# Is a Lorentz boost as a limit transformation of a separate time/space dilatation possible?

Given the covariant coordinate transformation to a rotating coordinate system, where you have a pure length dilatation (radius) .

\begin{eqnarray*} cT & = & ct\\ R & = & \frac{r}{\sqrt{1+\frac{\omega^{2}r^{2}}{c^{2}}}}\\ \varPhi & = & \phi-\omega t\\ Z & = & z \end{eqnarray*}

Here $\omega$ denotes the angular velocity. Coordinates are given in zylindrical coordinates. Capital coordinates are for the inertial reference frame. And the covariant coordinate transformation to an uniform accelerated reference frame , where you have a pure time dilatation. Can you understand the spacetime rotation of a Lorentz transformation as the limit of a combination of the above mentioned transformations, in a similar way in which you can interpret the straight line as a circle with infinite radius.

• I don't understand the whole question, but Lorentz transformations are spacetime rotations, whilst your transformation only transforms spatial coordinates and leaves time untouched. Thus, my answer is - probably not. – Prof. Legolasov Sep 9 '16 at 12:19
• Are you trying to unite special and general relativity? I am not sure if it is possible what you are trying to do, but sounds like an interesting idea to me. Post your answer here in case you figure something out=) – MsTais Sep 9 '16 at 14:02
• @MsTais Lorentz transformations are a special case of coordinate transformations from General Relativity with flat background spacetime. Thus, SR and GR are already "united", or, I would say, GR is a generalization of SR (thus the name). – Prof. Legolasov Sep 9 '16 at 17:58
• @v217 "And the covariant coordinate transformation to an uniform accelerated reference frame , where you have a pure time dilatation." How come? – udrv Sep 10 '16 at 17:55