A physical law or scientific law is, according to the Oxford English dictionary, "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.
The distinction between natural law in the political-legal sense and law of nature or physical law in the scientific sense is a modern one, both concepts being equally derived from physis, the Greek word (translated into Latin as natura) for nature.[2]
Contents [hide]
1 Description
2 Examples
3 Laws as definitions
4 Laws being consequences of mathematical symmetries
5 Laws as approximations
6 Physical laws derived from symmetry principles
7 History: religion, Greek philosophy, and the role of Roman law in the development of the concept of physical law
8 Other fields
9 See also
10 Notes
11 References
12 External links
[edit]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)
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.
[edit]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.
[edit]Laws as definitions
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.)
[edit]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, 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.
[edit]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.
[edit]Physical laws derived from symmetry principles
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.
Ras Kass or Krishna, I forget... prove that I'm wrong
