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In physics, a magnetic monopole is a hypothetical particle that may be loosely described as "a magnet with only one pole" (see electromagnetic theory for more on magnetic poles). In more accurate terms, it would have net magnetic charge. Interest in the concept stems from particle theories, notably Grand Unified Theories and superstring theories, that predict either the existence or the possibility of magnetic monopoles. Image File history File links Unbalanced_scales. ... This article needs additional references or sources for verification. ... Iron filings in a magnetic field generated by a bar magnet A magnet is a material or object that produces a magnetic field. ... Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... Particle physics is a branch of physics that studies the elementary constituents of matter and radiation, and the interactions between them. ... Grand unification, grand unified theory, or GUT is a theory in physics that unifies the strong interaction and electroweak interaction. ... Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. ...

Despite systematic searches since 1931, as of 2006, magnetic monopoles have never been observed.^[1] It therefore remains possible that monopoles do not exist at all. The failure of given experiments to find magnetic monopoles also places constraints on their possible properties and hence on the physical theories that predict them. Some current models suggest that while magnetic monopoles exist in principle, they are so massive that they may never be observed in practice. 2006 is a common year starting on Sunday of the Gregorian calendar. ...

Background

Unsolved problems in physics: Are there any particles that carry "magnetic charge", and if so, why are they so difficult to detect?

Magnets exert forces on one another, similarly to electric charges. Like poles will repel each other, and unlike poles will attract. When a magnet (an object conventionally described as having magnetic north and south poles) is cut in half across the axis joining those "poles", the resulting pieces are two normal (albeit smaller) magnets. Each has its own north pole and south pole. Image File history File links No higher resolution available. ... This is a list of some of the unsolved problems in physics. ... Iron filings in a magnetic field generated by a bar magnet A magnet is a material or object that produces a magnetic field. ... In physics, force is an influence that may cause an object to accelerate. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ...

Even atoms have tiny magnetic fields. In the Bohr model of an atom, electrons orbit the nucleus. The constant change in their motion gives rise to a magnetic field. Permanent magnets have measurable magnetic fields because the atoms and molecules in them are arranged in a way that their individual magnetic fields align, combining to form large aggregate fields. In this model, the lack of a single pole makes intuitive sense; cutting a bar magnet in half does nothing to the arrangement of the molecules within. The end result is two magnetic bars whose atoms have the same orientation as before, and therefore generate a magnetic field with the same orientation as the original larger magnet. Properties In chemistry and physics, an atom (Greek ἄτομος or átomos meaning indivisible) is the smallest particle still characterizing a chemical element. ... The Bohr model of the hydrogen atom, where negatively charged electrons confined to atomic shells encircle a small positively charged atomic nucleus, and that an electron jump between orbits must be accompanied by an emitted or absorbed amount of electromagnetic energy hν. The orbits that the electrons travel in are...

Maxwell's equations

Maxwell's equations of electromagnetism relate the electric and magnetic fields to the motions of electric charges. The standard form of the equations provide for an electric charge, but posit no magnetic charge. Except for this, the equations are symmetric under interchange of electric and magnetic field. In fact, symmetric equations can be written when all charges are zero, and this is how the wave equation is derived. In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ... Lasers used for visual effects during a musical performance. ...

Fully symmetric equations can also be written if one allows for the possibility of "magnetic charges" analogous to electric charges.[1] With the inclusion of a variable for these magnetic charges, say , there will also be "magnetic current" variable in the equations, . The extended Maxwell's equations, simplified by nondimensionalization, are as follows: In physics, Planck units are physical units of measurement defined exclusively in terms of the five universal physical constants shown in the table below in such a manner that all of these physical constants take on the numerical value of one when expressed in terms of these units. ...

Name	Without Magnetic Monopoles	With Magnetic Monopoles
Gauss's law:
Gauss' law for magnetism:
Faraday's law of induction:
Ampère's law (with Maxwell's extension):
Note: the Bivector notation embodies the sign swap, and these four equations can be written as only one equation.

If magnetic charges do not exist, or if they exist but where they are not present in a region, then the new variables are zero, and the symmetric equations reduce to the conventional equations of electromagnetism such as . Classically, the question is "Why does the magnetic charge always seem to be zero?" In physics and mathematical analysis, Gausss law is the electrostatic application of the generalized Gausss theorem giving the equivalence relation between any flux, e. ... Faradays law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ... An electric current produces a magnetic field. ... A bivector is an element of the antisymmetric tensor product of a tangent space with itself. ...

