87-442: In particle physics , quantum electrodynamics ( QED ) is the relativistic quantum field theory of electrodynamics . In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents
174-487: 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
261-402: 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
348-436: A positron moving forward in time.) Quantum mechanics introduces an important change in the way probabilities are computed. Probabilities are still represented by the usual real numbers we use for probabilities in our everyday world, but probabilities are computed as the square modulus of probability amplitudes , which are complex numbers . Feynman avoids exposing the reader to the mathematics of complex numbers by using
435-502: 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
522-1058: 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
609-465: A Feynman diagram could be drawn describing it. This implies a complex computation for the resulting probability amplitudes, but provided it is the case that the more complicated the diagram, the less it contributes to the result, it is only a matter of time and effort to find as accurate an answer as one wants to the original question. This is the basic approach of QED. To calculate the probability of any interactive process between electrons and photons, it
696-438: A better estimation for the total probability amplitude by adding the probability amplitudes of these two possibilities to our original simple estimate. Incidentally, the name given to this process of a photon interacting with an electron in this way is Compton scattering . There is an infinite number of other intermediate "virtual" processes in which more and more photons are absorbed and/or emitted. For each of these processes,
783-444: A finite value by experiments. In this way, the infinities get absorbed in those constants and yield a finite result in good agreement with experiments. This procedure was named renormalization . Based on Bethe's intuition and fundamental papers on the subject by Shin'ichirō Tomonaga , Julian Schwinger , Richard Feynman and Freeman Dyson , it was finally possible to get fully covariant formulations that were finite at any order in
870-441: A first order of perturbation theory , a problem already pointed out by Robert Oppenheimer . At higher orders in the series infinities emerged, making such computations meaningless and casting serious doubts on the internal consistency of the theory itself. With no solution for this problem known at the time, it appeared that a fundamental incompatibility existed between special relativity and quantum mechanics . Difficulties with
957-452: 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
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#17327720301921044-498: A later time) and a photon at D (yet another place and time)?". The simplest process to achieve this end is for the electron to move from A to C (an elementary action) and for the photon to move from B to D (another elementary action). From a knowledge of the probability amplitudes of each of these sub-processes – E ( A to C ) and P ( B to D ) – we would expect to calculate the probability amplitude of both happening together by multiplying them, using rule b) above. This gives
1131-436: A line, it breaks up into a collection of "simple" lines, each of which, if looked at closely, are in turn composed of "simple" lines, and so on ad infinitum . This is a challenging situation to handle. If adding that detail only altered things slightly, then it would not have been too bad, but disaster struck when it was found that the simple correction mentioned above led to infinite probability amplitudes. In time this problem
1218-845: 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. Robert Retherford From Misplaced Pages,
1305-430: 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,
1392-562: A perturbation series of quantum electrodynamics. Shin'ichirō Tomonaga, Julian Schwinger and Richard Feynman were jointly awarded with the 1965 Nobel Prize in Physics for their work in this area. Their contributions, and those of Freeman Dyson , were about covariant and gauge-invariant formulations of quantum electrodynamics that allow computations of observables at any order of perturbation theory . Feynman's mathematical technique, based on his diagrams , initially seemed very different from
1479-400: A set of asymptotic states that can be used to start computation of the probability amplitudes for different processes. In order to do so, we have to compute an evolution operator , which for a given initial state | i ⟩ {\displaystyle |i\rangle } will give a final state ⟨ f | {\displaystyle \langle f|} in such
1566-436: A simple but accurate representation of them as arrows on a piece of paper or screen. (These must not be confused with the arrows of Feynman diagrams, which are simplified representations in two dimensions of a relationship between points in three dimensions of space and one of time.) The amplitude arrows are fundamental to the description of the world given by quantum theory. They are related to our everyday ideas of probability by
