> On 2 Sep 2019, at 22:31, 'Brent Meeker' via Everything List > <[email protected]> wrote: > > > > On 9/2/2019 8:57 AM, Bruno Marchal wrote: >> Indeed that can be said illustrated from the fact that in string theory, to >> get the mass of the photon right, we use 1+2+3+4+5+… = -1/12, which is a >> statement about the prime numbers, just a little bit disguised > > I'm sure you know that equation depends on assumptions about how limits are > to be taken.
Of course. That is the most axing part: that we need to invoque the prime numbers, or equivalently the zeta function, to get a reasonable account of why it make sense to say that the sum on all natural numbers is -1/12. Now this “zeta-regularisation” has become common. To justify the mass of the photon, the string theorits needs sophisticated tools (yet still essentially arithmetical) from Number theory. It is essentially arithmetical by the fact that despite its use of complex analysis in its most common formulation, the Riemann Hypothesis (Conjecture RH) is an arithmetical sentence, indeed a pi_1 (the negation of a sigma_1 sentences). If the RH is false, then even the tiny Robinson Arithmetic, which cannot even prove that for all x 0 + x = x, is able to refute RH. That has been shown by Turing: if a non trivial zero of zeta is not on the critical line, a machine can find it. The existence of such zero is of (Post-Kleene)-complexity equal to “sigma_1". Bruno > > Brent > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/584572cc-75e9-ca69-303f-1a9f907f1601%40verizon.net. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/FA86C2F1-21BD-4EAB-826A-10B884EA45C1%40ulb.ac.be.
