A deterministic approach to quantum theory

Ralph Schiller

Asher Peres, Wojciech Hubert Zurek

Quantum theory has been criticized for not being deterministic and therefore not universal: it cannot completely describe a measurement aimed at verifying its predictions (although any given apparatus can be considered as a quantum system). We investigate the possible alternatives. Theories where the observed world is deterministic but the observer is not (whatever the reason for that) lead to Bell’s nonseparability theorem. If, on the other hand, the observer too is deterministic, the theory is not verifiable. It follows that quantum theory must be the logically preferred option. Its inability to completely describe the measurement process appears to be not a flaw of the theory but a logical necessity which is analogous to Gödel’s undecidability theorem.

Kristin Shrader‐Frechette

Earlier in this century, the physics community was wracked with a great debate between the determinists and the indeterminists over the status of quantum theory. Determinists like Einstein and Bohm argued that quantum theory would eventually be superseded by a deterministic theory having new state variables. Indeterminists like Heisenberg and Schrodinger, speaking for the Copenhagen School, disagreed. They maintained that the indeterminism in quantum theory was not merely a temporary setback, an epistemological problem to be overcome by means of a better scientific theory, but an accurate ontological representation of the matter.

Lev Vaidman A

Stephen Bruce Sontz

Juan Pablo Jorge, Federico Holik

In this work, we discuss the failure of the principle of truth functionality in the quantum formalism. By exploiting this failure, we import the formalism of N-matrix theory and non-deterministic semantics to the foundations of quantum mechanics. This is done by describing quantum states as particular valuations associated with infinite non-deterministic truth tables. This allows us to introduce a natural interpretation of quantum states in terms of a non-deterministic semantics. We also provide a similar construction for arbitrary probabilistic theories based in orthomodular lattices, allowing to study post-quantum models using logical techniques.