1653-451: A simple estimated overall probability amplitude, which is squared to give an estimated probability. But there are other ways in which the result could come about. The electron might move to a place and time E , where it absorbs the photon; then move on before emitting another photon at F ; then move on to C , where it is detected, while the new photon moves on to D . The probability of this complex process can again be calculated by knowing
1740-452: A single electroweak force . Near the end of his life, Richard Feynman gave a series of lectures on QED intended for the lay public. These lectures were transcribed and published as Feynman (1985), QED: The Strange Theory of Light and Matter , a classic non-mathematical exposition of QED from the point of view articulated below. The key components of Feynman's presentation of QED are three basic actions. These actions are represented in
1827-410: A way to have M f i = ⟨ f | U | i ⟩ . {\displaystyle M_{fi}=\langle f|U|i\rangle .} 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
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#17327720301921914-435: 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
2001-460: Is a constant, and is related to, but not the same as, the measured electron charge e . QED is based on the assumption that complex interactions of many electrons and photons can be represented by fitting together a suitable collection of the above three building blocks and then using the probability amplitudes to calculate the probability of any such complex interaction. It turns out that the basic idea of QED can be communicated while assuming that
2088-465: Is a matter of first noting, with Feynman diagrams, all the possible ways in which the process can be constructed from the three basic elements. Each diagram involves some calculation involving definite rules to find the associated probability amplitude. That basic scaffolding remains when one moves to a quantum description, but some conceptual changes are needed. One is that whereas we might expect in our everyday life that there would be some constraints on
2175-425: 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
2262-783: Is also credited with coining the term "quantum electrodynamics". Dirac described the quantization of the electromagnetic field as an ensemble of harmonic oscillators with the introduction of the concept of creation and annihilation operators of particles. In the following years, with contributions from Wolfgang Pauli , Eugene Wigner , Pascual Jordan , Werner Heisenberg and an elegant formulation of quantum electrodynamics by Enrico Fermi , physicists came to believe that, in principle, it would be possible to perform any computation for any physical process involving photons and charged particles. However, further studies by Felix Bloch with Arnold Nordsieck , and Victor Weisskopf , in 1937 and 1939, revealed that such computations were reliable only at
2349-895: Is an abelian gauge theory with the symmetry group U(1) , defined on Minkowski space (flat spacetime). The gauge field , which mediates the interaction between the charged spin-1/2 fields , is the electromagnetic field . The QED Lagrangian for a spin-1/2 field interacting with the electromagnetic field in natural units gives rise to the action S QED = ∫ d 4 x [ − 1 4 F μ ν F μ ν + ψ ¯ ( i γ μ D μ − m ) ψ ] {\displaystyle S_{\text{QED}}=\int d^{4}x\,\left[-{\frac {1}{4}}F^{\mu \nu }F_{\mu \nu }+{\bar {\psi }}\,(i\gamma ^{\mu }D_{\mu }-m)\,\psi \right]} where Expanding
2436-421: Is as follows: where a shorthand symbol such as x A {\displaystyle x_{A}} stands for the four real numbers that give the time and position in three dimensions of the point labeled A . A problem arose historically which held up progress for twenty years: although we start with the assumption of three basic "simple" actions, the rules of the game say that if we want to calculate
2523-554: 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
2610-532: 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
2697-595: 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
Quantum electrodynamics - Misplaced Pages Continue
2784-471: 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
2871-399: Is to say that their orientations in space and time have to be taken into account. Therefore, P ( A to B ) consists of 16 complex numbers, or probability amplitude arrows. There are also some minor changes to do with the quantity j , which may have to be rotated by a multiple of 90° for some polarizations, which is only of interest for the detailed bookkeeping. Associated with the fact that
2958-600: 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
3045-415: Is very important: it means that there is no observable feature present in the given system that in any way "reveals" which alternative is taken. In such a case, one cannot observe which alternative actually takes place without changing the experimental setup in some way (e.g. by introducing a new apparatus into the system). Whenever one is able to observe which alternative takes place, one always finds that
3132-549: Is written Expanding the covariant derivative in the Lagrangian gives For simplicity, B μ {\displaystyle B_{\mu }} has been set to zero. Alternatively, we can absorb B μ {\displaystyle B_{\mu }} into a new gauge field A μ ′ = A μ + B μ {\displaystyle A'_{\mu }=A_{\mu }+B_{\mu }} and relabel
