Dear John,
Thank you for your observations.
"your contribution is based on the assumption that spacetime is something real."
I don't know whether spacetime is real or not, and I haven't used this assumption. I am just trying to capture the relations between spacetime events, and these relations are mathematical. Spacetime may be reality or illusion, but from the viewpoint I presented, it doesn't matter, because the relations are still relations. Reality or illusion, it has a logic which we are trying to understand and to express mathematically.
"You implicitly use several time-dependent concept, in particular when you try to say something about the arrow of time."
Sure, when you tell a story, you may use verbs. Even if you describe a painting, no matter how static it may be, you may still use verbs. As long as we are concerned with the spacetime and matter only, the block spacetime view (in a broad meaning) is enough, and, in the mathematical description, there is no circularity about time. Only the verbal description is time-dependent, the mathematical description is not. If we want to discuss things above the material world, like the type of free-will from the final part of my essay, then the mathematical picture needs to be completed with something (I don't know what), and we remain with circular reference, I agree with that. In that case, I proposed an experiment to test this type of free-will. The experiment can give us back the free-will, or, if it disproves it, at least we are set free from the circular reference in the definition of time.
"I will appreciate if you can tell us, at the end of the day, what is time according to your contribution."
1. I don't know how the final theory will be (together with its version of time), I don't know yet the true nature of time, and I still want to discuss about time. To make these discussions more clear and precise, I propose a mathematical structure which can describe a large class of kinds of times, causal relations, and the relation of time with space and the physical law, in a way applicable to a wide class of physical theories.
2. I propose a version of a principle of causality, which may have implications about the beginning of time.
3. I propose an interpretation of the wavefunction collapse in Quantum Mechanics, which avoids the usual discontinuities, and have some implications on time. The world becomes a bunch, a sheaf of deterministic worlds, because of the to-be-determined initial conditions. Our choices (particularly, we choose the observable to be measured), and the outcome of the measurement, uses this freedom in the initial conditions, to choose them at the end. We choose the world, and our choice includes the past, as long as it does not contradict the precious choices. This feature is well known in QM, in my version is combined with a deterministic evolution. The only indeterminism occurs because we have not registered all the initial conditions.
4. I present a block view of time, and of the illusion of time flow, which is based on what is presently known. I do this to show that the free-will is not guaranteed by the indeterminism, and certainly not by the pure determinism. The free-will seems to have no place. Yet, I propose a place for the free-will, which employs the initial conditions freedom, or, alternatively, the freedom of indeterministic theories. This type of free-will, the only possible in a world that can be described mathematically, is based on something outside the spacetime. This is the feature with circular reference in explanation, and I agreed with that since the beginning. But this is the only type of free-will compatible with the world described there. The good news is that it can be tested experimentally.
On short, if we are not just algorithms frozen in the river of time, then this experiment should be able to show this.
I hope I answered to some of your questions, thanks for the opportunity to clarify some issues.
Best wishes,
Cristi Stoica
