# Scientists are looking for the elusive magnetic monopole

While theories such as the grand unified theories (GUTs), which combine electromagnetic, nuclear forces, and gravity into a single framework, predict the presence of magnetic monopole–like entities, it is unknown if magnetic monopoles exist. Nonetheless, the quest for them continues, and the results of two new trials will be very useful to other experimenters in the area.
ONE is aware that matter is made up of atoms, and that each atom is made up of a positively charged nucleus with negatively charged electrons orbiting it in certain orbits. Electric current is generated by the mobility of electrons in a conductor, as one was taught in school. That is, positive and negative charges exist in the cosmos as distinct entities that may exist independently. It was also taught that the passage of current in a wire creates a magnetic field around it (Ampere’s law), and that a changing magnetic field may induce an electric current to flow through a wire coil (Faraday’s law of induction). Maxwell’s equations (1864), which characterize the two as various expressions of one unified electromagnetic field, explain this unity and reciprocity between electricity and magnetism in classical physics. As a result, their characteristics may be defined using a single unified mathematical framework.

Despite this apparent similarity between electricity and magnetism, isolated magnetic charges are seldom discussed. One only speaks of magnets with one end designated as the north pole (N) and the other as the south pole (S), but never of the north and south poles as distinct entities. One recalls a school experiment using a bar magnet and iron filings to map the magnetic field produced by such a “dipole” magnet (Fig. 1a). The magnetic field lines are continuous loops that do not terminate at a source, as opposed to a positive (or negative) electric charge, where the electric field lines radiate from (or terminate at) the isolated charge’s point of location.

In fact, if one were to attempt to split a magnet in two, the two new ends would have opposing poles, resulting in two “dipole” magnets with north and south poles. This process may be repeated indefinitely without the formation of an isolated N or S pole, which would be a magnetic “monopole” (Fig. 1b). Even at the subatomic level, although a fundamental particle such as the electron has an isolated electric charge, its inherent magnetism is that of a dipole owing to a quantum mechanical feature known as spin. Every atom on the periodic table and every fundamental particle has a magnetic monopole charge of zero. Magnets, and the everyday phenomena of magnetism, emerge from the interaction of electric charges, electric currents, and the quantum mechanical inherent dipole magnetism of fundamental particles.

Electric charge quantification

Because isolated magnetic charges, or magnetic monopoles, are not seen empirically, James Clerk Maxwell did not include a word for magnetic charge (or source) equivalent to the electric charge term in his electromagnetism equations. As a result, the magnetic and electric components of Maxwell’s equations are not absolutely symmetric. If magnetic monopoles existed and a matching magnetic source component was included into Maxwell’s equations, the two sections would be completely symmetric, and the duality between electricity and magnetism would be complete (Figs 2a and b).

Pierre Curie was the first to speculate on the presence of magnetic monopoles in 1894. However, scientists started to take the notion seriously only when Paul Dirac, one of the creators of contemporary quantum theory, gave a scientific foundation for arguing why magnetic monopoles may exist. Charges, as we all know, can only have discrete values: they exist only as integral multiples of a unit e, which has a value of around 1.602 1019 coulombs and is equivalent to the charge of a proton or an electron (a proton has a charge of +1e and an electron has a charge of 1e). However, there is no comprehension of this quantisation of electric charge based on fundamental principles.

Dirac proposed, using basic quantum principles, that the presence of a magnetic monopole gave a natural explanation for this. He demonstrated how quantum mechanics restricted the values of the universe’s lowest electric and magnetic charges by requiring them to meet the formula eg = h/2, where g is the least magnetic charge and h is a number known as Planck’s constant. Meghnad Saha, an Indian physicist, later presented a simpler and more elegant explanation of this finding in 1936.

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The quantization of electric charge might thus be regarded as resulting from the possibility of a magnetic monopole of strength g existing somewhere in the cosmos. “Quantum mechanics does not rule out the existence of magnetic monopoles,” Dirac concluded in his seminal 1931 study, adding that he “would be shocked if Nature had not taken use of it.” Is the observable quantization of electric charge proof of the existence of magnetic monopoles? No, the Dirac quantisation requirement does not entail that monopoles must exist, just that they may.

However, a crucial consequence of the quantisation requirement is that, given the known value of e, the strength of the magnetic charge unit turns out to be quite strong. The magnetic force between two monopoles with the same magnetic charge g would be 4,700 times greater than the force between two electrons. With such a huge number for g, it is also challenging to compute the production rate of magnetic monopoles in elementary particle interactions, especially in high-energy particle accelerators, within the extremely successful Standard Model of particle physics. To construct a competent monopole search experiment, let alone understand the findings, reliable estimations are required.

