Generalising Unitary Time Evolution

Abstract

Abstract. In this third Quantum Interaction (QI) meeting it is time to examine our failures. One of the weakest elements of QI as a field, arises in its continuing lack of models displaying proper evolutionary dynamics. This paper presents an overview of the modern generalised approach to the derivation of time evolution equations in physics, showing how the notion of symmetry is essential to the extraction of operators in quantum theory. The form that symmetry might take in non-physical models is explored, with a number of viable avenues identified. Quantum Interactions are not EvolvingAs a field Quantum Interaction (QI) has progressed well in recent years [10,8]. It is clear that something is to be gained from applying the quantum formalism to the description of systems not generally considered physical [1,4,14,16,23]. However, despite this initial promise, there are many elements of quantum theory that have yet to be properly applied within this framework. Perhaps most notably, it is clear that time evolution has yet to be properly implemented (i.e. derived) for any of these systems. This is a very significant weakness. Without an appreciation of how an entangled quantum-like system might come about it becomes rather difficult to justify the quantum collapse model that is very often leveraged in the quantum interaction community. This paper will explore the notion of time evolution in standard quantum theory (QT), sketching out the modern approach to extracting Hamiltonians and unitary operators. We shall then utilise this approach to suggest some interesting avenues that might be pursued in the future extraction of a fully-fledged quantum-like theory capable of evolving, entangling and then collapsing.There is no apriori reason to expect that the Schrödinger equation is the only form of time evolution equation available in a quantum-like theory. This paper will discuss the reasons lying behind this, and propose ways in which the QI community might work to establish a new time dynamics, or to prove that the application of Schrödinger dynamics is appropriate. Even if some justification can be found for the application of the Schrödinger equation beyond the description of physical systems, it is highly unlikely that the common techniques used in the extraction of a quantum description will work. This is because the standard approach to constructing a quantum theory generally involves finding a 2 Kirsty Kitto, Peter Bruza, and Laurianne Sitbon

Extracting Spooky-Activation-at-a-Distance from Considerations of Entanglement

“…Given the large amount of data collected about word association norms [21] we might expect that experiments can be performed that might distinguish between the varying predictions of the different models, and work is underway to generate results here. A physically and cognitively motivated time evolution equation capable of generating the Bell-type state (10) is essential before we can consider this model to be truly quantum(like) and initial ruminations about how this might be achieved are presented in [9].…”

“…This seemingly innocuous state is one of the so-called Bell states in QT. It is impossible to write as a product state, thus it differs markedly from (9). The fact that entangled systems cannot be expressed as a product of the component states makes them non-separable.…”

Spectral Composition of Semantic Spaces

“…A related aspect of our approach is the quest to formalize corpus dynamics, in line with the recommendations spelled out by [16], also keeping the possible differences between language and quantum interaction systems in mind. We depart from the assumption that two types of dynamics characterize any text document collection: external forces leading to its expansion, and the inherent quality in terms and their agglomerates called their meaning.…”