Talk:Synchronous frame

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Physics: Relativity Low‑importance

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The contents of Synchronous coordinates was merged into Synchronous frame on 7 June 2017. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. For the discussion at that location, see its talk page.

Searching for a proof

I couldn't find a proof of the algebraic inequality

\varkappa _{\beta }^{\alpha }\varkappa _{\alpha }^{\beta }\geq {\frac {1}{3}}\left(\varkappa _{\alpha }^{\alpha }\right)^{2}

and that's why I tried to prove it myself. I found a partial numerical proof for the general non-symmetric case and a strict symbolic proof for the symmetric case. For the general case, I took the hint from Landau & Lifshitz and diagonalised the matrix. The proof is in the web page [1]. I haven't referenced it in the text because someone may think that I promote my site. This is not my intention.

If someone finds a proof, please include it in the article.Lantonov (talk) 17:37, 17 August 2020 (UTC)[reply]

As an idea, maybe use Cauchy-Schwarz inequality but haven't worked out details yet. Lantonov (talk) 18:30, 17 August 2020 (UTC)[reply]

I found a rigorous proof using the properties of Frobenius norm and Cauchy-Schwarz inequality and changed the web page [2] accordingly.Lantonov (talk) 09:38, 4 April 2024 (UTC)[reply]