null-strut-grid △▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽△▽ "All our assertions of spatio-temporal relations are reducible to individual observers' judgements of having collected several perceptions either together, or separately; i.e. determinations of space-time coincidence"
The drawing is of an (arbitrarily extended) "octet truss" 3D space frame ( open access taken from https://www.mdpi.com/2075-4701/12/3/410 ); see also tetrahedral-octahedral honeycomb.
ReplyDeleteInterpreted as illustration of a (3+1) dimensional null-strut-grid:
- each individual vertex depicts the individual time-like world line of a suitably selected "material point" (in the sense of [Einstein-1916]; [Minkowski-1908] ...); a.k.a. a "constituent" (of the null-strut-grid being shown), and
- each edge segment depicts continuous signal (front) exchange between relevant pairs of those material points; implying the causal structure of a "photon-2-surface", see [gr-qc/0306042];
or, being only a limited segement, rather: a "photon ribbon";
and thereby also a certain set of "null-struts" (in the sense of [Kheyfets-1988]).
In the corresponding (arbitrarily extended) null-strut-grid, for each constituent these null-struts are required (and selected such that) ping-coincidence relations are found and satisfied
- wrt. the 12 nearest neighbors,
- wrt. the 6 next-to-nearest neighbors,
- wrt. the 12 next-to-next-to-nearest neighbors, etc.
Each constituent is thereby also identified as "the middle between" (in the sense of [Comstock-1910] and of [Einstein-1917]) six different (and even disjoint) pairs of its nearest neighbors (where the two constituents making up any such pair are in turn next-to-next-to-nearest neighbors of each other).