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

c² +¹2 + x¹² + y^² + z²¹² ‡ c²₁² + x² + y² + z²
Transcribed Image Text:c² +¹2 + x¹² + y^² + z²¹² ‡ c²₁² + x² + y² + z²
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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