If it is not the sharing of "information" regarding each other's status, then how is one particle instantly effected by a measurement made on its entangled partner?
It isn't. It can be proven with the No-communication Theorem that no manipulation of the probabilities of a particle in an entangled pair can affect the probabilities of its partner as long as they are separated from one another. Entanglement must be created locally and then the interference effects between them can only be observed locally.
When you measure one of the entangled particles, you force it into a definite state. Due to their entanglement, the other particle’s state is instantly determined as well.
This is an assumption about the ontology of the mathematics, and the confusion you are having disappears if you drop this assumption.
Let's say we want to have a rather simple ontology and not posit the existence of anything we do not observe. If we measure the position of a particle, its momentum becomes uncertain due to the uncertainty principle, but more than this, if we are sticking with a simple ontology, we would have to say the particle really does not
have a momentum anymore. When we measure it and see it does have a momentum, then it would not have a position anymore.
Particles thus have real properties but not all those properties at all times. They sort of pass in and out of reality, become indeterminate and determinate under different conditions. So the question then becomes, what mathematical description actually corresponds to the ontology of the system, i.e. a real-world state, and which does not correspond to reality?
In the EPR paper, they put forward an assumption that absolute certainty corresponds to reality. That means if you cannot predict the state of a system with certainty, then that state has no element of reality, but if you can predict it with certainty, then it has an element of reality. Thus, the EPR paper concludes that if you have two systems with states that you can only describe probabilistically in a superposition of states, but they are entangled with one another, then if you measure one, you must be simulateously bringing both into reality at the same time, even if they are light years apart.
However, if we just define our ontology differently, then this problem goes away.
In contextual realist philosophy, reality is only
realized in context. As I interpret it, context is kind of like a reference frame whenever two systems interact, but specifically described from the reference frame of one of the systems partaking in the interaction. An "interaction" only makes sense from a third-person point of view, because you can only see two objects interacting if you are sitting outside of both of them. For example, if I look at a tree, you can describe the tree interacting with my eyeballs through reflecting light, but I cannot see this interaction because I cannot see my own eyeball, I
just see the tree.
Whatever system you use as the basis of your coordinate system thus effectively disappears from the picture. It's kind of like taring a scale. You set the beaker's mass to the center of the coordinate system, and then you can measure things as if it is not there. From the reference frame of a particular system, the system that is being used as the basis of that frame always would have all of its properties zero and would be unchanging, and thus effectively would not exist in the picture.
If it does not exist in the picture, then if two objects interact and you describe it from the reference frame of one of those two objects, then there could no longer even be an "interaction" as there would only be a single object in the picture, and a single object cannot interact with anything. Rather, what happens when we describe reality in this way we end up describing what properties of that one object are
realized in that
context. A third-party could describe the tree as interacting with my eyeballs, but from my own perspective, I would just describe the tree itself as something that is realized in front of me, in my own context.
Hence, for contextual realist philosophy, we would define the ontology a bit differently. The properties of systems are not realized just because certainty as to their values have reached 100%. They are only realized (1) if one physical system actually interacts with another, and (2) from the context of those two systems. The #2 point is also important because it means that if I interact with a system, from my context, the properties will be realized for me, but they are not realized for you. This is why you can have a "Wigner's friend" scenario whereby the properties are realized for one observer, but the other observer still has to describe it in a superposition of states.
If we adopt this different understanding of ontology, then the supposed nonlocal effects you speak of disappear. If you interact with a particle locally and update your prediction as to what the other one would be to 100%, that does not in any way suggest that both the local particle and the distant particle have both been simulateously realized. Rather, only the local particle has been realized, and you can not merely
predict what the distant particle would be
if you were to travel there yourself and observe it. It is ultimately still a
prediction for a
future event that has
yet to be realized.
In order for it to be realized, you would have to travel there locally yourself.
This is also true for
all physical systems. There is nothing special about human conscious observers in this picture. The fact our descriptions of a system may differ from different contexts is not due to the fact that we are observers, but in spite of it. It is due to the fact variable properties of particles are just contextual, kind of like how two different observers can observe the velocity of a train to be different, maybe because one is sitting on the ground and another is driving alongside it in a car. Quantum mechanics has nothing more to do with the fundamental nature of consciousness or observers any more than Galilean relativity does. Quantum theory is best understood as a
context-dependent theory rather than as an
observer-dependent theory.
