Abstract

Using the Heisenberg uncertainty principle in a semi-classical formalism, it is shown that mass and nuclear structure can be accounted for by the configuration of electric charge under only the Coulomb potential. In this approach, mass is accounted for by the confinement of electric charge. Tri-polar Coulomb interactions are responsible for the stability of the proton and the neutron, and bipolar Coulomb interactions provide the required stability for the nuclei. Initial calculations from this model are consistent with known nuclear binding energies and configuration. In addition, this approach gives an ab-initio estimates for the radius and mass of the quarks, and the radius of the proton. The estimated value for the radius of the proton is 1 fm, in close agreement with the known value of 0.83-0.88 fm. There is only electric charge (charge). That is the main idea of this work. It is meant in the sense that the distribution of charge is enough to explain the observable universe. To establish this novel claim, it will be argued that gravitational interactions and the interaction of sub-atomic particle can be explained by relatively simple considerations of the confinement and configuration of positive and negative charge. In this work the angular, magnetic , and spin degrees of freedom will be ignored. This aspect is left for future studies. A semi-classical approximation will be used where quarks are assumed to be "particles" with sharp boundaries. As a side note it is mentioned that any measurement would occur over a finite time interval, hence, the measured charge density will be smooth. The results of both Special and General Relativity are assumed. [1] They include the relationships between mass and energy, between space/time/momentum/energy, and as a general theory for gravitational interaction between mass. However, as will be discussed below, it is proposed that mass comes about from the potential energy of confined charge. Historically, mass entered physics at a very early stage since it is one of the most easily experienced physical measurements. Having the entrenched position in classical physics it is understandable how the notion that mass results from the quantum confinement of charge [2] is conceptually challenging. Similarly, the first observations of nuclear interactions [3, 4] involved protons and neutrons confined to a nucleus tiny in comparison to the size of the electron orbitals. [4, 5] Hence, it was unclear how this positive charge is confined and the strong nuclear force was conjured for an apparently missing "strong" attraction to hold the protons and nucleus together. [5] However, with the establishment of the quark model of the nucleons [6-8] it is possible to understand nuclear stability as a quantum outcome of Coulomb interactions , without the need for any addition interactions. Possibly the most fundamental idea of quantum mechanics is the Heisenberg Uncertainly Relations (HUR): [9-11] ∆x ∆p ħ. (1) ∆t ∆E ħ. (2) These expressions describe the smallest possible quantum states, with x the position, p the momentum, t time, E the energy of a state, and ħ the Planck constant. While the HUR have been around for almost 100 years, they still conceal many exciting discoveries. It is guessed that we still do not understand the mathematics and physics prescribed by the HUR. Here, their implications for charge systems will be used. For one thing, the HUR imply that nothing can have zero momentum in the quantum world. The HUR also hints to a finite minimal quantum state. States as such will be refereed to here as Minimal Quantum States (MQS). For these states an equality will be assumed for the inequality in Eqs. 1 and 2. An MQS is a