3219-594: The U ( 1 ) {\displaystyle {\text{U}}(1)} current j μ {\displaystyle j^{\mu }} as ∂ μ F μ ν = e j ν . {\displaystyle \partial _{\mu }F^{\mu \nu }=ej^{\nu }.} Now, if we impose the Lorenz gauge condition ∂ μ A μ = 0 , {\displaystyle \partial _{\mu }A^{\mu }=0,}
3306-488: The Shelter Island Conference . While he was traveling by train from the conference to Schenectady he made the first non-relativistic computation of the shift of the lines of the hydrogen atom as measured by Lamb and Retherford . Despite the limitations of the computation, agreement was excellent. The idea was simply to attach infinities to corrections of mass and charge that were actually fixed to
3393-442: The anomalous magnetic dipole moment . However, as Feynman points out, it fails to explain why particles such as the electron have the masses they do. "There is no theory that adequately explains these numbers. We use the numbers in all our theories, but we don't understand them – what they are, or where they come from. I believe that from a fundamental point of view, this is a very interesting and serious problem." Mathematically, QED
3480-462: The anomalous magnetic moment of the electron and the Lamb shift of the energy levels of hydrogen . It is the most precise and stringently tested theory in physics. The first formulation of a quantum theory describing radiation and matter interaction is attributed to British scientist Paul Dirac , who (during the 1920s) was able to compute the coefficient of spontaneous emission of an atom . He
3567-544: 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
Quantum electrodynamics - Misplaced Pages Continue
3654-446: The probability of the event is the sum of the probabilities of the alternatives. Indeed, if this were not the case, the very term "alternatives" to describe these processes would be inappropriate. What (a) says is that once the physical means for observing which alternative occurred is removed , one cannot still say that the event is occurring through "exactly one of the alternatives" in the sense of adding probabilities; one must add
3741-574: The quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction. In technical terms, QED can be described as a very accurate way to calculate the probability of the position and movement of particles, even those massless such as photons, and the quantity depending on position (field) of those particles, and described light and matter beyond the wave-particle duality proposed by Albert Einstein in 1905. Richard Feynman called it "the jewel of physics" for its extremely accurate predictions of quantities like
3828-401: 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
3915-932: The Hydrogen Atom by a Microwave Method" . Physical Review . 72 (3): 241–243. Bibcode : 1947PhRv...72..241R . doi : 10.1103/PhysRev.72.241 . ^ Schweber, Silvan (1994). "Chapter 5" . QED and the Men Who Did it: Dyson, Feynman, Schwinger, and Tomonaga . Princeton University Press. p. 215 . ISBN 978-0691033273 . Authority control databases [REDACTED] International VIAF National Germany Retrieved from " https://en.wikipedia.org/w/index.php?title=Robert_Retherford&oldid=1236627897 " Categories : 20th-century American physicists 1912 births 1981 deaths Columbia University alumni Hidden categories: Articles with short description Short description
4002-540: The Lagrangian contains no ∂ μ ψ ¯ {\displaystyle \partial _{\mu }{\bar {\psi }}} terms, we immediately get so the equation of motion can be written ( i γ μ ∂ μ − m ) ψ = e γ μ A μ ψ . {\displaystyle (i\gamma ^{\mu }\partial _{\mu }-m)\psi =e\gamma ^{\mu }A_{\mu }\psi .}
4089-408: 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
4176-571: 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
4263-438: The alternatives for E and F . (This is not elementary in practice and involves integration .) But there is another possibility, which is that the electron first moves to G , where it emits a photon, which goes on to D , while the electron moves on to H , where it absorbs the first photon, before moving on to C . Again, we can calculate the probability amplitude of these possibilities (for all points G and H ). We then have
4350-454: The amplitudes instead. Similarly, the independence criterion in (b) is very important: it only applies to processes which are not "entangled". Suppose we start with one electron at a certain place and time (this place and time being given the arbitrary label A ) and a photon at another place and time (given the label B ). A typical question from a physical standpoint is: "What is the probability of finding an electron at C (another place and
4437-564: The associated quantity is written in Feynman's shorthand as P ( A to B ) {\displaystyle P(A{\text{ to }}B)} , and it depends on only the momentum and polarization of the photon. The similar quantity for an electron moving from C {\displaystyle C} to D {\displaystyle D} is written E ( C to D ) {\displaystyle E(C{\text{ to }}D)} . It depends on
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#17327720301924524-597: 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
4611-408: The covariant derivative reveals a second useful form of the Lagrangian (external field B μ {\displaystyle B_{\mu }} set to zero for simplicity) where j μ {\displaystyle j^{\mu }} is the conserved U ( 1 ) {\displaystyle {\text{U}}(1)} current arising from Noether's theorem. It
