Discussion in 'Physics & Math' started by rpenner, Oct 5, 2011.
Aahhh! MY EYES!! The goggles do nothing!
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I was planning to start posting my results yesterday, but I decided to rework my derivation of the generalized Galilean transform. I didn't take enough care in defining the coordinate systems x,y,z,t and x',y',z',t' and then showing how certain basic symmetries must relate both systems. Once I did, I got the same results as I found a few days ago, except there was one remaining term I needed to set to zero, and I couldn't find a logical way to do it except to argue (in various equivalent forms) that space doesn't have a preferred orientation.
Anyhow, that's all done. I've tried to take care so everything's clear and simple as possible, and to simplify the maths as much as possible at every step so things don't become too messy, although for certain parts one will need a decent understanding of vector and multivariable calculus. I'm keeping my coordinate systems simple- the observers see each other moving along the x and x' axes in opposite directions, and I will show afterwards that any other results can be derived by spatial rotations, and it's easy to show that such spatial rotations in either frame will not change the resulting time coordinates. I feel I should be able to keep the maths fairly simple and straight-forward for the most part while still dealing with the most general possible situations (i.e. general charge/current distributions) whenever necessary.
Gotta sidetrack for the rest of this morning on real work, unfortunately, but then I should be ready to start writing it up tonight. I plan to post my derivations in stages, so hopefully tonight I'll have those generalized Galilean transforms up, then other stages will hopefully come soon after.
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