physical-laws-en-blog

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Fermat's principle

Fermat's principle leads to Snell's law; when the sines of the angles in the different media are in the same proportion as the propagation velocities, the time to get from P to Q is minimized. In optics, Fermat's principle or the principle of least time, named after French mathematician Pierre de Fermat, is the principle that the path taken between two points by a ray of light is the path that can be traversed in the least time. This principle is sometimes taken as the definition of a ray of light. However, this version of the principle is not general; a more modern statement of the principle is that rays of light traverse the path of stationary optical length with respect to variations of the path. In other words, a ray of light prefers the path such that there are other paths, arbitrarily nearby on either side, along which the ray would take almost exactly the same time to traverse. Fermat's principle can be used to describe the properties of light rays reflected off mirrors, refracted through different media, or undergoing total internal reflection. It follows mathematically from Huygens' principle (at the limit of small wavelength). Fermat's text Analyse des réfractions exploits the technique of adequality to derive Snell's law of refraction and the law of reflection. Fermat's principle has the same form as Hamilton's principle and it is the basis of Hamiltonian optics. More details Android, Windows

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Principle of least action

This article discusses the history of the principle of least action. For the application, please refer to action (physics). The principle of least action – or, more accurately, the principle of stationary action – is a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system. In relativity, a different action must be minimized or maximized. The principle can be used to derive Newtonian, Lagrangian and Hamiltonian equations of motion, and even general relativity (see Einstein–Hilbert action). It was historically called "least" because its solution requires finding the path that has the least change from nearby paths. Its classical mechanics and electromagnetic expressions are a consequence of quantum mechanics, but the stationary action method helped in the development of quantum mechanics. The principle remains central in modern physics and mathematics, being applied in thermodynamics, fluid mechanics, the theory of relativity, quantum mechanics, particle physics, and string theory and is a focus of modern mathematical investigation in Morse theory. Maupertuis' principle and Hamilton's principle exemplify the principle of stationary action. The action principle is preceded by earlier ideas in surveying and optics. Rope stretchers in ancient Egypt stretched corded ropes to measure the distance between two points. Ptolemy, in his Geography (Bk 1, Ch 2), emphasized that one must correct for "deviations from a straight course".[citation needed] In ancient Greece, Euclid wrote in his Catoptrica that, for the path of light reflecting from a mirror, the angle of incidence equals the angle of reflection.[citation needed] Hero of Alexandria later showed that this path was the shortest length and least time. Scholars often credit Pierre Louis Maupertuis for formulating the principle of least action because he wrote about it in 1744 and 1746. However, Leonhard Euler discussed the principle in 1744, and evidence shows that Gottfried Leibniz preceded both by 39 years. In 1932, Paul Dirac discerned the quantum mechanical underpinning of the principle in the quantum interference of amplitudes: for macroscopic systems, the dominant contribution to the apparent path is the classical path (the stationary, action-extremizing one), while any other path is possible in the quantum realm.[citation needed] More details Android, Windows

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Maupertuis' principle

In classical mechanics, Maupertuis' principle (named after Pierre Louis Maupertuis), is that the path followed by a physical system is the one of least length (with a suitable interpretation of path and length). It is a special case of the more generally stated principle of least action. Using the calculus of variations, it results in an integral equation formulation of the equations of motion for the system. More details Android, Windows

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CPT symmetry

"CPT theorem" redirects here. For the album by Greydon Square, see The C.P.T. Theorem. Charge, Parity, and Time Reversal Symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T). CPT is the only combination of C, P and T that is observed to be an exact symmetry of nature at the fundamental level. The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry. More details Android, Windows

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B − L

"B-L" redirects here. For other uses, see BL (disambiguation). In high energy physics, B − L (pronounced "bee minus ell") is the difference between the baryon number (B) and the lepton number (L). More details Android, Windows

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Conservation of energy

This article is about the law of conservation of energy in physics. For sustainable energy resources, see Energy conservation. In physics, the law of conservation of energy states that the total energy of an isolated system remains constant—it is said to be conserved over time. Energy can neither be created nor destroyed; rather, it transforms from one form to another. For instance, chemical energy can be converted to kinetic energy in the explosion of a stick of dynamite. A consequence of the law of conservation of energy is that a perpetual motion machine of the first kind cannot exist. That is to say, no system without an external energy supply can deliver an unlimited amount of energy to its surroundings. More details Android, Windows

