Nuclear force Force (in units of 10,000 N) between two nucleons as a function of distance as computed from the Reid potential (1968).[1] The spins of the neutron and proton are aligned, and they are in the S angular momentum state. The attractive (negative) force has a maximum at a distance of about 1 fm with a force of about 25,000 N. Particles much closer than a distance of 0.8 fm experience a large repulsive (positive) force. Corresponding potential energy (in units of MeV) of two nucleons as a function of distance as computed from the Reid potential. The nuclear force (or nucleon–nucleon interaction or residual strong force) is a force that acts between the protons and neutrons of atoms. The nuclear force is powerfully attractive between nucleons at distances of about 1 femtometre (fm, or 1.0 × 10−15 metres), but it rapidly decreases to insignificance at distances beyond about 2.5 fm. The nuclear force plays an essential role in storing energy that is used in nuclear power and nuclear weapons.
Wave equation Differential equation important in physics Spherical waves coming from a point source A solution to the 2D wave equation The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields – as they occur in classical physics – such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics. Single mechanical or electromagnetic waves propagating in a pre-defined direction can also be described with the first-order one-way wave equation, which is much easier to solve and also valid for inhomogeneous media. Introduction[edit] The (two-way) wave equation is a second-order partial differential equation describing waves, including traveling and standing waves; the latter can be considered as linear superpositions of waves traveling in opposite directions. The scalar wave equation is In other words:
Russell–Einstein Manifesto The Russell–Einstein Manifesto was issued in London on 9 July 1955 by Bertrand Russell in the midst of the Cold War. It highlighted the dangers posed by nuclear weapons and called for world leaders to seek peaceful resolutions to international conflict. The signatories included eleven pre-eminent intellectuals and scientists, including Albert Einstein, who signed it just days before his death on 18 April 1955. A few days after the release, philanthropist Cyrus S. Eaton offered to sponsor a conference—called for in the manifesto—in Pugwash, Nova Scotia, Eaton's birthplace. Background[edit] The first detonation of an atomic weapon took place on 16 July 1945 in the desert north of Alamogordo, New Mexico. On 18 August 1945, the Glasgow Forward published "The Bomb and Civilisation," the first known recorded comment by Bertrand Russell on atomic weapons, which he began composing the day Nagasaki was bombed. The prospect for the human race is sombre beyond all precedent. Synopsis[edit]
Heisenberg talks about Einstein. Werner Heisenberg was born in 1901 and died in 1976. He was four years old when Einstein formulated special relativity in 1905. Ten years later, when he was in high school, Heisenberg became interested in Einstein's theory and started his physics career out of his respect for Einstein.
Non-abelian group From Wikipedia, the free encyclopedia Group where ab = ba does not always hold Both discrete groups and continuous groups may be non-abelian. See also[edit] References[edit] Abelian group Commutative group (mathematics) Definition[edit] , together with an operation and of to form another element of denoted . is a general placeholder for a concretely given operation. Associativity For all , and in , the equation holds. Identity element There exists an element , such that for all elements Inverse element For each there exists an element such that , where is the identity element. Commutativity A group in which the group operation is not commutative is called a "non-abelian group" or "non-commutative group".[2]: 11 Facts[edit] Notation[edit] There are two main notational conventions for abelian groups – additive and multiplicative. Multiplication table[edit] To verify that a finite group is abelian, a table (matrix) – known as a Cayley table – can be constructed in a similar fashion to a multiplication table.[4]: 10 If the group is under the operation , the -th entry of this table contains the product The group is abelian if and only if this table is symmetric about the main diagonal. for all entry for all
Particle physics Study of subatomic particles and forces Particle physics or high-energy physics is the study of fundamental particles and forces that constitute matter and radiation. The field also studies combinations of elementary particles up to the scale of protons and neutrons, while the study of combination of protons and neutrons is called nuclear physics. Quarks cannot exist on their own but form hadrons. Particles have corresponding antiparticles with the same mass but with opposite electric charges. Practical particle physics is the study of these particles in radioactive processes and in particle accelerators such as the Large Hadron Collider. History[edit] Throughout the 1950s and 1960s, a bewildering variety of particles were found in collisions of particles from beams of increasingly high energy. Standard Model[edit] Subatomic particles[edit] Quarks and leptons[edit] Bosons[edit] Antiparticles and color charge[edit] Composite[edit] A normal atom is made from protons, neutrons and electrons.
