# Scientists’ search for the elusive magnetic monopole

### While theories such as the grand unified theories (GUTs), which unify electromagnetism, nuclear forces and gravity in one framework, predict the existence of magnetic monopole–like entities, one does not know whether magnetic monopoles exist. The hunt for them continues nonetheless, and the findings of two new experiments will be of great benefit to other experimenters in the field.

Published : Mar 16, 2022 06:00 IST

Figure 1a: A bar magnet and its dipole magnetic field.

ONE knows that matter is composed of atoms and that each atom is made up of a positively charged nucleus with negatively charged electrons moving around it in designated orbits. One was taught in school that electric current is due to the motion of electrons in a conductor. That is, one talks of positive and negative charges existing in the universe as separate entities that can exist in isolation. One was also taught that the flow of current in a wire results in a magnetic field around it (Ampere’s law), and similarly, a changing magnetic field can cause an electric current to flow through a coil of wire (Faraday’s law of induction). This unity and reciprocity between electricity and magnetism are described in classical physics by Maxwell’s equations (1864), according to which the two are different manifestations of one unified electromagnetic field. Their properties can, therefore, be described by a single unified mathematical framework.

But despite this apparent symmetry between electricity and magnetism, one never talks of isolated magnetic charges. One only talks of magnets with one end as the north pole (N) and the other end as the south pole (S) but never of north or south pole as separate entities. One would recall the school experiment with a bar magnet and iron filings to map the magnetic field due to such a “dipole” magnet (Fig. 1a). The magnetic field lines are continuous loops that do not end at a source unlike in the case of a positive (or negative) electric charge where the electric field lines radiate from (or end at) the point of location of the isolated charge.

In fact, if one were to try and break a magnet into two, the two new ends would have opposite poles such that one ends up having two “dipole” magnets, both having north and south poles. This process can be carried on ad infinitum without the emergence of an isolated N or S pole, what would be a magnetic “monopole” (Fig. 1b). Even at the subatomic level, while an elementary particle like the electron carries an isolated electric charge, its intrinsic magnetism, which is due to its quantum mechanical property called spin, is that of a dipole. All known matter—every atom on the periodic table and every elementary particle—has zero magnetic monopole charge. So magnets, and the ordinary phenomenon of magnetism, are not due to magnetic monopoles; they arise from the interplay of electric charges, electric currents and the quantum mechanical intrinsic dipole magnetism of elementary particles.

## Quantisation of electric charge

Because of the empirical fact that isolated magnetic charges, or magnetic monopoles, are not seen, James Clerk Maxwell did not introduce a term for magnetic charge (or source) analogous to the electric charge term in his equations of electromagnetism. The magnetic and electric parts of Maxwell’s equations are thus not strictly symmetric. If magnetic monopoles existed and if one were to introduce a corresponding magnetic source term in Maxwell’s equations, the two parts would be entirely symmetric and the duality between electricity and magnetism would be complete (Figs 2a and b).

In 1894, Pierre Curie was the first to discuss the possibility of the existence magnetic monopoles. But scientists only began to take the idea seriously after Paul Dirac, one of the architects of modern quantum theory, provided a physical basis to argue why magnetic monopoles can exist. One knows that charges can have only discrete values: they exist only as integral multiples of a unit e , which has a value of about 1.602 × 10−19 coulombs and is equal to the charge of a proton or an electron (a proton has the charge +1 e and an electron −1 e ). But there is no understanding of this quantisation of electric charge from basic principles.

Using fundamental quantum principles, Dirac posited that the existence of a magnetic monopole provided a natural explanation for this. He showed that quantum mechanics constrained the values of the smallest electric and magnetic charges in the universe by requiring that they satisfy the condition eg = h/2 , where g is the smallest magnetic charge and h is a constant known as Planck’s constant. Later, in 1936, the Indian physicist Meghnad Saha provided a simpler and more elegant derivation of this result.

Also read: Neutrinos may have saved the universe

Quantisation of electric charge can then be understood as arising from the possible existence of a magnetic monopole of strength g somewhere in the universe. “Quantum mechanics does not preclude the existence of magnetic monopoles,” Dirac concluded in his landmark 1931 paper and added that he “would be surprised if Nature had made no use of it”. So, is the observed quantisation of electric charge evidence for the existence of magnetic monopoles? Not quite, the Dirac quantisation condition does not imply that monopoles must exist but that they can .

However, an important consequence of the quantisation condition is that, given the known value of e , the strength of the unit of magnetic charge turns out to be very high. The magnetic force between two monopoles with unit magnetic charge g would be 4,700 times the force between two electrons. Such a large value for g also makes it difficult to calculate reliably the production rate of magnetic monopoles in elementary particle interactions, particularly in high-energy particle accelerators, within the highly successful Standard Model of particle physics. Reliable estimates are necessary to even design a suitable monopole search experiment let alone to interpret the results.

