On studies transition from state 1 to 2 to 3. Usual causality implies that you must first induce transition from state 1 to 2 - by suitable chosen pulse in the experiments: energy of photons in pulse must correspond to energy difference between 2 and 1. After than you can induce transition from 2 to 3 by second suitably chosen pulse. In quantum world you can make this in different order. First the pulse inducing transition 2 to 3 (state is 1 so that nothing happens). Then you generate pulse 1 and inducing transition 1 to 2 and transition 2 to 3 takes place! Weird! This might have profound implications for quantum information processing.
Layman description for this loop in causality is following. Suppose you must get out from parking hall. In classical world you first reverse the car and then drive away. In quantum world you can first drive away and then reverse the car! Good choice if you have a really big hurry! Maybe you should however not try this without the guidance of quantum physicist.
This is really crazy looking idea, which can be understood only in 4-D context. Zero Energy Ontology plus the fact that geometric time and subjective time (and therefore the corresponding causalities) are not one and the same thing explains the nicely. The "subjecively first" pulse represents 4-D wave as 4-D geometric entity (here time is geometric), which can induce the transition from state 2 to 3 if 2 is present in 4-D domain - causal diamond (CD) in TGD. Otherwise nothing happens: this is the case now! One kicks by second pulse state 1 to 2 "subjectively after" the first pulse. The state is 2 in entire CD and now the "subjectively first" pulse in CD can induce the transition from 2 to 3 in 4-D geometric space-time domain (CD)!
For a summary of earlier postings see Links to the latest progress in TGD.