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What about if the speed parameter in a Lorentz boost were in fact related nontrivially to a Galilean speed ?

More formally ##L(v_L)=G(v)\circ F## where L is a Lorentz boost with Lorentz speed ##v_L##, G is a Galileo transformation with speed ##v## and ##F## is still an unknown linear transformation that has to fulfill the previous matrix equation, which by solving should lead to a relationship ##v_L=g(v)## that possibly could have the property ##v_L=g(v\rightarrow\infty)\rightarrow c##.

More formally ##L(v_L)=G(v)\circ F## where L is a Lorentz boost with Lorentz speed ##v_L##, G is a Galileo transformation with speed ##v## and ##F## is still an unknown linear transformation that has to fulfill the previous matrix equation, which by solving should lead to a relationship ##v_L=g(v)## that possibly could have the property ##v_L=g(v\rightarrow\infty)\rightarrow c##.

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