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We describe a new paradigm for understanding both relativistic motions andparticle acceleration in the M87 jet: a magnetically dominated relativisticflow that naturally produces four relativistic magnetohydrodynamic (MHD) shocks(forward/reverse fast and slow modes). We apply this model to a set of opticalsuper- and subluminal motions discovered by Biretta and coworkers with the {\emHubble Space Telescope} during 1994 -- 1998. The model concept consists ofejection of a {\em single} relativistic Poynting jet, which possesses acoherent helical (poloidal + toroidal) magnetic component, at the remarkablyflaring point HST-1. We are able to reproduce quantitatively proper motions ofcomponents seen in the {\em optical} observations of HST-1 with the same modelwe used previously to describe similar features in radio VLBI observations in2005 -- 2006. This indicates that the quad relativistic MHD shock model can beapplied generally to recurring pairs of super/subluminal knots ejected from theupstream edge of the HST-1 complex as observed from radio to opticalwavelengths, with forward/reverse fast-mode MHD shocks then responsible forobserved moving features. Moreover, we identify such intrinsic properties asthe shock compression ratio, degree of magnetization, and magnetic obliquityand show that they are suitable to mediate diffusive shock acceleration ofrelativistic particles via the first-order Fermi process. We suggest thatrelativistic MHD shocks in Poynting-flux dominated helical jets may play a rolein explaining observed emission and proper motions in many AGNs.

A Magnetohydrodynamic Model of The M87 Jet. II. Self-consistent Quad-shock Jet Model for Optical Relativistic Motions and Particle Acceleration