Magnetic Monopoles
by Jan Seidel, visiting student at Sheffield University, 1998
... in this stone you should thoroughly comprehend there are two points of which one is called
the North, the remaining one the South. --- Petrus Peregrinus (1269 AD)
As early as in 1269 Petrus Peregrinus observed that all lines of force around a lodestone are
concentrated at two points which he named the north and south poles. Subsequent generations of
scientists have confirmed that all magnets have these two inseparable poles. All magnets are
dipoles. If one tries to split a magnet one will only get two pairs of magnetic poles, no matter
how small the pieces are. There is no way of getting two poles separated in this way. For a
mathematical description of this behaviour we have to look at one of the famous equations that
the Scottish physicist James Clerk Maxwell proposed in 1864:
div B = 0.
This means that the B field does not have any sources or sinks. In other words a magnetic field
always has closed field lines and the magnetic flux through any closed surface is always zero.
This implies that there are no singularities like magnetic north or south poles.
When we look at magnetism on an atomic level we imagine circulating currents which produce
a magnetic field. A current going round in a loop always produces a pair of magnetic poles.
This explains why it is not possible to take the poles apart, but does it mean, that single
magnetic poles are forbidden in nature? By looking again at Maxwell’s equations we can see that
they are not entirely symmetric. Electric fields are produced by electric charges or by changing
magnetic fields. Magnetic fields are only produced by changing electric fields. Is magnetism
therefore only a by-product of electricity? Why should magnetic charges not exist?
In 1929 P.A.M. Dirac answered the latter of the above questions. He related the existence of
monopoles to the phases of quantum waves and proposed that magnetic monopoles might exist with
multiples of the magnetic unit charge
. g=h*c/4*pi*e [1]
This clearly shows a coupling of electric and magnetic charges by means of fundamental constants
. If only one magnetic monopole was found, it would explain the value of e naturally.
However, systematic search for magnetic monopoles in rocks including some from the moon and
oceanic grounds, meteorites and other materials failed. This lead to the general opinion, that
there are no such things as single magnetic poles.
After the American Steven Weinberg and the Pakistani Abdus Salam succeeded in merging
electromagnetism and the weak nuclear force together into one single theory, namely the
electroweak force, in 1967, people were trying to include the strong nuclear force as well.
Many different versions of GUTs (Grand Unified Theories) were proposed. The necessity of
magnetic monopoles in these theories was shown by the Dutch physicist G. t’Hooft and by the
Russian physicist Alexander Polyakov. Almost all of those theories predicted a large abundance
of magnetic monopoles, which is in contradiction to observation. According to these GUTs there
should be as many magnetic monopoles as atoms in the universe. Apart from the fact that not
even one has been observed a very much lower limit on monopole flux in the universe is set by
the observed galactic magnetic field. An abundance of magnetic monopoles of more than
10E-16 per atom in the universe, or 10E-15 /cm*sr*s, would alter the observed
properties of this field drastically. This upper limit of monopole flux is called the
Parker bound [2]. Cosmology acted therefore as a testing ground for physics. This controversy
became known as "The Monopole Problem".
There have been many attempts to solve this problem. Probably the best explanation is provided
by an idea called "inflation". It was in 1979 when the American physicist Alan Guth firstly
suggested it. GUTs explain the differences between various kinds of particles as a consequence
of how they interact with something called the "Higgs field". At the unification energy, which
is the energy required to merge the three nongravitational forces together, the Higgs field was
symmetric. All particles were identical. As the Universe cooled down the symmetry was broken.
At this state the Higgs field created permanent "defects" that would behave just like single
magnetic poles. To suppress the creation of these monopoles Guth supposed that the symmetry
breaking "phase transition" was somehow delayed. In other words he claimed that the universe
underwent a process known as supercooling. Just like water, which can be supercooled below its
freezing point without becoming solid, the Higgs field could have done the same. This process
would have provided enough time for the universe to expand sufficiently before the field could
align itself. So the field would be much smoother, defects less abundant and monopoles scarcer.
Supercooling was perfect to solve the monopole problem.
Lets go back from cosmology to physics. Much theoretical work on magnetic monopoles was done
meanwhile. Its mass was predicted to be 10E-16 to 10E-17 GeV which is 10E16 proton masses or
a few micrograms. That means it would be as heavy as a bacterium [3]. Because of its mass it
is not surprising that no one has been observed in accelerator experiments. As this is not
supposed to happen in the foreseeable future the only way to find magnetic monopoles is to
search for them in cosmic rays. These monopoles can be regarded as relics of the early universe
when temperature was high enough to produce them. Furthermore a monopole would not be a
pointlike particle and it would posses a rather complex structure [4]. Its core size was
predicted to be approximately 10E28 m[5].
Its Compton wavelength would be much smaller than its spatial extension, hence it would be
essentially a "classical" object. A monopole is also supposed to be very penetrating.
The energy loss for a single magnetic pole with beta=v/c<=0.01 in rock has been calculated
to be dE/dx=100beta GeV/cm [6]. This shows that it is very unlikely for such a pole to be
trapped in terrestrial material and explains why search in rocks was not successful. Another
calculated property is that when a north pole and a south pole annihilate each other the energy
release of each pole would be .
