Onia
72-472: In particle physics , annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles, such as an electron colliding with a positron to produce two photons . The total energy and momentum of the initial pair are conserved in the process and distributed among a set of other particles in the final state. Antiparticles have exactly opposite additive quantum numbers from particles, so
144-431: A photon ( γ ), gluon ( g ), Z , or a Higgs boson ( H ). If the total energy in the center-of-momentum frame is equal to the rest mass of a real boson (which is impossible for a massless boson such as the γ ), then that created particle will continue to exist until it decays according to its lifetime . Otherwise,
216-487: A Hilbert space , which is also treated in quantum field theory . Following the convention of particle physicists, the term elementary particles is applied to those particles that are, according to current understanding, presumed to be indivisible and not composed of other particles. Ordinary matter is made from first- generation quarks ( up , down ) and leptons ( electron , electron neutrino ). Collectively, quarks and leptons are called fermions , because they have
288-433: A W boson . If the annihilating particles are composite , such as mesons or baryons , then several different particles are typically produced in the final state. The inverse of annihilation is pair production , the process in which a high-energy photon converts its energy into mass. If the initial two particles are elementary (not composite), then they may combine to produce only a single elementary boson , such as
360-402: A microsecond . They occur after collisions between particles made of quarks, such as fast-moving protons and neutrons in cosmic rays . Mesons are also produced in cyclotrons or other particle accelerators . Particles have corresponding antiparticles with the same mass but with opposite electric charges . For example, the antiparticle of the electron is the positron . The electron has
432-502: A quantum spin of half-integers (−1/2, 1/2, 3/2, etc.). This causes the fermions to obey the Pauli exclusion principle , where no two particles may occupy the same quantum state . Quarks have fractional elementary electric charge (−1/3 or 2/3) and leptons have whole-numbered electric charge (0 or 1). Quarks also have color charge , which is labeled arbitrarily with no correlation to actual light color as red, green and blue. Because
504-1058: A " Theory of Everything ", or "TOE". There are also other areas of work in theoretical particle physics ranging from particle cosmology to loop quantum gravity . In principle, all physics (and practical applications developed therefrom) can be derived from the study of fundamental particles. In practice, even if "particle physics" is taken to mean only "high-energy atom smashers", many technologies have been developed during these pioneering investigations that later find wide uses in society. Particle accelerators are used to produce medical isotopes for research and treatment (for example, isotopes used in PET imaging ), or used directly in external beam radiotherapy . The development of superconductors has been pushed forward by their use in particle physics. The World Wide Web and touchscreen technology were initially developed at CERN . Additional applications are found in medicine, national security, industry, computing, science, and workforce development, illustrating
576-415: A center of mass frame (or "rest frame" if the system is bound) exists. Thus, the mass of a system of several photons moving in different directions is positive, which means that an invariant mass exists for this system even though it does not exist for each photon. The invariant mass of a system includes the mass of any kinetic energy of the system constituents that remains in the center of momentum frame, so
648-452: A fourth generation of fermions does not exist. Bosons are the mediators or carriers of fundamental interactions, such as electromagnetism , the weak interaction , and the strong interaction . Electromagnetism is mediated by the photon , the quanta of light . The weak interaction is mediated by the W and Z bosons . The strong interaction is mediated by the gluon , which can link quarks together to form composite particles. Due to
720-898: A long and growing list of beneficial practical applications with contributions from particle physics. Major efforts to look for physics beyond the Standard Model include the Future Circular Collider proposed for CERN and the Particle Physics Project Prioritization Panel (P5) in the US that will update the 2014 P5 study that recommended the Deep Underground Neutrino Experiment , among other experiments. Rest energy The invariant mass , rest mass , intrinsic mass , proper mass , or in
