Prove that a metric tensor is symmetric.
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Assume . Because it’s irrelevant what letter we use for our indices,
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Then
So only the symmetric part of would survive the sum. As such we may as well take
to be symmetric in its definition.
— edited Jun 15 ’15 at 22:48
— rob
— answered Jun 15 ’15 at 17:52
— FenderLesPaul
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— Why is the metric tensor symmetric?
— Physics StackExchange
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1.
means that
So in
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we cannot cancel out on both sides. In other words, we do NOT assume that
in the first place.
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2.
means that
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3. “… only the symmetric part of would survive the sum” means that only the sum
is physically meaningful.
— Me@2020-08-14 03:34:05 PM
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2020.08.14 Friday (c) All rights reserved by ACHK