However, theories beyond the Standard Model, such as grand unified theories (GUTs), which unify electromagnetism, nuclear forces (both weak and strong) and gravity in one framework, predict the existence of magnetic monopole–like entities. It is well recognised that despite its current enormous success, the Standard Model is an incomplete theory because it does not accommodate gravity in its framework and does not account for dark matter, cosmological inflation and the preponderance of matter over antimatter in the universe. Magnetic monopoles arise as an inevitable mathematical consequence of grand unification (of forces of nature) in emergent formalisms such as GUTs and superstring theory.

However, unlike the Dirac monopole, which like electrons and other elementary particles is a point-like particle, GUT monopoles are “lumps” of quantum fields. They have a finite size and a substructure consisting of many elementary quanta. But, more importantly, GUT monopoles have a huge mass of about 1016 GeV (giga, or billion, electronvolt) energy equivalent, which is determined by the energy scale at which the forces unite. The mass of proton is about 1 GeV (energy equivalent), which means that GUT monopoles will be 10,000 trillion times heavier than the proton.

That clearly rules out their discovery in present-day particle accelerators and also in accelerators of the foreseeable future. At the Large Hadron Collider (LHC) at CERN (the European Organisation for Nuclear Research) in Geneva, the highest particle collision energy is only of the order of 104 GeV, or 10 trillion electronvolt (TeV). Of course, it is quite possible that the existence of magnetic monopoles has nothing to do with grand unification, and new physics beyond the Standard Model, which may get revealed in the near future, may admit monopoles that are point-like and/or are much lighter than GUT monopoles and would be accessible in today’s accelerators.

## The Parker bound

Since the fundamental laws of physics do not prohibit the existence of magnetic monopoles, they could have been produced during the Big Bang or soon afterwards in the early universe. The current monopole number density of the relic monopoles from the Big Bang would depend on the mass of the monopole. According to even very simple estimates in traditional Big Bang cosmology with no inflationary epoch, the number density of monopoles surviving in the universe today is much too high compared with present-day observations.

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

On the basis of certain theoretical considerations, astrophysical limits have been set on the monopole flux, or equivalently the number density, in the universe. The best such limit is known as the Parker bound. It was derived from considerations of the effect of monopoles streaming through the cosmos on the intergalactic magnetic field (IGMF). The basic argument here is that sufficiently light magnetic monopoles would be accelerated to high velocities by the IGMF, and this process would gradually drain away energy from the latter, resulting in its slow dissipation. The currently observed IGMF strength is used to set limits on the magnetic monopole flux in the universe. Parker set an upper limit to the monopole number at 10−15/cm2/sec/steradian (steradian is a measure of solid angle) for a monopole mass below 1017 GeV.

The Parker bound thus excludes all cosmological monopole densities predicted by non-inflationary Big Bang cosmology. With inflation in any case, as one has mentioned earlier, the density falls below experimentally detectable levels. Another astrophysical consideration is that if magnetic monopoles are present in the universe today they should have been seen in the cosmic ray flux arriving on the earth, but no cosmic ray experiment has found any such candidate event. MACRO, a cosmic ray experiment designed to specifically look for monopoles, and which ran from 1989 to 2000, put an upper limit of 10−16/cm2/sec/steradian on the relic cosmic monopole flux over a very wide monopole mass range. Later cosmic ray experiments with neutrino detectors such as ANITA, ANTARES and IceCube have been used to put upper bounds on the flux, and these are even tighter than MACRO. The search for monopoles has extended to polar rocks, moon rocks and seawater where researchers have looked for trapped monopoles. They have looked for tracks that monopoles could have left in mica. But in none of these searches, experimental or otherwise, has there been any evidence of monopoles.

## Neutrino telescope

Two very noteworthy monopole search experiments, one at the underground IceCube neutrino telescope in Antarctica (“ New window to the universe ”, Frontline , June 27, 2014) and the other at CERN, published their results in early February. They too have come up negative. However, they have put some stringent limits on monopole properties. IceCube has put an order of magnitude better upper bound on the relic monopole flux in the universe than its earlier result and the CERN experiment a strict lower bound on the monopole mass if it exists. This experiment is the first ever accelerator-based search that avoids the questionable monopole production rate calculations in the Standard Model because of monopole’s large coupling strength as mentioned earlier.

In its earlier round of monopole search, IceCube had arrived at an upper limit on the flux using only two years of detector data taken during 2008-09 and 2011-12. The results, which were published in 2015, enabled the IceCube team to set an upper bound of 1.55 × 10−18/cm2/sec/steradian on the flux of relativistic monopoles with velocities greater than half the velocity of light ( > 0.51 c ; c is velocity of light). This was already nearly three orders of magnitude stricter than the Parker bound. The latest results, which were published in Physical Review Letters on February 2, use eight years of IceCube data collected over 2,886 days during 2011-18. The analysis constrains the flux of relativistic monopoles in the velocity range between 0.75 c and 0.995 c at below 2.0 × 10−19/cm2/sec/steradian. This marks an order of magnitude improvement over the 2015 upper bound.

