Toy model for a relational formulation of quantum theory

TitleToy model for a relational formulation of quantum theory
Publication TypeJournal Article
Year of Publication2006
AuthorsPoulin, D
JournalInt. J. of Theor. Phys.
KeywordsFoundations, Gravity, Measurement, Quantum Theory, Reference frame
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 {\em 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 level. 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 semi-classical limit to derive the fully relational quantum theory) may offer interesting insights on the low energy limit of quantum gravity.
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