (say, fundamental law of mechanics - second Newton's law $F = frac\left\{dp\right\}\left\{dt\right\}$), or uncertainty principle, or least action principle, or causality - are absolutely correct simply by definition. They are extremely useful - because they can not be violated nor falsified.

## Laws being consequences of mathematical symmetries

Other laws reflect mathematical symmetries found in Nature (say, Pauli exclusion principle reflects identity of electrons, conservation laws reflect homogeneity of space, time, and rotational symmetry of space-time). Laws are constantly being checked experimentally to higher and higher degrees of accuracy. The fact that they have never been seen repeatably violated does not preclude testing them at increased accuracy, which is one of the 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 below), 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 better viewed as a series of improving and more precise generalizations.

## Laws as approximations

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 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.

## Origin of laws of nature

Some extremely important scientific laws are simply definitions of the observable laws of nature. For example, the central law of mechanics F = dp/dt (Newton's second "law" of mechanics) is just a mathematical definition of force. Although the concept of force predates Newton's law , there was no mathematical definition of force before Newton. The principle of least action (or principle of stationary action), Schroedinger equation, Heisenberg uncertainty principle, causality and a few other laws also fall into this category (of mathematical definitions).

Most of the other fundamental physical laws are mathematical consequences of various mathematical symmetries. Specifically, Noether's theorem connects any conservation law to certain symmetry. For example, conservation of energy is a consequence of the shift symmetry of time (no moment of time is different from any other), while conservation of momentum is a consequence of the symmetry (homogeneity) of space (no place in space is special, or different than any other). The indistinguishability of all particles of each fundamental type (say, electrons, or photons) results in the Dirac and Bose statistics which in turn result in the Pauli exclusion principle for fermions and in Bose-Einstein condensation for bosons. The rotational symmetry between time and space coordinate axes (when one is taken as imaginary, another as real) 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.

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

So to large extent scientific laws are mathematical expressions of certain observable simplicities (symmetries) of space, time, etc. In other words, there are quantities (e.g. the origin of the coordinates for time and space, the identity of a specific electron) upon which nothing depends. Currently the search for the most fundamental law(s) and most fundamental object(s) of nature is synonymous with the search for the most general mathematical symmetry group that can be applied to the fundamental interactions.

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, was limited by the belief in animism, and by the attribution of many effects that do not have readily obvious causes—such as meteorological, astronomical and biological phenomena— to the actions of various gods, spirits, holy ghosts, supernatural beings, etc. Early attempts to formulate laws in material terms were made by ancient philosophers, including Aristotle, but suffered both from lack of definitions and lack of accurate observations (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 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).

In essence, modern science aims at minimal speculation about metaphysics. This results in spectacular efficiency of science both in explaining how universe works and in making our life better, longer and more interesting (via building effective shelters, transportation, communication and entertainment as well as helping to feed population, cure diseases, etc).

## 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 and Einstein by the general populace as well.

## 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 sometimes 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.