Lorentz transformations: something like velocity, force, potential, momentum, energy, inertia.
Anyway we always intended to understand co- and contravariant stuff.
The other day general relativity came to our mind again. How can (in a 2 body system) the influence be described one piece has upon the other? It is related to the morphing group thing, where the morphing and Chess piece moves obviously resemble a lot. Is one Chess piece curving the spacetime for another piece? It would be the very simplest and natural way to describe dynamics, for let's say a linear force like a spring or some 1/r dependence would cause the very question of why this and not that. The morphing idea needs a mapping between the orbits of the morphed graph and the original, making the impression of some force or potential effect. Somehow the coordinate lines should change from straight to s.th. more elaborate.
How about a group containing all holonomy groups coming from all morphed states of a given graph together with those resulting when one dumps out the -q groups (more precisely directly their Schur covers) while the graph morphs underway. Then GAP™ could be able to find a homomorphism mapping the generators of a current vector group (belonging to some coordinate lines, telling what is straight) and new generators (thus more concretely actually new coordinate lines). We want a non-trivial result with curved orbits while obeying the Chess rules of piece movement. How can we relate the result to the single piece groups?
What are conformal transformations btw.?
The general equivalence theorem states that the physical laws have the same structure in all coordinate systems. Well, does that mean that there must be a Chess theory delivering the optimal play for all possible positions?