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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:
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, in terms of the more fundamental '''laws'''. Examples ''Main article'': 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 Law s, Ohm's Law , 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 ), 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 mathemetical definition of force (introduced first by Newton himself). The Principle Of Least Action (or Principle Of Stationary Action ), Heizenberg Uncertainty Principle , and a few other laws fall into this category. Most of the other laws are mathematical consequenses of various mathematical Symmetries (see Emmy Noether theorem as a proof of this), which physicists believe without justification. For example, conservation of energy is a consequence of the shift symmetry of time (no time moment is different than any other), while conservation of momentum is a consequence of the symmetry (homogeniety) of space (no place in space is different than any other). Indistinguishability of similar particles (say, electrons) results from Dirac and Bose statistics which in turn results from Pauli exclusion principle for fermions, leading to Bose condensation for bosons. Symmetry between Time and Space coordinate axis results in Lorentz Transformations (which in turn results in Special Relativity ). Symmetry between Inertial and gravitational Mass results in General Relativity and so on. So to some extent laws of nature are not laws of nature per se, but mathematical expressions of certain assumed simplicities (symmetries) of existing Universe. The application of these expressions to our needs has resulted in spectacular efficacy of science – its power to solve otherwise intractable problems, and made increasingly accurate predictions. History, and religious influence The idea that there are underlying laws 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—such as meteorological and astronomical phenomena—to the actions of Gods . Early attempts to formulate laws in material terms were made by ancient philosophers, including Aristotle , but suffered from various misconceptions, such as the assumption that observed effects were due to intrinsic properties of objects, e.g. "heaviness", "lightness", 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 institution of the use of the Scientific Method . Despite laymen belief that laws of nature are somehow God(s) given, there is little scientific evidence of that. However, it is questionable whether we can meaningfully speak of the scientific evidence for proposed origins of laws. To do so would surely require knowledge outside of the universe; by definition out of the realm of science. 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 of the 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. Other fields Some Mathematical Theorem s and Axiom s 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 . See also
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