Scientific law

Laws of science or scientific laws are statements that describe or predict a range of natural phenomena.[1] A scientific law is a statement based on repeated experiments or observations that describe some aspect of the natural world. The term law has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of natural science (physics, chemistry, biology, geology, astronomy, etc.). Laws are developed from data and can be further developed through mathematics; in all cases they are directly or indirectly based on empirical evidence. 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.[2]

Scientific laws summarize the results of experiments or observations, usually within a certain range of application. In general, the accuracy of a law does not change when a new theory of the relevant phenomenon is worked out, but rather the scope of the law's application, since the mathematics or statement representing the law does not change. As with other kinds of scientific knowledge, laws do not have absolute certainty (as mathematical theorems or identities do), and it is always possible for a law to be contradicted, restricted, or extended by future observations. A law can usually be formulated as one or several statements or equations, so that it can be used to predict the outcome of an experiment, given the circumstances of the processes taking place.

Laws differ from hypotheses and postulates, which are proposed during the scientific process before and during validation by experiment and observation. Hypotheses and postulates are not laws since they have not been verified to the same degree, although they may lead to the formulation of laws. Laws are narrower in scope than scientific theories, which may entail one or several laws.[3] Science distinguishes a law or theory from facts.[4] Calling a law a fact is ambiguous, an overstatement, or an equivocation.[5] The nature of scientific laws has been much discussed in philosophy, but in essence scientific laws are simply empirical conclusions reached by scientific method; they are intended to be neither laden with ontological commitments nor statements of logical absolutes.

Scientific law versus Scientific theories
Scientific theories explain why something happens, whereas scientific law records what happens.

Overview

A scientific law always applies under the same conditions, and implies that there is a causal relationship involving its elements. 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. As such, a law is limited in applicability to circumstances resembling those already observed, and may be found false when extrapolated. Ohm's law only applies to linear networks, Newton's law of universal gravitation only applies in weak gravitational fields, the early laws of aerodynamics such as Bernoulli's principle do not apply in case of compressible flow such as occurs in transonic and supersonic flight, Hooke's law only applies to strain below the elastic limit, Boyle's law applies with perfect accuracy only to the ideal gas, etc. These laws remain useful, but only under the conditions where they apply.

Many laws take mathematical forms, and thus can be stated as an equation; for example, the law of conservation of energy can be written as , where E is the total amount of energy in the universe. Similarly, the first law of thermodynamics can be written as , and Newton's Second law can be written as F = ​dpdt. While these scientific laws explain what our senses perceive, they are still empirical, and so are not like mathematical theorems (which can be proved purely by mathematics and not by scientific experiment).

Like theories and hypotheses, laws make predictions (specifically, they predict that new observations will conform to the law), and can be falsified if they are found in contradiction with new data.

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.

Laws are constantly being tested experimentally to higher and higher degrees of precision. This is one of the main goals of science. Just because laws have never been observed to be violated does not preclude testing them at increased accuracy or in 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 observed. 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. That is, the invalidated laws have been found to be only close approximations, 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.

Properties

Scientific laws are typically conclusions based on repeated scientific experiments and observations over many years and which have become accepted universally within the scientific community. 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."[7] The production of a summary description of our environment in the form of such laws is a fundamental aim of science.

Several general properties of scientific laws, particularly when referring to laws in physics, have been identified. They 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.[8]:82
  • Simple. They are typically expressed in terms of a single mathematical equation.
  • Absolute. Nothing in the universe appears to affect them.[8]:82
  • Stable. Unchanged since first discovered (although they may have been shown to be approximations of more accurate laws),
  • Omnipotent. Everything in the universe apparently must comply with them (according to observations).[8]:83
  • Generally conservative of quantity.[9]:59
  • Often expressions of existing homogeneities (symmetries) of space and time.[9]
  • Typically theoretically reversible in time (if non-quantum), although time itself is irreversible.[9]

The term "scientific law" is traditionally associated with the natural sciences, though the social sciences also contain laws.[10] For example, Zipf's law is a law in the social sciences which is based on mathematical statistics. In these cases, laws may describe general trends or expected behaviors rather than being absolutes.

Laws as consequences of mathematical symmetries

Some laws reflect mathematical symmetries found in Nature (e.g. the Pauli exclusion principle reflects identity of electrons, conservation laws reflect homogeneity of space, time, and Lorentz transformations reflect rotational symmetry of spacetime). 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.

Laws of physics

Conservation laws

Conservation and symmetry

Most significant laws in science are conservation laws. These fundamental laws follow from homogeneity of space, time and phase, in other words symmetry.

