Leibniz stated: "Thus committed to maintaining that if there were nothing more to motion than relative change of position, then, since motion could be ascribed with equal right to, say, Train A or Train B."

Is there a version of this that can extended to fields? (I suspect any realistic field with it's equations of motion automatically satisfy this criteria?)

  • 3
    Field relationalism has been developed recently by Barbour and Bertotti, see Pooley, Relationism Rehabilitated? II, p.4 for a philosophical discussion:"since space itself is supposed not to exist, this extended object should not be characterised in terms of the spatial locations of the various field intensities. Rather it is to be characterised by the relative dispositions of the field intensities: the infinite number of facts about the relative distances and angles between particular values of φ that fully capture the pattern of field intensities."
    – Conifold
    Nov 20, 2021 at 10:46
  • 1
    But the more common "Humean" strategy has been eliminative. Since fields manifest empirically only through their action on bodies one can eliminate them from the theory altogether, and reformulate it in terms of (delayed) interactions between bodies a la Feynman-Wheeler. See Vassallo, Leibnizian relationalism for general relativistic physics on applying this strategy to GR.
    – Conifold
    Nov 20, 2021 at 11:13


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