Interpretation Of Quantum State Research Articles

Propensity, Probability, and Quantum Theory

Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: (a) inferential probability, (b) ensemble probability, and (c) propensity. Class (a) is the basis of inductive logic; (b) deals with the frequencies of events in repeatable experiments; (c) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities (calculated from a state vector or density matrix) are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge.

REPLY TO: "ON COHEN'S CLASSICAL TELEPORTATION OF CLASSICAL STATES"

In response to a recently published protocol for classical teleportation of classical states [1], Hrasko [2] has made some remarks in connection with the impossibility of precise quantum teleportation if a classical mixture is used in place of the EPR state, and with regard to the epistemological interpretation of quantum states. The purpose of this note is to attempt to clarify these issues and their relevance for the argumentation presented in [1].

CLASSICAL TELEPORTATION OF CLASSICAL STATES

The standard quantum teleportation scheme is deconstructed, and those aspects of it that appear remarkable and "non-classical" are identified. An alternative teleportation scheme, involving only classical states and classical information, is then formulated, and it is shown that the classical scheme reproduces all of these remarkable aspects, despite the fact that they had seemed non-classical. This leads to a re-examination of quantum teleportation, which suggests that its significance depends on the interpretation of quantum states.

Statistical interpretation of the p-adic quantum field theory

A p-adic generalization of the frequency theory of probability is developed. Within the framework of this theory frequency meaning is imparted to probabilities belonging to the field of p-adic numbers. The Bargmann-Fock representation is constructed for the p-adic field theory. A frequency interpretation of quantum states in the Bargmann-Fock representation is proposed. The p-adic generalization is essentially an introduction of new quantum states which are meaningless from the point of view of the standard theory of probability based on Kolmogorov's axiomatics.