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Parity

In quantum mechanics, a parity transformation (also called parity inversion) is the flip in the sign of one spatial coordinate. In three dimensions, it is also often described by the simultaneous flip in the sign of all three spatial coordinates (a point reflection): P : ( x y z ) ↦ ( − x − y − z ) . {\displaystyle \mathbf {P} :{\begin{pmatrix}x\\y\\z\end{pmatrix}}\mapsto {\begin{pmatrix}-x\\-y\\-z\end{pmatrix}}.} It can also be thought of as a test for chirality of a physical phenomenon, in that a parity inversion transforms a phenomenon into its mirror image. A parity transformation on something achiral, on the other hand, can be viewed as an identity transformation. All fundamental interactions of elementary particles, with the exception of the weak interaction, are symmetric under parity. The weak interaction is chiral and thus provides a means for probing chirality in physics. In interactions that are symmetric under parity, such as electromagnetism in atomic and molecular physics, parity serves as a powerful controlling principle underlying quantum transitions. A matrix representation of P (in any number of dimensions) has determinant equal to −1, and hence is distinct from a rotation, which has a determinant equal to 1. In a two-dimensional plane, a simultaneous flip of all coordinates in sign is not a parity transformation; it is the same as a 180°-rotation. More details Android, Windows

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Strangeness

In particle physics, strangeness ("S") is a property of particles, expressed as a quantum number, for describing decay of particles in strong and electromagnetic interactions which occur in a short period of time. The strangeness of a particle is defined as: S = − ( n s − n s ¯ ) {\displaystyle S=-(n_{s}-n_{\bar {s}})} where n s represents the number of strange quarks ( s ) and n s represents the number of strange antiquarks ( s ). The terms strange and strangeness predate the discovery of the quark, and were adopted after its discovery in order to preserve the continuity of the phrase; strangeness of anti-particles being referred to as +1, and particles as −1 as per the original definition. For all the quark flavour quantum numbers (strangeness, charm, topness and bottomness) the convention is that the flavour charge and the electric charge of a quark have the same sign. With this, any flavour carried by a charged meson has the same sign as its charge. More details Android, Windows

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Charm

Charm (symbol C) is a flavour quantum number representing the difference between the number of charm quarks ( c ) and charm antiquarks ( c ) that are present in a particle: C = n c − n c ¯ .   {\displaystyle C=n_{\text{c}}-n_{\mathrm {\bar {c}} }.\ } By convention, the sign of flavour quantum numbers agree with the sign of the electric charge carried by the quark of corresponding flavour. The charm quark, which carries an electric charge (Q) of +2⁄3, therefore carries a charm of +1. The charm antiquarks have the opposite charge (Q = −2⁄3), and flavour quantum numbers (C = −1). As with any flavour-related quantum numbers, charm is preserved under strong and electromagnetic interaction, but not under weak interaction (see CKM matrix). For first-order weak decays, that is processes involving only one quark decay, charm can only vary by 1 (ΔC= ±1,0). Since first-order processes are more common than second-order processes (involving two quark decays), this can be used as an approximate "selection rule" for weak decays. More details Android, Windows

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Conservation of mass

Russian scientist Mikhail Lomonosov discovered the law of mass conservation in 1756 by experiments, and came to the conclusion that phlogiston theory is incorrect. Antoine Lavoisier's discovery of the Law of Conservation of Mass led to many new findings in the 19th century. Joseph Proust's law of definite proportions and John Dalton's atomic theory branched from the discoveries of Antoine Lavoisier. Lavoisier's quantitative experiments revealed that combustion involved oxygen rather than what was previously thought to be phlogiston. The law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as system mass cannot change quantity if it is not added or removed. Hence, the quantity of mass is "conserved" over time. The law implies that mass can neither be created nor destroyed, although it may be rearranged in space, or the entities associated with it may be changed in form, as for example when light or physical work is transformed into particles that contribute the same mass to the system as the light or work had contributed. Thus, during any chemical reaction, nuclear reaction, or radioactive decay in an isolated system, the total mass of the reactants or starting materials must be equal to the mass of the products. The concept of mass conservation is widely used in many fields such as chemistry, mechanics, and fluid dynamics. Historically, mass conservation was discovered in chemical reactions by Antoine Lavoisier in the late 18th century, and was of crucial importance in the progress from alchemy to the modern natural science of chemistry. The closely related concept of matter conservation was found to hold good in chemistry to such high approximation that it failed only for the high energies treated by the later refinements of relativity theory, but otherwise remains useful and sufficiently accurate for most chemical calculations, even in modern practice. In special relativity, needed for accuracy when large energy transfers between systems is involved, the difference between thermodynamically closed and isolated systems becomes important, since conservation of mass is strictly and perfectly upheld only for so-called isolated systems, i.e. those completely isolated from all exchanges with the environment. In this circumstance, the mass–energy equivalence theorem states that mass conservation is equivalent to total energy conservation, which is the first law of thermodynamics. By contrast, for a thermodynamically closed system (i.e., one which is closed to exchanges of matter, but open to exchanges of non-material energy, such as heat and work, with the surroundings) mass is (usually) only approximately conserved. The input or output of non-material energy must change the mass of the system in relativity theory, although the change is usually small, since relatively large amounts of such energy (by comparison with ordinary experience) carry only a small amount of mass (again by ordinary standards of measurement). In special relativity, mass is not converted to energy, since mass and energy cannot be destroyed, and energy in all of its forms always retains its equivalent amount of mass throughout any transformation to a different type of energy within a system (or translocation into or out of a system). Certain types of matter (a different concept) may be created or destroyed, but in all of these processes, the energy and mass associated with such matter remains unchanged in quantity (although type of energy associated with the matter may change form). In general relativity, mass (and energy) conservation in expanding volumes of space is a complex concept, subject to different definitions, and neither mass nor energy is as strictly and simply conserved as is the case in special relativity and in Minkowski space. For a discussion, see mass in general relativity. More details Android, Windows