  • Noether's theorem: Any quantity which has a continuous differentiable symmetry in the action has an associated conservation law.
  • Conservation of mass was the first law of this type to be understood, since most macroscopic physical processes involving masses, for example collisions of massive particles or fluid flow, provide the apparent belief that mass is conserved. Mass conservation was observed to be true for all chemical reactions. In general this is only approximative, because with the advent of relativity and experiments in nuclear and particle physics: mass can be transformed into energy and vice versa, so mass is not always conserved, but part of the more general conservation of mass-energy.
  • Conservation of energy, momentum and angular momentum for isolated systems can be found to be symmetries in time, translation, and rotation.
  • Conservation of charge was also realized since charge has never been observed to be created or destroyed, and only found to move from place to place.

Continuity and transfer

Conservation laws can be expressed using the general continuity equation (for a conserved quantity) can be written in differential form as:

where ρ is some quantity per unit volume, J is the flux of that quantity (change in quantity per unit time per unit area). 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 main article for details). In the table below, the fluxes, flows for various physical quantities in transport, and their associated continuity equations, are collected for comparison.

Physics, conserved quantity Conserved quantity q Volume density ρ (of q) Flux J (of q) Equation
Hydrodynamics, fluids
m = mass (kg) ρ = volume mass density (kg m−3) ρ u, where

u = velocity field of fluid (m s−1)

Electromagnetism, electric charge q = electric charge (C) ρ = volume electric charge density (C m−3) J = electric current density (A m−2)
Thermodynamics, energy E = energy (J) u = volume energy density (J m−3) q = heat flux (W m−2)
Quantum mechanics, probability P = (r, t) = ∫|Ψ|2d3r = probability distribution ρ = ρ(r, t) = |Ψ|2 = probability density function (m−3),

Ψ = wavefunction of quantum system

j = probability current/flux

More general equations are the convection–diffusion equation and Boltzmann transport equation, which have their roots in the continuity equation.

Laws of classical mechanics

Principle of least action

All of classical mechanics, including Newton's laws, Lagrange's equations, Hamilton's equations, etc., can be derived from this very simple principle:

where is the action; the integral of the Lagrangian

of the physical system between two times t1 and t2. The kinetic energy of the system is T (a function of the rate of change of the configuration of the system), and potential energy is V (a function of the configuration and its rate of change). The configuration of a system which has N degrees of freedom is defined by generalized coordinates q = (q1, q2, ... qN).

There are generalized momenta conjugate to these coordinates, p = (p1, p2, ..., pN), where:

The action and Lagrangian both contain the dynamics of the system for all times. The term "path" simply refers to a curve traced out by the system in terms of the generalized coordinates in the configuration space, i.e. the curve q(t), parameterized by time (see also parametric equation for this concept).

The action is a functional rather than a function, since it depends on the Lagrangian, and the Lagrangian depends on the path q(t), so the action depends on the entire "shape" of the path for all times (in the time interval from t1 to t2). Between two instants of time, there are infinitely many paths, but one for which the action is stationary (to the first order) is the true path. The stationary value for the entire continuum of Lagrangian values corresponding to some path, not just one value of the Lagrangian, is required (in other words it is not as simple as "differentiating a function and setting it to zero, then solving the equations to find the points of maxima and minima etc", rather this idea is applied to the entire "shape" of the function, see calculus of variations for more details on this procedure).[11]

Notice L is not the total energy E of the system due to the difference, rather than the sum:

The following[12][13] general approaches to classical mechanics are summarized below in the order of establishment. They are equivalent formulations, Newton's is very 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.

Laws of motion
Principle of least action:

The Euler–Lagrange equations are:

Using the definition of generalized momentum, there is the symmetry:

Hamilton's equations

The Hamiltonian as a function of generalized coordinates and momenta has the general form:

Hamilton–Jacobi equation
Newton's laws

Newton's laws of motion

They are low-limit solutions to relativity. Alternative formulations of Newtonian mechanics are Lagrangian and Hamiltonian mechanics.

The laws can be summarized by two equations (since the 1st is a special case of the 2nd, zero resultant acceleration):

where p = momentum of body, Fij = force on body i by body j, Fji = force on body j by body i.

For a dynamical system the two equations (effectively) combine into one:

in which FE = resultant external force (due to any agent not part of system). Body i does not exert a force on itself.

From the above, any equation of motion in classical mechanics can be derived.

Corollaries in mechanics
Corollaries in fluid mechanics

Equations describing fluid flow in various situations can be derived, using the above classical equations of motion and often conservation of mass, energy and momentum. Some elementary examples follow.

Laws of gravitation and relativity

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.

Modern laws

Special relativity

Postulates of special relativity are not "laws" in themselves, but assumptions of their nature in terms of relative motion.

Often two are stated as "the laws of physics are the same in all inertial frames" and "the speed of light is constant". However the second is redundant, since the speed of light is predicted by Maxwell's equations. Essentially there is only one.

The said posulate leads to the Lorentz transformations – the transformation law between two frame of references moving relative to each other. For any 4-vector

this replaces the Galilean transformation law from classical mechanics. The Lorentz transformations reduce to the Galilean transformations for low velocities much less than the speed of light c.

