I get that it’s values. It’s like, you assign a value to every point in space. But what “is” the electron field? It’s… what? I mean like a Kantian “field an sich”. Is the electron field the amount of electron-ness at a given point in space? What does that even mean beyond a calculation?
Are fields “real entities” with an objective physical reality? Or are they just mathematical abstractions that we use for calculation? Can you talk about fields without math? Does that even make sense? Like, I can talk about electrons without math. I can say they’re point particles that carry charge. But can you talk about the electron field outside of math? Or the EM field? Does it genuinely exist outside of an Electrodynamics calculation?
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Short answer: there is no satisfying answer to your question. We don’t know. And probably can’t know.
To me, this touches on the difference between mathematics and science. In pure mathematics, you start with some rules, and then you mix and match the rules to build up a complex game. But here in the real world, we have it in reverse. We’re already playing a game, and we don’t know what the rules are. So we make some rules that *look* like they describe the game we’re playing, and then we try everything we can think of to see if we can break that rule we came up with. If nothing breaks the rule, that doesn’t necessarily *prove* that it’s actually the rule, it just means we haven’t thought of anything that breaks it yet.
There was a time when it was common knowledge that water was a fundamental building block of the universe. Then we discovered molecules, and we thought the atoms that made them up were fundamental. Then we discovered atoms had electrons and a nucleus full of protons and neutrons, so we thought those were fundamental. Then, inside the protons and neutrons, we found quarks, and we thought those were fundamental. Now, we’ve came up with the idea of “fields”, which are currently our best description of how the world works so far. Does that make fields “real”? Or are they still something more fundamental and complex, that just *looks* like a field in all the ways we’ve poked at it so far? It’s not really an answerable question.
As to what these fields are “made of”, well… We’re talking about the most foundational layer of reality itself (that we know of). It isn’t “made of” anything. Everything else imaginable is *made of it*. It’s kind of like asking what the number “1” is “made of”. I could tell you that “2” is made of “1 plus 1”. But what is “1” itself? Hard to say. It just kind of *is*. Everything else is made of it. Without it, we don’t have anything else. But what it *is*… again, it’s not really an answerable question.
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