Abstract
We first show how the Temporal and Configurational Relationalism aspects of Background Independence can be implemented for field theories as well. We then consider the particular instance of Configurational Relationalism which occurs in general relativity. In this manner, we recover Wheeler’s much earlier Thin Sandwich formulation and recast it in Temporal Relationalism compatible form. Thus we arrive at full general relativity case of the current book’s main approach to the Problem of Time.
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Notes
- 1.
This book makes further systematic use of a number of further fonts to encode the role of the object in question (e.g. constraint or beable). If lost at any stage, consult the list of fonts in Appendix X.
- 2.
In fact, the first of these can be rewritten as \(\text{L}(t; \boldsymbol{Q}]\), which is a univariate functional due to \(\text{d}/\text{d} t\) acting on the \(\boldsymbol{Q}\) to form the velocities. However, this does not affect the types of derivatives that the theory has acting upon \(\text{L}\), so it does not disrupt the portmanteau.
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Anderson, E. (2017). Configurational Relationalism: Field Theory and GR’s Thin Sandwich. In: The Problem of Time. Fundamental Theories of Physics, vol 190. Springer, Cham. https://doi.org/10.1007/978-3-319-58848-3_18
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