Sometimes I read about connections between "advanced math" and quantum physics, but I am skeptical of these claims. I'm not an expert at math nor quantum physics but I will let the links speak for themselves: And others. Must I bring those other passports whenever I use the BNO one? If you pretend these were drawn from a random variable and calculate the correlations, you get the same result as if you just took a random Hermitian matrix like the kind that is used to model heavy nuclei. I can believe or understand the connections to calculus, vector calculus, differential equations, or linear algebra, but when I read about connections with prime numbers and the Riemann zeta function, I get very skeptical and confused. Riemann zeta function, function useful in number theory for investigating properties of prime numbers. Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. What is meant with energy levels? For all values of z>1 the function will coverage to a real value, which doesn’t go against our intuitive knowledge. Incidentally, I found this post that has a few more examples, including the two above. I suspect that Conway's use of the elements to label the "atomic" look and say sequences was a linguistic/numerical joke, not a serious connection to physics. The hypothesis is that, apart from some trivial exceptions, all of the zeros of this function lie on a straight line (known as the critical line). Now to prove the problem we started of with, 1+2+3+4+… Let this = S3. This is not to say that there are no connections/applications of Riemann Zeta to physics. Can someone provide a physical — not mathematical — intuition for the phase in a quantum wavefunction? We are going to add S2 to itself, but shift each term to the right. The sum depends on the term you stop at. Make a minimal and maximal 2-digit number from digits of two 3-digit numbers, Turning right but can't see cars coming (UK). Why did the F of "sneeze" and "snore" change to an S in English history? /MediaBox [0 0 612 792] What prevents chess engines from being undetectable? So the formula I quoted [tex]\zeta(z)=\sum_{n=1}^{\infty}1/n^{z}[/tex]. And one more thing guys, Happy New Year!! Proving that the sum of all real integers is -1/12. Hurwitz zeta function. But that is not a direct use of riemann zeta so maybe just a fun fact :-). So by simply dividing both sides by 2 we get S2=S1/2. ζ(z)= ∑(n^-z). The Riemann zeta function encodes information about the prime numbers —the atoms of arithmetic and critical to modern cryptography on which e-commerce is built. University of Bristol Luck, P ... 2.1 The Zeta function of Riemann. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. JavaScript is disabled. Honestly, I like his blog and his fascination with physics, and also I don't know enough to give you any worthwhile opinion of the complete link between the zeta to physics. If you pretend these were drawn from a random variable and calculate the correlations, you get the same result as if you just took a random Hermitian matrix like the kind that is used to model heavy nuclei. Usually pure mathematics supports physics, supplying the mathematical tools with which physical systems are analysed, but this is a case of the reverse: quantum physics is leading to new insights into number theory. Why echo request doesn't show in tcpdump? What aspects of image preparation workflows can lead to accidents like Boris Johnson's No. Change ). 2. Is this a correct proof of the Riemann Hypothesis. The calculation uses the wave functions that act as what we call smoothing functions in mathematics and we find the famous $\sum n=\frac{-1}{12}=\zeta(-1)$ as a proportionnality factor for the amplitude of the force. In his article "Statistical theory of numbers", Julia elaborates on the functional equation of the Riemann zeta function: "If one calls the theta function of the one-dimensional lattice one has: and one can show for Re(s) > 1 the remarkable formula: The Poisson summation formula implies (partly) the modularity of the theta function and leads to 3.) You used a summability method. However when we take values of z<1 things tend to stop making sense. Surprisingly enough… it converges to -1/12. My BNO passport lists my other passports under "observations." Queens Road What are you trying to do? �KYd�Y<0k��Y��>1&Ip�qE+l3�h�j��k|vb�cN$ �;��& �U��F;�ڟ@�X��mD���r�O���W�ܧ��՚j7=coq#h�yĘt�rh�\WC��&�+@y�����g�4i\�SI�gK�hЖG>�l��Jw�^ӵ�=U�����ti�� �Xu��mK����h���7R��p�X�-.��eN�5Ԭ܃,��%Ruz�p3�04#Հ�7gj-фzH������D˃OQ�PQ��@�5%W@�o zP���l�A���+�m��k����Z�~3���?_ �\�������Կ����C��C��.|){�����t��(����uP���)��x�J���#5gB�r�{/� J����A�o����w.�ab:BМ��%bS��*��[\�5>2j��6��������������\��3ًۀ�����7�hJ�!�R�"8#E�B(.�q$���*^��w�t?�ڲ>�.�S��vs��Q��H�KC��o����5��G��O�,� ����l��� q����dM`G[95`��̻G}�8�������j����e�R���#7��w�����'�eoS��H�$�-�t�뾁C%���Q�7����\���� �^}�o�g8��^)z�;K�e���$�]w��hM*�ՠS��}�#����\��MG��W��Dt�������L��g���Y�i����`9�s��/|�K Change ), You are commenting using your Google account. If you ask a different question about the Riemann zeta function, there is no reason for it to still keep this connection. So get another source, or another answer from this site...Without Riemann, building directly on the work of Gauss, we would not have General Relativity, but that was because his work was, Prime numbers are directly related to quantum physics, en.wikipedia.org/wiki/Look-and-say_sequence#Cosmological_Decay, Creating new Help Center documents for Review queues: Project overview, Feature Preview: New Review Suspensions Mod UX, Role of physics in the zeta function $\zeta$ and the Riemann hypothesis, Hamiltonian related to Riemann zeta function, Applications of the Spectral Theorem to Quantum Mechanics.
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