A discussion is given of the uncertainty principle in view of the introduction of a Gravitational Planck Constant. The need for such a gravitational constant is shown first. A reduced electromagnetic Planck constant and the analogous reduced gravitational Planck constant are defined as h/e^2 and H/m^2 respectively. An attempt is made to reconcile the quantum uncertainty concepts with a deterministic view of the physical world. This conclusion is achieved trough the detailed analysis of the measurement procedures of physical quantities.
A discussion is given of the uncertainty principle in view of the introduction of a Gravitational Planck Constant. The need for such a gravitational constant is shown first. A reduced electromagnetic Planck constant and the analogous reduced gravitational Planck constant are defined as h/e^2 and H/m^2 respectively. An attempt is made to reconcile the quantum uncertainty concepts with a deterministic view of the physical world. This conclusion is achieved trough the detailed analysis of the measurement procedures of physical quantities.
This paper presents a conceptual reinterpretation of the Heisenberg Uncertainty Principle within the relational framework developed in the preceding papers of this series. In conventional quantum mechanics, the uncertainty relation between position and momentum is typically understood as a limitation on the simultaneous precision with which these quantities can be measured. In this work, we explore an alternative interpretation in which the uncertainty principle reflects a structural constraint on the types of physical states that can exist within spacetime. Within the relational lens framework, physical systems exist between two fundamental limiting conditions: gravitational singularities, representing perfect spatial localization, and the speed of light, representing maximal propagation through spacetime. From this perspective, position and momentum can be interpreted as expressions of two complementary tendencies—localization and propagation—that define the allowable configurations of physical systems. Under this interpretation, the uncertainty relation expresses the minimum balance that must exist between these tendencies for a physical system to remain within spacetime. Planck’s constant (ħ) therefore represents the smallest relational scale separating these two boundary conditions. Rather than reflecting a limitation of measurement alone, the uncertainty principle may be understood as a structural feature of relational spacetime itself. This paper is conceptual in nature and does not introduce new empirical claims. Instead, it proposes a relational interpretation of the uncertainty principle that links quantum behavior with the broader boundary structure explored in earlier papers in this series.
Background: There has been altercation for and against Heisenberg uncertainty principles, whose earlier mathematical form has assumed other forms. This is despite the fact that the original form ought to be for the hydrogen atom only. Methods: the method is purely theoretical and computational, involving the use of spectroscopic data in the literature. Aim and objectives: The aim of the research was to show that half of reduced Planck’s constant (ℏ/2) cannot be restricted to a lower limit to the product of the uncertainty in the momentum and the uncertainty in the position. The objectives were: 1) to undertake the derivation of an equation unifying the Heisenberg uncertainty principle and atomic principles; and 2) to give evidence that half of the reduced Planck’s constant (ℏ/2) is strictly for hydrogen. Results and discussion: With hydrogen apart from other elements, fractions and multiples of ℏ/2, 0.0053–0.0264 corresponding to the radii ranging between a0/100 and a0/20 (a0 is the Bohr’s radius), and 5-26 corresponding to the radii ranging between 4a0 and 49a0 were demonstrated; the probability of locating the position and momentum increases with decreasing radii. Conclusion: The equations for the determination of the fractions and multiples of ℏ/2 were derived. Computation gave values less than and higher than ℏ/2; the latter was found to be restricted to hydrogen only. The possibility of linking the product of uncertainties in position and momentum to Pa may be reserved for a future study.
Initially it is proposed to interpret the fact that the delay of gravitational interaction in a binary system causes the emanation of gravitational waves, as a generalization of the Newtonian Principle of action and reaction. Then, the impact of such a concept is shown for a situation with mutual and simultaneously acting electromagnetic and inertia force, as well as consequences for a possible validity of the Mach principle. Further, the same phenomenon of retardation of the physical interactions is applied on the mechanistic Bohr model of the hydrogen atom together with the Indeterminacy principle, which results in a realistically adequate quantum description of the atom involving the pertinent de Broglie wave. Finally, the physical conclusions made before are discussed from a philosophical point of view; a new `para-deterministic' concept is presented being an alternative to both the deterministic and holistic views of our world.
Planck's constant h is considered to be a fundamental Universal constant of Physics. And although we can experimentally determine its value to great precision, the reason for its existence and what it really means is still a mystery. Quantum Mechanics has adapted it in its mathematical formalism, as it also has the Quantum Hypothesis. But QM does not explain its meaning or prove its existence. Why does the Universe need h and energy quanta? Why does the mathematical formalism of QM so accurately reflect physical phenomena and predict these with great precision? Ask any physicists and uniformly the answer is that's how the Universe works. The units of h are in energy-time and the conventional interpretation of h is as a quantum of action. But in this brief note we take a different view. We interpret h as the minimal accumulation of energy that can be manifested in our measurements. Certainly the units of h agree with such interpretation. Based on this we provide a plausible explanation for the existence of Planck's constant, what it means and how it comes about. We show that the existence of Planck's constant is not so much dictated by the Universe but rather by Mathematics and the inner consistence and calibrations of Physics.
In this paper, using two different formulations, we attempted to first provide an overview of mathematical interpretations of Heisenberg's uncertainty principle. This was done in order to emphasise the mathematical justification for the uncertainty principle's existence. First, we went over in detail the matrix formulation found in Schrodinger's original paper on uncertainty. Next, we reviewed the mathematical proof of the uncertainty principle in a Fourier series formulation and examined the results. We attempted to provide a comprehensive overview of the modified forms of the uncertainty relation in the Quantum Gravitational, Relativistic, and Entropic domains along with other variants after realizing that the most well-known uncertainty relation is not universal. All of these concepts also demonstrate a great deal of potential for use in the emerging new technologies. Our goal was to gather all of these dispersed variations of the uncertainty principle in one location. The current state of these theories, as well as their applications and limitations, are thoroughly discussed.
This paper is a small discussion about the uncertainty principle. With the great discoveries and researches made by predecessors, I try to answer some questions within the uncertainty principle. Using the definition of momentum, the momentum in de Broglie wave, the property of cosine function, the Euler’s formula, the basic property of plane wave, the law of derivative, the energy of quantum discovered by Max Planck, the photon energy discovered by Albert Einstein, the energy equation of a system and the Hamiltonian operator, I figure out the Schrodinger equation successfully. With the help of Schrodinger equation, the possibility density of a wave function, the concept of normalization, the average value of position and momentum, the Fourier transform, the integration by parts and the limit of normalized wave functions, I find the position operator and the momentum operator. Then using some knowledge of the standard deviation and the variance, the concept of inner product of vectors, some property of Dirac symbol, the law of calculation of complex number and the law of operator calculation, I obtain the general uncertainty relationship of abstract mathematical quantities. According to the general relationship, I get the inequality of uncertainty principle, and discuss the specific relationship between the position and the momentum. After getting the inequality, I use Heisenberg’s experiment of measuring an electron by using the γ ray to hit the electron to explain why we cannot measure the position and the momentum simultaneously. Based on Heisenberg’s experiment, I give my own explanation by discussing the earth and a spacecraft. Transforming the perspective, we can easily see how the accuracies of position and momentum change. In addition, I attempt to figure out why the uncertainty exists. However, I can only explain it by discussing the time and frequency in mathematical method and have no idea to work it out in a pure physics approach.