792-430: A negative electric charge, the positron has a positive charge. These antiparticles can theoretically form a corresponding form of matter called antimatter . Some particles, such as the photon , are their own antiparticle. These elementary particles are excitations of the quantum fields that also govern their interactions. The dominant theory explaining these fundamental particles and fields, along with their dynamics,
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#1732772385277864-431: A sea quark) to produce a gluon, after which the gluon together with the remaining quarks, antiquarks, and gluons will undergo a complex process of rearrangement (called hadronization or fragmentation ) into a number of mesons , (mostly pions and kaons ), which will share the total energy and momentum. The newly created mesons are unstable, and unless they encounter and interact with some other material, they will decay in
936-699: A series of reactions that ultimately produce only photons , electrons , positrons , and neutrinos . This type of reaction will occur between any baryon (particle consisting of three quarks) and any antibaryon consisting of three antiquarks, one of which corresponds to a quark in the baryon. (This reaction is unlikely if at least one among the baryon and anti-baryon is exotic enough that they share no constituent quark flavors.) Antiprotons can and do annihilate with neutrons , and likewise antineutrons can annihilate with protons, as discussed below. Reactions in which proton–antiproton annihilation produces as many as 9 mesons have been observed, while production of 13 mesons
1008-408: A system is equal to its total mass in that "rest frame". In other reference frames, where the system's momentum is nonzero, the total mass (a.k.a. relativistic mass ) of the system is greater than the invariant mass, but the invariant mass remains unchanged. Because of mass–energy equivalence , the rest energy of the system is simply the invariant mass times the speed of light squared. Similarly,
1080-1455: A system made of two massless particles whose momenta form an angle θ {\displaystyle \theta } has a convenient expression: M 2 = ( E 1 + E 2 ) 2 − ‖ p 1 + p 2 ‖ 2 = [ ( p 1 , 0 , 0 , p 1 ) + ( p 2 , 0 , p 2 sin θ , p 2 cos θ ) ] 2 = ( p 1 + p 2 ) 2 − p 2 2 sin 2 θ − ( p 1 + p 2 cos θ ) 2 = 2 p 1 p 2 ( 1 − cos θ ) . {\displaystyle {\begin{aligned}M^{2}&=(E_{1}+E_{2})^{2}-\left\|{\textbf {p}}_{1}+{\textbf {p}}_{2}\right\|^{2}\\&=[(p_{1},0,0,p_{1})+(p_{2},0,p_{2}\sin \theta ,p_{2}\cos \theta )]^{2}\\&=(p_{1}+p_{2})^{2}-p_{2}^{2}\sin ^{2}\theta -(p_{1}+p_{2}\cos \theta )^{2}\\&=2p_{1}p_{2}(1-\cos \theta ).\end{aligned}}} In particle collider experiments, one often defines
1152-423: A system without potential or kinetic energy can be added to a total mass). Consider the simple case of two-body system, where object A is moving towards another object B which is initially at rest (in any particular frame of reference). The magnitude of invariant mass of this two-body system (see definition below) is different from the sum of rest mass (i.e. their respective mass when stationary). Even if we consider
1224-404: A velocity depending on the reference frame used to view it). Thus, an observer can always be placed to move along with it. In this frame, which is the center-of-momentum frame, the total momentum is zero, and the system as a whole may be thought of as being "at rest" if it is a bound system (like a bottle of gas). In this frame, which exists under these assumptions, the invariant mass of the system
1296-435: A wide range of exotic particles . All particles and their interactions observed to date can be described almost entirely by the Standard Model. Dynamics of particles are also governed by quantum mechanics ; they exhibit wave–particle duality , displaying particle-like behaviour under certain experimental conditions and wave -like behaviour in others. In more technical terms, they are described by quantum state vectors in
1368-443: A wide variety of exotic heavy particles are created. The word "annihilation" takes its use informally for the interaction of two particles that are not mutual antiparticles – not charge conjugate . Some quantum numbers may then not sum to zero in the initial state, but conserve with the same totals in the final state. An example is the "annihilation" of a high-energy electron antineutrino with an electron to produce
