A lone magnetic pole - non-existent, according to classical electromagnetism. Paul Dirac proposed that monopoles could be present in quantum theories (1931), and they have been predicted in modern gauge theory (1974). Unified theories of fundamental forces predict monopoles of mass 1016 greater than proton mass. No monopoles have ever been detected.
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). 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.
Background
Unsolved problems in physics: Are there any particles that carry "magnetic charge", and if so, why are they so difficult to detect?‹The template Unsolved has been proposed for deletion here.›
The modern understanding of magnetism posits that all magnetic effects are actually due to the motion of charged particles; The magnetic force is actually due to the infinite speed of a disturbance of the electric field, the speed of light, which gives rise to forces that appear to be acting along a line at right angles to the charges. In effect, the magnetic force is the portion of the electric force directed to where the charge used to be. Permanent magnets have measurable magnetic fields because the atoms (and molecules) are arranged in a way that their individual tiny fields align and add up.
Since all known forms of magnetic phenomena involve the motion of electrically charged particles, and since no theory suggests that "pole" is, in that context, a thing rather than a convenient fiction, it may well be that nothing that could be called a magnetic monopole exists or ever did or could.
Maxwell's Equations
Maxwell's equations of electromagnetism relate the electric and magnetic fields to the motions of electric charges. The equations are very nearly symmetric under interchange of electric and magnetic field; in fact symmetric equations could be written if one allowed for the possibility of "magnetic charges" exactly analogous to the observed electric charges.
With the inclusion of these magnetic charges, say ρm, there will also be "magnetic current", Jm.
| 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): |
If indeed magnetic monopoles do exist, the inclusion of the magnetic current would validate the monopoles' existence as well as maintain the validity of Maxwell's Equations at the macroscopic level.
When no magnetic charges are present in a region, these symmetric equations reduce to the conventional equations of electromagnetism, that is, ( ∇·B = 0 ).
So, classically, the question is "Why does the magnetic charge always seem to be zero?" This has been a curiosity for a long time, but it has become more of a problem in recent years, when new theories of physics seem to predict the existence of magnetic monopoles.
Dirac's quantization
One of the defining advances in quantum theory was Paul Dirac's work on developing a relativistic quantum electromagnetism. This is because a system consisting of a single stationary electric monopole (an electron, say) and a single stationary magnetic monopole would have angular momentum. The magnitude of the angular momentum would depend only on the product of the electric charge (e) and "magnetic charge" (g) and would be independent of the distance between them. This means that if even a single magnetic monopole existed in the universe, all electric charges would then be quantized.
Dirac considered a point-like magnetic charge whose magnetic field behaves as μ / 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.
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. This phase is proportional to the electric charge qe of the probe, as well as to the magnetic charge qm of the source.
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:
This is known as the Dirac quantization condition. 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. (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.)
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.
The Dirac monopole is a singular solution of Maxwell's equation (because it requires removing the worldline from spacetime);
Mathematical approach to Dirac monopole
Classically, gauge theory is described by a connection over a principal G-bundle over spacetime. 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.
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. The charge on magnetic monopoles predicted by GUTs is either 1 or 2gD, depending on the theory.
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.
The dyons in these same theories are also stable, but for an entirely different reason. 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.
Many of the other particles predicted by these GUTs were beyond the abilities of current experiments to detect.
For this reason, monopoles became a major interest in the 1970s and 80s, along with the other "approachable" prediction of GUTs, proton decay.
Attempts to find monopoles
A number of attempts have been made to detect magnetic monopoles. 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.
Other experiments rely on the strong coupling of monopoles with photons, as is the case for any electrically charged particle as well. 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.
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.
User Comments Add a comment…