Question

show that the Lorentz transformation reduces to the Galilean transformation for v<<c​

Answer 1

Answer:

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Answer 2

Answer:

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.