by Lorenzo Maccone
One of the most puzzling aspects of our universe is the fact that its initial state had entropy so much lower than we see today, making the initial state highly unlikely. Joining the above hypothesis of a zero-entropy pure state of the universe with the second law considerations analyzed in this paper, it is clear that such puzzle can be resolved.
The universe may be in a zero entropy state, even though it appears (to us, internal observers) to possess a higher entropy: our situation is similar to the one of Alice, who, just after the measurement sees her lab in a nonzero entropy state, whereas to the super-observer Bob her lab maintains a zero-entropy state all along.
The arrow of time dilemma: the laws of physics are invariant for time inversion, whereas the familiar phenomena we see everyday are not (i.e. entropy increases).
I show that, within a quantum mechanical framework, all phenomena which leave a trail of information behind (and hence can be studied by physics) are those where entropy necessarily increases or remains constant. All phenomena where the entropy decreases must not leave any information of their having happened.
This situation is completely indistinguishable from their not having happened at all. In the light of this observation, the second law of thermodynamics is reduced to a mere tautology: physics cannot study those processes where entropy has decreased, even if they were commonplace.
