A physical law or scientific law is "a theoretical principle deduced from particular facts, applicable to a defined group or class of phenomena, and expressible by the statement that a particular phenomenon always occurs if certain conditions be present."[1] Physical laws are typically conclusions based on repeated scientific experiments and 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. These terms are not used the same way by all authors. Some philosophers, e.g. Norman Swartz, use "physical law" to mean the laws of nature as they truly are and not as they are inferred by scientists.[2]
Laws of nature are distinct from religious and civil law, and should not be confused with the concept of natural law, which deduces rules of moral behavior. Nor should "physical law" be confused with "laws of physics" - the term "physical law" usually covers laws in other sciences (e.g. biology) as well.
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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:
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.
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.
Some "scientific laws" appear to be mathematical definitions (e.g., Newton's Second law F = dp⁄dt, or the uncertainty principle, or the principle of least action, or causality). While these "scientific laws" explain what our senses perceive, they are still empirical and, thus, they are not "mathematical" facts. (Reference to a "law" often suggests a "fact", although "facts" do not exist scientifically a priori.)
Other laws reflect mathematical symmetries found in Nature (say, Pauli exclusion principle reflects identity of electrons, conservation laws reflect homogeneity of space, time, Lorentz transformations reflect rotational symmetry of space-time). Laws are constantly being checked experimentally to higher and higher degrees of precision. This is one of the main goals of science. The fact that laws have never been seen to be violated does not preclude testing them at increased accuracy or 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 seen. However, fundamental changes to the laws are extremely unlikely, 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.
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.
Many fundamental physical laws are mathematical consequences of various symmetries of space, time, or other aspects of nature. Specifically, Noether's theorem connects some conservation laws to certain symmetries. 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 quantum 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 result in special relativity theory. Symmetry between inertial and gravitational mass results in general relativity.
The inverse square law of interactions mediated by massless bosons is the mathematical consequence of the 3-dimensionality of space.
One strategy in the search for the most fundamental laws of nature is to search for the most general mathematical symmetry group that can be applied to the fundamental interactions.
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, 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.).
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.