Richard Feynman once said that nobody understands quantum mechanics. More than 100 years since it was first proposed as a theory, Feynman's remark still holds. One of the most puzzling aspects of quantum mechanics is its apparent incompatibility with the assumption that an objective reality exists independent of an observer. One can produce quantum states in the laboratory whose joint probability distribution for all measured quantities does not exist. This means that if we assume that an unmeasured observable exists, we arrive at absurd conclusions. Thus, it is often said that measuring a quantity does not reveal its value but creates it.
The nonexistence of joint probability distributions for quantum observables is even more puzzling if we consider states composed of particles that are far apart from each other. In the '30s, Albert Einstein, Boris Podolski, and Nathan Rosen (EPR) created a famous thought experiment. In their experiment, two particles are prepared in an entangled quantum state and then moved far away from each other. This state is such that when we measure a particle's property, we immediately know it for the other particle. Since nothing can be immediate, some "element of reality" common to the particles past had to be responsible for the observed quantities' value when they were far apart. However, later on, those "elements of reality" proposed by EPR were shown to be incompatible with experimental results. In other words, empirical evidence suggests that quantum systems are nonseparable; there are systems whose properties cannot be considered separately. Therefore, data seems to restrict our metaphysical worldviews. We cannot think of particles as individually separated objects; even when they are far apart, they still belong to a single whole, the quantum state.
There are many questions raised by quantum nonseparability. How can we tell whether a quantum system is separable or not? Does separability imply that quantum systems can be holistic? Can we create nonseparable systems that are classically correlated? Are there other ways in which quantum mechanics restrict our worldviews? How does it relate to the structure of spacetime? Can we find situations where we could distinguish ontological (non-local) interpretations from quantum mechanics' standard interpretation? What does quantum mechanics tell us about the ontology of our world? Does quantum ontology present problems to emerging properties, such as the mind? I approach these questions in two complementary ways.
In the first approach, I study nonlocality and contextuality in quantum mechanics using extended probability theory. When examining whether a quantum state is separable or not, one might check for the existence of the joint probability instead of checking for hidden variables, as both are, in some sense, equivalent. But can extended probability theories offer some insights into quantum mechanics that standard probabilities do not?
In the second approach, in collaboration with Décio Krause and Federico Holik, I use quasi-set theory to describe indistinguishability and non-identity in a quantum ontology. Our main question is whether the lack of identity for quantum particles leads to new ways of thinking about quantum contextuality and nonlocality. For instance, if we assume quantum particles have no identity, we can show that Kochen-Specker-type contradictions are not entailed. The same may hold true for nonlocality, but this still needs to be investigated.
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