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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A field is very similar to the concept of a function. You give it an input and it gives you an output. The input with a field is a point in space and time, the output could be a number, it could be a vector, or other more complicated things. The field itself is a mathematical abstraction. It is the math we’re using to describes some physical reality.
For example let’s look at an electric field. Charge particles feel an attractive or repulsive force between themselves proportional to the product of their charges and inversely proportional to the distance between them. So when we have a charged particle and we take some point in space and time it’s possible to come up with a number at any given point that represents the force another charged particle would feel at that point.
There’s nothing actually at that point. The electric force doesn’t exist until another particle actually enters the system. The field represents what a particle would feel if it was there. So the field is just a pure mathematical concept.
The field isn’t a real entity, but it does describe real behavior.
And just like if you have a function that describes some behavior of a system you can calculate properties of that system from it. You can do the same with fields. Probably the simplest example would be Gauss’s flux theorem. By finding the flux on an electric field over a closed surface (basically a surface integral of the electric field) you get the charge contained within that surface. The field isn’t real, but the charge is.
So the field is just math, but it’s math that describes real information about your system.
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.
Fields are pretty much the bedrock of the universe. If the universe is “made” of anything, it’s fields and spacetime. One way you can think of them is as a fluid that suffuses the entire universe. All the fields are everywhere.
When you keep asking the question of what something is made of you get smaller and smaller until you reach an elementary particle, like the electron or quarks.
These particles are the result of energy disturbing the field responsible for that particle. So if you have energy in the electron field, it produces an electron at the location of the energy.
You’ve probably heard that energy can’t be destroyed, but what does that mean? If you take an electron and a positron (anti-matter electron equivalent) and push them together then they annihilate each other and disappear with a burst of light(which is made of photons).
This is because you took two disturbances in the electron field with opposite charge and put them in the same place which pushed the energy they were made of out of the electron field and into the electromagnetic field which created the photons you saw appear when the electron and positron vanished.
So the energy that was the electron and positron got converted into photons because you changed the field that the energy was in.
Put simply fields are where particles come from, and to make particles you need to put energy into the relevant field.
Fields, at their most basic level, tell us what will happen in a region of space. In an electric field, we know that an electron will follow some specific set of behaviors that we map out onto what we call “electric field”. Neither the field, nor the electron, do anything to explain what is the *actual* mechanism or makeup of the universe. Fields answer “what will happen here” not “why will happen here”.
Some people will argue that there is no difference and the math is ultimately the “why” and the “what”
Why can’t fields be both real and mathematical abstractions? They refer to the same idea.
Your question has already been answered, but, just to fill-in two of the definitions a bit, you have already probably seen the way to calculate the gravitational force on an object of mass m as mg where g is the ‘gravitational acceleration’ of 10 m/s^2 , but the word ‘acceleration’ is wrong for a little technical reason that this holds true even if the object is sitting on a table. It is the Newton equation force=mass x acceleration, but there is no acceleration.
Hence one can make a tiny philosophical transformation and say, g is the acceleration which the object *would have* experienced if we’d removed the table.
If you take account of how the object could be anywhere on the earth, you obtain that g is not a scalar, rather, a vector at each point of space, and if we want it to be a force vector, it is defined to be the hypothetical acceleration vector of any object if it had been released, times its mass, and it is a bit strange that some of the comments say ‘we will never know what it is.’ I mean, I just gave the definition, but perhaps the point is that a mathematical definition does not ‘explain’ what it is.
That is called a ‘vector-field’ and mathematicians have — for many years — over time removed the need of having an ambient vector space like R^3 for this to make sense. There is a rigorous definition of a ‘vector-field’ on any manifold, and it is defined to be ‘a section of the tangent bundle’. Moreover the ‘tangent bunde’ has a nice coordinate-free definition for any manifold as does the `tangent space at a point’ https://en.wikipedia.org/wiki/Tangent_space#Definition_via_derivations
The reason for my replying was the dissonance in my mind between one person saying “consider this space of derivations” and giving a complete definition of it, and another person saying “But we will never know what it is.”
The theory of vector-fields, symmetry groups, Lie algebras etc is also the mathematical language to talk about ordinary differential equations.
It is most natural to visualize a vector-field as being a velocity vector-field, and this is always possible to do, though one has to keep the intuitions a bit separate. If we visualize the gravitational field of the earth as a velocity vector-field, we’d imagine objects drifting down at constant speed.
TL;DR The reason for my replying was the dissonance in my mind between one person saying “consider this space of derivations” and giving a complete definition of it, and another person saying “But we will never know what it is.”
A field is the thing that carries a force — it’s absolutely real. Drop iron filings on a magnet and you’ll see the field in the pattern.
Very precise knowledge of fields and how they work — that’s how MRIs work so well
The answer will likely depend on what type of field specifically in physics.
In the case of vector fields used in E&M/Gravitational, it is purely a made up mathematical concept we use to describe the physical phenomenon of physics (measured in a labratory). We “invented” the idea of vector fields to describe physics behavior
Physicist here. Field is a physical quantity (whatever a quantity is) with their main feature to be spatially and temporarily extent. The values of the field (at some point and time) can be numbers (pressure in a pipe) or vectors (velocity in a pipe). Physics then describes how these field evolve and interact, to ultimately give something that can ne observed or measured (and ideally being useful).
What are waves on the ocean made of?
It isn’t water – the molecules of water that are in waves kind of scurry back and forth/up and down, while the shape of a wave can move hundreds (even thousands) of miles without stopping or slowing down. If you were to dump a cup of dye into a wave while on a boat, that dye doesn’t get stuck in a wave to be carried hundreds of miles, but rather the dye disperses locally, roughly outward from where it was dropped. Waves that start in the middle of the Pacific don’t carry those same water molecules from Hawaii to Japan, but the shape/energy of the wave can travel that far. When a boat hits a wave, it doesn’t get “stuck” in the wave, to be carried hundreds of miles, but rather a boat can bob up or down as the waves go on beneath them.
Fields are the waves – in this case, we can visually see the value (height) of the wave going up or down on the surface of the water, it uses water as the carrier medium, but the wave itself is more like the energy that is being carried through the water, not the water itself.
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