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?"