How do particles know how to interact with other particles / fields? I attempted to ask this question previously here: How does the whole universe agree on the laws of physics? [duplicate]
 but I didn't make myself clear, and it ended in confusion. I will try again.
If we take two particles of the same type, say two electrons, we find that they behave the same way. They interact with other particles and fields in the same way. They are fungible. As far as we know, this is true (except perhaps very far away in time or space, but let's just talk locally for now).
Somehow they both know to behave in the same way. Now, I don't mean to imply they have sentience, but somehow they do behave the same.
We could say that these particles are made of something, quarks for example, and it is these particles that give our two protons their common behaviour, in the same way that two mechanical watches behave the same because they are made from the same type of parts. But that just moves the question down to the quarks. How do two of the same type of quark 'agree' on their behaviours.
And we can keep going down. If particles are just quanta of the fundamental fields, well, what makes a field have the same properties in two places?
Option 1: It's geometry
Perhaps there's simply no choice about these behaviours, and they are simply manifestations of geometry. The the same way that, presumably, Pi couldn't be different in different universes, perhaps there can't be universes with different laws of physics, and particles are manifestations of a pattern with a limited number of arrangements.
Option 2: The laws were baked in when the Big Bang happened
If the fields were created in the big bang, then became stretched out with the universe during inflation and since, then they have carried with them the 'information' (settings? configuration? memory?) of their properties. So, where is this information stored.
Option 3: Something else?

A note: It was hard to ask this question without using words like 'agree', 'information', 'stored'. Surely the fundamental fields don't have a configuration file with their parameters stored in YAML format, but I'm not sure what other terms to use.
Update: While I tried to make the question as clear as I could, there was still some room to misunderstand it, so I will try to clarify further:
Physics does not answer why questions: Firstly, yes it does. See for example: Why do diamonds shine?, Why do stickers curl?, Why aren't orbitals symmetric?, and so on. In fact, I thought that was one of the main reasons we did science, so we could answer 'why?' questions.
Here is a 'why?' question which is very similar to mine, and I'm sure you'll agree it's the kind of question which physics is able to address: Why is the cosmic microwave background radiation so smooth? And it has an answer: because of the inflationary period during the early universe.
So let me ask my question in a similar way: Why are the laws of physics so smooth across the universe?
I hope you'll agree that physics should consider this matter to be within its domain, even if the answer is: "we don't know and could never know".
Secondly: I actually didn't ask a why question. The question was: "How do particles know how to interact with other particles / fields?"
 A: 
How do particles know how to interact with other particles / fields ?

Interactions depend on the properties of particles. How do we know that, for example, the charge on an electron never changes ? This is an empirical fact - we have never seen this happen. How do we know that all electrons have the same charge ? Once again, experimental evidence.
Could we discover a particle that was identical to an electron except that it had a different charge ? Yes, but then it wouldn’t be an electron, by definition. A particle identical to an electron but with a positive charge is called a positron. A particle identical to an electron but with only half the charge has never been observed, but it could conceivably be discovered (although this would imply significant modifications to the Standard Model).
Could we discover a new fundamental force that interacts with some electrons differently from others - so that we could, say, distinguish pink electrons from blue electrons ? Again, yes, conceivably, but the Standard Model would have to be changed.
Is it possible to imagine a universe in which there are no fixed laws ? One in which the charge on an electron halves on alternate Tuesdays and the speed of light doubles whenever it rains and the mass of a proton changes if you stand on your head ? Yes, but it is unlikely that anything as complex as life could develop in such a chaotic universe.
The bottom line is that our brains seem to be conditioned to look for the sorts of regular patterns that do indeed occur in the external world. Throughout human history we have found more and more of these patterns, and extended them to wider and wider arenas. Since our brains are part of the universe that we are observing, this is probably not coincidence.
A: 
If particles are just quanta of the fundamental fields, well, what makes a field have the same properties in two places?

Physics is the discipline that models observations and measurements with mathematics so that it can describe data, and so as to also have a predictive tool for future data. Physics mathematical models need extra axioms to the mathematical ones, in order to pick up those mathematical solutions that describe the data.
Measurements means the axiomatically defined variables: Time, meter, second, mass.
To attain this, laws, principles,postulates are imposed as extra axioms to the mathematical theory, and in the present model of particle physics the particles in the table  are assumed axiomatically.
The mathematics make the field have the same properties in two places, so as to agree with the predictions of the standard model.
Physics does not answer "why" questions, physics theories show how the theory can describe data and future data.
Why questions can be asked, and they can be answered within the mathematical model, but then new why questions arise , because new why's arise if  one wants to dig deeper.
For example, the mathematical planetary model could not describe the spectra of  atoms, and a new axiomatic model was proposed by Bohr, quantizing the angular momentum: Why do electrons not fall on the nucleus? because of the angular momentum axiom. The quantum mechanical theory has more removed axioms, the answer to this  why becomes because there are bound states, and then "why bound states"? "because they fit the data" and the axioms of the theory were chosen so that "the mathematics fit the data".
Most probably new data will modify the model, and new theories may embed the model* and make new provable predictions and a new standard model, but the logic is the same, the mathematical model starts with extra axioms, fits the data and predicts new.
