Time (and Phase) Intervals vs Separation (and Wavelength) Distances in Transaction Geometry

Transaction geometry incorporates the frame independence of relativity that imposes additional constraints on forward scattering in a plasma.  Simultaneous, co-planar, and coherent phase field scattering events act as secondary indivisible emission/detection transactions that ultimately overwhelm and replace incident radiation.  The alternative perspectives of detections by a relatively moving electron that then collaterally ‘emits’ what is detected does not alter the phase (because of the constraint) but alters the wavelength.  The constraint virtually eliminates the possibility of a blueshift contribution to the secondary wave for scattering electrons moving counter to the direction of the incident radiation.

Detection events occur at times C_i(t +t_i) = A_i(t) + t_i; these times that are illustrated in the figure are related as: C₂ < ( C₁ = C₄ ) < C₃ because time intervals are related as: t₂ < ( t₁ = t₄ ) < t₃.  The quarter wavelength constraint of forward scattering allows a variance on these times of on the order of± dt = lambda/4c ~ 10^-16 seconds. (Lambda is wavelength.)

Since the velocity of light is the same constant value relative to the ‘observer’ (the detector and not the emitter or the locations of emitting and detecting), the amount of time it takes to propagate from A to C is the initial distance between A and B.  As shown for transaction 3 in the above figure, d₃ = c t₃ is the distance light must travel relative to the detecting agent initially at B₃ when light was emitted at A₃.  But where that occurs is atC₃ in the locally stationary frame of the incident radiation source and observer.

That is why and how radiation propagated through a plasma is redshifted.  The more intense the plasma pressure, the more the radiation is redshifted.  This produces the more extreme redshift dispersion of galaxy clusters, which then accumulates for radiation propagating through many clusters cells to effect the cosmological redshift that does not require dark matter, a big bang, or dark energy to drive acceleration.