The magnitudes of 4-vectors are invariants - not "conserved", but the same for all inertial frames (i.e. every observer in an inertial frame will agree on the same value), in particular if A is the four-momentum, the magnitude can derive the famous invariant equation for mass-energy and momentum conservation (see invariant mass):

in which the (more famous) mass-energy equivalence E = mc2 is a special case.

General relativity

General relativity is governed by the Einstein field equations, which describe the curvature of space-time due to mass-energy equivalent to the gravitational field. Solving the equation for the geometry of space warped due to the mass distribution gives the metric tensor. Using the geodesic equation, the motion of masses falling along the geodesics can be calculated.

Gravitomagnetism

In a relatively flat spacetime due to weak gravitational fields, gravitational analogues of Maxwell's equations can be found; the GEM equations, to describe an analogous gravitomagnetic field. They are well established by the theory, and experimental tests form ongoing research.[14]

Einstein field equations (EFE):

where Λ = cosmological constant, Rμν = Ricci curvature tensor, Tμν = Stress–energy tensor, gμν = metric tensor

Geodesic equation:

where Γ is a Christoffel symbol of the second kind, containing the metric.

GEM Equations

If g the gravitational field and H the gravitomagnetic field, the solutions in these limits are:

where ρ is the mass density and J is the mass current density or mass flux.

In addition there is the gravitomagnetic Lorentz force:

where m is the rest mass of the particlce and γ is the Lorentz factor.

Classical laws

Kepler's Laws, though originally discovered from planetary observations (also due to Tycho Brahe), are true for any central forces.[15]

Newton's law of universal gravitation:

For two point masses:

For a non uniform mass distribution of local mass density ρ (r) of body of Volume V, this becomes:

Gauss' law for gravity:

An equivalent statement to Newton's law is:

Kepler's 1st Law: Planets move in an ellipse, with the star at a focus

where

is the eccentricity of the elliptic orbit, of semi-major axis a and semi-minor axis b, and l is the semi-latus rectum. This equation in itself is nothing physically fundamental; simply the polar equation of an ellipse in which the pole (origin of polar coordinate system) is positioned at a focus of the ellipse, where the orbited star is.

Kepler's 2nd Law: equal areas are swept out in equal times (area bounded by two radial distances and the orbital circumference):

where L is the orbital angular momentum of the particle (i.e. planet) of mass m about the focus of orbit,

Kepler's 3rd Law: The square of the orbital time period T is proportional to the cube of the semi-major axis a:

where M is the mass of the central body (i.e. star).

Thermodynamics

Laws of thermodynamics
First law of thermodynamics: The change in internal energy dU in a closed system is accounted for entirely by the heat δQ absorbed by the system and the work δW done by the system:

Second law of thermodynamics: There are many statements of this law, perhaps the simplest is "the entropy of isolated systems never decreases",

meaning reversible changes have zero entropy change, irreversible process are positive, and impossible process are negative.

Zeroth law of thermodynamics: If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with one another.

Third law of thermodynamics:

As the temperature T of a system approaches absolute zero, the entropy S approaches a minimum value C: as T → 0, S → C.
For homogeneous systems the first and second law can be combined into the Fundamental thermodynamic relation:
Onsager reciprocal relations: sometimes called the Fourth Law of Thermodynamics
;
.
now improved by other equations of state

Electromagnetism

Maxwell's equations give the time-evolution of the electric and magnetic fields due to electric charge and current distributions. Given the fields, the Lorentz force law is the equation of motion for charges in the fields.

Maxwell's equations

Gauss's law for electricity

Gauss's law for magnetism

Faraday's law

Ampère's circuital law (with Maxwell's correction)

Lorentz force law:
Quantum electrodynamics (QED): Maxwell's equations are generally true and consistent with relativity - but they do not predict some observed quantum phenomena (e.g. light propagation as EM waves, rather than photons, see Maxwell's equations for details). They are modified in QED theory.

These equations can be modified to include magnetic monopoles, and are consistent with our observations of monopoles either existing or not existing; if they do not exist, the generalized equations reduce to the ones above, if they do, the equations become fully symmetric in electric and magnetic charges and currents. Indeed, there is a duality transformation where electric and magnetic charges can be "rotated into one another", and still satisfy Maxwell's equations.

Pre-Maxwell laws

These laws were found before the formulation of Maxwell's equations. They are not fundamental, since they can be derived from Maxwell's Equations. Coulomb's Law can be found from Gauss' Law (electrostatic form) and the Biot–Savart Law can be deduced from Ampere's Law (magnetostatic form). Lenz' Law and Faraday's Law can be incorporated into the Maxwell-Faraday equation. Nonetheless they are still very effective for simple calculations.

Other laws

Photonics

Classically, optics is based on a variational principle: light travels from one point in space to another in the shortest time.

In geometric optics laws are based on approximations in Euclidean geometry (such as the paraxial approximation).

In physical optics, laws are based on physical properties of materials.

In actuality, optical properties of matter are significantly more complex and require quantum mechanics.