Dirac's quantization

One of the defining advances in quantum theory was Paul Dirac's work on developing a relativistic quantum electromagnetism. Before his formulation, the presence of electric charge was simply "inserted" into QM, but in 1931 Dirac showed that a discrete charge naturally "falls out" of QM. Fig. ... Paul Adrien Maurice Dirac, OM, FRS (IPA: [dɪræk]) (August 8, 1902 – October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest...

Consider a system consisting of a single stationary electric monopole (an electron, say) and a single stationary magnetic monopole. Classically, the electromagnetic field surrounding them has a momentum density given by the Poynting vector, and it also has a total angular momentum, which is proportional to the product q_eq_m, and independent of the distance between them. The Poynting vector describes the energy flux (J·m−2·s−1) of an electromagnetic field. ... This gyroscope remains upright while spinning due to its angular momentum. ...

Quantum mechanics, dictates, however, that angular momentum is quantized in units of ħ, and therefore the product q_eq_m must also be quantized. This means that if even a single magnetic monopole existed in the universe, all electric charges would then be quantized. In physics, quantization is a procedure for constructing a quantum field theory starting from a classical field theory. ...

What are the units in which magnetic charge would be quantized? Although it would be possible simply to integrate over all space to find the total angular momentum in the above example, Dirac took a different approach, which led to new ideas. He considered a point-like magnetic charge whose magnetic field behaves as q_m / r² and is directed in the radial direction. Because the divergence of B is equal to zero almost everywhere, except for the locus of the magnetic monopole at r = 0, one can locally define the vector potential such that the curl of the vector potential A equals the magnetic field B. In vector calculus, a vector potential is a vector field whose curl is a given vector field. ... In vector calculus, curl is a vector operator that shows a vector fields rate of rotation: the direction of the axis of rotation and the magnitude of the rotation. ...

However, the vector potential cannot be defined globally precisely because the divergence of the magnetic field is proportional to the delta function at the origin. We must define one set of functions for the vector potential on the Northern hemisphere, and another set of functions for the Southern hemispheres. These two vector potentials are matched at the equator, and they differ by a gauge transformation. The wave function of an electrically charged particle (a probe) that orbits the equator generally changes by a phase, much like in the Aharonov-Bohm effect. This phase is proportional to the electric charge q_e of the probe, as well as to the magnetic charge q_m of the source. Dirac was originally considering an electron whose wave function is described by the Dirac equation. The Dirac delta function, introduced by Paul Dirac, can be informally thought of as a function δ(x) that has the value of infinity for x = 0, the value zero elsewhere, and a total integral of one. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... A wave function is a mathematical tool that quantum mechanics uses to describe any physical system. ... The Aharonov-Bohm effect, sometimes called the Ehrenberg-Siday-Aharonov-Bohm effect, is a quantum mechanical phenomenon by which a charged particle is affected by electromagnetic fields in regions from which the particle is excluded. ... e- redirects here. ... In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ...

Because the electron returns to the same point after the full trip around the equator, the phase exp(iφ) of its wave function must be unchanged, which implies that the phase φ added to the wave function must be a multiple of 2π:

, where Z is the set of integers

This is known as the Dirac quantization condition. In certain units, the condition is exactly given by the relation above. The hypothetical existence of a magnetic monopole would imply that the electric charge must be quantized in certain units; also, the existence of the electric charges implies that the magnetic charges of the hypothetical magnetic monopoles, if they exist, must be quantized in units inverse to the elementary electric charge.

At the time it was not clear if such a thing existed, or even had to. After all, another theory could come along that would explain charge quantization without need for the monopole. The concept remained something of a curiosity. However, in the time since the publication of this seminal work, no other widely accepted explanation of charge quantization has appeared. (The concept of local gauge invariance—see gauge theory below—provides a natural explanation of charge quantization, without invoking the need for magnetic monopoles; but only if the U(1) gauge group is compact, in which case we will have magnetic monopoles anyway.) In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ...