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Lepton number

In particle physics, the lepton number is a conserved quantum number representing the number of leptons minus the number of antileptons in an elementary particle reaction. In equation form, L = n ℓ − n ℓ ¯   , {\displaystyle L=n_{\ell }-n_{\overline {\ell }}~,} so all leptons have assigned a value of +1, antileptons −1, and non-leptonic particles 0. Lepton number (sometimes also called lepton charge) is an additive quantum number, which means that its sum is preserved in interactions (as opposed to multiplicative quantum numbers such as parity, where the product is preserved instead). Lepton number was introduced in 1953 and was invoked to explain the absence of reactions such as ν ¯ + n → p + e − {\displaystyle {\bar {\nu }}+n\rightarrow p+e^{-}} in the reactor Cowan–Reines neutrino experiment, which observed ν ¯ + p → n + e + {\displaystyle {\bar {\nu }}+p\rightarrow n+e^{+}} instead. Beside the leptonic number, leptonic family numbers are also defined: Le , the electronic number for the electron and the electron neutrino; Lμ , the muonic number for the muon and the muon neutrino; Lτ , the tauonic number for the tau and the tau neutrino; with the same assigning scheme as the leptonic number: +1 for particles of the corresponding family, −1 for the antiparticles, and 0 for leptons of other families or non-leptonic particles. An example is the muon decay. Like many lepton interactions, muon decay is a Weak Interaction. This is cited as a test for special relativity testing the time dilation effect More details Android, Windows

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Charge conservation

This article is about the conservation of electric charge. For a general theoretical concept, see charge (physics). In physics, charge conservation is the principle that electric charge can neither be created nor destroyed. The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved. The first written statement of the principle was by American scientist and statesman Benjamin Franklin in 1747. it is now discovered and demonstrated, both here and in Europe, that the Electrical Fire is a real Element, or Species of Matter, not created by the Friction, but collected only. — Benjamin Franklin, Letter to Cadwallader Colden, 5 June 1747 Charge conservation is a physical law that states that the change in the amount of electric charge in any volume of space is exactly equal to the amount of charge flowing into the volume minus the amount of charge flowing out of the volume. In essence, charge conservation is an accounting relationship between the amount of charge in a region and the flow of charge into and out of that region. Mathematically, we can state the law as a continuity equation: Q ( t 2 )   =   Q ( t 1 ) + Q I N − Q O U T . {\displaystyle Q(t_{2})\ =\ Q(t_{1})+Q_{\rm {IN}}-Q_{\rm {OUT}}.} Q(t) is the quantity of electric charge in a specific volume at time t, QIN is the amount of charge flowing into the volume between time t1 and t2, and QOUT is the amount of charge flowing out of the volume during the same time period. This does not mean that individual positive and negative charges cannot be created or destroyed. Electric charge is carried by subatomic particles such as electrons and protons, which can be created and destroyed. In particle physics, charge conservation means that in elementary particle reactions that create charged particles, equal numbers of positive and negative particles are always created, keeping the net amount of charge unchanged. Similarly, when particles are destroyed, equal numbers of positive and negative charges are destroyed. Although conservation of charge requires that the total quantity of charge in the universe is constant, it leaves open the question of what that quantity is. Most evidence indicates that the net charge in the universe is zero; that is, there are equal quantities of positive and negative charge. More details Android, Windows

