Looking back at the previous posts, we can see that if we begin with the relativity of the spatial component of movement, the Lorentz transformation turns out one way:
r´ = γ (r – vt) and its inverse r = γ (r´ + vt´)
along with a characteristic speed, c, in all reference frames: r = ct and r´ = ct´ leads to
γ² = 1 / (1 – v²/c²).
By substituting the expression for r´ and simplifying we get
t´ = γ (t – rv/c²) and its inverse t = γ (t´ + r´v/c²).
But if we begin with the relativity of the temporal component of movement, the Lorentz transformation turns out another way:
t´ = γ (t – r/v) and its inverse t = γ (t´ + r´/v)
along with a characteristic speed, c, in all reference frames: t = r/c and t´ = r´/c leads to
γ² = 1 / (1 – c²/v²).
By substituting the expression for t´ and simplifying we get
r´ = γ (r – tc²/v) and its inverse r = γ (r´ + t´c²/v).
So γ depends on v/c if space is relative, and γ depends on c/v if time is relative. But that also means v < c if space is relative and v > c if time is relative. Plus the converse: space is relative is v < c and time is relative if v > c.
But in fact space can be relative whether or not v < c and time can be relative whether or not v > c. So there is something artificially limiting about the Lorentz transformation.