The question is show that given two coordinate transformation matrices, that their product is also a coorindate transformation.(adsbygoogle = window.adsbygoogle || []).push({});

[itex]\Lambda^\alpha_\beta = \frac{\partial x'^\alpha}{\partial x_\beta}[/itex]

[itex]\widetilde{\Lambda}^\alpha_\beta = \frac{\partial \widetilde{x}^\alpha}{\partial x_\beta}[/itex]

[itex]\Lambda^\alpha_\gamma\widetilde{\Lambda}^\gamma_\beta = \frac{\partial x'^\alpha}{\partial x_\gamma}\frac{\partial \widetilde{x}^\gamma}{\partial x_\beta}[/itex]

Define [itex]\bar{x}^\alpha = x'^\alpha (\widetilde{x}^\gamma(x^\beta))[/itex]. Then by the chain rule we obtain

[itex]\frac{\partial \bar{x^\alpha}}{\partial x^\beta} = \frac{\partial x'^\alpha}{\partial \widetilde{x}^\gamma}\frac{\partial \widetilde{x}^\gamma}{\partial x^\beta}[/itex].

This differs from the previous expression by a tilde. Lightman et al shrug this off by saing that it makes no difference what symbol is used to represent the argument variable of a partial derivative. I don't understand this claim. Is anybody able to clarify this?

Thanks

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Lightman et al Question 3.10

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads for Lightman Question | Date |
---|---|

B Theoretical Question On The Twins Paradox and Heart Rate | Apr 9, 2018 |

I Some geometry questions re Schwarzschild metric | Mar 16, 2018 |

B Causality Question | Feb 23, 2018 |

I A question about the relativistic energy dispersion relation | Feb 20, 2018 |

Lightman et al Problem 3.24 | Jul 15, 2008 |

**Physics Forums - The Fusion of Science and Community**