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
As I take it from your explanations, you want to know why electromagnetism cannot randomly “change direction”. So not any sign choices, but why the resulting directions are always the same, not sometimes opposite.
This for example follows if one accepts that physics is _continuous_, stuff does not jump. That alone does not yet fully prove that magnetic fields cannot randomly “flip”, but it would require them to weaken down to 0 first. To actually get the compatibility and non-zero-ness, you can take a second electric/magnetic device and compare.
So why continuity? Well, at some point we reach an area where “why” is not a reasonable question anymore. Simply because the inherent nature of physics prevents us from ever knowing the root cause; if such a thing even exists. Even if we somehow guess rules that exactly predict everything, then the underlying mechanism might still be different. Our observations just match the physics we currently use, so it is “good enough”.
Depending on what kinds of guesses you accept this kind of question is either physics (when we at least _could_ check it with enough effort), metaphysics (when we cannot but try to find the simplest mechanism that could underlay it), or religion (when we just believe).
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