Hi Ding Jia,
Thanks for letting us in having a peak on your research of indefinite causal structure. I followed Lucien Hardy's work on operational approaches to physics a while and found it very interesting. But sadly I was never able to take the time to follow him in his roads to quantum gravity.
Can you make some qualitative phenomenological prediction that might follow from a indefinite causal structure? The causal structure seems to be somehow a priori in the sense that it is difficult (impossible?) to express scientific experience in a non definite causal structure. On the other hand it is surely good to critically question principles that might restrict the physical inquiry.
In my essay I argue that a causal description of events might be complementary to a realistic one (assignment of properties independently of a measurement).
During the work on my essay, where I tried study the conceptual structure of physics, I was speculating that gravity prevents the ability to define strictly separable free objects. And this might be the cause, why perturbative quantum field theoretical approaches might fail to renormalizable with a finite set of observable quantities.
Your essay surely deserves more attention a it seems to get.
Luca