PeterDonis
Mentor
- 27,090
- 7,307
Re: "Locally Lorentz"
But this transformation, if it is to be valid globally in a curved spacetime, cannot be a Lorentz transformation. If you insist on writing it in the form you gave, then the coefficients [itex]\beta[/itex] and [itex]\gamma[/itex] will vary from event to event in a curved spacetime (i.e., in the presence of gravity). A global Lorentz transformation must have constant coefficients.While the "globally lorentz" behavior applies to the global coordinates
[tex]\begin{pmatrix}
c t_{global}'
\\
x_{global}'
\end{pmatrix}=
\begin{pmatrix}
\gamma & -\beta \gamma \\
-\beta \gamma & \gamma
\end{pmatrix}
\begin{pmatrix}
c t_{global}
\\
x_{global}
\end{pmatrix}[/tex]