Detection of monopoles using IceCube, which is primarily designed to detect the elusive neutrinos, relies on the following principle. When a neutrino strikes an atom in the ice around the detector, it can produce a charged particle called a muon. When a charged particle travels through ice at a speed that is greater than the speed of light in the medium (ice), it generates a cone of blue radiation along its path called Cherenkov radiation (“ Cherenkov radiation and muons in IceCube ”, Frontline , April 9, 2021). This light triggers IceCube’s sensors as it traverses the ice and the detector, leaving a track of activated sensors whose signals give the particle’s energy and direction.

Like charged particles, magnetic monopoles whizzing through ice close to the speed of light also emit Cherenkov radiation. However, the nature and pattern of the emitted Cherenkov light are distinct from what a charged particle like the muon generates. For one, it is very bright. The Cherenkov light emitted by magnetic monopoles is about 8,000 times brighter than that emitted by muons. Two, unlike in the case of muons, the light emission is uniformly distributed along the monopole path (Fig. 3). The monopole signature in IceCube is thus clearly distinguishable from that of muons.

IceCube scientists first selected very bright and uniform emission events for signs of magnetic monopoles. Since magnetic monopoles can traverse the entire detector, tracks that started or stopped within the volume of IceCube were rejected. A machine learning event characterisation tool (a boosted decision tree) was then trained to differentiate magnetic monopole events from neutrino and muon events in the sample. Although the search did not come up with any monopole signature event, the data enabled the IceCube team to arrive at the tightest upper bound as yet on the cosmic monopole flux.

Until now, searches for monopoles in direct particle production in accelerators have been based only on collisions of elementary particles such as electrons and protons where monopoles could be produced through particle annihilation. Also, interpretation of results of searches in collider experiments have largely treated monopoles as point-like particles, thus ignoring the possibility of them being composite, particularly light ones, as predicted by some theories beyond the Standard Model. An international team of scientists working with the Monopole and Exotics Detector (MoEDAL) experiment at the LHC (Fig. 4) has been exploring the idea of monopole production in very high magnetic fields generated in heavy-ion collisions at the accelerator.

In 1951, Julian Schwinger proposed a mechanism (which now goes by his name) wherein, due to quantum theory, electrically charged particles could be spontaneously produced in the presence of intense electric fields. Given the electromagnetic duality, the MoEDAL team argued that, if monopoles exist, the magnetic analogue of the Schwinger mechanism should work in sufficiently strong magnetic fields and result in the production of monopoles. While this avoids the problem of unreliable Standard Model calculations for the monopole yield, the strong monopole coupling and the finite monopole size are expected to enhance their production a la Schwinger.

“A big advantage of the Schwinger mechanism is that we can calculate its rate more reliably than for any other production processes explored at the LHC so far,” said Oliver Gould, a MoEDAL physicist who performed theoretical calculations for this search, in a release. “This gives us a good idea about how many monopoles should be seen by the experiment as a function of their mass and magnetic charge. And since none have been seen, we can reliably say that magnetic monopoles must be heavier than a certain value.”

Collisions between lead ions at the LHC are known to briefly produce the strongest magnetic fields known in the universe (about 1016 tesla). Indeed, the highest magnetic field produced in this MoEDAL experiment was 10,000 times stronger than magnetic fields measured on the surface of neutron stars! The experiment used magnetic monopole trapping detectors made from the aluminium isotope Al-27, which can trap particles with magnetic charge (Fig. 5). The detectors were scanned for the presence of monopoles using a superconducting magnetometer. The experiment ruled out the existence of monopoles with a mass less than 75 GeV (energy equivalent) and with monopole charges g up to 3. The results were published on February 3 in Nature . Although this limit is much lower than the limits set by earlier proton-proton collision experiments at the LHC, which were of the order of a few thousand GeV, this bound is more reliable because it is based on perhaps the most unambiguous accelerator-based monopole search so far.

“This specific monopole search was pioneering and opened a new, promising avenue for further searches,” said Igor Ostrovskiy, a MoEDAL physicist. “Ours was the first search where magnetic monopoles with finite size—the type predicted by recent theories—were realistically detectable, and while we did not find any, we were able to set the first reliable [lower] limits on the monopole mass.”

So, do monopoles exist? One does not know, and magnetic monopole searches will, no doubt, continue. Even as these two new experiments improve their sensitivity further, they would also greatly benefit other experimenters in their searches as their objectives could be made more specific than before on the basis of the new findings.