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Givne the Lorentz transformations (LTs)}, [tex] x'^{\mu} = L_{\nu}^{\mu} x^{\nu} [/tex], between the coordinates, [tex] x^{\mu} = (ct , \vec{r}) [/tex] of an event as seen by O, and coordinates, [tex] x'^{\mu} = (ct', \vec{r'}) [/tex] of the same event as seen by an inertial observer O', show that if we write the inverse transformation as [tex] x^\alpha = \tilde{L}_{\beta}^{\alpha} x'^{\beta},\mbox{then} \ L_{\omega}^{\alpha} \tilde{L}_{\beta}^{\omega} = \delta_{\beta}^{\alpha}[/tex]

WELL from the inverse transformation we ca figure out that

1... [tex] \frac{\partial x^{\alpha}}{\partial x'^{\omega}} = \tilde{L}_{\beta}^{\alpha} \frac{\partial x'^{\beta}}{\partial x'^{\omega}} [/tex]

also

2... [tex] \frac{\partial x'^{\alpha}}{\partial x^{\omega}} =L_{\beta}^{\alpha} \frac{\partial x^{\beta}}{\partial x^{\omega}} [/tex]

there is a notation problem here that i am trying to resolve as well...

do i simply rearrange for L and tilde L andmultiply out??

mroe to come as i type it out

WELL from the inverse transformation we ca figure out that

1... [tex] \frac{\partial x^{\alpha}}{\partial x'^{\omega}} = \tilde{L}_{\beta}^{\alpha} \frac{\partial x'^{\beta}}{\partial x'^{\omega}} [/tex]

also

2... [tex] \frac{\partial x'^{\alpha}}{\partial x^{\omega}} =L_{\beta}^{\alpha} \frac{\partial x^{\beta}}{\partial x^{\omega}} [/tex]

there is a notation problem here that i am trying to resolve as well...

do i simply rearrange for L and tilde L andmultiply out??

mroe to come as i type it out

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