Fields aren't made of anything. When you feel static electricity, like when you rub a balloon against your hair, and your hair then stands up, that electric charge on the balloon and your hair is somehow being made evident across the space between the hair and the balloon. That communication of force electric charge happens over the electric (really, electromagnetic) field. It happens across air and vacuum alike. Nothing need be between the charged objects and yet the charge will be "felt" by them. That "field" is just the numeric electric charge felt at each point in space, for all points in space. It's just field strength -- a bunch of scalar values, one for every point in in space. We call that a field, but it's not an object made of stuff, just a mathematical object.

The book Waves in an Impossible Sea really goes into some depth on this (for a layman -- which I am) and tries to drive home the point that there are two perspectives one might take. There's the perspective of the medium and the perspective of the field.

Using wind, as an example, we can measure the wind speed/direction at various points in a given space. We don't need to know what wind is to feel its effects. Instead, we might view it as a force wave that propagates through space and interacts with everyday objects. The measurements of this force that we take at various points in space across a given area form what we might call the Wind Field. We don't need to know the nature of the medium these wind waves propagate through in order to study wind and how it interacts with other objects. This is the field perspective.

Of course, we know that wind is really an effect of air molecules moving through space. That is, the medium for wind is the atmosphere. This gives us deeper insight into what wind is and how it works. This is the medium perspective.

According to the book, we don't know what the media for the elementary particles are or if there even are any. Our intuition based on waves that we see in everyday life tell us that there must be some medium through which the wave can propagate, but thus far we have found no such medium for waves such as light.

We just know there are measurable properties that we can measure across points in space and we have created mathematical objects (fields) to represent this. From there, we can construct theories and make predictions based on these models.

I think that’s a tricky question. In one sense, they aren’t made of anything since they are elementary fields. Meaning they don’t have constituent parts. But one could still argue that it’s relevant to say that they are of some kind of substance in a sense. The nature of that substance is the domain of Theories of Everything and some argue that the discussion becomes either purely mathematical or somewhat philosophical in nature, more so than a matter of physics anymore. For example, some argue that the fields are all made of math, so to speak, or likewise that their differences are like geometric variations on the same substrate.

They aren’t made of anything (other than numbers). Fields are currently the fundamental ontology. They are mathematical objects.

I always thought the fields are just the mathematical representation of the respective force carrier particles travelling through space. Such particles (the photon is certainly the most relevant for us) are having such a big size due to their statistical nature that the fill space even though their own size when probed is tiny.

Particles don't actually exist, however. They're excitations in various fields. A proton, for example, is actually a sea of three quarks of different "colors" that continually exchange energy (and only have potential positions) via gluons, and those quarks and gluons themselves aren't particles, but excitations in fields

So we have a duality of fields and particles. Likely it doesn't make sense to give one representation precedence over the other.

QFT doesn't have a duality of particles and waves, it explains both as excitations in underlying fields. So even the particle in a double slit experiment is just the collapsed wave function, but we experience it as a particle. So precedence in this case is that QFT is the underlying explanation.

Yeah did everything forget about the double slit experiment? Why are fields any more real than particles? Is the updated science now resolved on wave particle duality then?

It's more like, particles are how we experience collapsed wave functions, and both are manifestations of excitations in the underlying quantum field.

Last I checked the theory of wave function collapse is still unresolved, with competing explanations. We don't know the answer and should not talk like we pretend we do. Unless you are personally one of those scientists or researchers endorsing one such theory, and even then you have to be clean and transparent and admit the matter is not settled by consensus yet.

What I'm describing is physics 102 and non-controversial. No one is pretending anything.

What you're referring to are competing interpretations for what it means when the superposition of eigenstates collapses into a single state, which we call wave function collapse. The most popular interpretation is the Copenhagen interpretation (observation causes collapse), and the second most probably the many worlds hypothesis (we only observe collapse due to being in one path among all real paths).

Quantum uncertainty doesn't mean you have to approach every topic going "ohh we just don't know! No one can be certain about anything! Leave this to the experts!" These are surface-level descriptions of basic quantum phenomena.

Afaik, the official answer is that they are made of nothing because they are fundamental. That's how scientists say "we don't know". But when a fridge magnet sticks to a fridge, something holds it there and it's not nothing. It's not photons either. It's the magnetic field itself, the one that's made of "nothing". Photons are like waves in the magnetic field "water", but water isn't made of waves. Equations of magnetic field have a curious similarity with the flow of something in 4 dimensions (I mean that kaluza-klein theory), but nobody has managed to make that theory work yet, so there must be something else. Iirc, Einstein himself spent half of his life on this idea, but didn't succeed.