4698-1014: The derivatives this time are ∂ ν ( ∂ L ∂ ( ∂ ν A μ ) ) = ∂ ν ( ∂ μ A ν − ∂ ν A μ ) , {\displaystyle \partial _{\nu }\left({\frac {\partial {\mathcal {L}}}{\partial (\partial _{\nu }A_{\mu })}}\right)=\partial _{\nu }\left(\partial ^{\mu }A^{\nu }-\partial ^{\nu }A^{\mu }\right),} ∂ L ∂ A μ = − e ψ ¯ γ μ ψ . {\displaystyle {\frac {\partial {\mathcal {L}}}{\partial A_{\mu }}}=-e{\bar {\psi }}\gamma ^{\mu }\psi .} Substituting back into ( 3 ) leads to which can be written in terms of
4785-450: 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
4872-441: The early 1960s and attained its present form in the 1970s work by H. David Politzer , Sidney Coleman , David Gross and Frank Wilczek . Building on the pioneering work of Schwinger , Gerald Guralnik , Dick Hagen , and Tom Kibble , Peter Higgs , Jeffrey Goldstone , and others, Sheldon Glashow , Steven Weinberg and Abdus Salam independently showed how the weak nuclear force and quantum electrodynamics could be merged into
4959-404: The electron can be polarized is another small necessary detail, which is connected with the fact that an electron is a fermion and obeys Fermi–Dirac statistics . The basic rule is that if we have the probability amplitude for a given complex process involving more than one electron, then when we include (as we always must) the complementary Feynman diagram in which we exchange two electron events,
5046-677: The equations reduce to ◻ A μ = e j μ , {\displaystyle \Box A^{\mu }=ej^{\mu },} which is a wave equation for the four-potential, the QED version of the classical Maxwell equations in the Lorenz gauge . (The square represents the wave operator , ◻ = ∂ μ ∂ μ {\displaystyle \Box =\partial _{\mu }\partial ^{\mu }} .) This theory can be straightforwardly quantized by treating bosonic and fermionic sectors as free. This permits us to build
5133-495: The field-theoretic, operator -based approach of Schwinger and Tomonaga, but Freeman Dyson later showed that the two approaches were equivalent. Renormalization , the need to attach a physical meaning at certain divergences appearing in the theory through integrals , has subsequently become one of the fundamental aspects of quantum field theory and has come to be seen as a criterion for a theory's general acceptability. Even though renormalization works very well in practice, Feynman
5220-478: 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
5307-408: The form of visual shorthand by the three basic elements of diagrams : a wavy line for the photon, a straight line for the electron and a junction of two straight lines and a wavy one for a vertex representing emission or absorption of a photon by an electron. These can all be seen in the adjacent diagram. As well as the visual shorthand for the actions, Feynman introduces another kind of shorthand for
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#17327720301925394-476: The 💕 American physicist (1912–1981) Robert Curtis Retherford Born 1912 ( 1912 ) Died 1981 (aged 68–69) Citizenship United States Alma mater Columbia University Known for Lamb shift Scientific career Fields Physics Institutions Columbia University Doctoral advisor Willis Lamb Robert Curtis Retherford (1912–1981)
5481-538: 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
5568-424: 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
5655-433: 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
5742-497: 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
5829-400: The momentum and polarization of the electron, in addition to a constant Feynman calls n , sometimes called the "bare" mass of the electron: it is related to, but not the same as, the measured electron mass. Finally, the quantity that tells us about the probability amplitude for an electron to emit or absorb a photon Feynman calls j , and is sometimes called the "bare" charge of the electron: it
5916-559: The new field as A μ . {\displaystyle A_{\mu }.} From this Lagrangian, the equations of motion for the ψ {\displaystyle \psi } and A μ {\displaystyle A_{\mu }} fields can be obtained. These arise most straightforwardly by considering the Euler-Lagrange equation for ψ ¯ {\displaystyle {\bar {\psi }}} . Since
6003-478: The numerical quantities called probability amplitudes . The probability is the square of the absolute value of total probability amplitude, probability = | f ( amplitude ) | 2 {\displaystyle {\text{probability}}=|f({\text{amplitude}})|^{2}} . If a photon moves from one place and time A {\displaystyle A} to another place and time B {\displaystyle B} ,
6090-483: 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
6177-414: The points to which a particle can move, that is not true in full quantum electrodynamics. There is a nonzero probability amplitude of an electron at A , or a photon at B , moving as a basic action to any other place and time in the universe . That includes places that could only be reached at speeds greater than that of light and also earlier times . (An electron moving backwards in time can be viewed as
6264-426: 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
