Quantum computing rests upon two theoretical pillars: superposition and entanglement. But some physicists say that this is a very shaky foundation and quantum computing success will have to be based on a different theoretical foundation. The g-qubit theory supports that point of view. Current article is the first one of two and about the superposition principle. Quantum superposition principle states that any two quantum wave functions can be superposed, and the result be another valid wave function. It specifically refers to linearity of the Schrodinger equation. In the g-qubit theory quantum wave functions are identified by points on the surface of three-dimensional sphere . That gives different, more physically feasible, not mysterious, explanation of what the superposition is.
Quantum computing rests upon two theoretical pillars: superposition and entanglement. But some physicists say that this is a very shaky foundation and quantum computing success will have to be based on a different theoretical foundation. The g-qubit theory supports that point of view. Current article is the first one of two and about the superposition principle. Quantum superposition principle states that any two quantum wave functions can be superposed, and the result be another valid wave function. It specifically refers to linearity of the Schrodinger equation. In the g-qubit theory quantum wave functions are identified by points on the surface of three-dimensional sphere . That gives different, more physically feasible, not mysterious, explanation of what the superposition is.
Quantum computing rests upon two theoretical pillars: entanglement and superposition. But some physicists say that this is a very shaky foundation and quantum computing success will have to be based on a different theoretical foundation. The g-qubit theory supports this point of view. Current article is the second one of the two and about the entanglement. It gives different, more physically feasible, not mysterious, explanation of what the entanglement is. The suggested formalism demonstrates that the core of future quantum computing should not be in entanglement which only formally follows in conventional quantum mechanics from representation of the many particle states as tensor products of individual states. The core of quantum computing scheme should be in manipulation and transferring of wave functions on as operators acting on observables and formulated in terms of geometrical algebra. In this way quantum computer will be a kind of analog computer keeping and processing information by sets of objects possessing infinite number of degrees of freedom, contrary to the two value bits or two-dimensional Hilbert space elements, qubits.
Superposition and entanglement are two theoretical pillars quantum computing rests upon. In the g-qubit theory quantum wave functions are identified by points on the surface of three-dimensional sphere S3. That gives different, more physically feasible explanation of what superposition and entanglement are. The core of quantum computing scheme should be in manipulation and transferring of wave functions on S3 as operators acting on observables and formulated in terms of geometrical algebra. In this way quantum computer will be a kind of analog computer keeping and processing information by sets of objects possessing infinite number of degrees of freedom, contrary to the two value bits or two-dimensional Hilbert space elements, qubits.
Quantum mechanics stands as one of the most profound and successful theories in the history of physics. This paper provides a comprehensive review of the foundational principles, mathematical formalism, and modern applications of quantum mechanics. Beginning with the historical development of the theory, we examine core postulates including wave-particle duality, the Heisenberg Uncertainty Principle, and the Schrödinger equation. We further explore quantum entanglement, quantum tunneling, and spin, and discuss their roles in cutting-edge technologies such as quantum computing, quantum cryptography, and quantum sensing. Diagrams and mathematical representations are included to aid conceptual clarity. This review aims to serve both as an educational reference and a bridge to current research frontiers.
Abstract Quantum mechanics is spectacularly successful on the technical level but the meaning of its rules remains shrouded in mystery even more than seventy years after its inception. Quantum-mechanical probabilities are often considered as fundamentally different from classical probabilities, in disre-gard of the work of Cox (1946) -and of Schrödinger (1947) -on the foundations of probability theory. One central question concerns the superposition principle, i. e. the need to work with inter-fering wave functions, the absolute squares of which are probabilities. Other questions concern the relationship between spin and statistics or the collapse of the wave function when new data become available. These questions are reconsidered from the Bayesian point of view. The superposition principle is found to be a consequence of an apparently little-loiown mathematical theorem for non-negative Fourier polynomials published by Fejer in 1915 that implies wave-mechanical inter-ference already for classical probabilities. Combined with the classical Hamiltonian equations for free and accelerated motion, gauge invariance and particle indistinguishability, it yields all basic quantum features -wave-particle duality, operator calculus, uncertainty relations, Schrödinger equation, CPT invariance and even the spin-statistics relationship -which demystifies quantum mechanics to quite some extent.
Lying in the core of the conceptual scheme of current quantum theory, the notion of quantum superposition is a consequence of the quantum-mechanical superposition principle. However, relying on precise but not attainable space or time coordinates, quantum superposition makes little sense physically if we use it to describe or explain experimental results obtained by measurement. Space or time is usually modeled by a metric space endowed with the usual distance function. Irrelevant to instrument precision and measurement accuracy, unattainability of precise coordinates is a well-established mathematical fact following from properties of the corresponding metric topology, and hence rules out completely, in principle, the possibility for us to obtain precise coordinates by measurement in actually performed experiments. In classical mechanics, unattainability of precise coordinates is hardly noticeable, and measurement results obtained in classical physics can still be reasonably explained even though precise coordinates are unattainable. However, when we explain measurement results obtained in quantum physics, unattainability of precise coordinates should not be omitted. In the conceptual scheme of current quantum theory, omission of unattainability of precise coordinates is an unfortunate flaw, which is largely responsible not only for the invalidity of quantum superposition in description of the physical world but also for various ineligible applications of quantum mechanics. Nevertheless, in no sense does the flaw imply quantum mechanics as a successful theory failing to be correct. As shown in this article, the flaw is repairable. By taking into account unattainability of precise coordinates, we can reinterpret the meaning of quantum superposition to repair the flaw without affecting eligible applications of quantum mechanics while avoiding all the ineligible applications.
The principle of superposition of states requires that the states of a dynamical system form a linear vector space. This hypothesis of linearity has usually been regarded as a fundamental postulate in quantum mechanics, of a kind that cannot be explained by classical concepts. Indeed, Dirac [2, p. 14] comments that "the superposition that occurs in quantum mechanics is of an essentially different nature from any occurring in the classical theory, as is shown by the fact that the quantum superposition principle demands indeterminacy in the results of observations in order to be capable of a sensible physical interpretation."