The Conjugate Entangled Manifold of Space-Time Induced by the Law of Unity of Contradiction

摘要

The mechanism of the contradiction between two different objects u and v is attributed to a mechanism that their opposite position information "x_u" and "x_v" of u and v are transmitted, respectively, from the initial time t_0 , at different speeds x_u(t) and x_v(t) (x_v = －ζx_u(t)), and is meeting at the contradiction point t = t_λ and x = x_λ. Because the coordinate of contradiction point can be noted by z_λ(t_λ,x_λ) and z_λ~*(x_λ,t_λ) in two space time Complex Coordinates Systems which origins are z_0(0_t,0_x) and z_0~*(1_t,1_t), respectively, such that the time t_λ and the position x_λ of the contradictory points can be expressed as the sum of the complex numbers z_λ(t_λ,x_λ) and its conjugate z_λ(t_λ,x_λ) : t_λ = z_λ(t_λ,x_λ) + z_λ(t_λ,x_λ) = w_λ(z_λ,z_λ), and the difference of z_λ~*(x_λ,t_λ) and its conjugate: z_λ~*(x_λ,t_λ) : x_λ = Z_λ~*(x_λ,t_λ) - z_λ~*(x_λ,t_λ) = w_λ~*(z_λ~*,z_λ~*). By synthesizing the time-space coordinate and the space-me coordinate, such their time axis [0_t, 1_t] and the space axis [1_x,0_x] of the two complex coordinate systems are coincide with the intervals [u,v], respectively, then the contradiction point can be expressed in the synthesis Coordinate System to be a wave function: ψ(w_λ, w_λ~*) = t_λ － ix_λ = w_λ － iw_λ~*. Because of the varying direction of two information "x_u" and "x_v" and their increments Δx_u(Δ_ut) = x_u(Δ_ut)Δ_ut and Δx_v(Δ_vt) = x_v(Δ_vt)Δ_vt with time t and increment Δt = t － 0_t are opposite each other, so the t_λ of the wave function ψ is on the time axis [0_t, 1,] and the x_λ on the space axis [1_x,0_x]. constructed a pair of information transmission streams entangled in opposite directions appear, such that the interval [u, v] constitutes a space-time conjugate entangled manifold. The invariance of the contradiction point or wave function ψ(w_λ, w_λ~*), under the unit scale transformation of time and distance measurement, not only make all points z(t,x) ∈ [u,v] is contradiction point, and makes λ=(~1/_2) and ζ = (~λ/_1) ‐ λ It is also shown that since λ changes from 0 to (~1/_2) is equivalent to the integral for the on t_λ and x_λ in wave function ψ from 0 to (~1/_2), respectively, by it not only the inner product ψ of the ψ and the time component t_λ, respectively ψ(w, w*).t_λ, and the outer product of ψ and the spatial component ψ(w, w*) ∧ x_λ can be get, but also their sum: ψ(w, w*) ψ_t + ψ(w, w*) ∧ψ_x can be gotten too.