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I've noticed that a very easy way to generate the Lorentz transformation is to draw Cartesian coordinate axes in a plane, label then ix and ct, rotate them clockwise some angle [itex] \theta [/itex] producing axes ix' and ct', use the simple rotation transformation to produce ix' and ct', then just divide out the i and c accordingly. I assume this works because rotation keeps the components of the metric tensor constant, and applying a kind of pseudo-Euclidean metric [itex]
ds^2 = d(ix)^2 + d(ct)^2 = d(ix')^2 + d(ct')^2 [/itex] is consistent with the premise of special relativity.
My question is, what other linear transformations in a plane maintain the
[ 1 0
0 1 ]
metric tensor form?
Thanks.
ds^2 = d(ix)^2 + d(ct)^2 = d(ix')^2 + d(ct')^2 [/itex] is consistent with the premise of special relativity.
My question is, what other linear transformations in a plane maintain the
[ 1 0
0 1 ]
metric tensor form?
Thanks.