In this paper the following results are achieved: at first we demonstrate that Heisenberg's indeterminacy principle is based on a mathematical model that is unsound because of an inadequate use of the Fourier development and we prove a new mathematical model. In second place we show that with regard to physical quantities there isn�t theoretical indeterminacy and only the inadequacy of measuring instruments can cause working indeterminacy. Then we prove within the ambit of the new theory: the stability of orbital motions of atomic electrons, the quantized wave equation, the fine and hyperfine structure of atoms, the Lamb shift as a consequence of the relativistic correction. Results on these subjects are concordant with experimental data and are obtained without making use of probabilistic concepts. We think that only the most adequate use of mathematical models can allow a further evolution of our scientific knowledges that must be adapted to the examined physical event and supported with more valid analyses.
In this paper the following results are achieved: at first we demonstrate that Heisenberg's indeterminacy principle is based on a mathematical model that is unsound because of an inadequate use of the Fourier development and we prove a new mathematical model. In second place we show that with regard to physical quantities there isn�t theoretical indeterminacy and only the inadequacy of measuring instruments can cause working indeterminacy. Then we prove within the ambit of the new theory: the stability of orbital motions of atomic electrons, the quantized wave equation, the fine and hyperfine structure of atoms, the Lamb shift as a consequence of the relativistic correction. Results on these subjects are concordant with experimental data and are obtained without making use of probabilistic concepts. We think that only the most adequate use of mathematical models can allow a further evolution of our scientific knowledges that must be adapted to the examined physical event and supported with more valid analyses.
Abstract Modern developments of atomic theory have required alterations in some of the most fundamental physical ideas. This has resulted in its being usually easier to discover the equations that describe some particular phenomenon than just how the equations are to be interpreted. The quantum mechanics of Heisenberg and Schrodinger was first worked out for a number of simple examples, from which a general mathematical scheme was constructed, and afterwards people were led to the general physical principles governing the interpretation, such as the superposition of states and the indeterminacy principle. In this way a satisfactory non-relativistic quantum mechanics was established.
The Heisenberg uncertainty principle constitutes one of the foundational pillars of quantum mechanics and represents a definitive rupture with the deterministic ideal of classical physics. This work develops a comprehensive analysis of the uncertainty principle from a mathematical, physical, and philosophical perspective, demonstrating that it should not be interpreted as an instrumental or epistemological limitation, but rather as an ontological property inherent to the formalstructure of quantum theory.Within the framework of Hilbert spaces, self-adjoint operators, and non-commutative algebras, it is shown that uncertainty emerges necessarily as a consequence of the structural incompatibility between conjugate observables. The study articulates the uncertainty principle with classical chaos theory and the sciences of complexity, establishing a fundamental distinction between epistemological unpredictability and ontological indeterminacy. While classical chaos preserves well-defined trajectories that are practically inaccessible, quantum mechanics eliminates the very notion of trajectory as a fundamental entity.This rupture manifests itself in the granularity of phase space, the impossibility of defining exact initial conditions, and the consequent reformulation of determinism. Contemporary experimental developments designed to exclude instrumental disturbances are analyzed, reinforcing the ontological interpretation of the uncertainty principle.Finally, the implications for simulation, predictability, and quantumOverall, this work argues that the uncertainty principle does not undermine scientific rationality, but rather redefines itsscope and deepens our understanding of physical reality. Keywords: uncertainty principle; quantum mechanics; mathematical structure; non-commutative operators; chaos theory; complexity; determinism; physical ontology.
The following two questions are examined: 1o Do the unobservable parameters possess precise, though unknown, values ? 2o If these unobservable values were known, would it be possible to make precise predictions of the reults of later measurements ? The answer is shown to be negative; the questions, therefore, are not meaningless, being capable of a falsification. The inquiry leads to the establishment of a principle of anomaly, more precisely speaking, of causal anomaly, which is to be added to Heisenberg's principle of indeterminacy. This principle states that the principle of action by contact is violated whenever definite values are assigned to the unobserved quantities, i. e., when an exhaustive interpretation of quantum mechanics is used. The two most important exhaustive interpretations are given by the corpuscle and the wave interpretation; each leads to causal anomalies, though for different places. The causal anomalies can be eliminated by the use of a restrictive interpretation, which separates statements about unobserved quantities, as a third propositional class, from true or false statements. Bohr and Heisenberg have called such statements meaningless, without being able to eliminate them completely; these statements arte thus merely shifted into the metalanguage. In another version of the restrictive interpretation such statements are assigned a third truth value, the value indeterminate, and quantum mechanics is then presented in the form of a three-valued logic. The inquiry is carried through without the presupposition of any philosophical conception; every interpretation is examined with respect to the consequences to which it leads. - H. R.'
Quantum theory comprises a number of physical concepts and methods of calculation applicable to bodies on an atomic scale and consequently to the explanation of the properties of macroscopic bodies in terms of the behaviour of their constituent particles. In advanced work the theory is highly mathematical, but at an elementary level the difficulties lie mostly in the appreciation of the relevant physical ideas. Wave-particle duality, indeterminacy, the nature of a quantized state of a system and the exclusion principle cause most conceptual problems.
The initial purpose is to add two physical origins for the outstandingly clear mathematical description that Dirac has left in his Principles of Quantum Mechanics. The first is the “internal motion” in the wave function of the electron that is now expressed through dispersion dynamics; the second is the physical origin for mathematical quantization. Bohr’s model for the hydrogen atom was “the greatest single step in the development of the theory of atomic structure.” It leads to the Schrodinger equation which is non-relativistic, but which conveniently equates together momentum and electrostatic potential in a representation containing mixed powers. Firstly, we show how the equation is expansible to approximate relativistic form by applying solutions for the dilation of time in special relativity, and for the contraction of space. The adaptation is to invariant “harmonic events” that are digitally quantized. Secondly, the internal motion of the electron is described by a stable wave packet that implies wave-particle duality. The duality includes uncertainty that is precisely described with some variance from Heisenberg’s axiomatic limit. Harmonic orbital wave functions are self-constructive. This is the physical origin of quantization.
Quantum mechanics is based on the concepts of indeterminacy , indistinguishability probability amplitudes , probabilities , reversibility , superposition , and uncertainty . And yet that is only part of the essence of quantum mechanics. Using the words attached to the concepts just described provides only a partial description of what quantum mechanics really is. The other part is provided by a set of physical and mathematical principles annexed to the mentioned concepts. The beauty is that quantum mechanics becomes workable and functional just by observing its mathematical principles. There is no need for any particular interpretation. Not even the orthodox interpretation. Here, fifteen mathematical-physical principles of quantum mechanics are listed and succinctly explained.