1440-425: Is a particle physics theory suggesting that systems with higher energy have a smaller number of dimensions. A third major effort in theoretical particle physics is string theory . String theorists attempt to construct a unified description of quantum mechanics and general relativity by building a theory based on small strings, and branes rather than particles. If the theory is successful, it may be considered
1512-797: Is also used in inelastic scattering experiments. Given an inelastic reaction with total incoming energy larger than the total detected energy (i.e. not all outgoing particles are detected in the experiment), the invariant mass (also known as the "missing mass") W of the reaction is defined as follows (in natural units): W 2 = ( ∑ E in − ∑ E out ) 2 − ‖ ∑ p in − ∑ p out ‖ 2 . {\displaystyle W^{2}=\left(\sum E_{\text{in}}-\sum E_{\text{out}}\right)^{2}-\left\|\sum \mathbf {p} _{\text{in}}-\sum \mathbf {p} _{\text{out}}\right\|^{2}.} If there
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#17327723852771584-554: Is called the Standard Model . The reconciliation of gravity to the current particle physics theory is not solved; many theories have addressed this problem, such as loop quantum gravity , string theory and supersymmetry theory . Practical particle physics is the study of these particles in radioactive processes and in particle accelerators such as the Large Hadron Collider . Theoretical particle physics
1656-455: Is equal to the total system energy (in the zero-momentum frame) divided by c . This total energy in the center of momentum frame, is the minimum energy which the system may be observed to have, when seen by various observers from various inertial frames. Note that for reasons above, such a rest frame does not exist for single photons , or rays of light moving in one direction. When two or more photons move in different directions, however,
1728-532: Is explained by the Standard Model , which gained widespread acceptance in the mid-1970s after experimental confirmation of the existence of quarks . It describes the strong , weak , and electromagnetic fundamental interactions , using mediating gauge bosons . The species of gauge bosons are eight gluons , W , W and Z bosons , and the photon . The Standard Model also contains 24 fundamental fermions (12 particles and their associated anti-particles), which are
1800-404: Is forbidden by momentum conservation—a single photon would carry nonzero momentum in any frame , including the center-of-momentum frame where the total momentum vanishes. Both the annihilating electron and positron particles have a rest energy of about 0.511 million electron-volts (MeV). If their kinetic energies are relatively negligible, this total rest energy appears as the photon energy of
1872-490: Is from fusion of two gluons (via annihilation of a heavy quark pair), while two quarks or antiquarks produce more easily identified events through radiation of a Higgs by a produced virtual vector boson or annihilation of two such vector bosons. Particle physics 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
1944-595: Is in model building where model builders develop ideas for what physics may lie beyond the Standard Model (at higher energies or smaller distances). This work is often motivated by the hierarchy problem and is constrained by existing experimental data. It may involve work on supersymmetry , alternatives to the Higgs mechanism , extra spatial dimensions (such as the Randall–Sundrum models ), Preon theory, combinations of these, or other ideas. Vanishing-dimensions theory
2016-411: Is one dominant particle which was not detected during an experiment, a plot of the invariant mass will show a sharp peak at the mass of the missing particle. In those cases when the momentum along one direction cannot be measured (i.e. in the case of a neutrino, whose presence is only inferred from the missing energy ) the transverse mass is used. In a two-particle collision (or a two-particle decay)
2088-495: Is the energy associated with a particle's invariant mass. The rest energy E 0 {\displaystyle E_{0}} of a particle is defined as: E 0 = m 0 c 2 , {\displaystyle E_{0}=m_{0}c^{2},} where c {\displaystyle c} is the speed of light in vacuum . In general, only differences in energy have physical significance. The concept of rest energy follows from
2160-466: Is the same in all frames of reference (see also special relativity ). This equation says that the invariant mass is the pseudo-Euclidean length of the four-vector ( E , p ) , calculated using the relativistic version of the Pythagorean theorem which has a different sign for the space and time dimensions. This length is preserved under any Lorentz boost or rotation in four dimensions, just like
