Two broad scenarios for extended linear Lorentz transformations (ELTs) are modeled in Section 2 for mixing subluminal and superluminal sectors resulting in standard or deformed energy-momentum dispersions. The first scenario is elucidated in the context of four diverse realizations of a continuous functionf(v), with0≤f(v)≤1andf(0)=f(c)=1, which is fitted in the ELT. What goes in the making of the ELT in this scenario is not the boost speedv, as ascertained by two inertial observers in uniform relative motion (URM), butv×f(v). The second scenario infers the preexistence of two rest-mass-dependent superluminal speeds whereby the ELTs are finite at the light speedc. Particle energies are evaluated in this scenario atcfor several particles, including the neutrinos, and are auspiciously found to be below the GKZ energy cutoff and in compliance with a host of worldwide ultrahigh energy cosmic ray data. Section 3 presents two broad scenarios involving a number of novel nonlinear LTs (NLTs) featuring small Lorentz invariance violations (LIVs), as well as resurrecting the notion of simultaneity for limited spacetime events as perceived by two observers in URM. These inquiries corroborate that NLTs could be potent tools for investigating LIVs past the customary LTs.
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