Laws of quantum mechanics

Quantum mechanics has its roots in postulates. This leads to results which are not usually called "laws", but hold the same status, in that all of quantum mechanics follows from them.

One postulate that a particle (or a system of many particles) is described by a wavefunction, and this satisfies a quantum wave equation: namely the Schrödinger equation (which can be written as a non-relativistic wave equation, or a relativistic wave equation). Solving this wave equation predicts the time-evolution of the system's behaviour, analogous to solving Newton's laws in classical mechanics.

Other postulates change the idea of physical observables; using quantum operators; some measurements can't be made at the same instant of time (Uncertainty principles), particles are fundamentally indistinguishable. Another postulate; the wavefunction collapse postulate, counters the usual idea of a measurement in science.

Quantum mechanics, Quantum field theory

Schrödinger equation (general form): Describes the time dependence of a quantum mechanical system.

The Hamiltonian (in quantum mechanics) H is a self-adjoint operator acting on the state space, (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's constant.

Wave-particle duality

Planck–Einstein law: the energy of photons is proportional to the frequency of the light (the constant is Planck's constant, h).

De Broglie wavelength: this laid the foundations of wave–particle duality, and was the key concept in the Schrödinger equation,

Heisenberg uncertainty principle: Uncertainty in position multiplied by uncertainty in momentum is at least half of the reduced Planck constant, similarly for time and energy;

The uncertainty principle can be generalized to any pair of observables - see main article.

Wave mechanics

Schrödinger equation (original form):

Pauli exclusion principle: No two identical fermions can occupy the same quantum state (bosons can). Mathematically, if two particles are interchanged, fermionic wavefunctions are anti-symmetric, while bosonic wavefunctions are symmetric:

where ri is the position of particle i, and s is the spin of the particle. There is no way to keep track of particles physically, labels are only used mathematically to prevent confusion.

Radiation laws

Applying electromagnetism, thermodynamics, and quantum mechanics, to atoms and molecules, some laws of electromagnetic radiation and light are as follows.

Laws of chemistry

Chemical laws are those laws of nature relevant to chemistry. Historically, observations led to many empirical laws, though now it is known that chemistry has its foundations in quantum mechanics.

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. Modern physics shows that it is actually energy that is conserved, and that energy and mass are related; a concept which becomes important in nuclear chemistry. Conservation of energy leads to the important concepts of equilibrium, thermodynamics, and kinetics.

Additional laws of chemistry elaborate on the law of conservation of mass. Joseph Proust's law of definite composition says that pure chemicals are composed of elements in a definite formulation; we now know that the structural arrangement of these elements is also important.

Dalton's law of multiple proportions says that these chemicals will present themselves in proportions that are small whole numbers; although in many systems (notably biomacromolecules and minerals) the ratios tend to require large numbers, and are frequently represented as a fraction.

More modern laws of chemistry define the relationship between energy and its transformations.

Reaction kinetics and equilibria
  • In equilibrium, molecules exist in mixture defined by the transformations possible on the timescale of the equilibrium, and are in a ratio defined by the intrinsic energy of the molecules—the lower the intrinsic energy, the more abundant the molecule. Le Chatelier's principle states that the system opposes changes in conditions from equilibrium states, i.e. there is an opposition to change the state of an equilibrium reaction.
  • Transforming one structure to another requires the input of energy to cross an energy barrier; this can come from the intrinsic energy of the molecules themselves, or from an external source which will generally accelerate transformations. The higher the energy barrier, the slower the transformation occurs.
  • There is a hypothetical intermediate, or transition structure, that corresponds to the structure at the top of the energy barrier. The Hammond–Leffler postulate states that this structure looks most similar to the product or starting material which has intrinsic energy closest to that of the energy barrier. Stabilizing this hypothetical intermediate through chemical interaction is one way to achieve catalysis.
  • All chemical processes are reversible (law of microscopic reversibility) although some processes have such an energy bias, they are essentially irreversible.
  • The reaction rate has the mathematical parameter known as the rate constant. The Arrhenius equation gives the temperature and activation energy dependence of the rate constant, an empirical law.
Thermochemistry
Gas laws
Chemical transport

Geophysical laws

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, and 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.

History

The observation that there are underlying regularities in nature dates from 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.

According to a positivist view, when compared to pre-modern accounts of causality, laws of nature replace the need for divine causality on the one hand, and accounts such as Plato's theory of forms on the other.

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,[16] 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.[17]

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 forms of mathematics. During this period, natural philosophers such as Isaac Newton were influenced by a religious view which held that God had instituted absolute, universal and immutable physical laws.[18][19] In chapter 7 of The World, René Descartes described "nature" as matter itself, unchanging as created by God, thus changes in parts "are to be attributed to nature. The rules according to which these changes take place I call the 'laws of nature'."[20] 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).