2232-471: Is the study of these particles in the context of cosmology and quantum theory . The two are closely interrelated: the Higgs boson was postulated by theoretical particle physicists and its presence confirmed by practical experiments. The idea that all matter is fundamentally composed of elementary particles dates from at least the 6th century BC. In the 19th century, John Dalton , through his work on stoichiometry , concluded that each element of nature
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2304-423: Is theoretically possible. The generated mesons leave the site of the annihilation at moderate fractions of the speed of light and decay with whatever lifetime is appropriate for their type of meson. Similar reactions will occur when an antinucleon annihilates within a more complex atomic nucleus , save that the resulting mesons, being strongly interacting , have a significant probability of being absorbed by one of
2376-600: Is used to extract the parameters of the Standard Model with less uncertainty. This work probes the limits of the Standard Model and therefore expands scientific understanding of nature's building blocks. Those efforts are made challenging by the difficulty of calculating high precision quantities in quantum chromodynamics . Some theorists working in this area use the tools of perturbative quantum field theory and effective field theory , referring to themselves as phenomenologists . Others make use of lattice field theory and call themselves lattice theorists . Another major effort
2448-544: The atomic nuclei are baryons – the neutron is composed of two down quarks and one up quark, and the proton is composed of two up quarks and one down quark. A baryon is composed of three quarks, and a meson is composed of two quarks (one normal, one anti). Baryons and mesons are collectively called hadrons . Quarks inside hadrons are governed by the strong interaction, thus are subjected to quantum chromodynamics (color charges). The bounded quarks must have their color charge to be neutral, or "white" for analogy with mixing
2520-401: The weak interaction , and the strong interaction . Quarks cannot exist on their own but form hadrons . Hadrons that contain an odd number of quarks are called baryons and those that contain an even number are called mesons . Two baryons, the proton and the neutron , make up most of the mass of ordinary matter. Mesons are unstable and the longest-lived last for only a few hundredths of
2592-408: The Standard Model during the 1970s, physicists clarified the origin of the particle zoo. The large number of particles was explained as combinations of a (relatively) small number of more fundamental particles and framed in the context of quantum field theories . This reclassification marked the beginning of modern particle physics. The current state of the classification of all elementary particles
2664-571: The aforementioned color confinement, gluons are never observed independently. The Higgs boson gives mass to the W and Z bosons via the Higgs mechanism – the gluon and photon are expected to be massless . All bosons have an integer quantum spin (0 and 1) and can have the same quantum state . Most aforementioned particles have corresponding antiparticles , which compose antimatter . Normal particles have positive lepton or baryon number , and antiparticles have these numbers negative. Most properties of corresponding antiparticles and particles are
2736-474: The angular position of a particle in terms of an azimuthal angle ϕ {\displaystyle \phi } and pseudorapidity η {\displaystyle \eta } . Additionally the transverse momentum, p T {\displaystyle p_{T}} , is usually measured. In this case if the particles are massless, or highly relativistic ( E ≫ m {\displaystyle E\gg m} ) then
2808-471: The annihilation (or decay) of an electron–positron pair into a single photon can occur in the presence of a third charged particle, to which the excess momentum can be transferred by a virtual photon from the electron or positron. The inverse process, pair production by a single real photon, is also possible in the electromagnetic field of a third particle. When a proton encounters its antiparticle (and more generally, if any species of baryon encounters
2880-420: The case of bound systems simply mass , is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, it is a characteristic of the system's total energy and momentum that is the same in all frames of reference related by Lorentz transformations . If a center-of-momentum frame exists for the system, then the invariant mass of
