Scientific law
Scientific laws or laws of science are statements, based on
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, scientific laws do not express absolute certainty, as mathematical
A law can often be formulated as one or several statements or
Overview
A scientific law always applies to a
Laws differ from
Many laws take
Like theories and hypotheses, laws make predictions; specifically, they predict that new observations will conform to the given law. Laws 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 increasing degrees of precision, which is one of the main goals of science. The fact that 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
Several general properties of scientific laws, particularly when referring to laws in physics, have been identified. Scientific 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.[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),
- All-encompassing. Everything in the universe apparently must comply with them (according to observations).
- Generally conservative of quantity.[9]: 59
- Often expressions of existing homogeneities (
- Typically theoretically reversible in time (if non-quantum), although time itself is irreversible.[9]
- Broad. In physics, laws exclusively refer to the broad domain of matter, motion, energy, and force itself, rather than more specific systems in the universe, such as living systems, e.g. the mechanics of the human body.[10]
The term "scientific law" is traditionally associated with the
In natural science, impossibility assertions come to be widely accepted as overwhelmingly probable rather than considered proved to the point of being unchallengeable. The basis for this strong acceptance is a combination of extensive evidence of something not occurring, combined with an underlying theory, very successful in making predictions, whose assumptions lead logically to the conclusion that something is impossible. While an impossibility assertion in natural science can never be absolutely proved, it could be refuted by the observation of a single counterexample. Such a counterexample would require that the assumptions underlying the theory that implied the impossibility be re-examined.
Some examples of widely accepted impossibilities in
Laws as consequences of mathematical symmetries
Some laws reflect mathematical symmetries found in Nature (e.g. the
The
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
- Noether's theorem: Any quantity with a continuously differentiable symmetry in the action has an associated conservation law.
- Conservation of mass was the first law 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.
- symmetries in time, translation, and rotation.
- Conservation of chargewas 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 the 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 fieldof 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 =
wavefunctionof quantum systemj = probability current/flux
More general equations are the
Laws of classical mechanics
Principle of least action
Classical mechanics, including
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
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. They are equivalent formulations. 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.
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 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.
- Archimedes' principle
- Bernoulli's principle
- Poiseuille's law
- Stokes's law
- Navier–Stokes equations
- Faxén's law
Laws of gravitation and relativity
Some of the more famous laws of nature are found in
Modern laws
The two postulates of special relativity are not "laws" in themselves, but assumptions of their nature in terms of relative motion.
They can be stated as "the laws of physics are the same in all
The said postulates lead to the
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 is governed by the
- 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
Einstein field equations (EFE): where Λ =
Ricci curvature tensor, Tμν = Stress–energy tensor, gμν = metric tensorGeodesic 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.[16]
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. - 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
- Newton's law of cooling
- Fourier's law
- Ideal gas law, combines a number of separately developed gas laws;
- now improved by other equations of state
- Dalton's law (of partial pressures)
- Boltzmann equation
- Carnot's theorem
- Kopp's law
Electromagnetism
Maxwell's equations Gauss's law for electricity
Ampère's circuital law (with Maxwell's correction)
Lorentz force law: photons, see Maxwell's equationsfor 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
- Ohm's law
- Kirchhoff's laws
- Joule's law
Photonics
Classically, optics is based on a variational principle: light travels from one point in space to another in the shortest time.
In
- Law of reflection
- Law of refraction, Snell's law
In physical optics, laws are based on physical properties of materials.
- Brewster's angle
- Malus's law
- Beer–Lambert law
In actuality, optical properties of matter are significantly more complex and require quantum mechanics.
Laws of quantum mechanics
Quantum mechanics has its roots in
- The state of a physical system, be it a particle or a system of many particles, is described by a wavefunction.
- Every physical quantity is described by an operator acting on the system; the measured quantity has a probabilistic nature.
- The wavefunction obeys the Schrödinger equation. Solving this wave equation predicts the time-evolution of the system's behavior, analogous to solving Newton's laws in classical mechanics.
- Two identical particles, such as two electrons, cannot be distinguished from one another by any means. Physical systems are classified by their symmetry properties.
These postulates in turn imply many other phenomena, e.g., uncertainty principles and the Pauli exclusion principle.
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 operatoracting on the state space, (seePlanck's constant.Wave–particle duality Planck's constant, h).De Broglie wavelength: this laid the foundations of wave–particle duality, and was the key concept in the Schrödinger equation,
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.
- Stefan–Boltzmann law
- Planck's law of black-body radiation
- Wien's displacement law
- Radioactive decay law
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.
