Magnetic Monopoles and Magnetism: The Alliteration Choice of Champions

Recently, I was reading this article about doomsday, law suits and the Large Hadron Collider. I admit that I’m intrigued and would kind of like to read a rigorous version of the theories behind these doomsday scenarios. It struck me how difficult a problem it is for courts to sort out such things, what with the high level of prerequisite knowledge a person must possess to understand enough about these concerns to make an informed decision about them. I suppose that’s what expert witnesses are for. Still, I think it is important to try to bridge the knowledge gap between scientific experts and folks with only as much science background as their learning institutions required them to learn to graduate in another field. Our society is pretty lacking in those bridges, I think, and I’m going to try to build more.

One of the fears in the article seems to be that the exotic and frighteningly named “magnetic monopoles”, if created, will be malignant and alter all matter they touch in upsetting ways, Ice-Nine style. Having just reinserted the topic of magnetic monopoles into my brain a couple months ago in my class on electricity and magnetism, I’m feeling the spirit to type about them on the internet.

The article sums up a magnetic monopole as a particle with “only one magnetic pole — only north, or only south, but not the north-south magnetism that dominates nature.” This is true, but a deceptively simple thought nugget for a reader to carry around and apply to future contexts. When I’m musing about some aspect of physics to my biologist coworker, I summarize some pieces of mathematics when going through it point by point would detract from the discussion at hand. She usually gives me permission to proceed by saying “I’m sure its more complicated than that.” This is her way of indicating she’s understood conceptually what I’ve said and is willing to take on faith that my simplistic model can be trusted in the realms I apply it to. This is a common understanding of physics: whatever portion is conceptually comprehensible must be a simplified version of how a physicist would explain what’s going on to another physicist. This, too, is true, but with a catch: the complication of physics frequently lies in the elaborate mathematical and conceptual apparatus required to solve specific physics problems. Physicists are trained be begat physics, not just to understand what has come before. The concepts themselves are frequently not super complicated for non-physicists to understand, when explained using English and pictures rather than math.

So what is a magnetic monopole, in plain English? It’ll be a meandering adventure through electromagnetism to get there, so if you’re in the mood for a leisurely Sunday discovery jaunt, let’s go. First off, what’s a magnet? If a three-year-old asked you what a magnet is, every adult of sound mind would (correctly) give the answer with confidence. But if a physicist asked you what a magnet is, you might be hesitant and second guess yourself before answering, assuming the answer should contain more complexity. On some level I suppose it does, but your intuitive response, the one you gave to the three-year-old, is still entirely correct; we just need to emphasize specific properties of a magnet and hold them in our heads to have a thorough understanding of what a magnetic monopole is, and how it fits into the larger picture of nature. (The point, after all, is to have this enriched understanding, not just to accumulate the intellectual equivalent of cute party tricks.) So what’s a monopole? Well, if it occurred to you that “mono” means “one” or “single”, then you’re on the right track. You might be reminded of the North and South pole of the Earth when you read the word “pole”, or even recall that bar magnets, like the ones you stick on your refrigerator, the ones you told the three-year-old about, have “North” and “South poles”, and again, you’re on the right track.

So what does a magnet do? You know this: it attracts or repels some objects, such as a refrigerator or another magnet. In other words, from physics 101, it exerts a force on some objects and not on others. A magnet doesn’t have to touch the refrigerator to be pulled toward it either. It seems to exert its force from a distance. This seems a little odd compared to the way other familiar applications of force work. For example, you couldn’t knock your roommate onto the floor or pull him tight to you by throwing punches or grabby hands from your side of the couch when your hands only connect with the air between you. Likewise, it seems a little weird that a magnet would leap through the air to the fridge when you let go of it close by, but not touching. It turns out there’s another actor that mediates this force: the magnetic field. A magnetic field exerts a magnetic force on some materials, particularly metal ones. Iron filings on paper illustrate the location and direction of the magnetic field of a bar magnet. Physicists have figured out tons of details about these interactions, and have created mathematical models such that the behavior of all sorts of objects under the influence of magnetic fields generated by a variety of means can be predicted. Not knowing these details does not imply a lesser understanding of the underlying principle though; a magnetic field carries the magnetic force, some objects feel a push or pull from this force, and a bar magnet can create a magnetic field, which is the carrier of this force.

Before we get too carried away parsing words and examining our Chipclips, let’s think about why some materials, such as iron, react to a magnetic field, and others, such as wood, do not. This will lead us to a bigger picture. It turns out that only objects that have charge are affected by magnetic fields. If this seems weird, let’s go back to a more intuitive situation involving force. In the roommate shoving analogy, you apply a force to shove an object (your roommate), who has mass, off the couch. He falls to the floor because he has mass and the Earth has mass, and the gravitational force of the Earth — the force exerted by the Earth’s gravity that we’re all familiar with — exerts a force on your roommate that pulls him toward the Earth. The gravitational force only acts on objects that have mass, and the magnetic force only acts on charge.