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Baryon number

In particle physics, the baryon number is a strictly conserved additive quantum number of a system. It is defined as B = 1 3 ( n q − n q ¯ ) , {\displaystyle B={\frac {1}{3}}\left(n_{\text{q}}-n_{\bar {\text{q}}}\right),} where nq is the number of quarks, and nq is the number of antiquarks. Baryons (three quarks) have a baryon number of +1, mesons (one quark, one antiquark) have a baryon number of 0, and antibaryons (three antiquarks) have a baryon number of −1. Exotic hadrons like pentaquarks (four quarks, one antiquark) and tetraquarks (two quarks, two antiquarks) are also classified as baryons and mesons depending on their baryon number. More details Android, Windows

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Continuity equation

A continuity equation in physics is an equation that describes the transport of some quantity. It is particularly simple and particularly powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described using continuity equations. Continuity equations are a stronger, local form of conservation laws. For example, a weak version of the law of conservation of energy states that energy can neither be created nor destroyed—i.e., the total amount of energy is fixed. This statement does not immediately rule out the possibility that energy could disappear from a field in Canada while simultaneously appearing in a room in Indonesia. A stronger statement is that energy is locally conserved: Energy can neither be created nor destroyed, nor can it "teleport" from one place to another—it can only move by a continuous flow. A continuity equation is the mathematical way to express this kind of statement. For example, the continuity equation for electric charge states that the amount of electric charge at any point can only change by the amount of electric current flowing into or out of that point. Continuity equations more generally can include "source" and "sink" terms, which allow them to describe quantities that are often but not always conserved, such as the density of a molecular species which can be created or destroyed by chemical reactions. In an everyday example, there is a continuity equation for the number of people alive; it has a "source term" to account for people being born, and a "sink term" to account for people dying. Any continuity equation can be expressed in an "integral form" (in terms of a flux integral), which applies to any finite region, or in a "differential form" (in terms of the divergence operator) which applies at a point. Continuity equations underlie more specific transport equations such as the convection–diffusion equation, Boltzmann transport equation, and Navier–Stokes equations. More details Android, Windows

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Noether's theorem

This article is about Emmy Noether's first theorem, which derives conserved quantities from symmetries. For other uses, see Noether's theorem (disambiguation). Emmy Noether was an influential mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics. Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proven by mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action. Noether's theorem is used in theoretical physics and the calculus of variations. A generalization of the formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian alone (e.g. systems with a Rayleigh dissipation function). In particular, dissipative systems with continuous symmetries need not have a corresponding conservation law. More details Android, Windows

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Conservation law

This article is about conservation in physics. For the legal aspects of environmental conservation, see Environmental law and Conservation movement. For other uses, see Conservation (disambiguation). In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric charge. There are also many approximate conservation laws, which apply to such quantities as mass, parity, lepton number, baryon number, strangeness, hypercharge, etc. These quantities are conserved in certain classes of physics processes, but not in all. A local conservation law is usually expressed mathematically as a continuity equation, a partial differential equation which gives a relation between the amount of the quantity and the "transport" of that quantity. It states that the amount of the conserved quantity at a point or within a volume can only change by the amount of the quantity which flows in or out of the volume. From Noether's theorem, each conservation law is associated with a symmetry in the underlying physics. More details Android, Windows

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Lenz's law

Lenz's law /ˈlɛnts/ is named after a Russian physicist of Baltic German descent Heinrich Lenz in 1834, and says: The direction of current induced in a conductor by a changing magnetic field due to Faraday's law of induction will be such that it will create a field that opposes the change that produced it. Lenz's law is shown by the negative sign in Faraday's law of induction: E = − ∂ Φ ∂ t , {\displaystyle {\mathcal {E}}=-{\frac {\partial \Phi }{\partial t}},} which indicates that the induced voltage ( E {\displaystyle {\mathcal {E}}} ) and the change in magnetic flux ( ∂ Φ {\displaystyle \partial \Phi } ) have opposite signs. It is a qualitative law that specifies the direction of induced current but says nothing about its magnitude. Lenz's Law explains the direction of many effects in electromagnetism, such as the direction of voltage induced in an inductor or wire loop by a changing current, or why eddy currents exert a drag force on moving objects in a magnetic field. Lenz's law can be seen as analogous to Newton's third law in classic mechanics. For a rigorous mathematical treatment, see electromagnetic induction and Maxwell's equations. More details Android, Windows