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The Casimir effect is a force arising from quantum effects; it shows that QFT allows the energy density in certain regions to be < 0 relative to the vacuum energy. Many physicists therefore argue that such effects might make it possible to stabilize a traversable wormhole.https://twitter.com/usmankayaniphd/status/1184642301714423808 …
The statement ζ(-3) = 1³ + 2³ + 3³ + ... = 1/120 is not true. The equals sign should not be used here.
But remember this is Twitter; due to the limited characters I can't go into these nuanced details. When I first saw "1+2+3+.. = -1/12" I knew it wasn't quite right and I wanted to learn more. I hope others will do the same. Thank you for clarifying though!
I know that it isn't true, strictly speaking. The Riemann zeta function summation only applies for Re(s) > 1 while the right hand side is assigned uniquely via analytic continuation for Re(s) < 1.https://twitter.com/usmankayaniphd/status/1184567831414870016 …
"1³ + 2³ + 3³ + ... = 1/120" isn't true (maybe I should have used quotes) as it doesn't make sense.... But there is a unique sense in which they are related even if they aren't equal; that's why we replace divergent sums with the Riemann zeta function in certain calculations.
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