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Definitions [used, set] by Howell
Note that here I use "convenience definitions" for [γ_JJ, γ_TB] as extyensions of the commonly-used γ_KL. I assume that Einstein actually first defined γ_JJ, but I will have to check on that ... (28Oct2019).
The Lorentz (relativistic) factor, γ_KL, is commonly used :
I call this the Konrad Lorentz relativistic correction factor (see wikipedia) :
γ_KL = (1 - β^2)^(-1/2)
I assume that this arose from the Lorentz transformations, and the Lorentz-Poincare original theory of relativity.
The John Jackson relativistic correction factor, γ_JJ, probably a misnomer as Einstein would have developed it? :
John David Jackson 1999 "Classical Electrodynamics, 3rd Edition", John Wiley & Sons, 808pp, ISBN 978-0-471-30932-1, p560 equation 11.154 :
γ_JJ = (1 - β^2)/(1 - β^2*sin(Aθpc(POIo(t),t=0))^2)^(3/2)
The Thomas Barnes relativistic correction factor, γ_JJ, was derived on the basis of [E, B] field beedbacks between reference frames :
γ_TB = (1 - β^2)/(1 - β^2*sin(Aθpc(POIo(t),t=0))^2)^(3/2)
As state by Lucas, this is the SAME as γ_JJ.
γ_TB = γ_JJ
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Comparisons
Note the comparison of the factors at extremes of sinθ :
- As sinθ -> 1 then :
- γ_JJ = γ_TB = γ_KL = (1 - β^2)^(-1/2)
- As sinθ -> 0 then :
- γ_TB -> (1 - β^2)
- γ_TB -> (1 - β^2)
- but γ_KL remains = (1 - β^2)^(-1/2)
- That is a huge difference for significant β, so I assume that γ_TB is only applicable to POIo that are directly on the path of the particle?