Magnetic monopoly

A magnetic monopole is an imaginary magnet that has only one pole, i.e. only the north or only the south pole. According to its effects, a single magnetic pole can be imagined as one end of a long bar magnet (see pole strength ) if its other end is so far away that the forces emanating from there are negligibly small.

Electronic structures ( quasiparticles ) have been detected in certain solids , which resemble a mixture of exactly the same number of individual and freely moving north and south poles. Although these are called magnetic monopoles, they can only occur in pairs, not individually, and cannot exist as free particles.

A real magnetic monopole for which there is no opposite pole has not yet been observed. If it existed as a particle, it would be a carrier of a magnetic charge corresponding to the electric charge ; magnetic charges would be sources and sinks of the magnetic field (see also monopole (physics) ). Considerations about such magnetic monopoles existed and existed in various areas of theoretical physics. In the observed nature, however, we only know magnetic fields with closed field lines that have no sources and sinks.

Quasiparticles in solids as apparent magnetic monopoles

So-called monopoles have been observed and researched in solids of the spin-ice type since 2009. They are monopole-like quasiparticles in the shape of the two ends of long chains of "connected" electron spins . Like gas molecules, they can move freely through the solid and behave in many ways like real individual magnetic monopoles. However, they can only appear in pairs as north and south poles. Therefore, they can be viewed locally as sources of magnetization , but globally the magnetic field remains source-free .

After preliminary conceptual work by Castelnovo, Moessner and Sondhi, a team from the Helmholtz-Zentrum Berlin, together with other researchers, was able to observe such so-called monopoles in solid matter for the first time using neutron diffraction in a dysprosium titanate crystal (Dy ₂ Ti ₂ O ₇ ).

In 2010 the Paul Scherrer Institute also succeeded in mapping these quasi-monopoles using synchrotron radiation .

In 2013, researchers from the Technical Universities of Dresden and Munich discovered that the quasi-monopolies can play a role in the breakdown of Skyrmion - "crystals". This effect could be important in the future use of skyrmions in data storage technology.

In 2014, researchers working with David Hall (University of Amherst) and Mikko Möttönen (University of Aalto) succeeded in recreating quasi-monopoles in a ferromagnetic Bose-Einstein condensate .

The Dirac string

A Dirac string (English string = thread) is an imaginary line that starts from a magnetic monopole. For an electrically charged particle that moves in the magnetic field of the monopole, the phase of the quantum mechanical wave function on this line is singular and the probability of its location is zero. If there is a magnetic monopole, the existence of such a line must also be assumed, since particles outside the line would otherwise have no clear phase. Such a string would have to be observable because of the vanishing probability of being on it and has actually been observed at the quasi monopolies. In the publications on the quasi monopolies, these are therefore also called “Dirac monopolies”; But it is not a question of monopoles in the sense of elementary particles, an idea that also goes back to Paul Dirac .

Magnetic monopoles as elementary particles

Dirac's elementary particle monopoly

Paul Dirac speculated that the magnetic monopole could exist as an elementary particle , which would be the magnetic counterpart to the electron . There are two arguments in favor of this idea:

• The strange asymmetry between the otherwise similar phenomena magnetism and electricity - visible e.g. B. in the Maxwell equations - would be fixed.
• It would be easy to explain why the electric charge is always only “quantized” , ie. H. occurs in integer multiples of the elementary charge.

Both arguments are explained in the following sections. Despite intensive efforts, however, the existence of such a particle has not yet been proven.

Maxwell's equations and symmetry

Symmetries play a fundamental role in physics. The Maxwell equations formulated in the 19th century, which describe the electrical and magnetic phenomena, show an unnatural-appearing asymmetry between the vectors of the electrical field strength and the magnetic flux density . While the electrical charges appear as charge density and the associated current density , due to the non-existence of magnetic charges, the corresponding magnetic quantities are equal to zero: ${\displaystyle {\vec {E}}}$ ${\displaystyle {\vec {B}}}$ ${\displaystyle \rho _{e}}$ ${\displaystyle {\vec {j}}_{e}}$

The classic Maxwell equations in a vacuum in cgs units

${\displaystyle {\vec {\nabla }}\cdot {\vec {E}}=4\pi \rho _{e}}$		${\displaystyle {\vec {\nabla }}\cdot {\vec {B}}=0}$
${\displaystyle {\vec {\nabla }}\times {\vec {E}}=-{\frac {1}{c}}{\frac {\partial {\vec {B}}}{\partial t}}}$		${\displaystyle {\vec {\nabla }}\times {\vec {B}}={\frac {4\pi }{c}}{\vec {j}}_{e}+{\frac {1}{c}}{\frac {\partial {\vec {E}}}{\partial t}}}$

