Related papers: Physical interpretation of the Riemann hypothesis
A formulation of quaternionic quantum mechanics ($\mathbb{H}$QM) is presented in terms of a real Hilbert space. Using a physically motivated scalar product, we prove the spectral theorem and obtain a novel quaternionic Fourier series. After…
The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and…
The relational interpretation of quantum mechanics (RQM) has received a growing interest since its first formulation in 1996. Usually presented as an interpretational layer over the usual quantum mechanics formalism, it appears as a…
We discuss new approaches to fundamental problems of mathematics and mathematical physics such as mathematical foundation of quantum field theory, the Riemann hypothesis, and construction of noncommutative algebraic geometry.
A variant for the Hilbert and Polya spectral interpretation of the Riemann zeta function is proposed. Instead of looking for a self-adjoint linear operator H, whose spectrum coincides with the Riemann zeta zeros, we look for the complex…
An attempt is made to formulate quantum mechanics (QM) in physical rather than in mathematical terms. It is argued that the appropriate conceptual framework for QM is "contextual objectivity", which includes an objective definition of the…
It is demonstrated that the reason for the diversity of interpretations of quantum mechanics is that they are not connected by continuity relations with classical physics, and also the reason is the impossibility of operationalist…
This paper proposes a reformulation of the Riemann Xi function in order to investigate its properties. The reformulated function, which depicts the Xi function as the weighted sum of incomplete gamma functions, is validated, and a number of…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
It is argued that the usual postulates of quantum mechanics are too strong. It is conjectured that it is possible to interpret all experiments if we maintain the formalism of quantum theory without modification, but weaken the postulates…
A GGC (Generalized Gamma Convolution) representation of Riemann's Xi-function is constructed.
In this tenth paper of the series we aim at showing that our formalism, using the Wigner-Moyal Infinitesimal Transformation together with classical mechanics, endows us with the ways to quantize a system in any coordinate representation we…
This note states and proves a representation theorem for regular quantity functions, based on the theory of quantity spaces, thereby giving a new perspective on dimensional analysis and the classical $\pi$ theorem.
Quantum Mechanics, the physical theory describing the microworld, represents one of science's greatest triumphs. It lies at the root of all modern digital technologies and offers unparalleled correspondence between prediction and…
The ongoing progress in quantum theory emphasizes the crucial role of the very basic principles of quantum theory. However, this is not properly followed in teaching quantum mechanics on the graduate and undergraduate levels of physics…
We propose an interpretation of physics named potentiality realism. This view, which can be applied to classical as well as to quantum physics, regards potentialities (i.e. intrinsic, objective propensities for individual events to obtain)…
The probabilistic prediction of quantum theory is mystery. I solved the mystery by a geometrical interpretation of a wave function. This suggests the unification between quantum theory and the theory of relativity. This suggests Many-Worlds…
Through a new interpretation of Special Theory of Relativity and with a model given for physical space, we can find a way to understand the basic principles of Quantum Mechanics consistently from Classical Theory. It is supposed that…
As well known, the study of Riemanns zeta function {\zeta}(s) involves the related entire function {\xi}(s). A close relative of {\zeta}(s) is the alternating zeta function {\eta}(s). Similar to {\zeta}(s), also {\eta}(s) has a…
The Riemann Hypothesis is not proved yet and this article gives a possible proof for the hypothesis which confirms that the only possible nontrivial zeros of the Riemann zeta-function has its real value equal to 1/2. From the result, the…