To the memory of Jacob Klien and Alexander Koyre
Fifth Impression—"M": The implications for prime number distribution as "formally Indicated" in my previous four papers—explorations of conics,
Or the final royal road to Reimann's hypothesis
In this final attempt to confront the reasoning which I have previously offered for the "resolution" of the Riemann Hypothesis, I would like—in a paper I believe may be the last of my short life—to point the way, if I can, to those mathematicians and cosmologists of the future, possibly, to Dr. Debranges, to work out fully what time has not permitted me to fully elucidate; because I am not a professional physicist or a mathematician—
In fact, The University of Chicago has these days kept me busy worrying mostly about my checking account balance as well as a legacy of inherited diseases that were not well treated early in my life (but such are the costs of attempting to create a "Master Race," and its associated "Fall-out," a tremendous amount of human carnage, by my estimate:—
Shivas and Vishnus do not worry about destroying worlds or the associated human carnage: As my girlfriend, Laura Deluna, whom I love more than time could ever allow me to express, said to me once, "Maybe God just creates," that is in the abscence of moral considerations—as Nietzschean will-to-power as art, "Beyond Good and Evil," world and cosmos formation have a prerequisite—of world and cosmos destruction!)—I cannot give the final "proof" of the Reimann Hypothesis, but, at best, can show which Hamiltonian and Hermitian operator must be the focus of the solution, if the ground is to be gained at last.
I have already pre-figured everything in my previous papers, but in this note, want to carry just a bit further my suggestion about Dirac's centrality in that I believe his system to contain the final key to the Riemann Hypothesis, and, if I am right, we will be able finally to transform the "hypothesis" in to a "proof"—a proof beuatifully embodied in the paradoxically simplest, because, on my analysis, the atom which contains within itself all other atoms and all atomic states, the hydrogen atom: This atom is special, I have indicated, because it has a "neutrino" concealed within its heavy proton (which is why I suspect that all neutrino detectors use water as the source of detection: After all, the Ionic philosopher Thales may have been right in his assertion that "All is water,").
And this neutrino, if my reasoning is sound, contains within it, an electron and positron, which together, when liberated from the heavy proton nucleus—as happened in the New Mexico desert at the advent of the Manhattan Project—create a dual-light cone or conic geometry that is the literal articulation of all space-time paths that are possible, with one particle moving in one time direction, the opposite in the other direction—thus articulating the "Universal Wave Function":—
Which is to say, that the Erwin Schrodinger's "Time dependent" equation is the necessary prerequisite to the articulation of the "Universal Wave Function," which culminates in the creation of the "state of all states"—i.e., the comprehensive elaboration of a conic geometry, that allows one to see—from a "horizon," interfacing the two cones, space-time events, ex hypothesi, from the present moving forward and, from the future, paradoxically, moving backward.
This has the most significant implication—and if I am right—holds the key to the solution—at last, after a hundred and fifty years of searching (but I think the University of Chicago had that key as well as the entire Hilbert program as early as, if not earlier than, 1959, the year of the publication of Leo Strauss' "Thoughts on Machivelli and the year that Riemann (Maimonides) propounded the hypothesis; this is, i conjecture, further related to Strauss' subsequent study "Socrates and Aristophanes," published one hundred years exactly after the death of Riemann and in my own birth year, 1966.
The conic or dual light-cone geometry expressed when the hydrogen nucleus is liberated, as it were, has the ability to have all of its space-time points mapped one onto the other, and since these values are opposites—one a set of real integers, one a set of imaginary complex numbers—they cancel each other exactly—thereby creating the "critical strip" of zeros that are the inbuilt zeta function of the periodicity of the hydrogen nucleus: The Hamiltonian and Hermitian operater, therefore, has to be sought in the critical limit or Chandraskar limit principle, which is exactly the quantum gravitational point at which a sun collapses into a black hole, and creates a Nietschean eternally-recurring cyclical cosmos, which continually expands or redshifts as Hubble observed in the early 2oth century:—
It is precisely this process that gaurentees the infinity of the primes and their non-random distribution, for they are the complete collection of ever-expanding space-time points on the expanding—and eternally-recurring— light cones and their topographic tranformations (as may be implcit in the Poincare conjecture and, by extension, in Stephen Hawking's "no boundary principle" of quantum cosmology). The Hamiltonian and Hermitian operators, therefore, should already be contained in Einstien's Special and "General Theory of Relativity," at the region discovered by Chandraskarr, which should be the gravitational unit theorized and calculated by Paul Dirac when he offered his "Large Numbers Conjecture."
The infinite cycling of this system, as I have already indicated, explains or offers a theory for 1) the Strong Nuclear Force; 2) the deep reason for the "Heisenberg Uncertainty Principle"—namely, that an energy/mass conversion takes place within the hydrogen atom—indeed within all matter as implied by L. Debroglie—, which transfers its energy, in nanosecond peridicity, from the particle-like nucleus, to the wave-like energy expressed by the electrons and positrons, thereby disallowing simultaneous measurement of position and velocity, for the two do not, on this model, co-exist, but exist by alternation between states of energy and mass conversion, as Einstien predicted in his famous relation; 3) An explanation of so called "dark matter"—which, on this view, is the energy that exists in the never completely vacuous space time which is always receiving bursts of energy from these nuclei undergoing transition from energy to mass and mass to energy; 4) The non-commutative algerbra of Heisenberg's Matrix Mechnics, for the Matrix Mechanics, on my view, embodies the Dirac particle/anti-particle duality, and this involves particles moving in two directions of time, and so, cause events that are non-commuting—cause to effect is not the same as effect to cause; 5) Moreover, the deep geometric basis and genesis of the distribution of the prime numbers, for on certain areas of the dual-light cones there will be a large number of primes, while on other areas of the matrix they will be less evenly spaced, but always in such a way that a one-to-one mapping can be performed, which produces—to eternity in potential—the infinity of the zeros of the zeta function; 6) Because this system infinity recurs—in each cycle rebinding the heavy hydrogen nuclei and its composite neutrino (consisting of an electron/positron), the second Law of Thermodynamics is violated, allowing our cosmos to cycle to eternity. As Stephen Hawking expressed it profoundly: "God created the Integers," which is an echo of Plato's statement in his "laws": God Geometrizes"!