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.[21]

See also

References

  1. ^ "law of nature". Oxford English Dictionary (3rd ed.). Oxford University Press. September 2005. (Subscription or UK public library membership required.)
  2. ^ William F. McComas (30 December 2013). The Language of Science Education: An Expanded Glossary of Key Terms and Concepts in Science Teaching and Learning. Springer Science & Business Media. p. 58. ISBN 978-94-6209-497-0.
  3. ^ "Definitions from". the NCSE. Retrieved 2019-03-18.
  4. ^ "The Role of Theory in Advancing 21st Century Biology: Catalyzing Transformative Research" (PDF). Report in Brief. The National Academy of Sciences. 2007.
  5. ^ Gould, Stephen Jay (1981-05-01). "Evolution as Fact and Theory". Discover. 2 (5): 34–37.
  6. ^ Honderich, Bike, ed. (1995), "Laws, natural or scientific", Oxford Companion to Philosophy, Oxford: Oxford University Press, pp. 474–476, ISBN 0-19-866132-0
  7. ^ "Law of nature". Oxford English Dictionary (3rd ed.). Oxford University Press. September 2005. (Subscription or UK public library membership required.)
  8. ^ a b c Davies, Paul (2005). The mind of God : the scientific basis for a rational world (1st Simon & Schuster pbk. ed.). New York: Simon & Schuster. ISBN 978-0-671-79718-8.
  9. ^ a b c Feynman, Richard (1994). The character of physical law (Modern Library ed.). New York: Modern Library. ISBN 978-0-679-60127-2.
  10. ^ Andrew S. C. Ehrenberg (1993), "Even the Social Sciences Have Laws", Nature, 365:6445 (30), page 385.(subscription required)
  11. ^ Feynman Lectures on Physics: Volume 2, R.P. Feynman, R.B. Leighton, M. Sands, Addison-Wesley, 1964, ISBN 0-201-02117-X
  12. ^ Encyclopaedia of Physics (2nd Edition), R.G. Lerner, G.L. Trigg, VHC Publishers, 1991, ISBN (Verlagsgesellschaft) 3-527-26954-1 (VHC Inc.) 0-89573-752-3
  13. ^ Classical Mechanics, T.W.B. Kibble, European Physics Series, McGraw-Hill (UK), 1973, ISBN 0-07-084018-0
  14. ^ Gravitation and Inertia, I. Ciufolini and J.A. Wheeler, Princeton Physics Series, 1995, ISBN 0-691-03323-4
  15. ^ 2.^ Classical Mechanics, T.W.B. Kibble, European Physics Series, McGraw-Hill (UK), 1973, ISBN 0-07-084018-0
  16. ^ 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 (12 October 2012).
  17. ^ Sedley, "When Nature Got Its Laws", Times Literary Supplement (12 October 2012).
  18. ^ Davies, Paul (2007-11-24). "Taking Science on Faith". The New York Times. ISSN 0362-4331. Retrieved 2016-10-07.
  19. ^ Harrison, Peter (8 May 2012). "Christianity and the rise of western science". ABC.
  20. ^ "Cosmological Revolution V: Descartes and Newton". bertie.ccsu.edu. Retrieved 2016-11-17.
  21. ^ 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].

Further reading

  • John Barrow (1991). Theories of Everything: The Quest for Ultimate Explanations. (ISBN 0-449-90738-4)
  • Dilworth, Craig (2007). "Appendix IV. On the nature of scientific laws and theories". Scientific progress : a study concerning the nature of the relation between successive scientific theories (4th ed.). Dordrecht: Springer Verlag. ISBN 978-1-4020-6353-4.
  • Francis Bacon (1620). Novum Organum.
  • Hanzel, Igor (1999). The concept of scientific law in the philosophy of science and epistemology : a study of theoretical reason. Dordrecht [u.a.]: Kluwer. ISBN 978-0-7923-5852-7.
  • Daryn Lehoux (2012). What Did the Romans Know? An Inquiry into Science and Worldmaking. University of Chicago Press. (ISBN 9780226471143)
  • Nagel, Ernest (1984). "5. Experimental laws and theories". The structure of science problems in the logic of scientific explanation (2nd ed.). Indianapolis: Hackett. ISBN 978-0-915144-71-6.
  • R. Penrose (2007). The Road to Reality. Vintage books. ISBN 0-679-77631-1.
  • Swartz, Norman (20 February 2009). "Laws of Nature". Internet encyclopedia of philosophy. Retrieved 7 May 2012.

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Dehradun

Dehradun (), also spelled Dehra Dun, is the interim capital of Uttarakhand, a state in India. Located in the Garhwal region, it lies 236 kilometres (147 mi) north of India's capital New Delhi and 168 kilometres (104 mi) from Chandigarh. It is one of the "Counter Magnets" of the National Capital Region (NCR) being developed as an alternative centre of growth to help ease the migration and population explosion in the Delhi metropolitan area and to establish a smart city at Dehradun. During the days of British Raj, the official name of the town was Dehra. At present, Gairsain, a hill-town between Garhwal and Kumaon regions and centrally located in Uttarakhand, is being developed as permanent capital of the state.

