Use Lorentz transformations to prove the following (show work). c² +¹2 + x¹² + y^² + z²¹² ‡ c²₁² + x² + y² + z²

Answered: z²+zí+z*+z¹z³ #ziz+zık +zıx + zitza

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Use Lorentz transformations to prove the following (show work).

Expert Solution

Step 1

We know that by Lorentz equation for a moving inertial frame with velocity v with respect to a other inertial frame.

x'=[1/√(1-v²/c²)](x-vt)

y'=y

z'=z

t'=[1/√(1-v2/c2)](t-vx/c²)

We can proof the given relation by help of Lorentz transformation.

We can take Left hand side of given relation as following and further solving

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