Invariance of Maxwell's equation under Lorentz transformation and validity of Space-time

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Rigorous calculation of transformation Maxwell's equations under Lorentz transformation using tensor algebra and invariance of space-time interval. This lays down the groundwork for defining special relativity in 4 dimension.
This should be the the 2nd video of the special relativity series although I haven't uploaded the 1st one yet.
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Although I understand the derivation at 11:45, left panel, it is illegal in a tensor equation to have the same index four times in one term. The first two should have been another Greek letter like nu but not mu. You also have a Kronecker delta with both indices alpha, it should have been Kronecker delta sub mu sup nu.

danielvolinski