If we maximally extend the definition of the vector potential for the Southern hemisphere, it will be defined everywhere except for a semi-infinite line stretched from the origin in the direction towards the Northern pole. This semi-infinite line is called the Dirac string and its effect on the wave function is analogous to the effect of the solenoid in the Aharonov-Bohm effect. The quantization condition comes from the requirement that the phases around the Dirac string are trivial, which means that the Dirac string must be unphysical. The Dirac string is merely an artifact of the coordinate chart used and should not be taken seriously. In physics, a Dirac string is a fictitious one-dimensional curve in space, stretched from a magnetic monopole - also called the Dirac monopole - to infinity. ... Various solenoid actuators from Trombetta Motion Technologies A solenoid is a loop of wire, often wrapped around a metallic core, which produces a magnetic field when an electrical current is passed through it. ... The Aharonov-Bohm effect, sometimes called the Ehrenberg-Siday-Aharonov-Bohm effect, is a quantum mechanical phenomenon by which a charged particle is affected by electromagnetic fields in regions from which the particle is excluded. ...

The Dirac monopole is a singular solution of Maxwell's equation (because it requires removing the worldline from spacetime); in more complicated theories, it is superseded by a smooth solution such as the 't Hooft-Polyakov monopole. In theoretical physics, the t Hooft-Polyakov monopole is a topological soliton similar to the Dirac monopole but without any singularities. ...

Mathematical approach to Dirac monopole

Classically, gauge theory is described by a connection over a principal G-bundle over spacetime. Ordinary spacetime has the topology of R⁴, which is topologically trivial. So, the space of all possible connections over the principal G-bundle is connected. But consider what happens when we remove a timelike worldline from spacetime. The resulting spacetime is homotopically equivalent to the topological sphere S². So, it suffices to classify the connected components of the space of all connections over a principal G-bundle over S². To do this, consider covering S² by two charts, each homeomorphic to the open 2-ball such that their intersection is homeomorphic to the strip S¹×I. 2-balls are homotopically trivial and the strip is homotopically equivalent to the circle S¹. So a topological classification of the possible connections is reduced to classifying the transition functions, which is given by the first homotopy group of G. In other words, a gauge theory can only admit Dirac monopoles provided G is not simply connected. For instance, U(1), which has quantized charges is not simply connected and can have Dirac monopoles while R, its universal covering group, is simply connected, doesn't have quantized charges and does not admit Dirac monopoles even in principle. In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In mathematics, and specifically differential geometry, the connection form captures the invariant aspects of the connection on principal bundles, vector bundles and line bundles. ... In mathematics, a principal bundle is a mathematical object which formalizes some of the essential features of a Cartesian product X × G of a space X with a group G. Analogous to the Cartesian product, a principal bundle P is equipped with An action of G on P, analogous to... Connected and disconnected subspaces of R². The space A at top is connected; the shaded space B at bottom is not. ... In physics and mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einsteins theory of special relativity is most conveniently formulated. ... A world line of an object or person is the sequence of events labeled with time and place, that marks the history of the object or person. ... The two bold paths shown above are homotopic relative to their endpoints. ... A sphere is, roughly speaking, a ball-shaped object. ... In topology, an atlas describes how a complicated space is glued together from simpler pieces. ... This word should not be confused with homomorphism. ... In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. ... A geometrical object is called simply connected if it consists of one piece and doesnt have any circle-shaped holes or handles. Higher-dimensional holes are allowed. ... The universal covering space of a topological group is also a topological group. ...

It is easy to see how this argument generalizes to d + 1 dimensions with . We look at the homotopy group π_d−2(G).

Grand Unified Theories

In more recent years, a new class of theories has also suggested the presence of a magnetic monopole.

In the early 1970s, the successes of quantum field theory and gauge theory in the development of electroweak and the strong nuclear force led many theorists to move on to attempt to combine them in a single theory known as a grand unified theory, or GUT. Several GUTs were proposed, most of which had the curious feature of suggesting the presence of a real magnetic monopole particle. More accurately, GUTs predicted a range of particles known as dyons, of which the most basic state is a monopole. The charge on magnetic monopoles predicted by GUTs is either 1 or 2gD, depending on the theory. Quantum field theory (QFT) is the quantum theory of fields. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ... The strong nuclear force or strong interaction (also called color force or colour force) is a fundamental force of nature which affects only quarks and antiquarks, and is mediated by gluons in a similar fashion to how the electromagnetic force is mediated by photons. ... Grand unification, grand unified theory, or GUT is a theory in physics that unifies the strong interaction and electroweak interaction. ... In physics, a dyon is a hypothetical particle with both electric and magnetic charges. ...