However, theories that go beyond the Standard Model, such as grand unified theories (GUTs), which combine electromagnetism, nuclear forces (both weak and strong), and gravity into a single framework, predict the presence of magnetic monopole–like entities. Despite its present huge success, it is widely acknowledged that the Standard Model is an incomplete theory since it does not account for gravity in its framework and does not account for dark matter, cosmic inflation, or the universe’s predominance of matter over antimatter. Magnetic monopoles are an unavoidable mathematical result of grand unification (of natural forces) in emergent formalisms like GUTs and superstring theory.

GUT monopoles, on the other hand, are “lumps” of quantum fields, as opposed to the Dirac monopole, which, like electrons and other fundamental particles, is a point-like particle. They are finite in size and have a substructure made up of numerous fundamental quanta. More critically, GUT monopoles have a massive mass of about 1016 GeV (giga, or billion, electronvolt) energy equivalent, which is defined by the energy scale at which the forces combine. The proton has an energy equivalent mass of around 1 GeV, which indicates that GUT monopoles will be 10,000 trillion times heavier than the proton.

This definitely rules out their finding in current particle accelerators as well as future accelerators. The maximum particle collision energy in the Large Hadron Collider (LHC) at CERN (the European Organization for Nuclear Research) in Geneva is only on the order of 104 GeV, or 10 trillion electronvolts (TeV). Of course, the existence of magnetic monopoles may have nothing to do with grand unification, and new physics beyond the Standard Model, which may be revealed in the near future, may admit monopoles that are point-like and/or much lighter than GUT monopoles and are accessible in today’s accelerators.

Parker’s bound

Because magnetic monopoles are not forbidden by the basic principles of physics, they might have been created at the Big Bang or shortly thereafter in the early cosmos. The present monopole number density of remnant monopoles from the Big Bang would be determined by the monopole’s mass. Even very basic calculations in orthodox Big Bang cosmology with no inflationary period suggest that the number density of monopoles surviving in the universe today is much too high in comparison to current findings.

However, if the universe went through an inflationary phase soon after the Big Bang, as current cosmological theories predict, when the universe suddenly went through an accelerated expansion phase, the pre-inflationary high monopole density (regardless of monopole mass) would have rapidly declined to below observational limits, thereby avoiding the high monopole density problem entirely.

Astrophysical limitations on the monopole flux, or equivalently the number density, in the universe have been imposed based on certain theoretical considerations. The Parker bound is the best such limit. It was generated from calculations of the cosmic magnetic field’s influence on monopoles flowing across the universe (IGMF). The primary assumption here is that the IGMF would accelerate suitably light magnetic monopoles to high velocities, and this process would progressively drain away energy from the latter, culminating in its slow disintegration. The present IGMF strength is used to constrain the magnetic monopole flux in the cosmos. Parker specified a monopole number upper limit of 1015/cm2/sec/steradian (steradian is a measure of solid angle) for monopole masses less than 1017 GeV.

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As a result, the Parker limit eliminates any non-inflationary Big Bang cosmological monopole densities. As previously stated, with inflation, the density decreases below empirically measurable levels. Another astrophysical aspect is that if magnetic monopoles exist in the universe today, they should be visible in cosmic ray flux arriving on Earth, but no cosmic ray investigation has discovered any such candidate event. MACRO, a cosmic ray experiment that operated from 1989 to 2000 and was particularly intended to seek for monopoles, set an upper limit of 1016/cm2/sec/steradian on the relic cosmic monopole flux across a very large monopole mass range. Later cosmic ray experiments using neutrino detectors, such as ANITA, ANTARES, and IceCube, have established upper constraints on the flux that are even tighter than MACRO. Researchers have searched for trapped monopoles in polar rocks, moon rocks, and saltwater. They sought for traces in mica that monopoles could have left. However, no evidence of monopoles has been found in any of these searches, experimental or otherwise.

Neutrino observatory

In early February, the findings of two notable monopole search experiments, one at the subsurface IceCube neutrino observatory in Antarctica (“New window to the cosmos,” Frontline, June 27, 2014) and the other at CERN, were released. They, too, have returned negative results. They have, however, imposed strict limitations on monopoly assets. IceCube has set an order of magnitude greater upper constraint on the universe’s relic monopole flux than its previous finding, while the CERN experiment has established a stringent lower bound on the monopole mass assuming it exists. This is the first accelerator-based search that avoids the dubious monopole production rate estimates in the Standard Model due to the monopole’s high coupling strength, as previously discussed.

