The Dirac monopole

While preparing some educational material for the MoEDAL experiment, I found I needed to illustrate what Dirac's hypothesised magnetic monopole looks like. The monopole has magnetic charge, and so one can draw magnetic field lines emerging from the monopole just like you can for an isolated electric charge. Unable to find a good quality, rights-free image that would do the job, and inspired by Figure 2 of (Preskill, 1984), I made the figure below:

A schematic representation of Dirac’s magnetic monopole, inspired by Figure 2 of (Preskill, 1984).

Normally when you draw magnetic field lines you can only draw complete loops, as (experimentally, at least) there are no isolated magnetic charges. Dirac's monopole circumvents this problem by imagining an infinitely long and infinitely thin "string" that carry the looping field lines away, making the monopole appear to behave like an isolated magnetic charge. You can read more about it in Dirac's original paper (Dirac, 1931) or in MoEDAL Collaboration theorist Arttu Ranjantie's review paper (Rajantie, 2012).

If an infinitely long, infinitely thin string sounds a bit odd, well, yes. Yes it is. But that's almost the point; in order to make such a string undetectable in an experiment (which, after all, is all that matters) electric charge must be quantised - i.e. free charged particles that we observe have to have whole numbers of electric charge. Of course, we know that this is the case experimentally - which is why, when writing his paper, Dirac himself remarked: would be surprised if Nature had made no use of it.
— Paul A. M. Dirac, 1931 (

That's certainly what those of us working on the MoEDAL experiment are hoping, anyway!

If you would like to use this image, it has been published on Zenodo and released under a Creative Commons 4.0 license. Enjoy!

Citing the LHC experiments: BibTeX code

Need to cite the "Big Four" LHC experiments in your next paper? In 2008, The Journal of Instrumentation (JINST) published four papers describing the ALICE, ATLAS, CMS and LHCb experiments (along with a fifth describing the LHC itself). And here's the BibTeX code you'd need in your LaTeX document:

Of course, the idea is that rather than having to describe the experimental setup in each paper published by the respective collaboration, the paper can be cited and referred to by the interested reader. (It's also nice, therefore, that the papers are Open Access, as are all LHC results). Enjoy!

Hints, warnings and information boxes

Over the past few years I've been writing a lot of documentation and user guides for various projects - experimental equipment, grid software, etc. - and one technique I've often borrowed from great guide writers like Hartl is the use of little pop-out boxes to make certain points stand out. Specifically, I like to add Hints, Warnings, and Points of Information, as shown in the image below.

Fortunately these are pretty trivial to add in LaTeX thanks to the tcolorbox package and a macro or three inspired by this TeX StackExchange post. I've embedded a Minimal Working Example in the Gist below to give you an idea of how it works (which also generated the above image). Pretty handy, eh?

The MoEDAL Bibliography

So here's that bibliography I was talking about in the monopole discovery post. It's basically an annotated list of all (well, most) of the papers referenced by other MoEDAL publications to date generated using a BibTeX file and the bibtexparser Python module. You can download it from CERN's Zenodo repository here.

OK, so it's a little more than just a list:

  • bibliography.tex is the base TeX file containing the LaTeX document class, title stuff, etc. that also \inputs various snippets from /common/tools for recurring CERN@school document features;
  • However, a Python script is used to generate a LaTeX table containing summary information about each paper;
  • The generated autotable.tex file is \input into the main TeX file bibliography.tex, which is then used to generate the document itself;
  • One of the columns in the summary tables is the citation of the paper itself, so every paper then gets listed in the BibTeX-generated bibliography at the end of the document as usual;
  • Another of the columns is a "Notes" section, which contains a one line summary of the paper's contents;
  • The hyperlinked Digitial Object Identifier (DOI) of each paper (or URL if no DOI is available) is also included for each paper so you can simply click on it to get to the paper on the publishing journal's website.

What's more, thanks to GitHub and Zenodo both the bibliography itself and the code used to generate it have DOIs themselves. This means that they can both be cited in other papers, grant reports - anything that needs a permanent, unique identifier rather than some transient URL on some organisation's website. As I understand it, this is largely thanks to @arfon - who you may remember from the Zooniverse. He certainly wrote this fantastic guide to making your code citable that I used.

I'm going to be using it a lot over the next few weeks, anyway...

