In Zero Energy Ontology (ZEO), the basic geometric structure is causal diamond (CD), which is a subset of M4× CP2 identified as an intersection of future and past directed light cones of M4 with points replaced with CP2. Poincare symmetries are isometries of M4× CP2 but CD itself breaks Poincare symmetry.

Whether Poincare transformations can act as global symmetries in the "world of classical worlds" (WCW), the space of space-time surfaces - preferred extremals - connecting 3-surfaces at opposite boundaries of CD, is not quite clear since CD itself breaks Poincare symmetry. One can even argue that ZEO is not consistent with Poincare invariance. By holography one can either talk about WCW as pairs of 3-surfaces or about space of preferred extremals connecting the members of the pair.

First some background.

Poincare transformations act symmetries of space-time surfaces representing extremals of the classical variational principle involved, and one can hope that …

Whether Poincare transformations can act as global symmetries in the "world of classical worlds" (WCW), the space of space-time surfaces - preferred extremals - connecting 3-surfaces at opposite boundaries of CD, is not quite clear since CD itself breaks Poincare symmetry. One can even argue that ZEO is not consistent with Poincare invariance. By holography one can either talk about WCW as pairs of 3-surfaces or about space of preferred extremals connecting the members of the pair.

First some background.

Poincare transformations act symmetries of space-time surfaces representing extremals of the classical variational principle involved, and one can hope that …