The majority of particles appearing in any quantum field theory are unstable, and decay into other particles in a variety of reactions that have to conserve various values. Stable particles are stable because there are no lighter particles to decay into that still conserve these values. For instance, the electron has a lepton number of 1 and an electric charge of 1, and there are no lighter particles that conserve these values. On the other hand, the muon, essentially a heavy electron, can decay into the electron and is therefore not stable. In high energy physics, the lepton number is the number of leptons minus the number of antileptons. ... The muon (from the letter mu (μ)--used to represent it) is an elementary particle with negative electric charge and a spin of 1/2. ...

The dyons in these same theories are also stable, but for an entirely different reason. The dyons are expected to exist as a side effect of the "freezing out" of the conditions of the early universe, or symmetry breaking. In this model the dyons arise due to the vacuum configuration in a particular area of the universe, according to the original Dirac theory. They remain stable not because of a conservation condition, but because there is no simpler topological state for them to decay to. Promotional picture Symmetry Breaking is a rock band from Northern New Jersey, in the United States. ... A Möbius strip, an object with only one surface and one edge; such shapes are an object of study in topology. ...

The length scale over which this special vacuum configuration exists is called the correlation length of the system. A correlation length cannot be larger than causality would allow, therefore the correlation length for making magnetic monopoles must be at least as big as the horizon size determined by the metric of the expanding universe. According to that logic, there should be at least one magnetic monopole per horizon volume as it was when the symmetry breaking took place. This leads to a direct prediction of the amount of monopoles in the universe today, which is about 10¹¹ times the critical density of our universe. The universe appears to be close to critical density, so monopoles should be fairly common. For this reason, monopoles became a major interest in the 1970s and 80s, along with the other "approachable" prediction of GUTs, proton decay. The apparent problem with monopoles is resolved by cosmic inflation that greatly reduces the expected abundance of magnetic monopoles. Causality describes the relationship between causes and effects, and is fundamental to all natural science, especially physics. ... In mathematics, the metric tensor is a symmetric tensor field of rank 2 that is used to measure distance in a space. ... The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. ... In cosmology, the Big Crunch is a hypothesis that states the universe will stop expanding and start to collapse upon itself; a counterpart to the Big Bang. ... In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, usually a neutral pion and a positron. ... In physical cosmology, cosmic inflation is the idea that the nascent universe passed through a phase of exponential expansion that was driven by a negative-pressure vacuum energy density. ...

Many of the other particles predicted by these GUTs were beyond the abilities of current experiments to detect. For instance, a wide class of particles known as the X and Y bosons are predicted to mediate the coupling of the electroweak and strong forces, but these particles are extremely heavy and well beyond the capabilities of any reasonable particle accelerator to create. In particle physics, the X and Y bosons are hypothetical elementary particles analogous to the W and Z bosons, but corresponding to a new type of force, such as the forces predicted by grand unified theory. ... For the DC Comics Superhero also called Atom Smasher, see Albert Rothstein. ...

Attempts to find monopoles

A number of attempts have been made to detect magnetic monopoles. One of the simplest is to use a loop of superconducting wire that can look for even tiny magnetic sources, a so-called "superconducting quantum interference detector", or SQUID. Given the predicted density, loops the size of a soup can would expect to see about one monopole event per year. Although there have been tantalizing events recorded, in particular the event recorded by Blas Cabrera on the night of February 14, 1982 (thus, sometimes referred to as the "Valentine's Day Monopole"), there has never been reproducible evidence for the existence of magnetic monopoles. The lack of such events places a limit on the number of monopoles of about 1 monopole per 10²⁹ nucleons. Superconductivity is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of electrical resistance and the damping of the interior magnetic field (the Meissner effect. ... Suborders †Plesioteuthididae (incertae sedis) Myopsina Oegopsina Squid are a large, diverse group of marine cephalopods. ... Blas Cabrera is a physicist at Stanford University who was searching for magnetic monopoles; on the night of February 14, 1982, the detector recorded an event which had the perfect signature hypothesized for a magnetic monopole. ... Insert non-formatted text here{| style=float:right; |- | paul is so hot sophie loves him |- | |} is the 45th day of the year in the Gregorian calendar. ... Year 1982 (MCMLXXXII) was a common year starting on Friday (link displays the 1982 Gregorian calendar). ... In physics a nucleon is a collective name for two baryons: the neutron and the proton. ...

