iSoul In the beginning is reality

# Limits of the Lorentz transformation

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:

= γ (r – vt) and its inverse r = γ (r´ + vt´)

along with a standard (characteristic) speed, c, in all reference frames: r = ct and r´ = ct´ leads to

γ² = 1 / (1 – v²/c²).

By substituting the expression for and simplifying we get

= 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:

= γ (t – r/v) and its inverse t = γ (t´ + r´/v)

along with a standard 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 and simplifying we get

= 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.