Geodesic Deviation: Deriving Formula with Schtuz's Book

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The discussion focuses on deriving the formula for geodesic deviation using Schutz's book as a reference. Participants highlight that the approach can be straightforward, albeit mathematically impure due to the assumption of a convenient coordinate system. One contributor mentions their derivation process, which began as a translation from Ohanian's book, indicating that some concepts were challenging to grasp. They provide a link to their webpage for further clarification on the topic. Overall, the conversation emphasizes the importance of understanding the derivation process while acknowledging the complexities involved.
Terilien
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Can someone explain how to derive the formula for geodesic deviation? i didn't quite understand it. I'm using schtuz's book.
 
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You can try, for instance, http://www.mth.uct.ac.za/omei/gr/chap6/node11.html

This seems like a rather direct and straightforwards approach to me, even more direct than MTW's. Of course it is a bit mathematically impure, in that it assumes a convenient coordinate system, but I think assuming an inertial coordinate system for one of the observers makes the physics more apparent.
 
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Terilien said:
Can someone explain how to derive the formula for geodesic deviation? i didn't quite understand it. I'm using schtuz's book.
The derivation I placed on my web page at

http://www.geocities.com/physics_world/gr/geodesic_deviation.htm

started out being a translation from Ohanian's book to my web page. However it seemed to end up being Ohanian's book and part of what I had to say since Ohanian made somethings hard to understand there. Enjoy. Any problems then e-mail me so we can set straight if there is something wrong.

Pete
 

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In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...
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