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 above picture of an octet-truss layer and unit cell is by "open access" from https://link.springer.com/article/10.1007/s00170-022-10051-3
ReplyDeleteThe regular octahedron (red in the octet-truss unit cell), interpreted as illustration of a small section of a null-strut-grid, corresponds to the time-like world lines of six constituents (shown as one "top" vertex, one "bottom" vertex, four vertices "in the center plane"; in the following called constituents $T, B, J, K, P Q$), and to 12 mutually exchanged signal fronts ("photon ribbons") between the 12 next-neighbor pairs (shown as the octahedron edges).
This partial grid of causal relations is consistent with (although not necessarily determinative of) repeated instances of a pattern whose relevance has been recently recognized [gr-qc:2302.12209], and named the "well-stitchedness" relation between a total of 8 suitable events. Namely:
each event of a group of 4 distinct events being light-like separated (or in other words: connetced by a null-strut) to each event of another (disjoint) group of 4 distinct events
See A. V. Nenashev, S. D. Baranovskii, How to detect the spacetime curvature without rulers and clocks [gr-qc:2302.12209]
The applicable configuration is shown there as Fig. 1(d).
In terms of signal fronts being exchanged between six constituents of a null-strut-grid, as identified above, this "well-stitchedness" relation can be satisfied e.g. by
- $T$ stating a certain signal (indication $T_s$) and receiving (and recognizing) the corresponding signal front reflections from $J, K, P$ as well as $Q$ together (i.e. in coincidence)
along with
- $B$ stating a certain signal (indication $B_{\sigma}$) and receiving (and recognizing) the corresponding signal front reflections from $J, K, P$ as well as $Q$ together (i.e. in coincidence),
such that
- $J$ had received the two signal fronts of indications $T_s$ and $B_{\sigma}$ together (i.e. in coincidence); and likewise $K$, $P$ and $Q$, too.
(As far as the octahedra in drawings of octet trusses are understood to be
regular octahedra, this may be mistaken as suggesting that all coincidence requirements listed above being guaranteed and readily satisfied. That's not my claim, however. Instead, those required coincidence determinations would actually have to be asserted by the six relevant observers involved, instance by instance, in order to conclude that a "well-stitchedness" relation obtained among them.
Considering the example case above, this presents the "practical problem" of certain indications $T_s$ and $B_{\sigma}$ being identifiable, in general.)