Other experiments rely on the strong coupling of monopoles with photons, as is the case for any electrically charged particle as well. In experiments involving photon exchange in particle accelerators, monopoles should be produced in reasonable numbers, and detected due to their effect on the scattering of the photons. The probability of a particle being created in such experiments is related to their mass—heavier particles are less likely to be created—so by examining such experiments limits on the mass can be calculated. The most recent such experiments suggest that monopoles with masses below 600 GeV/c² do not exist, while upper limits on their mass due to the existence of the universe (which would have collapsed by now if they were too heavy) is about 10¹⁷ GeV/c². In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ...

Non-inflationary Big Bang cosmology suggests that monopoles should be plentiful, and the failure to find magnetic monopoles is one of the main problems that led to the creation of cosmic inflation theory. In inflation, the visible universe was much smaller in the period before inflation, and despite the very short time before inflation, it would have been small enough for the whole visible universe to have been within the horizon, and thus not requiring many monopoles, perhaps only one. At the moment, versions of inflation seem to be the most likely cosmological theories. According to the Big Bang model, the universe developed from an extremely dense and hot state. ... In physical cosmology, cosmic inflation is the idea that the nascent universe passed through a phase of exponential expansion that was driven by a negative-pressure vacuum energy density. ...

Interestingly, the other major prediction of GUTs, proton decay, has also not been observed. The absence of these two key pieces of evidence has generally led to a decline in work on "classic" GUTs, and the introduction of more "radical" proposals, such as superstrings. In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, usually a neutral pion and a positron. ... Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. ...

See also

• Dirac string
• Dyon
• Felix Ehrenhaft
• Halbach array
• Instanton
• Meron
• Soliton
• 't Hooft-Polyakov monopole
• Wu-Yang monopole

In physics, a Dirac string is a fictitious one-dimensional curve in space, stretched from a magnetic monopole - also called the Dirac monopole - to infinity. ... In physics, a dyon is a hypothetical particle with both electric and magnetic charges. ... Felix Ehrenhaft (April 24, 1879 - March 4, 1952) was an Austrian-Hungarian physicist known for his maverick style and controversy. ... A Halbach array is a special arrangement of permanent magnets which augments the magnetic field on one side of the device while cancelling the field to near zero on the other side. ... This article or section is in need of attention from an expert on the subject. ... A meron or half-instanton is a Euclidean space-time solution of the Yang-Mills field equations. ... A topological soliton is a solution of a system of partial differential equations (or alternatively, a quantum field theory), not so much because of the nature of the PDEs themselves, but because of the boundary conditions entailing the existence of homotopically distinct solutions. ... In theoretical physics, the t Hooft-Polyakov monopole is a topological soliton similar to the Dirac monopole but without any singularities. ... The Wu-Yang monopole was the first solution, found in 1968 by Wu and Yang, to the Yang-Mills field equations. ...

References

• Brau, Charles A. (2004). Modern Problems in Classical Electrodynamics. Oxford University Press. ISBN 0-19-514665-4. 
• Milton, Kimball A. (June 2006). "Theoretical and experimental status of magnetic monopoles". Reports on Progress in Physics 69 (6): 1637-1711. DOI:10.1088/0034-4885/69/6/R02. 
• Shnir, Yakov M. (2005). Magnetic Monopoles. Springer-Verlag. ISBN 3-540-25277-0. 

A digital object identifier (or DOI) is a standard for persistently identifying a piece of intellectual property on a digital network and associating it with related data, the metadata, in a structured extensible way. ...

External links

• Magnetic Monopole Searches (lecture notes)
• Particle Data Group summary of magnetic monopole search
• 'Race for the Pole' Dr David Milstead Freeview 'Snapshot' video by the Vega Science Trust and the BBC/OU.