The most fundamental concept in chemistry is the
Additional laws of chemistry elaborate on the law of conservation of mass.
The law of definite composition and the law of multiple proportions are the first two of the three laws of stoichiometry, the proportions by which the chemical elements combine to form chemical compounds. The third law of stoichiometry is the law of reciprocal proportions, which provides the basis for establishing equivalent weights for each chemical element. Elemental equivalent weights can then be used to derive atomic weights for each element.
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 energydependence of the rate constant, an empirical law.
- Gas laws
- Chemical transport
Laws of biology
Ecology
- Competitive exclusion principle or Gause's law
Genetics
- Mendelian laws(Dominance and Uniformity, segregation of genes, and Independent Assortment)
- Hardy–Weinberg principle
Natural selection
Whether or not
Laws of Earth sciences
Geography
Geology
- Archie's law
- Buys-Ballot's law
- Birch's law
- Byerlee's law
- Principle of original horizontality
- Law of superposition
- Principle of lateral continuity
- Principle of cross-cutting relationships
- Principle of faunal succession
- Principle of inclusions and components
- Walther's law
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
History
The observation and detection of underlying regularities in nature date from
In Europe, systematic theorizing about nature (
For the Romans . . . the place par excellence where ethics, law, nature, religion and politics overlap is the
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. During this period,
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.[24]
See also
- Empirical research
- Empirical statistical laws
- Formula
- List of laws
- Law (principle)
- Nomology
- Philosophy of science
- Physical constant
- Scientific laws named after people
- Theory
References
- ^ "law of nature". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
- ISBN 978-94-6209-497-0.
- ^ "Definitions from". the NCSE. Retrieved 2019-03-18.
- ISBN 978-0-309-11249-9.
- ^ Gould, Stephen Jay (1981-05-01). "Evolution as Fact and Theory" (PDF). Discover. 2 (5): 34–37.
- ISBN 0-19-866132-0
- ^ "Law of nature". Oxford English Dictionary (Online ed.). Oxford University Press. (Subscription or participating institution membership required.)
- ^ ISBN 978-0-671-79718-8.
- ^ ISBN 978-0-679-60127-2.
- S2CID 122262641.
- ^ Andrew S. C. Ehrenberg (1993), "Even the Social Sciences Have Laws", Nature, 365:6445 (30), page 385.(subscription required)
- ISBN 0-201-02117-X
- ^ 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
- ISBN 0-07-084018-0
- ISBN 0-691-03323-4
- ISBN 0-07-084018-0
- ^ Reed ES: The lawfulness of natural selection. Am Nat. 1981; 118(1): 61–71.
- ^ a b Byerly HC: Natural selection as a law: Principles and processes. Am Nat. 1983; 121(5): 739–745.
- ^ 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).
- ^ Sedley, "When Nature Got Its Laws", Times Literary Supplement (12 October 2012).
- ISSN 0362-4331. Retrieved 2016-10-07.
Isaac Newton first got the idea of absolute, universal, perfect, immutable laws from the Christian doctrine that God created the world and ordered it in a rational way.
- ^ Harrison, Peter (8 May 2012). "Christianity and the rise of western science". ABC.
Individuals such as Galileo, Johannes Kepler, Rene Descartes and Isaac Newton were convinced that mathematical truths were not the products of human minds, but of the divine mind. God was the source of mathematical relations that were evident in the new laws of the universe.
- ^ "Cosmological Revolution V: Descartes and Newton". bertie.ccsu.edu. Retrieved 2016-11-17.
- ^ 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
- 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). ISBN 978-0-679-77631-4.
- Swartz, Norman (20 February 2009). "Laws of Nature". Internet encyclopedia of philosophy. Retrieved 7 May 2012.
External links
- Physics Formulary, a useful book in different formats containing many or the physical laws and formulae.
- Eformulae.com, website containing most of the formulae in different disciplines.
- Stanford Encyclopedia of Philosophy: "Laws of Nature" by John W. Carroll.
- Baaquie, Belal E. "Laws of Physics : A Primer". Core Curriculum, National University of Singapore.
- Francis, Erik Max. "The laws list".. Physics. Alcyone Systems
- Pazameta, Zoran. "The laws of nature". Committee for the scientific investigation of Claims of the Paranormal.
- The Internet Encyclopedia of Philosophy. "Laws of Nature" – By Norman Swartz
- "Laws of Nature", In Our Time, BBC Radio 4 discussion with Mark Buchanan, Frank Close and Nancy Cartwright (Oct. 19, 2000)