What is a charge? Well, physicists like to break things down as simply as possible, and the most simple charge model is that of a static point charge, which is a charge that has a particular location, but no volume, and is not moving. The closest you get to one of these in real life is an electron, the particle that orbits the nucleus of an atom. You may recall that an atom has a nucleus that contains protons, which are “positively charged”. Orbiting around the nucleus are electrons, which are “negatively charged”. In a metal, the outer electrons in each atom have more freedom to move than in a material that magnet don’t stick to. The electrons are free to align themselves with the magnetic field that radiates from a magnet, causing the object to feel a push or pull from the magnet.

Modeling an electron as a static point charge is a total lie, by the way. An electron doesn’t stand still, and it occupies a volume, but cannot be precisely located in space, so it pretty much fails as a static point charge on all counts. The trick with physics models, and the source of much confusion for all the regular folks trying to learn a bit about science, is this: it doesn’t actually matter that the electron utterly fails as a static point charge or that point charges, a prominent and indispensable tool in the study of electricity and magnetism, do not exist in reality, because perpetuating this falsehood allows us to create accurate models of nature under certain conditions. The model of an electron as a point charge fits some applications quite well, so we tend to use that fact to our advantage in realms where it works, and abandon the lie in realms where its falsehood becomes apparent. Additionally, point charges are tools for thinking about electric and magnetic effects in the simplest terms possible, and from these simple terms, physicists build up larger models of nature that are tested again and again by experiment and pass every time. Hopefully you’ve bought this argument, but I encourage you to be skeptical and think it through.

So a mass exerts a gravitational force on another mass. Does a charge exert a magnetic force on another charge? If the charges were moving, it would. A still charge exerts an electric force on another charge, but not a magnetic force. Magnetic and electric fields have parallel properties, and are interrelated, but there are some key differences. A point charge can also be thought of as an electric monopole. It’s a single charge with a uniform electric field radiating out from it in all directions, and this field carries the electric force. An electric dipole, “di” meaning “two”, can be most simply modeled as one positive charge some short distance from one negative charge. The electric fields are drawn toward each other and orient themselves in a pattern much like the iron filings in the magnetic field of a bar magnet, going from one charge to the other.

A magnetic field springs forth from moving charges, with the field itself curling around a wire on which charge flows, and the magnetic force pointing radially outward from that wire. If you have a circular loop of wire with charges moving along it, aka, a wire with an electric current flowing through it, the magnetic field will still curl around the wire, such that the magnetic field is all pointing upward from the center of the loop, and downward around the outside (diagram). Now, this is getting somewhat taxing to visualize, but if it were possible to have an electric dipole where the distance between the two charges was zero, its electric field would look exactly the same as the magnetic field of the current loop if the radius of the loop was zero! See what interesting “coincidences” we find when we use oversimplified theories full of lies? The current loop is actually a magnetic dipole. As far as we can tell though, there is no magnetic monopole.

The electrons in a material spin, and this spinning, like current going around a loop, creates a magnetic field. These spins are usually oriented randomly through the material, so there’s not net magnetic field outside because all the tiny magnetic fields points in all directions and cancel each other out. In bar magnet, however, these spins are all oriented in the same direction, creating a magnetic field outside the material. Similarly, the path of the electrons around the nucleus creates a current loop, and these loops can also become aligned to create a net magnetic field.

One large reason physicist search for magnetic monopoles is that Maxwell’s Equations, the equations which, coupled with Lorentz’s Force Law, describe all of classical electrodynamics, would be more symmetrical if they existed. I am serious. Physicists want nature to be simple and beautiful and symmetrical–probably because it is, in many cases–and search for new ways in which it is so. There are other reasons too, but do not underestimate the sort of aesthetically pleasing equation OCD physics get into their heads.

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2 Responses to “Magnetic Monopoles and Magnetism: The Alliteration Choice of Champions”

  1. Jenn Says:

    This is an excellent description of magnetism — I probably could’ve used it before launching headfirst into quantum magnetism. I also like the way you’ve phrased the points about accurate models and mathematical vs. conceptual/pictorial ways of describing things. I think lack of understanding the latter is part of what keeps people like my parents from ever asking what I actually do. 🙂

    One thing, though. I still don’t understand what a magnetic monopole would be. Is it a small particle, like an electron? That is–does it necessarily have to be some kind of inherent magnetism that isn’t caused by electrons/motion of electrons? It’s early in the morning and I may not have read carefully enough, though–sorry if that’s the case.

  2. dyslexicmathematician Says:

    Thanks for the input. And the compliments; flattery will get you everywhere. 😛

    Point well taken about magnetic monopoles. I was getting tired of typing and brain-wandery by the end of this, and perhaps forgot to really wrap things up. I started writing a response to you on this, but I think it really deserves its own post. So stay tuned…

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