[1] The term law has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of natural science (physics, chemistry, astronomy, geoscience, biology).
It is generally understood that they implicitly reflect, though they do not explicitly assert, causal relationships fundamental to reality, and are discovered rather than invented.
Laws differ from hypotheses and postulates, which are proposed during the scientific process before and during validation by experiment and observation.
Social sciences such as economics have also attempted to formulate scientific laws, though these generally have much less predictive power.
Factual and well-confirmed statements like "Mercury is liquid at standard temperature and pressure" are considered too specific to qualify as scientific laws.
A central problem in the philosophy of science, going back to David Hume, is that of distinguishing causal relationships (such as those implied by laws) from principles that arise due to constant conjunction.
[6] Laws differ from scientific theories in that they do not posit a mechanism or explanation of phenomena: they are merely distillations of the results of repeated observation.
Laws are constantly being tested experimentally to increasing degrees of precision, which is one of the main goals of science.
Well-established laws have indeed been invalidated in some special cases, but the new formulations created to explain the discrepancies generalize upon, rather than overthrow, the originals.
A scientific law is "inferred 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".
Some examples of widely accepted impossibilities in physics are perpetual motion machines, which violate the law of conservation of energy, exceeding the speed of light, which violates the implications of special relativity, the uncertainty principle of quantum mechanics, which asserts the impossibility of simultaneously knowing both the position and the momentum of a particle, and Bell's theorem: no physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics.
Special relativity uses rapidity to express motion according to the symmetries of hyperbolic rotation, a transformation mixing space and time.
The inverse square law of interactions mediated by massless bosons is the mathematical consequence of the 3-dimensionality of space.
Intuitively, the divergence (denoted ∇⋅) of a vector field is a measure of flux diverging radially outwards from a point, so the negative is the amount piling up at a point; hence the rate of change of density in a region of space must be the amount of flux leaving or collecting in some region (see the main article for details).
[12] Notice L is not the total energy E of the system due to the difference, rather than the sum: The following[13][14] general approaches to classical mechanics are summarized below in the order of establishment.
Newton's is commonly used due to simplicity, but Hamilton's and Lagrange's equations are more general, and their range can extend into other branches of physics with suitable modifications.
Solving the equation for the geometry of space warped due to the mass distribution gives the metric tensor.
Kepler's laws, though originally discovered from planetary observations (also due to Tycho Brahe), are true for any central forces.
Other laws : Classically, optics is based on a variational principle: light travels from one point in space to another in the shortest time.
(see Dirac notation) is the instantaneous quantum state vector at time t, position r, i is the unit imaginary number, ħ = h/2π is the reduced Planck constant.
Quantitative analysis : The most fundamental concept in chemistry is the law of conservation of mass, which states that there is no detectable change in the quantity of matter during an ordinary chemical reaction.
[17][18] Henry Byerly, an American philosopher known for his work on evolutionary theory, discussed the problem of interpreting a principle of natural selection as a law.
[18] His approach was to express relative fitness, the propensity of a genotype to increase in proportionate representation in a competitive environment, as a function of adaptedness (adaptive design) of the organism.
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 physical phenomena—to the actions of gods, spirits, supernatural beings, etc.
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.
According to [historian and classicist Daryn] Lehoux's persuasive narrative,[19] the idea was made possible by the pivotal role of codified law and forensic argument in Roman life and culture.
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.
[20]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 the development of advanced forms of mathematics.
"[23] The modern scientific method which took shape at this time (with Francis Bacon (1561–1626) and Galileo (1564–1642)) contributed to a trend of separating 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 scholars such as Grotius (1583–1645), Spinoza (1632–1677), and Hobbes (1588–1679).)