Theorists of reconciliation generally recognize that reconciliation is a "scalar" concept, which allows for minimal and maximal versions of improved relationships (Crocker 1999, Griswold 2007).
Indeed, if the scalar field is everywhere non-negative, then this particular choice of dynamics puts ironclad constraints on the value of the field at v and w: the field there must be zero (assuming Wvx and Wwy to be non-zero), and similarly all nodes in their past must have field value zero.
Friedman et al. 1990 examined the case of source free non-self-interacting scalar fields traveling through such a time travel wormhole and found that no constraints on initial conditions in the non-time travel region are imposed by the existence of such time travel wormholes.
It's true that vector and tensors can be defined in terms of coordinates and scalar fields, and one could imagine telling a formal story about these along the lines sketched for the scalar field: the equations governing them take an especially simple — and Lorentz invariant — form in certain coordinates.
Indeed, if what matters is supposed to be the degree of continuity, it might seem to make more sense simply to focus on the more obviously scalar relation in which continuity consists, viz., connectedness, as delivering the units of significance in the form of selves.
These are \(S\), the scalar interaction; \(P\), pseudoscalar; \ V\), vector; \(A\), axial vector; and \(T\), tensor.
In such theories as the unified model of electroweak interactions, the SSB responsible (via the Higgs mechanism) for the masses of the gauge vector bosons is because of the symmetry-violating vacuum expectation values of scalar fields (the so-called Higgs fields) introduced ad hoc in the theory.
This suggests that from that level of abstraction the laws governing motion (not contingencies for Gassendi) are intended to be scalar invariant.
Finally, Gassendi subscribes to a seamless compositionality of matter and scalar invariance regarding the nature and laws of motion, each of which lead him into murky waters.
Φ is the topological anti-dual of Φx, meaning that it is the complete set of continuous anti-linear functionals on Φx; it is anti-linear rather than linear because multiplication by a scalar is defined in terms of the scalar's complex conjugate.
It is a scalar field that "pulls back" moving and interacting particles.
