What do we get if we sum all the natural numbers? This was the question we asked in our recent Numberphile video. The answer we gave was, to the surprise of many I'm sure, −1/12 . It's by no means obvious, but this is the only sensible value one can attach to this divergent sum. Infinity is not a sensible value. In my opinion, as a physicist, infinity has no place in physical observables, and therefore no place in Nature. David Hilbert, one of the founding fathers of quantum mechanics, described infinity as "a mathematical abstraction that does not have a physical content". I think most physicists would firmly agree with this sentiment. The trouble is that divergent sums like the one we discuss in the video do appear in calculations of physical observables, such as the Casimir energy, or in the dimensionality of the Universe in bosonic string theory. Therefore, only a very brave individual would dream of attaching the value infinity to sums like this. Minus a twelfth is far less crazy a value when you start talking about Physics.
Fonte: aqui
Postagens
