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Proof of Space time invariance using Lorentz transformation

1. Use the Lorentz transformations to show that the spacetime interval is invariant, s'2 =s2 for relative motion along one direction.

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Space time invariance has been proved using Lorentz transformation. I have shown each and every step in this proof. I have used equation editor to type expressions so that the solution is neat and easy to read and understand.