Temporal Asymmetry (Theorem V*)
Definition
Theorem V* of ODTOE establishes temporal asymmetry of past and future states in H: the past is indestructible (norm conservation under Φ-iterations), the future is constructible (not fixed). Projectors π_past and π_future are mutually orthogonal, which gives the arrow of time from first principles and connects to Penrose's CCC and Wheeler's delayed-choice.
Related Terms
Time as Derivative of Observation
Time in ODTOE is not a fundamental parameter but the iteration counter of the self-observation map Φ — the «tact frequency» of a strange loop. Cesium-133 atomic time and a heartbeat are both legitimate τ₀ calibrations at different observer levels; the transcendence of π guarantees the arrow of time.
Spacetime Genesis at Observer Birth
ODTOE's composite spacetime genesis theorem ST.T1 states that time and space arise simultaneously with the birth of an observer Ô as structural consequences of spontaneous symmetry breaking and KAM selection. Both temporal projectors π_past and π_future are instantiated symmetrically at τ_obs = τ₀, resolving the chicken-and-egg paradox of observer vs spacetime.
π as Structural Invariant
In ODTOE π is the continuous-phase invariant of self-consistent observation — the form of the observation cycle. Its transcendence (Lindemann 1882) guarantees that the φ-torus trajectory never closes, which produces the arrow of time and the eternal expansion of the universe.
Source Articles
Temporal Asymmetry of Indestructibility in ODTOE: Theorem V* on Conservation of the Past and Constructibility of the Future
Theorem V* on temporal asymmetry of past and future states in H. Past is indestructible (norm conservation under Φ-iterations), future is constructible (not fixed). Resolves the «arrow of time» problem from first principles. Temporal projectors π_past and π_future with mutual orthogonality. Connection to Penrose's CCC and Wheeler's delayed-choice.
Birth of Time and Space at Observer Birth: Composite Spacetime Genesis Theorem in ODTOE
Closes four related questions: (i) time and space emerge simultaneously with observer Ô birth as structural consequences of SSB+KAM selection; (ii) both temporal projectors π_past and π_future instantiated symmetrically at τ_obs=τ₀; (iii) formal resolution of chicken-and-egg paradox via anti-circularity audit; (iv) teleological selection of realized world-line via goal-functional A_goal [CONJECTURE]. Composite theorem ST.T1 in five claims.