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
One explanation of magnetic fields around a conductor is that they are actually electric fields that appear because of relativistic length-contraction when charges are moving.
Because your motion relative to the moving negatively charged electrons in the conductor is different to the stationary positively charged atomic nuclei. Thus you will perceive length contraction on the electrons to be different than the atomic nuclei, either compressing or expanding the distance between the electrons, changing the apparent charge density of the electrons and the nuclei, and thereby creating an electrical field.
The right-hand rule and all that are consequences of the direction of motion etc.
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I probably explained that terribly. [Here’s a video that does a better job](https://www.youtube.com/watch?v=1TKSfAkWWN0).
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