Dehradun is located in the Doon Valley on the foothills of the Himalayas nestled between the river Ganges on the east and the river Yamuna on the west. The city is famous for its picturesque landscape and slightly milder climate and provides a gateway to the surrounding region. It is well connected and in proximity to Himalayan tourist destinations such as Mussoorie, and Auli and the Hindu holy cities of Haridwar and Rishikesh along with the Himalayan pilgrimage circuit of Chota Char Dham.

Dehradun Municipal Corporation is locally known as Nagar Nigam Dehradun. Other urban entities involved in civic services and city governance and management include Mussoorie Dehradun Development Authority (MDDA), Special Area Development Authority (SADA), Jal Sansthan, and Jal Nigam among others. Dehradun is also known for its Basmati rice and bakery products.

Empirical statistical laws

An empirical statistical law or (in popular terminology) a law of statistics represents a type of behaviour that has been found across a number of datasets and, indeed, across a range of types of data sets. Many of these observances have been formulated and proved as statistical or probabilistic theorems and the term "law" has been carried over to these theorems. There are other statistical and probabilistic theorems that also have "law" as a part of their names that have not obviously derived from empirical observations. However, both types of "law" may be considered instances of a scientific law in the field of statistics. What distinguishes an empirical statistical law from a formal statistical theorem is the way these patterns simply appear in natural distributions, without a prior theoretical reasoning about the data.

Fact, Fiction, and Forecast

Fact, Fiction, and Forecast is a book by Nelson Goodman in which he explores some problems regarding scientific law and counterfactual conditionals and presents his New Riddle of Induction. Hilary Putnam described the book as "one of the few books that every serious student of philosophy in our time has to have read." According to Jerry Fodor, "it changed, probably permanently, the way we think about the problem of induction, and hence about a constellation of related problems like learning and the nature of rational decision." Noam Chomsky and Hilary Putnam attended some of the lectures on which the book is based as undergraduate students at the University of Pennsylvania, leading to a lifelong debate between the two over the question of whether the problems presented in the book imply that there must be an innate ordering of hypotheses.

Fitts's law

Fitts's law (often cited as Fitts' law) is a predictive model of human movement primarily used in human–computer interaction and ergonomics. This scientific law predicts that the time required to rapidly move to a target area is a function of the ratio between the distance to the target and the width of the target. Fitts's law is used to model the act of pointing, either by physically touching an object with a hand or finger, or virtually, by pointing to an object on a computer monitor using a pointing device.

Fitts's law has been shown to apply under a variety of conditions; with many different limbs (hands, feet, the lower lip, head-mounted sights, eye gaze), manipulanda (input devices), physical environments (including underwater), and user populations (young, old, special educational needs, and drugged participants).

Homeopathy

Homeopathy or homœopathy is a system of alternative medicine created in 1796 by Samuel Hahnemann, based on his doctrine of like cures like (similia similibus curentur), a claim that a substance that causes the symptoms of a disease in healthy people would cure similar symptoms in sick people. Homeopathy is a pseudoscience – a belief that is incorrectly presented as scientific. Homeopathic preparations are not effective for treating any condition; large-scale studies have found homeopathy to be no more effective than a placebo, indicating that any positive effects that follow treatment are not due to the treatment itself but instead to factors such as normal recovery from illness, or regression toward the mean.Hahnemann believed the underlying causes of disease were phenomena that he termed miasms, and that homeopathic preparations addressed these. The preparations are manufactured using a process of homeopathic dilution, in which a chosen substance is repeatedly diluted in alcohol or distilled water, each time with the containing vessel being struck against an elastic material, commonly a leather-bound book. Dilution typically continues well past the point where individual doses would not contain molecules of the original substance. Homeopaths select homeopathics by consulting reference books known as repertories, and by considering the totality of the patient's symptoms, personal traits, physical and psychological state, and life history.Homeopathy is not a plausible system of treatment, as its claims about drugs, illness, the human body, liquids, and solutions are contradicted by a wide range of discoveries across biology, psychology, physics and chemistry made in the two centuries since its invention. Although some clinical trials produce positive results, multiple systematic reviews have shown that this is because of chance, flawed research methods, and reporting bias. Homeopathic practice has been described as unethical because it discourages the use of effective treatments, with the World Health Organization warning against using homeopathy to try to treat severe diseases such as HIV and malaria. The continued practice of homeopathy, despite a lack of evidence of efficacy, has led to it being characterized within the scientific and medical communities as nonsense, quackery, and a sham.There have been four large scale assessments of homeopathy by national or international bodies: the Australian National Health and Medical Research Council; the United Kingdom's House of Commons Science and Technology Committee; the European Academies' Science Advisory Council; and the Swiss Federal Health Office. Each concluded that homeopathy is ineffective, and recommended against the practice receiving any further funding. The National Health Service in England has announced a policy of not funding homeopathic medicine because it is "a misuse of resources". They called on the UK Department of Health to add homeopathic remedies to the blacklist of forbidden prescription items, and the NHS ceased funding homeopathic remedies in November 2017.