2952-597: The constituents of all matter . Finally, the Standard Model also predicted the existence of a type of boson known as the Higgs boson . On 4 July 2012, physicists with the Large Hadron Collider at CERN announced they had found a new particle that behaves similarly to what is expected from the Higgs boson. The Standard Model, as currently formulated, has 61 elementary particles. Those elementary particles can combine to form composite particles, accounting for
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3024-421: The corresponding antibaryon ), the reaction is not as simple as electron–positron annihilation. Unlike an electron, a proton is a composite particle consisting of three " valence quarks " and an indeterminate number of " sea quarks " bound by gluons . Thus, when a proton encounters an antiproton, one of its quarks, usually a constituent valence quark, may annihilate with an antiquark (which more rarely could be
3096-523: The decay products of a single particle is equal to the mass of the particle that decayed. The mass of a system of particles can be calculated from the general formula: ( W c 2 ) 2 = ( ∑ E ) 2 − ‖ ∑ p c ‖ 2 , {\displaystyle \left(Wc^{2}\right)^{2}=\left(\sum E\right)^{2}-\left\|\sum \mathbf {p} c\right\|^{2},} where The term invariant mass
3168-450: The development of nuclear weapons . Throughout the 1950s and 1960s, a bewildering variety of particles was found in collisions of particles from beams of increasingly high energy. It was referred to informally as the " particle zoo ". Important discoveries such as the CP violation by James Cronin and Val Fitch brought new questions to matter-antimatter imbalance . After the formulation of
3240-478: The first experimental deviations from the Standard Model, since neutrinos do not have mass in the Standard Model. Modern particle physics research is focused on subatomic particles , including atomic constituents, such as electrons , protons , and neutrons (protons and neutrons are composite particles called baryons , made of quarks ), that are produced by radioactive and scattering processes; such particles are photons , neutrinos , and muons , as well as
3312-538: The gravitational interaction, but it has not been detected or completely reconciled with current theories. Many other hypothetical particles have been proposed to address the limitations of the Standard Model. Notably, supersymmetric particles aim to solve the hierarchy problem , axions address the strong CP problem , and various other particles are proposed to explain the origins of dark matter and dark energy . The world's major particle physics laboratories are: Theoretical particle physics attempts to develop
3384-424: The hundreds of other species of particles that have been discovered since the 1960s. The Standard Model has been found to agree with almost all the experimental tests conducted to date. However, most particle physicists believe that it is an incomplete description of nature and that a more fundamental theory awaits discovery (See Theory of Everything ). In recent years, measurements of neutrino mass have provided
3456-402: The hypothesized tachyon ), and these do not appear to exist. Any time-like four-momentum possesses a reference frame where the momentum (3-dimensional) is zero, which is a center of momentum frame. In this case, invariant mass is positive and is referred to as the rest mass. If objects within a system are in relative motion, then the invariant mass of the whole system will differ from the sum of
3528-433: The interactions between the quarks store energy which can convert to other particles when the quarks are far apart enough, quarks cannot be observed independently. This is called color confinement . There are three known generations of quarks (up and down, strange and charm , top and bottom ) and leptons (electron and its neutrino, muon and its neutrino , tau and its neutrino ), with strong indirect evidence that
3600-482: The invariant mass becomes: M 2 = 2 p T 1 p T 2 ( cosh ( η 1 − η 2 ) − cos ( ϕ 1 − ϕ 2 ) ) . {\displaystyle M^{2}=2p_{T1}p_{T2}(\cosh(\eta _{1}-\eta _{2})-\cos(\phi _{1}-\phi _{2})).} Rest energy (also called rest mass energy )
3672-431: The invariant mass of a system may be greater than sum of the invariant masses (rest masses) of its separate constituents. For example, rest mass and invariant mass are zero for individual photons even though they may add mass to the invariant mass of systems. For this reason, invariant mass is in general not an additive quantity (although there are a few rare situations where it may be, as is the case when massive particles in
