%0 Generic %1 poulin2005model %A Poulin, David %D 2005 %K Relational mechanics quantum %R 10.1007/s10773-006-9052-0 %T Toy Model for a Relational Formulation of Quantum Theory %U http://arxiv.org/abs/quant-ph/0505081 %X In the absence of an external frame of reference 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 to demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental level, from which the original "non-relational" theory emerges in a semi-classical limit. According to this thesis, the non-relational theory is therefore an approximation of the fundamental relational theory. We propose four simple rules that can be used to translate an örthodox" quantum mechanical description into a relational description, independent of an external spacial reference frame or clock. The techniques used to construct these relational theories are motivated by a Bayesian approach to quantum mechanics, and rely 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, there is no need for a "collapse of the wave packet" in our model: the probability interpretation is only 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.

@misc{poulin2005model, abstract = {In the absence of an external frame of reference 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 to demonstrate using elementary quantum theory how any quantum mechanical experiment admits a purely relational description at a fundamental level, from which the original "non-relational" theory emerges in a semi-classical limit. According to this thesis, the non-relational theory is therefore an approximation of the fundamental relational theory. We propose four simple rules that can be used to translate an "orthodox" quantum mechanical description into a relational description, independent of an external spacial reference frame or clock. The techniques used to construct these relational theories are motivated by a Bayesian approach to quantum mechanics, and rely 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, there is no need for a "collapse of the wave packet" in our model: the probability interpretation is only 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.}, added-at = {2019-08-02T10:36:46.000+0200}, author = {Poulin, David}, biburl = {https://www.bibsonomy.org/bibtex/2b38f8cb506c51b16bfb9c23d7d8896c0/guiguisat}, description = {Toy Model for a Relational Formulation of Quantum Theory}, doi = {10.1007/s10773-006-9052-0}, interhash = {634b84f8db5d7d5a6a729a33a5f76e9d}, intrahash = {b38f8cb506c51b16bfb9c23d7d8896c0}, keywords = {Relational mechanics quantum}, note = {cite arxiv:quant-ph/0505081Comment: References added, extended discussion}, timestamp = {2019-08-02T10:36:46.000+0200}, title = {Toy Model for a Relational Formulation of Quantum Theory}, url = {http://arxiv.org/abs/quant-ph/0505081}, year = 2005 }