Index of philosophy of science articles

An index list of articles about the philosophy of science.

Inductive reasoning

Inductive reasoning is a method of reasoning in which the premises are viewed as supplying some evidence for the truth of the conclusion; this is in contrast to deductive reasoning. While the conclusion of a deductive argument is certain, the truth of the conclusion of an inductive argument may be probable, based upon the evidence given.Many dictionaries define inductive reasoning as the derivation of general principles from specific observations, though there are many inductive arguments that do not have that form.

Naomi Weisstein

Naomi Weisstein (1939 – March 2015) was an American professor of psychology, a neuroscientist, and an author.

Natural law (disambiguation)

Natural law is law that exists independently of the positive law of a given political order, society or nation-state.

Natural law may also refer to:

"Natural Law" (Star Trek: Voyager), a Star Trek: Voyager episode

Natural-law argument, an argument for the existence of God

Natural Law Party, a trans-national union of political parties, with national branches in over 80 countries

Natural Law Party of Canada

Natural Law Party (Ireland)

Natural Law Party of Israel

Natural Law Party of New Zealand

Natural Law Party of Ontario

Natural Law Party of Quebec

Natural Law Party (Trinidad and Tobago)

Natural Law Party (United States)

Scientific law, statements based on experimental observations that describe some aspect of the world

Physics

Physics (from Ancient Greek: φυσική (ἐπιστήμη), romanized: physikḗ (epistḗmē), lit. 'knowledge of nature', from φύσις phýsis "nature") is the natural science that studies matter, its motion, and behavior through space and time, and that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over much of the past two millennia, physics, chemistry, biology, and certain branches of mathematics, were a part of natural philosophy, but during the Scientific Revolution in the 17th century these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics which are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy.

Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism, solid-state physics, and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

Principle

A principle is a proposition or value that is a guide for behavior or evaluation. In law, it is a rule that has to be or usually is to be followed, or can be desirably followed, or is an inevitable consequence of something, such as the laws observed in nature or the way that a system is constructed. The principles of such a system are understood by its users as the essential characteristics of the system, or reflecting system's designed purpose, and the effective operation or use of which would be impossible if any one of the principles was to be ignored. A system may be explicitly based on and implemented from a document of principles as was done in IBM's 360/370 Principles of Operation.

Examples of principles are, entropy in a number of fields, least action in physics, those in descriptive comprehensive and fundamental law: doctrines or assumptions forming normative rules of conduct, separation of church and state in statecraft, the central dogma of molecular biology, fairness in ethics, etc.

In common English, it is a substantive and collective term referring to rule governance, the absence of which, being "unprincipled", is considered a character defect. It may also be used to declare that a reality has diverged from some ideal or norm as when something is said to be true only "in principle" but not in fact.

Science and technology in Jamaica

Since the late 3477, the Jamaican government has set an agenda to push the development of technology in Jamaica. The goal is to make Jamaica a significant player in the arena of information technology.

Jamaica was among the earliest developing countries to craft a scientific law to guide the use of Science & Technology for the exploitation of domestic natural resources. In fact, the island was among the first in the American hemisphere to gain electricity, build a railway and to use research results to boost sugar cane production. The Jamaican Science and Technology Policy have two missions; 1) to improve science, technology and engineering and 2) to leverage its use to enhance societal needs.

Efforts to develop its Science and Technology educative system, through institutions such as The University of Technology, has been successful but it has been difficult to translate the results into domestic technologies, products and services because of national budgetary constraints.

Sigmund Freud

Sigmund Freud ( FROYD; German: [ˈziːkmʊnt ˈfʁɔʏt]; born Sigismund Schlomo Freud; 6 May 1856 – 23 September 1939) was an Austrian neurologist and the founder of psychoanalysis, a clinical method for treating psychopathology through dialogue between a patient and a psychoanalyst.Freud was born to Galician Jewish parents in the Moravian town of Freiberg, in the Austrian Empire. He qualified as a doctor of medicine in 1881 at the University of Vienna. Upon completing his habilitation in 1885, he was appointed a docent in neuropathology and became an affiliated professor in 1902. Freud lived and worked in Vienna, having set up his clinical practice there in 1886. In 1938 Freud left Austria to escape the Nazis. He died in exile in the United Kingdom in 1939.

In founding psychoanalysis, Freud developed therapeutic techniques such as the use of free association and discovered transference, establishing its central role in the analytic process. Freud's redefinition of sexuality to include its infantile forms led him to formulate the Oedipus complex as the central tenet of psychoanalytical theory. His analysis of dreams as wish-fulfillments provided him with models for the clinical analysis of symptom formation and the underlying mechanisms of repression. On this basis Freud elaborated his theory of the unconscious and went on to develop a model of psychic structure comprising id, ego and super-ego. Freud postulated the existence of libido, a sexualised energy with which mental processes and structures are invested and which generates erotic attachments, and a death drive, the source of compulsive repetition, hate, aggression and neurotic guilt. In his later works, Freud developed a wide-ranging interpretation and critique of religion and culture.

