Dear Luca,
Thank you for your essay, as it has inspired the following thoughts:
It would seem that if the future were deterministic, we could determine it, at least approximately. But then we could change it. There is no reason to suppose this 'ability' to be peculiar to humanity, or even life, but to operate, to some degree, at all scales. That is, the future is 'perceived' at a higher level of entropy, and then changed, symmetry breaking, to a lower state of entropy, which becomes the present. This would 'create' information. The direction of time, therefore, is the result of successive symmetry breaking.
Conservation of information says there is no (actual) symmetry breaking.
If the future were determined, the map from present to future would be a function, one to one, and not one to (many possible) states. Mapping into the past seems to be determined, different values of the present mapping onto ever fewer values going back, until just one at the quantum fluctuation. If the map onto the future is one to one, this would imply the backward mapping also one to one. That is also, no information is destroyed going backward.
I have trouble with the Everett interpretation of quantum mechanics, as it seems to imply the universe is still expanding exponentially, just in (exponential) dimensions we cannot see. In terms of symmetry breaking, it says all possible states are chosen: The pencil standing on its tip falls in every direction, each direction creating a new universe, only one of which we, looking back, exist in. The creation of matter in extra dimensions would seem to be energetically difficult, but perhaps I am mistaken. What, after all, is energy, aside from being, at least locally, conserved? It seems as if the inflationary process which generated this cosmos would be merely twisted, and not extinguished, when inflation appeared to stop.
Thanks again. Best of luck in the competition.
Charles
