As we know through experiment, the magnetic force around a current carrying wire always points in the same direction given the direction of current, and this direction is described with the ‘right hand rule.’ What is it about the universe that has this ‘preference’ for this, and only this, direction?
Or from a mathematics perspective, why are our electromagnetic vector coordinates the way they are, and not the other way around? It seems the direction of fields is axiomatic to the equations, and something we tack on at the end after calculating magnitudes. For instance, “we just used ampere’s law to calculate the force at this distance from the wire, now to know the direction, let’s use the right hand rule.” Nowhere in the math does it say that the direction is a necessity.
It seems to just be an observed fact, and we have to include this fact in our equations. But this fact is not derived from the equations. For context, I understand that the electromagnetic equations can be solved with either a right or left convention. My question does not pertain to this convention, but the underlying nature of the universe and its ‘preference’ to follow the same direction every time given a direction of current. If it’s said the angular momentum of the vector causes this direction, then still it remains why this direction and not the other?
It all seems so asymmetric and arbitrary.
In: Physics
It’s just a convention. When you go between any two actual measurable quantities, you apply the right hand rule an even number of times, so they cancel out and the convention itself is totally arbitrary.
For example, you can’t measure the “direction” of a magnetic field, you can just see the lines, but there’s no inherent arrow saying that they go in one direction or the other, we just chose to call one end north and the other south, and say that the lines point at the south pole.
If we used the left hand rule instead, the direction of the magnetic field would reverse in our diagrams, but the physical system is unchanged. If you tried to actually do a measurement to demonstrate the change, you could drop an electric charge into the field and see how it moves – but you’d be using the left hand rule to determine the direction of the magnetic force on your charge, so at the end of the day the charge would move in the same direction it always has.
It doesn’t fundamentally matter whether you use the right hand rule or left hand rule as long as you use the same one through your whole calculation – consistency is the key.
See also: [pseudovectors](https://en.wikipedia.org/wiki/Pseudovector), which all the quantities you’re concerned about actually are, not normal vectors
Latest Answers