Though in overall decline as a diagnostic and clinical practice, psychoanalysis remains influential within psychology, psychiatry, and psychotherapy, and across the humanities. It thus continues to generate extensive and highly contested debate with regard to its therapeutic efficacy, its scientific status, and whether it advances or is detrimental to the feminist cause. Nonetheless, Freud's work has suffused contemporary Western thought and popular culture. In the words of W. H. Auden's 1940 poetic tribute to Freud, he had created "a whole climate of opinion / under whom we conduct our different lives."

Sustainable agriculture

Sustainable agriculture is farming in sustainable ways (meeting society's food and textile needs in the present without compromising the ability of future generations to meet their own needs) based on an understanding of ecosystem services, the study of relationships between organisms and their environment. It is a long-term methodological structure that incorporates profit, environmental stewardship, fairness, health, business and familial aspects on a farm setting. It is defined by 3 integral aspects which are: economic profit, environmental stewardship and social responsibility. Sustainability focuses on the business process and practice of a farm in general, rather than a specific agricultural product. The integrated economic, environmental, and social principles are incorporated into a “triple bottom line” (TBL); when the general impacts of the farm are assessed. Unlike a traditional approach where the profit-margin is the single major factor; Agriculture sustainability is also involved with the social and environmental factors.

Theorem

In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms. A theorem is a logical consequence of the axioms. The proof of a mathematical theorem is a logical argument for the theorem statement given in accord with the rules of a deductive system. The proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally deductive, in contrast to the notion of a scientific law, which is experimental.Many mathematical theorems are conditional statements. In this case, the proof deduces the conclusion from conditions called hypotheses or premises. In light of the interpretation of proof as justification of truth, the conclusion is often viewed as a necessary consequence of the hypotheses, namely, that the conclusion is true in case the hypotheses are true, without any further assumptions. However, the conditional could be interpreted differently in certain deductive systems, depending on the meanings assigned to the derivation rules and the conditional symbol.

Although they can be written in a completely symbolic form, for example, within the propositional calculus, theorems are often expressed in a natural language such as English. The same is true of proofs, which are often expressed as logically organized and clearly worded informal arguments, intended to convince readers of the truth of the statement of the theorem beyond any doubt, and from which a formal symbolic proof can in principle be constructed. Such arguments are typically easier to check than purely symbolic ones—indeed, many mathematicians would express a preference for a proof that not only demonstrates the validity of a theorem, but also explains in some way why it is obviously true. In some cases, a picture alone may be sufficient to prove a theorem. Because theorems lie at the core of mathematics, they are also central to its aesthetics. Theorems are often described as being "trivial", or "difficult", or "deep", or even "beautiful". These subjective judgments vary not only from person to person, but also with time: for example, as a proof is simplified or better understood, a theorem that was once difficult may become trivial. On the other hand, a deep theorem may be stated simply, but its proof may involve surprising and subtle connections between disparate areas of mathematics. Fermat's Last Theorem is a particularly well-known example of such a theorem.

Utilitarianism

Utilitarianism is a family of consequentialist ethical theories that promotes actions that maximize happiness and well-being for the majority of a population. Although different varieties of utilitarianism admit different characterizations, the basic idea behind all of them is to in some sense maximize utility, which is often defined in terms of well-being or related concepts. For instance, Jeremy Bentham, the founder of utilitarianism, described utility as

that property in any object, whereby it tends to produce benefit, advantage, pleasure, good, or happiness...[or] to prevent the happening of mischief, pain, evil, or unhappiness to the party whose interest is considered.Utilitarianism is a version of consequentialism, which states that the consequences of any action are the only standard of right and wrong. Unlike other forms of consequentialism, such as egoism and altruism, utilitarianism considers the interests of all beings equally.

Proponents of utilitarianism have disagreed on a number of points, such as whether actions should be chosen based on their likely results (act utilitarianism) or whether agents should conform to rules that maximize utility (rule utilitarianism). There is also disagreement as to whether total (total utilitarianism), average (average utilitarianism) or minimum utility should be maximized.

Though the seeds of the theory can be found in the hedonists Aristippus and Epicurus, who viewed happiness as the only good, the tradition of utilitarianism properly began with Bentham, and has included John Stuart Mill, Henry Sidgwick, R. M. Hare, David Braybrooke, and Peter Singer. It has been applied to social welfare economics, the crisis of global poverty, the ethics of raising animals for food and the importance of avoiding existential risks to humanity.

Vern Poythress

Vern Sheridan Poythress (born 1946) is an American Calvinist philosopher, theologian, and New Testament scholar.

Von Babo's law

Von Babo's law (sometimes styled Babo's law) is a scientific law formulated by German chemist Lambert Heinrich von Babo. It states that the vapor pressure of solution decreases according to the concentration of solute.

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