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#17327723852773744-404: The kinetic energy of the molecules in a bottle of gas to be part of invariant mass of the bottle, and thus also its rest mass. The same is true for massless particles in such system, which add invariant mass and also rest mass to systems, according to their energy. For an isolated massive system, the center of mass of the system moves in a straight line with a steady subluminal velocity (with
3816-497: The models, theoretical framework, and mathematical tools to understand current experiments and make predictions for future experiments (see also theoretical physics ). There are several major interrelated efforts being made in theoretical particle physics today. One important branch attempts to better understand the Standard Model and its tests. Theorists make quantitative predictions of observables at collider and astronomical experiments, which along with experimental measurements
3888-408: The objects' rest masses. This is also equal to the total energy of the system divided by c . See mass–energy equivalence for a discussion of definitions of mass. Since the mass of systems must be measured with a weight or mass scale in a center of momentum frame in which the entire system has zero momentum, such a scale always measures the system's invariant mass. For example, a scale would measure
3960-413: The ordinary length of a vector is preserved under rotations. In quantum theory the invariant mass is a parameter in the relativistic Dirac equation for an elementary particle. The Dirac quantum operator corresponds to the particle four-momentum vector. Since the invariant mass is determined from quantities which are conserved during a decay, the invariant mass calculated using the energy and momentum of
4032-409: The particle kinetic energies as calculated by an observer is smallest in the center of momentum frame (again, called the "rest frame" if the system is bound). They will often also interact through one or more of the fundamental forces , giving them a potential energy of interaction, possibly negative . In particle physics , the invariant mass m 0 is equal to the mass in the rest frame of
4104-705: The particle, and can be calculated by the particle's energy E and its momentum p as measured in any frame, by the energy–momentum relation : m 0 2 c 2 = ( E c ) 2 − ‖ p ‖ 2 {\displaystyle m_{0}^{2}c^{2}=\left({\frac {E}{c}}\right)^{2}-\left\|\mathbf {p} \right\|^{2}} or in natural units where c = 1 , m 0 2 = E 2 − ‖ p ‖ 2 . {\displaystyle m_{0}^{2}=E^{2}-\left\|\mathbf {p} \right\|^{2}.} This invariant mass
4176-483: The photon or gluon, have no antiparticles. Quarks and gluons additionally have color charges, which influences the strong interaction. Quark's color charges are called red, green and blue (though the particle itself have no physical color), and in antiquarks are called antired, antigreen and antiblue. The gluon can have eight color charges , which are the result of quarks' interactions to form composite particles (gauge symmetry SU(3) ). The neutrons and protons in
4248-400: The photon. When a low-energy electron annihilates a low-energy positron (antielectron), the most probable result is the creation of two or more photons , since the only other final-state Standard Model particles that electrons and positrons carry enough mass–energy to produce are neutrinos , which are approximately 10,000 times less likely to produce, and the creation of only one photon
4320-428: The photons produced. Each of the photons then has an energy of about 0.511 MeV. Momentum and energy are both conserved, with 1.022 MeV of photon energy (accounting for the rest energy of the particles) moving in opposite directions (accounting for the total zero momentum of the system). If one or both charged particles carry a larger amount of kinetic energy, various other particles can be produced. Furthermore,
4392-444: The possibility for triggering a significant number of secondary fission reactions in a subcritical mass and may potentially be useful for spacecraft propulsion . In collisions of two nucleons at very high energies, sea quarks and gluons tend to dominate the interaction rate, so neither nucleon need be an anti-particle for annihilation of a quark pair or "fusion" of two gluons to occur. Examples of such processes contribute to
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#17327723852774464-426: The primary colors . More exotic hadrons can have other types, arrangement or number of quarks ( tetraquark , pentaquark ). An atom is made from protons, neutrons and electrons. By modifying the particles inside a normal atom, exotic atoms can be formed. A simple example would be the hydrogen-4.1 , which has one of its electrons replaced with a muon. The graviton is a hypothetical particle that can mediate