This is by a factor of 1000 higher than the energy release of a nuclear fusion process [7].
At the 14th of February 1982 something unexpected happened. Blas Cabrera, a physicist at
Stanford University, got a signal from his detector which was built to find magnetic monopoles.
This signal was consistent with a magnetic monopole. What he used was a superconducting coil
of niobium wire with a diameter of five centimetres. This coil was surrounded by a
superconducting magnetic shield to protect it from smaller influences of the environment.
There was no current in the coil. After a magnetic monopole eventually traversed the coil
there would be a change in magnetic flux. A persistent current of predictable value would be
induced. This is exactly what Cabrera observed. But was it a magnetic monopole or just a
experimental effect? Other scientists suggested that it could have been a heavy nucleus
traversing the coil. However, this was the only event he observed and since it could not be
reproduced doubts arose.
One more signal was obtained at Imperial College London some time later using a similar
experimental set-up but again it could not be reproduced. More recent experiments including
the one at Gran Sasso Laboratory, Italy, have been using huge detectors covering areas of
several hundred square metres. This is due to the fact that maximum monopole rates on earth
of up to 200 km^-2 per year were predicted using the Parker bound. But the search for magnetic
monopoles remained without success. This detector at Gran Sasso Lab., which is called MACRO
(Monopole, Astrophysics and Cosmic Ray Observatory), uses liquid scintillation counters as
well as streamer tubes and track-etch detectors. It is being improved at the time.
Another interesting experiment was performed by the Russian physicist V.F. Mikhailov
in 1996 [8]. What he did was the magnetic equivalence of Millikan’s famous oil drop experiment
although he was not the first one to have this idea. The first one to try this was Felix
Ehrenhaft (1879-1952). Surprisingly he succeeded and got a value for the magnetic charge in
the range of 10E-9 to 10E-14 Gauss/cm^2. Although he had a positive result concerning magnetic
charges, interest in his work waned. This is due to the fact that his measured value did not
agree with Dirac’s theoretical value of 3.29E-8 Gauss/cm^2 . Mikhailov did a similar version of
this experiment using ferromagnetic aerosols created by electrospark sputtering. A uniform
magnetic field was provided by Helmholtz coils. Like in Millikan’s experiment the falling
aerosol was observed using a microscope while it was placed in an intense light beam. Mikhailov
observed lateral motion of an approximately equal number of magnetic north and south poles.
He also recognised that increasing either the magnetic field or the intensity of the light beam
increased the lateral rate of travel. Using particles that were electrically charged as well as
magnetically he was able to compare the electrostatic quantum of charge and the magnetic quantum
of charge. His value for the magnetic charge quantum
g'=a*e/6=a^2*g/3=5.84E-13 Gauss/cm^2,
where a is the fine structure constant and g the theoretical value of Dirac, did agree with
Ehrenhaft’s work. However, the monopoles of Ehrenhaft and Mikhailov are not monopole particles
in the conventional sense. To quote Mikhailov: "Magnetic charges are experimentally observed
only in the presence of two components: light and ferromagnetic particles. It seems therefore,
that magnetic charges are created as a consequence of an interaction between photons and
ferromagnetic particles, and moreover, such charges cannot exist without these physical
conditions: without light a magnetic particle loses magnetic charge almost instantaneously."[8].
He also draws the conclusion that lateral motion in a uniform magnetic field would clearly
violate Maxwell’s equation
div B = 0.
Of course the existence of a magnetic monopole would also discard this equation and so
Mikhailov might have found indirect evidence for the existence of magnetic monopoles.
However, the magnetic monopole itself remains undiscovered so far. The work of many scientists
around the world is still concentrated on this subject and it might be possible to find strong
evidence for the existence of such particles in the future. It would support the Big Bang
model and also the theory of inflation. Furthermore it would be another part of the infinite
large puzzle that describes the world and that scientists try to reveal.
References
[1] J.D. Jackson, Classical Electrodynamics, 2nd ed., John Wiley, New York, 1975,
p. 254.
[2] D.H. Perkins, Introduction to High Energy Physics, 3rd ed., Addison Wesley,
Menlo Park California, 1987, p. 345.
[3] Jeon and Longo. Phys. Rev. Let., Aug. 21, 1995.
[4] Paul Davies, Superforce, Penguin Books Ltd., London, 1995, p. 139ff.
[5] Doris Teplitz, Electromagnetism: paths to research, Plenum, New York and London,
1982.
[6] Jiangtao Hong, Search for GUT Magnetic Monopoles and other Supermassive
Particles with the MACRO Detector, Ph.D. thesis, California Institut of Technology,
Pasadena, 1993.
[7] Frank Close, Michael Marten and Christine Sutton, The Particle Explosion, Oxford
University Press, Oxford, 1994, p. 204.
[8] Terrence W. Barrett and Dale M. Grimes, Advanced Electromagnetism Foundations,
Theories and Applications, World Scientific Publishing, 1995, p. 593ff.