Basic Concepts and Their Interpretation

Abstract

The superposition principle forms the most fundamental kinematical concept of quantum theory. Its universality seems to have first been postulated by Dirac as part of the definition of his "ket-vectors", which he proposed as a complete 1 and general concept to characterize quantum states regardless of any basis of representation. They were later recognized by von Neumann as forming an abstract Hilbert space. The inner product (also needed to define a Hilbert space, and formally indicated by the distinction between "bra" and "ket" vectors) is not part of the kinematics proper, but required for the probability interpretation, which may be regarded as dynamics (as will be discussed). The third Hilbert space axiom (closure with respect to Cauchy series) is merely mathematically convenient, since one can never decide empirically whether the number of linearly independent physical states is infinite in reality, or just very large.According to this kinematical superposition principle, any two physical states, |1 and |2 , whatever their meaning, can be superposed in the form c 1 |1 +c 2 |2 , with complex numbers c 1 and c 2 , to form a new physical state (to be be distinguished from a state of information). By induction, the principle can be applied to more than two, and even an infinite number, of states, and appropriately generalized to apply to a continuum of states. After postulating the linear Schrödinger equation in a general form, one may furthermore

A “Potency-Act” Interpretation of Quantum Physics

“…Interactions of the system with the environment and the apparatus appear both as the "causal agent" determining the collapse from coherence of the wave function. Such interaction, which may be even "non-local", is recognized as the physical basis of entanglement [10].…”

Subsystems and time in quantum mechanics

“…In the early days of quantum mechanics, Schrödinger used it in an attempt to interpret particles as stable wave packets [134,135]. More recently, its importance for decoherence theory has been repeatedly emphasized by Zeh [68,[148][149][150][151][152][153][154][155], and the basic idea has been developed extensively by Zurek under such names as the predictability sieve [156,157], einselection [69,158,159], the existential interpretation [156,158,159], and quantum Darwinism [159,160].…”

“…An answer to this objection can be found in the growing consensus [32,[61][62][63][64][65][66][67][68][69][70][71][72][73][74][75] that most (if not all) superselection rules are pragmatic expressions of practical limitations on experimental capabilities rather than fundamental laws of nature. This suggests that, at the level of fundamental theory, the superposition principle should be taken seriously, not lightly brushed aside [154].…”

The Problem With the "Measurement Problem"

“…Everett's Many-World interpretation argues that the collapse never occurs and there is no measurement problem 4 . Likewise, several other theories have been presented, such as De Broglie-Bohm theory 5 , Ghiradi-Rimini-Weber theory 6,7 and Quantum Decoherence phenomena 8,9 .…”