However, if one assumes the existence of magnetic charges (monopoles), then there would also be a magnetic charge density and magnetic current density other than zero ; the equations would then be: ${\displaystyle \rho _{m}}$ ${\displaystyle {\vec {j}}_{m}}$

The modified Maxwell equations in vacuum in cgs units

${\displaystyle {\vec {\nabla }}\cdot {\vec {E}}=4\pi \rho _{e}}$		${\displaystyle {\vec {\nabla }}\cdot {\vec {B}}=4\pi \rho _{m}}$
${\displaystyle {\vec {\nabla }}\times {\vec {E}}=-{\frac {4\pi }{c}}{\vec {j}}_{m}-{\frac {1}{c}}{\frac {\partial {\vec {B}}}{\partial t}}}$		${\displaystyle {\vec {\nabla }}\times {\vec {B}}={\frac {4\pi }{c}}{\vec {j}}_{e}+{\frac {1}{c}}{\frac {\partial {\vec {E}}}{\partial t}}}$

One would thus obtain a theory that would remain unchanged under the following transformations (so-called symplectic symmetry ):

${\displaystyle {\vec {E}}\rightarrow {\vec {B}}}$		${\displaystyle \rho _{e}\rightarrow \rho _{m}}$		${\displaystyle {\vec {j}}_{e}\rightarrow {\vec {j}}_{m}}$
${\displaystyle {\vec {B}}\rightarrow -{\vec {E}}}$		${\displaystyle \rho _{m}\rightarrow -\rho _{e}}$		${\displaystyle {\vec {j}}_{m}\rightarrow -{\vec {j}}_{e}}$

The existence of magnetic monopoles would therefore further reduce the differences between electric and magnetic fields, electric and magnetic phenomena would be strictly "dual" to one another.

Potentials and covariant formulation

As in the case of Maxwell's equations without magnetic monopoles, potentials can be introduced which are helpful for the construction of solutions to the respective differential equations and which satisfy certain new differential equations. In addition to the electromagnetic quadruple potential , a second, “magnetoelectric” quadruple potential is introduced . The potentials are chosen in such a way (whereby there is a certain arbitrariness, insofar as it is possible) that the field strength tensor appears as a differential form ${\displaystyle A}$ ${\displaystyle C}$

${\displaystyle F=\mathrm {d} A-*\mathrm {d} C}$

results, or in index notation as

${\displaystyle F^{\mu \nu }=\partial ^{\mu }A^{\nu }-\partial ^{\nu }A^{\mu }-\epsilon ^{\mu \nu \alpha \beta }\partial _{\alpha }C_{\beta }}$.

The Maxwell equations take the following form ( understood as four-vectors): ${\displaystyle j_{m},j_{e}}$

${\displaystyle *\mathrm {d} F=4\pi j_{m}}$

${\displaystyle *\mathrm {d} *F=4\pi j_{e}}$

The continuity equations result from this :

${\displaystyle \mathrm {d} *j_{m}=0}$

${\displaystyle \mathrm {d} *j_{e}=0}$

For the potentials this means:

${\displaystyle *\mathrm {d} *\mathrm {d} C=4\pi j_{m}}$

${\displaystyle *\mathrm {d} *\mathrm {d} A=4\pi j_{e}}$

This means that exactly as in the case without magnetic monopoles it behaves independently of , and the components of completely analog in each component satisfy the wave equation with magnetic charge or current as inhomogeneity. The theory also has an additional gauge invariance : for scalar fields it is not only invariant under the transformation ${\displaystyle A}$ ${\displaystyle j_{m}}$ ${\displaystyle C}$ ${\displaystyle \phi ,\psi }$

${\displaystyle A\rightarrow A+\mathrm {d} \phi }$,

but also under

${\displaystyle C\rightarrow C+\mathrm {d} \psi }$.

The above-mentioned symmetry transformation can be understood in this notation as a transformation using the Hodge-Star operator from the field strength tensor to the dual field strength tensor, as well as through the transitions and . ${\displaystyle F\rightarrow *F}$ ${\displaystyle j_{e}\rightarrow j_{m}}$ ${\displaystyle j_{m}\rightarrow -j_{e}}$

The quantization of the electric charge

Besides the angular momentum , the electrical charge is also quantized, i.e. H. it occurs only as an integral multiple of the elementary charge . According to Dirac, the existence of magnetic monopoles would easily explain this fact: An electron moving in the field of a monopole is deflected onto a curved path. The change in angular momentum associated with the deflection can only be quantized in certain discrete steps, but must be proportional to the electrical charge. Hence the quantization of the angular momentum together with the existence of the magnetic monopole directly leads to the quantization of the electric charge. The same consideration would also apply to the magnetic charge. The monopole would be the carrier of the elementary magnetic charge.

