I'm not 100% sure what other evidence backs up the idea of "lines of force" other than the iron filings
My apologies for not making it more clear previously, but my argument is that the evidence for "lines of force" (in this context) comes directly from conservation of angular momentum. I will give a chain of custody for this entire response and then if you would like to contend anything in that chain - I will be happy to accommodate it.
but fundamentally I'm very against the idea simply because of two things:
Lines are not real things, they are abstractions
All words and by extension all languages are abstractions. It does not seem viable to arbitrarily select one abstraction from all the other abstractions you are using in your communication and reject it for being identical to the others.
For example, I don't think you would agree it is a viable argument to say I reject "red" because it is a color while I are perfectly fine with "green" (even though it is also a color).
For words or languages to be anything other than abstractions you would need objective, unimpeachable first hand knowledge. That is not available to any human by definition. For example, you cannot disprove "the Matrix". You might not be who you think you are - you could be a brain in a box whose reality is a simulation.
While this is a fun idea for a movie, it has no practical use or value in the context of knowledge. The best we can do is assume we are not in a matrix and try to communicate using shared or common experience. As humans, we abstract those shared experiences into words and language.
The best you can do then is argue that you are not familiar with the concept of a line and we do not have a shared experience with the concept. Is that true though? It simply signifies an arrangement of things - like a line of trees or a line of ducks. I think we have those experiences in common.
Obviously in this case we are talking about the mathematical definition of a line, which fortunately applies to lines of trees and lines of ducks - so basically if you compare and contrast the differences between a line of trees and a line of ducks and remove every difference between those two cases - whatever is left is a mathematical line.
Force is not an entity in and of itself. Force is applied when one thing interacts with another.
A force is a push or a pull. I think you have a common experience pushing and pulling things. When you type you are pushing on the keys - when you breath you are pulling on the air.
We simply can't see the agent that moves around the iron filings much like how children don't know that puppets are controlled via strings from above.
A better example might be to consider a person living insolation or confinement about air. They might not believe it exists because they dont have the shared experience of wind or tornados. How do you convince a person that has never experienced wind that air can destroy entire cities?
Even more so - when a bomb explodes the vast majority of the damage comes from displaced air in the form of wind that pushes with lines of force outward from the explosion. Do we not have that shared experience with explosions and lines of force?
It looks to me like you are trying to say that bombs don't work because you reject the words "line" and "force". I apologize if that sounds snarky - this is simply the most honest and clear way I can express my interpretation of your position.
At best we have visualizations via iron filings or ferrocells which probably can't show us everything.
My apologies, but this is not correct. "We" have all the evidence of every working electrical device and in reality all of chemistry as well. That is to say - every aspect of the computing device you are using to read this passage relies on the mathematics of Maxwells equations to describe these "ferrocells" or "lines of force". Humans only have Maxwells equations and nothing else to not just design and build computers, but to allow them to communicate with each other.
Furthermore, the entirety of chemistry and biology also rely 100% on Maxwell's equations to describe the finest available details in each field. Why does salt dissolve in water? Maxwells equations. Why are you eyes able to detect light waves? Maxwells equations. Why does DNA unravel during cellular mitosis? Maxwells equations.
There is literally no direct experience available to you in principle that is not evidence that Maxwells equations are accurate and correct. In turn, Maxwells equations are noting more than the result of conservation of linear and angular moment along "lines of force."
That said, just because I postulated that the magnetic field runs perpendicular to the lines of force, doesn't mean that they don't have a real basis in some way.
I dont understand why you are using "lines of force" here after you have claimed to reject them. Let me give one last simple example of a "line of force" in our common experience. It would be difficult to argue that when you are typing on a keyboard - the push/force you use is linear or a line of force, but if you dropped something like a ball in a room with still air - the ball would follow the lines of force from gravity and those gravitational lines of force would push/force the ball to intern push/force the keys on your keyboard.
I dont know how you can reject this specific description of a ball falling onto your keyboard, but it is no different than the description of magnetic forces that arise from Maxwells equations.
OK - I promised a chain of custody. The exclusion of contradiction comes from Aristotle 2,300 years ago - it is well known. It is the foundation of both math, logic, and in turn reason itself. The point of these pursuits is directly that - to exclude contradiction. Contradiction provides the only objective basis for the concept of wrong.
This is the first step in the chain of custody. There is nothing that is logical, reasonable, or mathematically correct that also contains a contradiction.
Natural languages arise without consideration of logic and so they are obliged to hold logic as a principle. They can be haphazard and contradictory. We can try to impose logic upon natural languages, but the vague and contradictory definitions of the words in a natural language always leave large gaps and confusion when applying logic.
Math on the other hand is a language in which clarification of each definition happens before the conversation. Math excludes contradiction necessarily before it is available for use as a language. It therefore is the only reliable second step in the chain of custody for knowledge.
This is why math is so powerful and so vital for communicating science. All objective knowledge can be reduced to math as it provides the only reliable path back to the exclusion of contradiction. And there is little math in the entirety of human history and personal experience that is more reliable and successful than Maxwell's equations concerning lines of force. It certainly surpasses Einstein's work.