show that the Lorentz transformation reduces to the Galilean transformation for v<<c
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The Galilean transformations are :
x'=x-vt
y'=y γ
z'=z
t'=t
Explanation:
From the Lorentz transformations :
x' = γ(x - vt) , y' = y , z' = z , t' = γ(t-(vx/c^2)) , γ = 1 / (1 - (v^2/c^2))^(1/2)
when v<<c | c- speed of light , v- the velocity with which the primed frame moves in the x direction with reference to the unprimed frame. γ
thus, γ = 1/(1-0)^(1/2) = 1
substituting for γ in the Lorentz transformation equations
x' = x-vt , y' = y, z' = z, t' = (t-0)(1)= t
Lorentz transformation converges to Galilean transformation when v<<c.
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