Forest Relativity Notes

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Lorentz Transformations

ForestRelativityLorentzFrame.jpg

xμ=3ν=0Λμνxν

where

x0ct
x1x
x2y
x3z
Λ=[γγβ00γβγ0000100001]
β=vc
γ=11β2
example
x0=2ν=0Λ0νxν=Λ00x0+Λ01x1Λ02x2+Λ03x2
ct=γx0γβx1+0x2+0x3=γctγβx=γ(ctβx)
Or in matrix form the tranformation looks like
(ctxyz)=[γγβ00γβγ0000100001](ctxyz)