Derive the Lorentz transformations for time from the transformations for space.

Expert Solution

Inverse Lorentz from formation

x = γ(x' + vt'), r = 1/√1 – v2/c2

and

x' = γ(x – vt)

⇒ x = γ(γx – γvt + γt')

x(1 – γ2) = - γ2vt + γvt'

1 – γ2 = 1 – 1/1 – v2/c2 = -v2/c2/(1 – v2/c2) = - γ2v2/c2

- γ2v2/c2 x + γ2vt = γvt1

t1 = γ(t – vx/c2), For v/c → 0, γ → 1

⇒ t1 = t

Junaid answered 2 years ago

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