Magnetic monopoles as solitons

An indication of the existence of magnetic monopoles may possibly arise from the so-called theories of great unification (GUT). These theories describe the unification of the electroweak force with the strong force at high energies, as they existed in our universe up to about 10 ⁻³⁶ seconds after the Big Bang. Due to the cooling of the expanding universe, the typical particle energy sank below a critical value of about 10 ¹⁵  GeV (this corresponds to about 10 ²⁸ Kelvin ). This triggered the symmetry breaking of the unified force into the separate forces strong interaction and electroweak interaction. Among other things, stable punctiform topological defects of the calibration field , so-called solitons , occurred - the magnetic monopoles. This mechanism can be roughly compared with the processes in solidifying liquids. The crystallization starts simultaneously at different points in space. If two crystals grow together, lattice defects arise on the contact surfaces. The density of the resulting monopoles can be estimated at about 10 ⁸²  m ⁻³ at the time of their formation . The fact that the particle density is significantly lower today is also seen as another indication of a strong inflationary phase in the early universe. In these theories the structure and properties of a GUT monopoly are described in detail.

construction

A GUT monopole has a mass of around 10 ¹⁶  GeV, a diameter of around 10 ⁻¹⁵  m and a defined onion-like substructure. Accordingly, near the center, i. H. in the range of 10 ⁻³¹  m, a GUT-symmetrical vacuum is present. This is followed by a shell of the so-called electro-weak union with particles such as the gauge bosons of the weak interaction W ⁺ , W ^- and Z ⁰ . At about 10 ⁻¹⁸  m, this zone merges into the confinement shell, which is filled with gluons and photons. The outermost shell is made up of fermion-antifermion pairs.

Violation of time reversal invariance

If one examines the deflection of a charged particle in the vicinity of a monopole, one finds that such an arrangement violates the time-reversal invariance . This means that if the time direction is reversed, the process does not proceed in the same way. For a long time, this fact spoke directly against the existence of magnetic monopoles. However, after the CP violation in the decay of the K mesons could be demonstrated in 1964, the existence of T-invariance violating processes follows from the CPT theorem .

Catalysis of proton decay

Due to the internal structure mentioned above, GUT monopoles can catalyze proton and neutron decay . The theories predict the following reactions ( M stands for monopoly):

${\displaystyle M+p\rightarrow M+e^{+}+\pi ^{+}+\pi ^{-}}$
${\displaystyle M+n\rightarrow M+e^{+}+\pi ^{0}+\pi ^{-}}$

The monopoly itself does not break down in these reactions. Through these decay processes, he is able to influence the stability of matter.

Experimental search for GUT monopolies

Because of the very high rest energy of the GUT monopoly mentioned above - its mass is comparable to that of a bacterium - it can not be generated and detected directly even in colliding beam experiments . Therefore, when looking for monopoles, one has to rely on their naturally existing flux density, which, however, is predicted by current theories as very low.

One possible experiment to detect the hypothetical particle is based on the use of superconducting coils. When a monopole passes through such a coil, the change in the magnetic flux induces a ring current that can be detected. Such a circulating current can actually only be generated by means of magnetic monopoles and not by the field of a conventional dipole magnet. However, the relatively high susceptibility to interference of such experiments requires careful implementation.

Further experiments, such as Super-Kamiokande (the Kamiokande follow -up experiment ), aim to demonstrate the monopole-induced proton decay described above. Several (ten) thousand tons of ultrapure water, for example, serve as proton carriers. However, estimating the expected rate of decay requires knowledge of the typical cross-section of the decay reaction.

A single event was observed in a coil experiment by Blas Cabrera (Stanford University, USA) in 1982 . However, it cannot be ruled out that this is a faulty signature. Current experiments therefore always specify upper limits for the particle flux which, depending on the method used, are currently in the range of 10 ⁻¹⁶  s ⁻¹ cm ⁻² . This means that an area of ​​1 m ^{2 is} crossed by a monopoly at most every 30,000 years on average.

Expected frequency

Using the lifetime of galactic magnetic fields, an upper limit for the frequency of GUT monopoles hitting earth can be determined. This is estimated at an average of at most one monopoly per square meter of the earth's surface and 31,700 years, which corresponds to the so-called Parker limit of F _M  <10 ⁻¹⁶  cm ⁻² s ⁻¹ .

