Related papers: Quantum mechanics based on real numbers: A consist…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
The necessity of complex numbers in quantum mechanics has long been debated. This paper develops a real Kahler space formulation of quantum mechanics [19], asserting equivalence to the standard complex Hilbert space framework. By mapping…
A formulation of quantum mechanics, which begins by postulating assertions for individual physical systems, is given. The statistical predictions of quantum mechanics for infinite ensembles are then derived from its assertions for…
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…
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 mathematical formulation of Quantum Mechanics is derived from purely operational axioms based on a general definition of "experiment" as a set of transformations. The main ingredient of the mathematical construction is the postulated…
Complex numbers are an intrinsic part of the mathematical formalism of quantum theory, and are perhaps its most mysterious feature. In this paper, we show that the complex nature of the quantum formalism can be derived directly from the…
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
Since its inception at the beginning of the twentieth century, quantum mechanics has challenged our conceptions of how the universe ought to work; however, the equations of quantum mechanics can be too computationally difficult to solve…
Physicists describe nature using mathematics as the natural language, and for quantum mechanics, it prefers to use complex numbers. However, whether complex numbers are really necessary for the theory has been debated ever since its birth.…
The widely accepted basis for quantum computing advantage is derived from the entanglement and superposition properties of the probabilistic interpretation of the underlying quantum mechanical formalism which in turn is widely accepted…
The fundamental principles of quantum mechanics, such as its probabilistic nature, allow for the theoretical ability of quantum computers to generate statistically random numbers, as opposed to classical computers which are only able to…
The best mathematical arguments against a realistic interpretation of quantum mechanics - that gives definite but partially unknown values to all observables - are analysed and shown to be based on reasoning that is not compelling. This…
Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
Numerical simulation of quantum systems is crucial to further our understanding of natural phenomena. Many systems of key interest and importance, in areas such as superconducting materials and quantum chemistry, are thought to be described…
Wave-particle duality is one of the basic features of quantum mechanics, giving rise to the use of complex numbers in describing states of quantum systems, their dynamics, and interaction. Since the inception of quantum theory, it has been…
The quantum mechanical measurement problem does not arise in the quantum real number approach to quantum measurements of the first kind. The attributes of individual microscopic systems in the experimental ensemble always have qr-number…
Several concrete examples in quantum information are discussed to demonstrate the importance of proper modeling that relates the mathematical description to real-world applications. In particular, it is shown that some commonly accepted…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…