IceCube reached an upper limit on the flux in its last round of monopole search utilizing just two years of detector data from 2008-09 and 2011-12. The IceCube team was able to put an upper limit of 1.55 1018/cm2/sec/steradian on the flux of relativistic monopoles with velocities larger than half the velocity of light (>0.51c; c is the velocity of light) thanks to the data, which were published in 2015. This was roughly three orders of magnitude more stringent than the Parker bound. The most recent findings, published in Physical Review Letters on February 2, are based on eight years of IceCube data gathered over 2,886 days from 2011 to 2018. The study limits the flux of relativistic monopoles in the velocity range of 0.75 c to 0.995 c to less than 2.0 1019/cm2/sec/steradian. This is an order of magnitude better than the top limit set in 2015.

The detection of monopoles using IceCube, which was built mainly to detect elusive neutrinos, is based on the following idea. When a neutrino collides with an atom in the ice surrounding the detector, a charged particle known as a muon is produced. When a charged particle travels faster than the speed of light through ice, it creates a cone of blue radiation along its route known as Cherenkov radiation (“Cherenkov radiation and muons in IceCube,” Frontline, April 9, 2021). This light activates IceCube’s sensors as it moves through the ice and detector, creating a trail of active sensors whose signals provide the particle’s energy and direction.

Magnetic monopoles, like charged particles, produce Cherenkov radiation when they pass through ice at near to the speed of light. However, the type and pattern of the produced Cherenkov radiation differ from that of a charged particle such as the muon. For starters, it is really bright. Cherenkov light generated by magnetic monopoles is about 8,000 times brighter than muon light. Second, unlike muons, light emission is consistently distributed throughout the monopole route (Fig. 3). Thus, the monopole signal in IceCube can be distinguished from muon signatures.

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IceCube scientists began by looking for magnetic monopoles in particularly bright and homogeneous emission episodes. Tracks that began or ended inside the volume of IceCube were excluded because magnetic monopoles may traverse the whole detector. Then, in the sample, a machine learning event characterization tool (a boosted decision tree) was trained to distinguish magnetic monopole events from neutrino and muon events. Although the search did not yield any monopole signature events, the data allowed the IceCube team to calculate the tightest upper limit on the cosmic monopole flux to date.

Until date, searches for monopoles in accelerators have relied only on collisions of elementary particles such as electrons and protons, where monopoles might be generated by particle annihilation. Furthermore, the interpretation of data from collider experiments has primarily interpreted monopoles as point-like particles, neglecting the potential that they are composite, especially light ones, as predicted by certain theories outside the Standard Model. An worldwide team of scientists working with the LHC’s Monopole and Exotics Detector (MoEDAL) experiment (Fig. 4) has been investigating the possibility of monopole generation under very high magnetic fields created by heavy-ion collisions.

In 1951, Julian Schwinger postulated a process (which now bears his name) by which electrically charged particles may be generated spontaneously in the presence of high electric fields, according to quantum theory. Given the electromagnetic duality, the MoEDAL team claimed that if monopoles exist, the magnetic equivalent of the Schwinger process should function in sufficiently strong magnetic fields to produce monopoles. While this avoids the issue of incorrect Standard Model predictions for monopole yield, the strong monopole coupling and limited monopole size are projected to boost their generation à la Schwinger.

“A significant benefit of the Schwinger mechanism is that we can determine its rate more accurately than for any other production process examined at the LHC so far,” said Oliver Gould, a MoEDAL scientist who did theoretical calculations for this search, in a release. “This provides us a decent estimate of how many monopoles the experiment should observe as a function of their mass and magnetic charge.” Because none have been seen, we may confidently assert that magnetic monopoles must be heavier than a specific value.”

Collisions between lead ions at the LHC are known to create the greatest magnetic fields known in the cosmos for a limited period of time (about 1016 tesla). In fact, the strongest magnetic field created in this MoEDAL experiment was 10,000 times greater than magnetic fields reported on the surface of neutron stars! Magnetic monopole trapping detectors consisting of the aluminum isotope Al-27, which can trap particles with magnetic charge, were employed in the experiment (Fig. 5). A superconducting magnetometer was used to scan the detectors for the presence of monopoles. The experiment ruled out the occurrence of monopoles with masses less than 75 GeV (energy equivalent) and monopole charges g ranging from 1 to 3. The findings were published in Nature on February 3rd. Although this limit is significantly lower than previous proton-proton collision tests at the LHC, which were in the range of a few thousand GeV, it is more credible since it is based on what is perhaps the most unequivocal accelerator-based monopole search to date.

“This particular monopole search was pioneering and created a new, promising channel for future studies,” stated MoEDAL scientist Igor Ostrovskiy. “Ours was the first search in which magnetic monopoles of limited size, as anticipated by contemporary theories, were actually visible, and although we did not discover any, we were able to place the first credible [lower] limits on the monopole mass.”

So, are there monopolies? Nobody knows, and magnetic monopole searches will undoubtedly continue. While these two new trials boost their sensitivity even more, they would also substantially aid other experimenters in their searches since their aims might be set more precise than previously based on the new discoveries.