# Physical law

### Physical law

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.

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

• Description 1
• Examples 2
• Laws as definitions 3
• Laws being consequences of mathematical symmetries 4
• Laws as approximations 5
• Physical laws derived from symmetry principles 6
• History 7
• Other fields 8
• Notes 10
• References 11

## 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.

## Examples

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

Some "scientific laws" appear to be mathematical definitions (e.g., Newton's Second law F = dpdt, 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.)

## 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.

## 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.

## 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.

## History

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.

The observation that there are underlying regularities in nature dates to prehistoric times, since the recognition of cause-and-effect relationships is an implicit recognition that there are laws of nature. The recognition of such regularities as independent scientific laws per se, though, was limited by their entanglement 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. Observation and speculation about nature were intimately bound up with metaphysics and morality.

In Europe, systematic theorizing about nature (physis) began with the early Greek philosophers and scientists and continued into the Hellenistic and Roman imperial periods, during which times the intellectual influence of Roman law increasingly became paramount.
The formula "law of nature" first appears as "a live metaphor" favored by Latin poets Lucretius, Virgil, Ovid, Manilius, in time gaining a firm theoretical presence in the prose treatises of Seneca and Pliny. Why this Roman origin? According to [historian and classicist Daryn] Lehoux's persuasive narrative,[3] the idea was made possible by the pivotal role of codified law and forensic argument in Roman life and culture.
For the Romans . . . the place par excellence where ethics, law, nature, religion and politics overlap is the law court. When we read Seneca's Natural Questions, and watch again and again just how he applies standards of evidence, witness evaluation, argument and proof, we can recognize that we are reading one of the great Roman rhetoricians of the age, thoroughly immersed in forensic method. And not Seneca alone. Legal models of scientific judgment turn up all over the place, and for example prove equally integral to Ptolemy's approach to verification, where the mind is assigned the role of magistrate, the senses that of disclosure of evidence, and dialectical reason that of the law itself.[4]

The precise formulation of what are now recognized as modern and valid statements of the laws of nature dates from the 17th century in Europe, with the beginning of accurate experimentation and development of advanced form of mathematics.. The modern scientific method which took shape at this time (with Francis Bacon and Galileo) aimed at total separation of science from theology, with minimal speculation about metaphysics and ethics. Natural law in the political sense, conceived as universal (i.e., divorced from sectarian religion and accidents of place), was also elaborated in this period (by Grotius, Spinoza, and Hobbes, to name a few).

## 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.

## Notes

1. ^ "Law of Nature".
2. ^ Some modern 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. See Norman Swartz, The Concept of Physical Law (New York: Cambridge University Press), 1985. Second edition available online [1].
3. ^ in Daryn Lehoux, What Did the Romans Know? An Inquiry into Science and Worldmaking (Chicago: University of Chicago Press, 2012), reviewed by David Sedley, "When Nature Got its Laws", Times Literary Supplement (October 12, 2012).
4. ^ Sedley, "When Nature Got Its Laws", Times Literary Supplement (October 12, 2012).

## References

• Novum Organum.
• John Barrow (1991). Theories of Everything: The Quest for Ultimate Explanations. (ISBN 0-449-90738-4)
• Davies, Paul (1992) The Mind of God. (ISBN 0-671-79718-2)
• Feynman, Richard (1965) The Character of Physical Law. (ISBN 0-679-60127-9)
• Daryn Lehoux (2012). What Did the Romans Know? An Inquiry into Science and Worldmaking. University of Chicago Press. (ISBN 9780226471143)