Gauge boson The Standard Model of elementary particles, with the gauge bosons in the fourth column in red In particle physics, a gauge boson is a force carrier, a bosonic particle that carries any of the fundamental interactions of nature.[1][2] Elementary particles, whose interactions are described by a gauge theory, interact with each other by the exchange of gauge bosons—usually as virtual particles. Gauge bosons in the Standard Model[edit] The Standard Model of particle physics recognizes three kinds of gauge bosons: photons, which carry the electromagnetic interaction; W and Z bosons, which carry the weak interaction; and gluons, which carry the strong interaction.[3] Isolated gluons do not occur at low energies because they are color-charged, and subject to color confinement. Multiplicity of gauge bosons[edit] Massive gauge bosons[edit] According to the Standard Model, the W and Z bosons gain mass via the Higgs mechanism. Beyond the Standard Model[edit] Grand unification theories[edit] See also[edit]
W and Z bosons The W bosons are named after the weak force. The physicist Steven Weinberg named the additional particle the "Z particle",[3] and later gave the explanation that it was the last additional particle needed by the model. The W bosons had already been named, and the Z bosons have zero electric charge.[4] The two W bosons are verified mediators of neutrino absorption and emission. The Z boson mediates the transfer of momentum, spin and energy when neutrinos scatter elastically from matter (a process which conserves charge). Basic properties[edit] These bosons are among the heavyweights of the elementary particles. Weak nuclear force[edit] The W and Z bosons are carrier particles that mediate the weak nuclear force, much as the photon is the carrier particle for the electromagnetic force. W bosons[edit] The W bosons are best known for their role in nuclear decay. 60 27Co → 60 28Ni+ + e− + ν e This reaction does not involve the whole cobalt-60 nucleus, but affects only one of its 33 neutrons.
Sheldon Lee Glashow Sheldon Lee Glashow (/ˈɡlæʃoʊ/; born December 5, 1932) is a Nobel Prize winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University and Eugene Higgins Professor of Physics, Emeritus, at Harvard University, and is a member of the Board of Sponsors for the Bulletin of the Atomic Scientists. Birth and education[edit] Sheldon Lee Glashow was born in New York City, to Jewish immigrants from Russia, Bella (née Rubin) and Lewis Gluchovsky, a plumber.[1] He graduated from Bronx High School of Science in 1950. Glashow was in the same graduating class as Steven Weinberg, whose own research, independent of Glashow's, would result in Glashow, Weinberg, and Abdus Salam sharing the 1979 Nobel Prize in Physics (see below).[2] Glashow received a Bachelor of Arts degree from Cornell University in 1954 and a Ph.D. degree in physics from Harvard University in 1959 under Nobel-laureate physicist Julian Schwinger. Research[edit] Personal life[edit] Notes
Electroweak interaction In particle physics, the electroweak interaction is the unified description of two of the four known fundamental interactions of nature: electromagnetism and the weak interaction. Although these two forces appear very different at everyday low energies, the theory models them as two different aspects of the same force. Above the unification energy, on the order of 100 GeV, they would merge into a single electroweak force. Thus if the universe is hot enough (approximately 1015 K, a temperature exceeded until shortly after the Big Bang) then the electromagnetic force and weak force merge into a combined electroweak force. Formulation[edit] The pattern of weak isospin, T3, and weak hypercharge, YW, of the known elementary particles, showing electric charge, Q, along the weak mixing angle. The spontaneous symmetry breaking causes the W0 and B0 bosons to coalesce together into two different bosons – the Z0 boson, and the photon (γ) as follows: Where θW is the weak mixing angle. The where ) and
Georgi–Glashow model (For a more elementary introduction to how the representation theory of Lie algebras are related to particle physics, see the article Particle physics and representation theory.) This model suffers from the doublet-triplet splitting problem.[clarification needed] Breaking SU(5)[edit] SU(5) breaking occurs when a scalar field, analogous to the Higgs field, and transforming in the adjoint of SU(5) acquires a vacuum expectation value proportional to the weak hypercharge generator[why?] When this occurs SU(5) is spontaneously broken to the subgroup of SU(5) commuting with the group generated by Y. Under the unbroken subgroup the adjoint 24 transforms as giving the gauge bosons of the standard model. The standard model quarks and leptons fit neatly into representations of SU(5). . (dc and l) (q, uc and ec) (νc) Since the homotopy group this model predicts 't Hooft–Polyakov monopoles. These monopoles have quantized Y magnetic charges. Minimal supersymmetric SU(5)[edit] Spacetime[edit] Z2 (matter parity)