Progress

  • Major theoretical work on internon theory has now been completed. 
  • Internon theory is a new theory of quantum state evolution
    • Not an interpretation
    • Extends the measurement and unitary postulates and unifies them within a single consistent theoretical framework.
    • Methodology completed for determining the regimes of unitary and non-unitary evolution
    • Several physical examples completed
  • Publication is now proceeding
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Publications

Current plans for documenting internon theory

Papers Completed

Complementary Relationships between Entanglement and Measurement

Complementary relationships exist among interference properties of particles such as pattern visibility, predictability, and distinguishability. Additionally relationships between average information gain Ḡ and measurement disturbance F for entangled spin pairs are well established. This article examines whether a similar complementary relationship exists between entanglement and measurement. For qubit systems, both measurements on a single system and measurements on a bipartite system are considered in regard to entanglement. It is proven that Ē + D ≤ 1 holds, where Ē is the average entanglement after a measurement is made and D is a measure of the measurement disturbance of a single measurement. Assuming measurements on a bipartite system shared by Alice and Bob, it is shown that Ē + Ḡ ≤ 1, where Ḡ is the maximum average information gain that Bob can obtain regarding Alice’s result. These results are generalized to arbitrary initial mixed states and non-Hermitian operators and direct results are found for the case of maximally entangled initial states. We conclude that the amount of disturbance and average information gain one can achieve is strictly limited by entanglement.

Papers in Planning

Discrimination of Unitary Evolution and the Measurement Process: Theory and Implications

In von Neumann’s theory of quantum mechanics, two postulates exist—a measurement postulate by which the quantum state evolution changes by a discontinuous and non-deterministic process and a unitary postulate by which the quantum state evolution changes by a continuous and deterministic process. These two disparate processes form the basis of the quantum measurement problem. It is found that von Neumann’s two postulates perhaps are necessary, but cannot be considered to be sufficient to provide a complete theory. Furthermore, it is seen that the quantum measurement problem arises naturally from the ability, within the same theory, to discriminate these two processes. This is shown to lead to the incompleteness of quantum mechanics. A variety of test configurations are discussed which are capable of distinguishing whether the state evolution is occurring via unitary evolution or via measurement, a Unitary versus Measurement Discrimination Test (UMDT). A formal investigation of the theory of the discrimination of these two processes is undertaken and results are shown that the UMDT must lack commutation with the effects of the hypothesized measurement. The practical utility of UMDTs is demonstrated via several examples. Furthermore, von Neumann’s consistency argument of quantum mechanics is examined. It is shown that von Neumann utilized an assumption in his proof that limits the class of applicable Hamiltonians. It is proven that the constrained Hamiltonian class always results in commutivity of states throughout the chain. Von Neumann left out non-commuting processes in order to obtain his consistency result, which exposes a major flaw in that they are necessary for UMDTs.

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