TGD View on Quantum Computations without Definite Causal Structure

Abstract

The notions of causal order and indefiniteness of causal order have popped up in information science. One can construct quantum computations, which cannot be carried out in fixed causal order: the simplest one is SWITCH which changes the causal order. It has been reported that the SWITCH has been realized experimentally with almost 7 sigma accuracy. In standard physics causal order is fixed and SWITCH is impossible so that the implications could be world view changing. In TGD Zero Energy Ontology (ZEO) replaces ordinary ontology and the arrow of time is not fixed, and it is interesting to see whether superposition of different causal orders related by time inversion T for causal diamond (CD) and SWITCH could be realized in ZEO. The twistor lift of TGD leads to the proposal that CD is accompanied by a Minkowskian generalization of self-dual Kahler form J(CD). Although the moduli space of CDs allows to avoid breaking of Poincare invariance, self-duality of J(CD) leads to violation of T implying that different causal orders correspond to disjoint sectors of world of classical worlds. This makes possible also superposition of different causal orders and SWITCH would map these sectors to each other.