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