The presence of symmetries in physical theories implies a pernicious form of underdetermination. In order to avoid this theoretical vice, philosophers often espouse a principle called Leibniz Equivalence, which states that symmetry-related models represent the same state of affairs. Moreover, philosophers have claimed that the existence of non-trivial symmetries motivates us to accept the Invariance Principle, which states that quantities that vary under a theory’s symmetries aren’t physically real. Leibniz Equivalence and the Invariance Principle are often seen as part of the same package. I argue that this is a mistake: Leibniz Equivalence and the Invariance Principle are orthogonal to each other. This means that it is possible to hold that symmetry-related models represent the same state of affairs whilst having a realist attitude towards variant quantities. Various arguments have been presented in favour of the Invariance Principle: a rejection of the Invariance Principle is inter alia supposed to cause indeterminism, undetectability or failure of reference. I respond that these arguments at best support Leibniz Equivalence.

Shifts are a well-known feature of the literature on spacetime symmetries. Recently, discussions have focused on so-called dynamic shifts, which by analogy with static and kinematic shifts enact arbitrary linear accelerations of all matter (as well as a change in the gravitational potential). But in mathematical formulations of these shifts, the analogy breaks down: while static and kinematic shift act on the matter field, the dynamic shift acts on spacetime structure instead. I formulate a different, ‘active’ version of the dynamic shift which does act on matter, and analyse the consequences of this reformulation for Newton-Cartan Theory and Maxwell Gravitation.

It is now standard to interpret symmetry-related models of physical theories as representing the same state of affairs. Recently, a debate has sprung up around the question when this interpretational move is warranted. In particular, Moller-Nielsen (2017) has argued that one is only allowed to interpret symmetry-related models as physically equivalent when one has a characterisation of their common content. I disambiguate two versions of this claim. On the first, a perspicuous interpretation is required: an account of the models' common ontology. On the second, stricter, version of this claim, a perspicuous formalism is required in addition: one whose mathematical structures 'intrinsically' represent the physical world, in the sense of Field (1980). Using Dewar (2019)'s distinction between internal and external sophistication as a case study, I argue that the second requirement is decisive. This clarifies the conditions under which it is warranted to interpret symmetry-related models as physically equivalent.Acknowledgements: I would like to thank Marta Bielińska, Adam Caulton, Neil Dewar, Henrique Gomes, Oliver Pooley and James Read for their insightful comments and discussions. I would also like to thank an audience at the Philosophy of Physics Graduate Lunch Seminar in Oxford and a helpful anonymous reviewer.

In this journal, Middleton and Murgueitio Ramírez argue that absolute velocity is measurable, contrary to the received wisdom. Specifically, they claim that 'there exists at least one reasonable analysis of measurement according to which the speedometer in [a world called 'the Basic World'] measures the absolute velocity of the car'. In this note I critically respond to this claim: the analysis of measurement that Middleton and Murgueitio Ramírez propose is neither reasonable, nor does it entail that absolute velocities are measurable.

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