Chapter 4: Minkowski Space-Time: A Glorious Non-Entity

Mass–Energy–Momentum: Only there Because of Spacetime?

“…The last section has discussed how mass-energy-momentum density tensors can be derived in a Lagrangian framework, and that indeed this is only 33 In the 'constructive' approach towards special relativity, it has been argued that the metric should not be seen as an entity in its own right, but as merely encoding certain properties of the matter fields; see Brown [2005] and Brown and Pooley [2004] for advocacy, and Norton [2008] and Janssen [2007] for criticism of this position. An argument in support is that an unsatisfactory element of special relativity is believed to be that the metric seems to violate the action-reaction principle by acting without being acted upon: a feature we get rid of if the metric is conceived as encoding properties of the fully interacting matter fields.…”

The Dynamical Approach as Practical Geometry

“…Brown has assured me that (Brown and Pooley 2006) From this we see that Pooley's reminder above (p.5) is apt: the dynamical approach to special relativity needn't account for all geometrical structure by an appeal to the symmetries of the dynamical laws, and indeed Brown seems to have had in mind a primitive sub-metrical structure all along. The dynamical approach's arrow of explanation from dynamics to geometry can then be understood along the lines above: as an application of Einstein's practical geometry to a topological (or differentiable) space of field values, which finds Minkowski geometry to supervene upon the symmetries of the best-system dynamical laws.…”

Why Constructive Relativity Fails

“…Brown asserts (p. 141)"…the space-time structures [of Newtonian theory and special relativity] … are not real entities in their own right at all" and (p. 142); that the 4-connection of these theories is "a codification of certain key aspects of the behaviour of particles and fields"; and (p. 100) that "I see the absolute geometrical structures of Minkowski space-time as parasitic on the relativistic properties of the dynamical matter fields." These sentiments are captured more vividly in the earlier slogan of Brown and Pooley (2004) of Minkowski spacetime as a "glorious non-entity." This would make…”