# Why is it not possible to distinguish left from right by means of a coil?

Why is it not possible to explain to an alien "at the phone" which side is left and which is the right side by defining a simple experimental setup using induction? Defining for instance downwards should not be a problem, or is it?

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What is "f.i."? –  Mark Eichenlaub Jul 23 '13 at 20:57
for instance? (I hope) –  Emilio Pisanty Jul 23 '13 at 20:57
confirm for instance, sorry.. –  Mirc Breitschuh Jul 23 '13 at 21:39

Say you want to explain to your Martian friend what "clockwise" means. You instruct him to look down and place a coil of wire on the floor, and connect it to the battery so that the current flows in what he hopes is clockwise (the hope being that if something comes out wrong, he can then reverse this). You can then, and you do, tell him that the magnetic field inside the coil is now pointing down. So far so good: electric current is a vector and it $+/-$ charges can be independently verified, and we can assume he knows what "down" is.

However, once he's done that, he phones back and says "OK, but how do I actually confirm that the magnetic field is pointing down?". "Well," you say, "fling a positive charge horizontally through the field. It should curve left."

... and you can imagine his response: "so what was 'left', again?".

What this illustrates is that while some electromagnetic quantities, like the magnetic field, do depend on a convention for left/right handedness, and therefore transform to themselves after a space inversion, these are not directly physically observable. All pseudo-vector quantities in electromagnetism couple through a cross product to make physical observables, which means that mirror versions of the same apparatus will have magnetic fields going opposite ways but all forces, positions and velocities will behave identically.

Of course, this is absolutely necessary. If you begin with a parity-invariant theory, then all subsequent physical observables will be parity invariants. To transmit chiral information, you need to use physical observables from a chiral theory; the standard example is the weak interaction. There you can make an apparatus that will transmit a sense of handedness to an alien friend, with the caveat that, since the weak interaction is $CP$ invariant, if your friend is made of antimatter then he'll get it the wrong way round.

I'll just finish by saying that if you didn't read about this first directly from the Feynman lecture, you really should go read that.

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I thought one could argue by the direction of current (or motion of electrons) in a 2nd, closed conductor that goes through the coil. A change in flux of the magnetic field should then induce a current, or electron motion in the closed loop cunductor. But maybe I mix things up here... –  Mirc Breitschuh Jul 23 '13 at 21:34
do you mean two interlinked loops? Then the induced current must be zero. If you have two parallel loops, then the induced current will mimic the applied one, and you learn nothing. –  Emilio Pisanty Jul 23 '13 at 21:44
the coin has dropped. Thank you! –  Mirc Breitschuh Jul 23 '13 at 22:15
And of course, the resolution is to find a phenomena that is described by a theory that is not parity (or charge-parity if you can't confirm matterness) invariant. Alas, E&M is not that theory. –  dmckee Jul 23 '13 at 23:11
In the back of my mind is something I read, I don't remember if it was in a Feynman lecture or not but, it had to do with the fact that, if a magnetic monopole existed, it, in combination with an electric charge would establish, IIRC, an absolute CW versus CCW (or something). I'm still trying to find it so I may be completely off the mark but... –  Alfred Centauri Jul 24 '13 at 3:04