An Interesting Discovery (or Not)

In writing up the bibliography for an upcoming paper on the background radiation environment measured by the MoEDAL Timepix detector array, I was going through the collaboration's bibliography - the list of papers that are typically cited in the papers that we publish. These include things like the MoEDAL Technical Design Report [1] and physics programme [2], but also key theory papers like Dirac's original prediction [3] (which you can read for free here) and Polyakov's [4] and 't Hooft's [5] GUT monopole papers. Julian Schwinger - who shared the 1965 Nobel Prize for Physics with Tomonaga and Feynman for his work on Quantum Electrodynamics (QED) - also has a paper in this list; in Magnetic charge and the charge quantization condition [6] he talks about dyons - particles that have both magnetic and electric charge. We are looking for these with MoEDAL too; these are one of the "Exotics" represented by the "E".

Anyway, in reading the paper to check exactly where dyons are mentioned, I noticed the following throwaway paragraph placed inconspicuously at the very end:

Added note: At long last there is experimental evidence for magnetic charge. P. B. Price, E. K. Shirk, W. Z. Osborne, and L. S. Pinsky [Phys. Rev. Lett. 35, 487 (1975)] have detected a very heavily ionizing particle that has all the characteristics of a particle with magnetic charge...
— J. Schwinger, Phys. Rev. D 12 3105 (1975)

Now, I wasn't aware that there was any experimental evidence for magnetic monopoles - MoEDAL would be a very different proposition if there had been, and I'm pretty sure I'd have remembered it from my undergraduate degree - so I thought I'd check out the cited paper. Lo and behold:

The paper itself can be found here [7]. In short, in the last flight of a balloon-borne stack of Cerenkov film, emulsion, and Lexan polycarbonate sheets, the authors spotted a very heavily-ionising track that they believed had all the characteristics of a magnetic monopole. The paper itself is a nice read; you can almost imagine the authors sitting around carefully preparing and sorting through the emulsion plates and plastic sheets, half-jokingly discussing what they’d wear on stage for the ceremony in Stockholm. As one would expect, the figures very much resemble the sort of thing we’re looking for with the MoEDAL Nuclear Track Detectors (NTDs) - etch-pit cones aligned along the path of the particle through the Lexan layers of the stack. We would certainly get very excited if we saw something similar in our layers of NTD plastic.

So what happened? Had they found experimental evidence for a magnetic monopole? Well, no. An alternative explanation for their signal would have been a very fast, very heavy ion fragment (Z>100ish) reaching the atmosphere from space. Price et al. claim to rule this out in the paper, but in the same journal a fellow balloon-stack experimentalist shows how [8], once you take into account saturation effects in the Lexan and the ambiguities introduced by only having one layer of emulsion (their lab always used two or more in their balloon stacks, apparently), a heavy ion fragment cannot be ruled out.

And so, I suppose, it wasn’t.

However, it wasn’t just the monopole discovery claim that had caught my eye. One of the authors in the citation was listed as L. S. Pinsky. As I read it, I thought, "could this be the L. S. Pinsky, friend of the Institute for Research in Schools and keynote speaker at the 2015 CERN@school Research Symposium? Could the world be so small that the supporting scientist for IRIS’s TimPix project was an author on a magnetic monopole discovery paper from back in 1975?"

Yes! Yes it was! And perhaps it shouldn’t be too surprising, really - after all, Professor Pinsky is one of the world’s leading experts on heavy ion fragments from space at the University of Houston (where he was in 1975!) and NASA’s Space Radiation Analysis Group at the Johnson Space Centre. And of course both they and MoEDAL are using the Medipix Collaborations’s Timepix detectors to study highly ionising particles on the International Space Station and at the Large Hadron Collider respectively - and both are offering projects for school students with us at Institute for Research in School’s CERN@school programme.

So at least I'd made one interesting discovery from going through the bibliography. And who knows - perhaps one day we’ll publish our own monopole discovery paper!


  1. The MoEDAL Collaboration, "Technical Design Report of the Moedal Experiment", CERN-LHCC-2009-006 (2009)
  2. The MoEDAL Collaboration, “The Physics Programme Of The MoEDAL Experiment At The LHC”, Int. J. Mod. Phys. A 29 1430050 (2014)
  3. P. A. M. Dirac, “Quantised Singularities in the Electromagnetic Field”, Proc. Roy. Soc. A 133 60 (1931)
  4. A. M. Polyakov, “Particle Spectrum in the Quantum Field Theory”, JETP Lett. 20 194 (1974)
  5. G. ’t Hooft, “Magnetic Monopoles in Unified Gauge Theories”, Nucl. Phys. B 79 27690486-6) (1974)
  6. J. Schwinger, "Magnetic charge and the charge quantization condition", Phys. Rev. D 12 3105 (1975)
  7. P. B. Price et al., "Evidence for Detection of a Moving Magnetic Monopole", Phys. Rev. Lett. 35 487 (1975)
  8. M. W. Friedlander, "Comments on the Reported Observation of a Monopole", Phys. Rev. Lett. 35 1167 (1975)