Abstract
Rovelli’s “Why Gauge?” offers a parable to show that gauge-dependent quantities have a modal and relational physical significance. We subject the morals of this parable to philosophical scrutiny and argue that, while Rovelli’s main point stands, there are important disanalogies between his parable and Yang-Mills type gauge theory.
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Notes
For a review and analysis of the orthodox point of view, see chapters 3 and 4 of Healey (2007). See also Earman (2004) (and references therein), where the orthodox view it is taken as a starting point for posing a philosophical problem about the Higgs mechanism, i.e. ‘How does mass emerge from descriptive fluff?’
This latter point can be fully appreciated by considering the role that such transformations play in determining the existence of gauge anomalies.
Here Rovelli has in mind local gauge theories.
Since this is a brief note on Rovelli’s paper, we will restrict ourselves to discussing Yang-Mills theories with respect to Rovelli’s parable. A discussion of the case of General Relativity, on the other hand, would have to distinguish between two senses of ‘gauge’ that could be analyzed with respect to Rovelli’s parable: the broad sense, in which ‘diffeomorphism invariance’ is considered to be a ‘gauge symmetry’, and the narrow sense of ‘Yang-Mills type gauge theory’, according to which General Relativity is not generally considered to be a gauge theory (e.g. see Teh (2014) and Wallace (2014) for a review and analysis of this claim). Furthermore, let us note that a more comprehensive discussion of Rovelli’s concept of a ‘partial observable’ would include an analysis of his application of Dirac’s constrained Hamiltonian approach to ‘gauge’. For a discussion of the latter, see Earman (2003).
For two interpretations of Rovelli’s relationism – one semantic and one ontological – see Dorato (2013).
Here we follow Rovelli in adopting the following shorthand: x n is a vector in \(\mathbb {R}^{m}\), and (⋅)2 is defined by the Euclidean metric of \(\mathbb {R}^{m}\).
For a survey of the merits and implications of these two different ways of thinking about fields, see Section 5.3 of Belot’s ‘Geometry and Motion’, British Journal for the Philosophy of Science 51 (2000): 561–595.
I thank Carlo Rovelli for this example.
This can be done in a manner akin to Galileo’s Ship, see Teh (2015).
I thank an anonymous referee for raising this example and suggesting that I address it.
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Acknowledgments
The author thanks three anonymous referees, as well as Carlo Rovelli, David Wallace, and Jeremy Butterfield for helpful discussions about this article.
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This comment refers to the article available at: http://dx.doi.org/10.1007/s10701-013-9768-7.
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Teh, N.J. A Note on Rovelli’s ‘Why Gauge?’. Euro Jnl Phil Sci 5, 339–348 (2015). https://doi.org/10.1007/s13194-015-0109-x
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DOI: https://doi.org/10.1007/s13194-015-0109-x