Other theories and research

In other gauge theories , the field strength tensor can be split into magnetic and electrical components. Magnetic monopoles can then also exist in these theories. One example is quantum chromodynamics or SU (3) - Yang-Mills theory . So-called chromomagnetic monopoles are associated with the confinement hypothesis. They come into question for possible explanatory scenarios, but have so far been of a purely theoretical nature.

The Russian astrophysicist Igor Novikov assumes that the fields of macroscopic black holes can also be magnetic monopoles. In this case, it would be the mouth of an Einstein-Rosen bridge .

literature

• R. Moessner: Magnetic monopoles in spin ice. Physik Journal 13 (2014) No. 6, pp. 41-47

Individual evidence

1. ^ C. Castelnovo, R. Moessner, SL Sondhi: Magnetic monopoles in spin ice . In: Nature . tape 451 , no. 42 , 2008, p. 42–45 , doi : 10.1038 / nature06433 , arxiv : 0710.5515 .
2. ↑ Magnetic monopoles discovered in a magnetic solid ( memento from December 20, 2015 in the Internet Archive ). In: News and press releases 2009. Helmholtz-Zentrum Berlin, September 3, 2009, accessed on March 10, 2010.
3. ^ DJP Morris, DA Tennant, SA Grigera, B. Klemke, C. Castelnovo, R. Moessner, C. Czter-nasty, M. Meissner, KC Rule, J.-U. Hoffmann, K. Kiefer, S. Gerischer, D. Slobinsky, RS Perry: Dirac Strings and Magnetic Monopoles in Spin Ice Dy2Ti2O7 . In: Science . tape 326 , no. 5951 , 2009, p. 411-414 , doi : 10.1126 / science.1178868 .
4. ↑ ^{a b} physorg.com - Scientists capture first direct images of theoretically predicted magnetic monopoles , last accessed on October 23, 2010
5. ↑ P. Milde et al .: Unwinding of a Skyrmion Lattice by Magnetic Monopoles. Science Vol. 340 pp. 1076-1080 (2013)
6. ↑ Press release of the Technical University of Munich, May 2013 .
7. ↑ Rainer Scharf: Dirac Monopoly in the Bose-Einstein Condensate, Physik Journal, January 2014
8. ↑ MW Ray, E. Ruokokoski, S. Kandel, M. Möttönen, DS Hall Dirac monopole in a synthetic magnetic field , Nature, Vol 505, 2014 657th
9. ↑ ^{a b c d} Yakov M. Shnir: Magnetic Monopoles. Springer, 2006, ISBN 3-540-25277-0
10. ↑ ^{a b} http://www.pro-physik.de/details/news/5791621/Dirac-Monopol_im_Bose-Einstein-Kondensat.html
11. ^ Richard P. Feynman, Steven Weinberg: Elementary Particles and the Laws of Physics: The 1986 Dirac Memorial Lectures . Cambridge University Press, 1987, ISBN 0-521-65862-4 , pp. 48-54
12. ^ Frédéric Moulin: Magnetic monopoles and Lorentz force . In: Nuovo Cimento B . tape 116 B, no. 8 , 2001, p. 869-877 , arxiv : math-ph / 0203043v1 .
13. ↑ Erwyn van der Meer: Magnetic Monopoles in Gauge Field Theories . On the realization of global symmetries on moduli spaces. 1997, p. 8 ( online ( memento of February 22, 2014 in the Internet Archive ) ( GZIP ; 1.1 MB) [accessed on June 4, 2013]). Magnetic Monopoles in Gauge Field Theories ( Memento of the original from February 22, 2014 in the Internet Archive ) Info: The archive link was automatically inserted and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.  
14. ↑ Cabrera et al. a. First results from a superconducting detector for moving magnetic monopoles , Physical Review Letters, Vol. 48, 1982, p. 1378
15. ↑ EN Parker: Cosmical magnetic fields: Their origin and their activity . Clarendon Press, New York 1979.
16. ↑ Green Site J .: The confinement trouble in lattice gauge theory . In: Progress in Particle and Nuclear Physics . tape 51 , no. 1 , 2003, p. 1-83 , doi : 10.1016 / S0146-6410 (03) 90012-3 .
17. ↑ "If the structures of the magnetic fields appear to be magnetic monopoles, that are macroscopic in size, then this is a wormhole." From All About Space , Issue No. 24, April 2014, article "Could wormholes really exist?"