Phenomenological Determinisms
Résumé
The arrow of time is revisited. It is proposed that it arises from the existence in the cosmos of a phenomenological determinism within the fundamental determinism expressed by the Liouville or Liouville-von Neumann equations. The latter link exactly the fundamental information present in the cosmos at any different times. The proposed phenomenological determinism is expressed by phenomenological laws which allow the observers to deduce, from the phenomenological fraction of the fundamental information accessible to observation at a time t, the same phenomenological information at a times t', but only along the arrow of time t'>t. It is first shown, in a simplified cosmos, that this phenomenological determinism can exist under two conditions : an initial condition weighing on the fundamental information at a primordial time of the cosmos, which introduces the arrow of time aimed from the primordial time to the observers' times ; a structural condition specifying in fine the nature of the phenomenological information, which imposes that any information which does not become phenomenological very rapidly becomes disconnected forever. It is then shown that these conditions are fulfilled, and the phenomenological determinism exists, thanks to a canonical representation of the phase space in the vicinity of the hamiltonian trajectories, which highlights purely hyperbolic or elliptic motions of the cosmos.
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