The limitations of inertial frame spacetime functionalism

Abstract

For Knox, 'spacetime' is to be defined functionally, as that which picks out a structure of local inertial frames. Assuming that Knox is motivated to construct this functional definition of spacetime on the grounds that it appears to identify that structure which plays the operational role of spacetime-i.e., that structure which is actually surveyed by physical rods and clocks built from matter fields-we identify in this paper important limitations of her approach: these limitations are based upon the fact that there is a gap between inertial frame structure and that which is operationally significant in the above sense. We present five concrete cases in which these two notions come apart, before considering various ways in which Knox's spacetime functionalism might be amended in light of these issues.

Relativity without miracles

“…8 See the development of this argument in [40], section 4.1 9 Claims like this one, pertaining to the original formulation of the DA, might be too crude: the chronogeometrical significance of the metric must presuppose, beyond the SEP, the existence of stable rods and clocks. According to this, the structure recovered through the equivalence principle is what [41] call theoretical spacetime, distinct from the operational spacetime that would presuppose the existence of stable rod and clocks. 10 The question and its answer here refer to theoretical reasons; without any doubt, the miracles view admits empirical reasons for the validity of SEP. 11 Further clarification about the relation of minimal coupling and SEP seems necessary.…”

“…If something like this is assumed, the miracle claims would regard the spatiotemporal character of spacetime as a brute unexplained feature in the DA. For more on the relation between the operational perspective of the DA and its relations to Knox' spacetime functionalism see [41] Principle of Equivalence. Inertia and gravity are phenomena identical in nature.…”

“…See [17] for a precise characterisation of the notion of approximate local spacetime symmetry. 41 A Killing field λ with respect a metric g ab is defined as a smooth vector field for which the Lie derivative of g ab associated with it vanishes: £ λ g ab = 0. The (local) flow maps determined by the Killing fields are isometries of the metric.…”

“…See[26], p. 348 16. According to Read and Menon's distinction[41] mentioned above this would be theoretical (not operational) spacetime 17. This can be understood as an idealisation of the notion of force free-body (a body for which interactions are turned off) which incorporates, first, the possibility of universal interactions like gravity and also a field theoretical formulation.…”

In Search of the Holy Grail: How to Reduce the Second Law of Thermodynamics

“…But in the case of spacetime, there is controversy over the correct functional role, cf. Knox (2019), Baker (2018), Read and Menon (2019).…”