1.
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.
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Given.
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2.
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metric tensor
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3.
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Lorentz transformation
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4.
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Lorentz transformation
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5.
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Substitute 3 and 4 into 2.
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6.
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metric tensor
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7.
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From 5, 1, and 6.
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8.
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Rearrange 7.
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9.
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∴
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From 8, since and may be arbitrary.
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10.
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Kronecker delta
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11.
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Multiply both sides of 9 by , then apply 10.
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12.
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Contracting the indices in 11.
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13.
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Contracting the indices in 12.
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14.
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Swap the order of indices in order to transpose the first of 13.
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15.
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∴
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14 may be paraphrased as .
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