The book’s proposed correspondence
Ultimate Symmetry uses super symmetry for the proposed complementarity of physical and psychical domains. Its introduction connects those domains with two temporal orientations and treats them as parts of a larger account of manifestation. The two-arrows excerpt preserves the author’s original notation and discussion.
The central reading question is what establishes the correspondence: which states are paired, which operation relates them, and which properties the pairing preserves. Naming two complementary domains leaves these details open. A mathematical realization would make them explicit and would explain how the proposed pairing affects observable results.
Comparison with particle-physics supersymmetry
In particle physics, supersymmetry relates bosonic and fermionic degrees of freedom. It predicts partner states with spins differing by one half. CERN’s introduction to supersymmetry describes this usage and the motivation for investigating it.
A correspondence between two domains would have to recover the relevant particle states, transformations and dynamical relations before it could establish that physical supersymmetry. Likewise, a reversal or exchange of temporal labels does not by itself determine the spin or interactions of a partner state. These are specific questions a proposed model can address.
A concrete comparison to pursue
Begin by choosing a state space for each domain and a map between them. Ask whether applying the map twice returns the original state, whether it changes any measured quantum numbers, and whether it preserves the evolution law. If it exchanges observables, state how an observer can compare the two results.
These tests separate a useful formal correspondence from a merely visual similarity. The gauge and spacetime symmetry guide explains why transformations acting on different structures need different definitions. The spin guide connects rotational transformations with the structures used to describe spin.
For the author’s wider interpretation, return to the book introduction and follow the online contents in order.
