Temporal Asymmetry (Theorem V*)
Temporal Asymmetry (Theorem V*)
定义
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.
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.
相关术语
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.
源文章
ODTOE中不可摧毁性的时间不对称：关于过去保存和未来可构造性的V*定理
关于H中过去和未来状态时间不对称的V*定理。过去是不可摧毁的（Φ迭代下的范数守恒），未来是可构造的（未固定）。从第一性原理解决「时间箭头」问题。时间投影算子π_past和π_future具有相互正交性。
观察者诞生时时间与空间的诞生：ODTOE中的复合时空起源定理
关闭四个相关问题：(i) 时间和空间与观察者Ô诞生同时出现，作为SSB+KAM选择的结构性后果；(ii) 两个时间投影算子π_past和π_future在τ_obs=τ₀时对称实例化；(iii) 通过反循环审计正式解决鸡与蛋悖论；(iv) 通过目标泛函A_goal的目的论选择。五点复合定理ST.T1。