6351-437: The probability amplitude for an electron to get from A to B , we must take into account all the possible ways: all possible Feynman diagrams with those endpoints. Thus there will be a way in which the electron travels to C , emits a photon there and then absorbs it again at D before moving on to B . Or it could do this kind of thing twice, or more. In short, we have a fractal -like situation in which if we look closely at
6438-516: The probability amplitudes for the photon and the electron respectively. These are essentially the solutions of the Dirac equation , which describe the behavior of the electron's probability amplitude and the Maxwell's equations , which describes the behavior of the photon's probability amplitude. These are called Feynman propagators . The translation to a notation commonly used in the standard literature
6525-405: The probability amplitudes of each of the individual actions: three electron actions, two photon actions and two vertexes – one emission and one absorption. We would expect to find the total probability amplitude by multiplying the probability amplitudes of each of the actions, for any chosen positions of E and F . We then, using rule a) above, have to add up all these probability amplitudes for all
6612-456: The resulting amplitude is the reverse – the negative – of the first. The simplest case would be two electrons starting at A and B ending at C and D . The amplitude would be calculated as the "difference", E ( A to D ) × E ( B to C ) − E ( A to C ) × E ( B to D ) , where we would expect, from our everyday idea of probabilities, that it would be a sum. Finally, one has to compute P ( A to B ) and E ( C to D ) corresponding to
6699-444: 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
6786-622: 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 ,
6873-534: The simple rule that the probability of an event is the square of the length of the corresponding amplitude arrow. So, for a given process, if two probability amplitudes, v and w , are involved, the probability of the process will be given either by or The rules as regards adding or multiplying, however, are the same as above. But where you would expect to add or multiply probabilities, instead you add or multiply probability amplitudes that now are complex numbers. Addition and multiplication are common operations in
6960-411: The square of the total of the probability amplitudes mentioned above ( P ( A to B ), E ( C to D ) and j ) acts just like our everyday probability (a simplification made in Feynman's book). Later on, this will be corrected to include specifically quantum-style mathematics, following Feynman. The basic rules of probability amplitudes that will be used are: The indistinguishability criterion in (a)
7047-432: The theory increased through the end of the 1940s. Improvements in microwave technology made it possible to take more precise measurements of the shift of the levels of a hydrogen atom , now known as the Lamb shift and magnetic moment of the electron. These experiments exposed discrepancies which the theory was unable to explain. A first indication of a possible way out was given by Hans Bethe in 1947, after attending
7134-415: The theory of complex numbers and are given in the figures. The sum is found as follows. Let the start of the second arrow be at the end of the first. The sum is then a third arrow that goes directly from the beginning of the first to the end of the second. The product of two arrows is an arrow whose length is the product of the two lengths. The direction of the product is found by adding the angles that each of
7221-423: The two have been turned through relative to a reference direction: that gives the angle that the product is turned relative to the reference direction. That change, from probabilities to probability amplitudes, complicates the mathematics without changing the basic approach. But that change is still not quite enough because it fails to take into account the fact that both photons and electrons can be polarized, which
7308-399: Was "fixed" by the technique of renormalization . However, Feynman himself remained unhappy about it, calling it a "dippy process", and Dirac also criticized this procedure as "in mathematics one does not get rid of infinities when it does not please you". Within the above framework physicists were then able to calculate to a high degree of accuracy some of the properties of electrons, such as
7395-601: Was an American physicist . He was a graduate student of Willis Lamb at Columbia Radiation Laboratory . Retherford and Lamb performed the famous experiment (now known as the Lamb–Retherford experiment ) revealing Lamb shift in the fine structure of hydrogen, a decisive experimental step toward a new understanding of quantum electrodynamics . See also [ edit ] Quantum electrodynamics Lamb shift References [ edit ] ^ Lamb, Jr, W. E. ; Retherford, R. C. (1947). "Fine Structure of
7482-682: 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
7569-441: Was never entirely comfortable with its mathematical validity, even referring to renormalization as a "shell game" and "hocus pocus". Thence, neither Feynman nor Dirac were happy with that way to approach the observations made in theoretical physics, above all in quantum mechanics. QED has served as the model and template for all subsequent quantum field theories. One such subsequent theory is quantum chromodynamics , which began in
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