## Degrees of Freedom

The boundless dimensions of math and physics

# Why There's No Such Thing as North and South

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Spot the cultural bias

The human mind often confuses familiarity with understanding.

You've learned the basics of a field. You've memorized the rules and used them so many times they have become second nature, or "common sense"--which means that you have stopped asking yourself why they should be true. And now it's often harder for you to learn a new concept than it would be if you were to start from tabula rasa.

That is why many of us who studied science or engineering or mathematics at university find it hard to convince ourselves that electromagnetism--one of the four fundamental forces of nature--does not have a preferred handedness. (which in particular implies that one cannot use the laws of electromagnetism to explain our concept of left and right to far away aliens, or explain it to Martians over the phone, as Richard Feynman put it).

The first time many of us had to face the formal concept of handedness was, in fact, precisely in electromagnetism class.

In EM class, students learn that an electric current generates a magnetic field. That field swirls around the space surrounding the wire similar to how the pattern of wind velocity in a hurricane wraps itself around the eye of the storm. To remember which way the field goes, students are taught something called the right-hand rule.

The association of the right hand rule with electromagnetism gets so ingrained that, in one's mind, EM theory can become the mental picture of handedness itself--the quintessential example of a theory that has a specific handedness built in.

Then someone comes along and claims that electromagnetism has nothing to do with handedness after all. You listen to their words but all the while your brain keeps blocking them out and instead visualizing the picture of the magnetic field around a wire. How could it ever be, your inner voice keeps repeating, that the theory of the right hand rule cannot tell left from right?

The reason is simple: the idea that the magnetic field itself points in a well-defined direction--the idea that there is a north and a south--is purely a convention. To see why, it helps to look at what a magnetic field actually does. A static magnetic field enters in essentially two (not entirely unrelated) types of phenomena. The first is that it puts a torque on permanent magnets, for example, on the needle of a compass: more on this later.

The second is that it deflects moving electric charges: hence the curved trajectories you see in some of the tracks coming out of atom smashers such as the LHC. Particle physicists embed their detectors in powerful superconducting magnets because they can can glean lots of information just by looking at how those tracks are bent.

The first high-energy collision recorded by a detector at the LHC. Electrically charged particles (such as electrons) have curved trajectories because the detector is bathed in a strong magnetic field.

The magnetic field pushes the electron in a direction that's at 90 degrees both to the elctron's motion and to the magnetic field itself. This is called the Lorentz force, and its exact direction is described again by a right-hand rule.

Here is what happens in a very simple case: say you have a vertical wire in which current is running in the "up" direction. According to the right hand rule, the wire produces a magnetic field that looks more or less like this (pardon the extremely low-tech illustration):

Now an electron shows up and it's moving vertically. The field then acts on the electron with a Lorentz force that's at 90 degrees both to the field itself and to the motion of the electron. That force is directed away from the wire, and looks as follows:

To figure out which way the force pushes the electron, one applies the right hand rule once to get the direction of the magnetic field, and then once more to calculate the corresponding force. The end result is a force pointing in a direction that has nothing to do with any left or right hand: it just points towards or away from the wire.

"When we actually predict how matter moves due to magnetic fields, we use the right-hand rule twice, so it cancels out." explains John Baez, a mathematical physicist at the University of California, Riverside. "We use the right-hand rule once when describing how a current or changing electric field produces a magnetic field, and again when describing how a magnetic field pushes on matter!"

If we had used the opposite convention (a left-hand rule) for defining the magnetic field, but also to calculate the resulting Lorentz force, "we'd get the same answer," Baez points out.

But is the orientation of the magnetic field really aribitrary? After all, doesn't a bar magnet point in a definite direction? In fact, one way to define the magnetic field is by observing its effects on bar magnets, in particular on a compass. You place the compass at a point in space and you take note of which way the "N" points. If you walk your compass around the electric wire the S->N direction is always that of the magnetic field, as defined by the right-hand rule.

There is one small problem, though. Our very definition of magnetic north is itself a convention. It would not be any easier to explain to an alien what we mean by north than it would be to explain our concept right-handed.

We are accustomed to looking at maps in which north is up and south is down (although the North Pole of maps does not quite coincide with the North Magnetic Pole, which complicates things a bit). Maps point north perhaps because they were invented by people in the Northern Hemisphere, who may have found it convenient because they used the North Star for navigation. If you look at the North Star while holding up a map in front of you, it helps to be able to read the labels on the map without having to tilt your head. According to some, the tradition of putting north up and south down dates back to Ptolemy.

But there is a perfect symmetry between the north and south magnetic pole of the Earth. Nothing moves preferentially from south to north--or from north to south--except in our imagination. Auroras don't happen any differently at the South Magnetic Pole than they do at the North Magnetic Pole. An alien arriving at Earth would certainly be able to measure the geomagnetic field, but from that he could never guess which way we have conventionally decided to point the arrow on our compasses.

 This post is part of a series on handedness. Here are the all the posts in the series:  Galactic Challenge, Part II: The Richard Feynman Files Galactic Challenge Part III: The “Easy” SolutionsWhy There’s No Such Thing as North and SouthStill to come: The "hard solutions" to the challenge

The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings: Third Revised Edition. By Martin Gardner​. 2005.

The Handedness of the Universe. Roger A. Hegstrom and Dilip K. Kondepudi in Scientific American, Vol. 262, pages 108-115; January 1990.

Alien Pizza, Anyone? Davide Castelvecchi in Science News, Vol. 172, No. 7, pages 107-; August 18, 2007

Image credits: Steele Hill/NASA; National High Magnetic Field Laboratory

The views expressed are those of the author and are not necessarily those of Scientific American.