May 25, 2023 update: abstract
May 30, 2023 update
Feynman, Helmholtz, Kramers, Rollnik, Schpolski, Spatschek, Treder
Dec 2, 2020
The mathematical-dynamic and the statistical physical-mechanical "realities"
The proposed model of perpendicular (mechanical, potential, and ground state energy) worlds is about a purely mathematical dynamical world (electrinos & positrinos, quanta information) and a physical-mathematical kinematical and potential anergy world (physical space, physical time, physical mass / matter, physical forces, and actions), including a biological-physical world (atoms & molecules, viruses & cells, biological information, Schrödinger’s concept of biologically relevant repeated differentials (*), Husserl's concept of internal time-consciousness, (HuE)).
The „two-mechanical vs. dynamical realities“ fit to M. Planck‘s distinction between physical-statistical type of laws and „dynamical“ laws, (PlM), and to E. Schrödinger’s two principles, „order from order“ and „order from disorder“ differentiating between the two related underlying mechanisms of biological and physical laws governing regular courses of events, (ScE).
The „energetical world decomposition“ model in combination with concepts like potentials, potential operators, hyperboloids in Krein space theory and least action principles also supports A. Unzicker’s vision „to form a consistent picture of (a mathematical) reality by observing nature from cosmos to elementary particles“, (UnA), (UnA1), (UnA2).
Home | Alexander Unzicker (alexander-unzicker.de)
The current paradigm/narrative of physical systems
- "the behavior of a physical system depends on a scale (of energies, distances, momenta, etc.) at which the behavior is studied. Very generally speaking, the method of renormalization group is a method designed how to describe how the dynamics of some system changes when we change the scale (distance, energies) at which we probe it,. … Physics is scale dependent (requiring only a mathematical metric space framework, which has no geometric structure at all), and at each scale, we have different degrees of freedom and different dynamics, i.e. physics at a large scale decouples from the physics at a smaller scale. ...
… In classical mechanics there are three scales of distance, time, and mass. In non-relativistic quantum theory there are two scales: the mass can be expressed through «time» and «distance» using the Planck constant) and classical relativity («time» can be expressed via «distance» using the speed of light). In relativistic quantum theory there is only the scale of distance (or equivalently – the scale of (its inverse) momenta), (DeP) p. 551.
In the current narrative the physics is scale dependent and decoupling. The down (complexity) causality thinking results into a degrease of the number of scales, while the number of «Nature» constants increases. The effect of the required auxiliary scales, cutoffs, etc. on the physics is encoded into the renormalization group equation. The "case" if there is no related (G-invariant) renormalization realisation (example ground state energy) is called "symmetry break down", (DeP1) p. 1119 ff.. THe first quantization was about Einstein's discrete energy parcels, the photons, the second quantization was about Dirac's electron spin 1/2 model, where the fine structure constant becomes an error term with regards to the Lamb shift phenomenon, which is not in line with the Dirac model
The new paradigm/narrative
The proposed two complementary mechanical and dynamical energy field "Worlds" are built by an orthogonal sum of apropriately defined kinetical, potential, and ground state energy "worlds". There are four groups of related mechanical and dynamical energy quanta. Those energy quanta are appropriately composed by two fundamental mathematical quanta, electrinos and positrinos, governed by appropriately chosen sets of quantum numbers. The corresponding rules to build the sets of composed quanta numbers from the fundamental two quanta are purely governed by mathematical rules motivated by number theory.
The new "complementary energy worlds", which are compactly embedded into an overall fractional total energy "world" enable a solution of the 3D-Navier-Stokes millennium problem of the Clay Mathematics Institute. At the same time, the new quanta energy element concept distinguishing between kinematical and dynamical quanta types governed by "world"-specific least action potential function approximations makes the Yang-Mills equations obsolete, i.e., the related "mass gap (millennium) problem" disappears.
The link of the proposed plasma quanta potential model to the Riemann Hypothesis is when "Number Theory Meets Quantum Mechanics", (DeJ). Or more specifically, this is, when number theory meets plasma quantum dynamics providing an appropriate mathematical model for the (physical) Montgomery-Odlyzko law (where the action of the Leray-Hopf operator on Gaussian functions meets confluent hpergeometric functions of first kind), and where the Hilbert-Polya conjecture meets the Berry-Keating conjecture:
Following the idea of the above, which is in line with Planck's concept of a statistical and a dynamical physical world, the underling operator of the Hilbert-Polya conjecture (accompanied by a properly defined domain) may be represented by the sum of two Hermitian operators, where one operator is in line with the (statistical relevant) Montgomey-Odlyzko law and a second operator represents a related "chaotic dynamical" operator. Then, both operators together provide an alternative operator to the Berry-Keating "quantized" classical Hamiltonian operator of a particle of mass m that is moving under the influence of a potential V(x).