Relational time for systems of oscillators

Using an elementary example based on two simple harmonic oscillators, we show how a relational time may be defined that leads to an approximate Schrodinger dynamics for subsystems, with corrections leading to an intrinsic decoherence in the energy eigenstates of the subsystem.

Toy model for a relational formulation of quantum theory

In the absence of an external frame of reference-i.e., in background independent theories such as general relativity-physical degrees of freedom must describe relations between systems. Using a simple model, we investigate how such a relational quantum theory naturally arises by promoting reference systems to the status of dynamical entities. Our goal is twofold. First, we demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental. Second, we describe how the original non-relational theory approximately emerges from the fully relational theory when reference systems become semi-classical. Our technique is motivated by a Bayesian approach to quantum mechanics, and relies on the noiseless subsystem method of quantum information science used to protect quantum states against undesired noise. The relational theory naturally predicts a fundamental decoherence mechanism, so an arrow of time emerges from a time-symmetric theory. Moreover, our model circumvents the problem of the collapse of the wave packet as the probability interpretation is only ever applied to diagonal density operators. Finally, the physical states of the relational theory can be described in terms of spin networks introduced by Penrose as a combinatorial description of geometry, and widely studied in the loop formulation of quantum gravity. Thus, our simple bottom-up approach (starting from the semiclassical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.

Developing relational navigation to effectively understand software

Effective comprehension of complex software systems requires understanding of both the individual documents that represent software and the complex relationships that exist within and between documents. Relationships of all kinds play a vital role in a software engineer's comprehension of, and navigation within and between, software documents. User-determined relationships have the additional role of enabling the engineer to create and maintain relational documentation that cannot be generated by tools or derived from other relationships. We argue that for a software development environment to effectively support the understanding of complex software systems, relational navigation must be supported at both the document-focused (intra-document) and relation-focused (inter-document) levels. The need for a relation-focused approach is highlighted by an evaluation of an existing document-focused relational interface. We conclude with the requirements for a relation-focused approach to relational navigation. These requirements focus on the user's perspective when interacting with a collection of related documents. We define the requirements for a software development environment that effectively supports the understanding of the software documents and relationships that define a complex software system.