4536-401: The process is understood as the initial creation of a boson that is virtual , which immediately converts into a real particle + antiparticle pair. This is called an s-channel process. An example is the annihilation of an electron with a positron to produce a virtual photon, which converts into a muon and anti-muon. If the energy is large enough, a Z could replace
4608-519: The production of the long-sought Higgs boson . The Higgs is directly produced very weakly by annihilation of light (valence) quarks, but heavy t or b sea or produced quarks are available. In 2012, the CERN laboratory in Geneva announced the discovery of the Higgs in the debris from proton–proton collisions at the Large Hadron Collider (LHC). The strongest Higgs yield
4680-405: The remaining "spectator" nucleons rather than escaping. Since the absorbed energy can be as much as ~2 GeV , it can in principle exceed the binding energy of even the heaviest nuclei. Thus, when an antiproton annihilates inside a heavy nucleus such as uranium or plutonium , partial or complete disruption of the nucleus can occur, releasing large numbers of fast neutrons. Such reactions open
4752-419: The same system from center-of-momentum frame, where net momentum is zero, the magnitude of the system's invariant mass is not equal to the sum of the rest masses of the particles within it. The kinetic energy of such particles and the potential energy of the force fields increase the total energy above the sum of the particle rest masses, and both terms contribute to the invariant mass of the system. The sum of
4824-444: The same, with a few gets reversed; the electron's antiparticle, positron, has an opposite charge. To differentiate between antiparticles and particles, a plus or negative sign is added in superscript . For example, the electron and the positron are denoted e and e . When a particle and an antiparticle interact with each other, they are annihilated and convert to other particles. Some particles, such as
4896-622: The scale of protons and neutrons , while the study of combination of protons and neutrons is called nuclear physics . The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) and bosons (force-carrying particles). There are three generations of fermions, although ordinary matter is made only from the first fermion generation. The first generation consists of up and down quarks which form protons and neutrons , and electrons and electron neutrinos . The three fundamental interactions known to be mediated by bosons are electromagnetism ,
4968-757: The square of the invariant mass (in natural units ) is M 2 = ( E 1 + E 2 ) 2 − ‖ p 1 + p 2 ‖ 2 = m 1 2 + m 2 2 + 2 ( E 1 E 2 − p 1 ⋅ p 2 ) . {\displaystyle {\begin{aligned}M^{2}&=(E_{1}+E_{2})^{2}-\left\|\mathbf {p} _{1}+\mathbf {p} _{2}\right\|^{2}\\&=m_{1}^{2}+m_{2}^{2}+2\left(E_{1}E_{2}-\mathbf {p} _{1}\cdot \mathbf {p} _{2}\right).\end{aligned}}} The invariant mass of
5040-421: The sums of all quantum numbers of such an original pair are zero. Hence, any set of particles may be produced whose total quantum numbers are also zero as long as conservation of energy , conservation of momentum , and conservation of spin are obeyed. During a low-energy annihilation, photon production is favored, since these particles have no mass. High-energy particle colliders produce annihilations where
5112-410: The total energy of the system is its total (relativistic) mass times the speed of light squared. Systems whose four-momentum is a null vector (for example, a single photon or many photons moving in exactly the same direction) have zero invariant mass and are referred to as massless . A physical object or particle moving faster than the speed of light would have space-like four-momenta (such as
5184-682: Was composed of a single, unique type of particle. The word atom , after the Greek word atomos meaning "indivisible", has since then denoted the smallest particle of a chemical element , but physicists later discovered that atoms are not, in fact, the fundamental particles of nature, but are conglomerates of even smaller particles, such as the electron . The early 20th century explorations of nuclear physics and quantum physics led to proofs of nuclear fission in 1939 by Lise Meitner (based on experiments by Otto Hahn ), and nuclear fusion by Hans Bethe in that same year; both discoveries also led to
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