International Journal of Physics, 2014, Vol. 2, No. 3, 86-95 Available online at http://pubs.sciepub.com/ijp/2/3/4 © Science and Education Publishing DOI:10.12691/ijp-2-3-4 The Rest Mass of a Particle in a Field and a General Mass Equation Mohamed Ahmed Hassan * Department of Mathematics, Faculty of Science, Ain-Shams University, Cairo, Egypt *Corresponding author: el_hmam.1113@Yahoo.com Received May 26, 2014; Revised June 07, 2014; Accepted June 22, 2014 Abstract Using a modified version of the mass vector model, Hassan (1997), we explain that the particle mass decreases (increases) if the particle in attractive (repulsive) field. The concepts of the free rest mass and the rest mass in a field are introduced. We conclude that the mass of a particle in a field changes according to the rule 2 0 / 1 ( / ) f f v c m m = − , where 0 f m is the rest mass of the particle in the field. This result is consistent with the existence of the Higgs field through the space and it causes existing particles to acquire mass. The confined theory is explained. General mass equations of a particle and of a composite particle in terms of different four forces of nature are obtained. Some applications of the general mass equation of composite particle (nucleus) are presented and discussed. Keywords: mass vector- charge vector- mass space of a force-rest mass in a field- general mass space- general mass equation Cite This Article: Mohamed Ahmed Hassan, “The Rest Mass of a Particle in a Field and a General Mass Equation.” International Journal of Physics, vol. 2, no. 3 (2014): 86-95. doi: 10.12691/ijp-2-3-4. 1. Introduction In 1997 Hassan [1] suggested a model where a one object (vector) represents the mass of the particle and its own field. He introduced the total mass of the particle concept which was defined to be t m m W = + , where m is the measured mass of the particle and W is the virtual mass which is related to the field of the particle. This idea is similar, in some sense, to the idea of the electromagnetic mass [2], where the electromagnetic field contributes to the mass of charged particles. Also, the binding energy of composite particle can be considered as the part of the mass which represents the field. In the present work we try, suggesting a general definition for the charge of any force, to give a relation between the mass and the charge of the particle. To formulate the suggested definition for the charge a mathematical model for the mass of the particle with its own field is needed. This model was given by (Hassan, 1997) [1]. A modified and extended version of this model is presented in section 3. Using this model we try to answer the question: Is there a difference between the rest mass of a free particle and its rest mass in a field? Also, we try to compare between the semi-empirical Weizsäcker mass formula, [3], of nuclei and a general mass equation which is obtained by the modified mass vector model. 2. The Charge Between electric charged particles there is electromagnetic force, without the electric charge the electromagnetic force between the particles does not exist. This means that, “the charge is the source of the force “. Also, between any two nucleons there is a nuclear (strong) force, and we have a question: What is the source of the nuclear force? We can, as in the case of electromagnetic force, suppose that a nuclear charge is the source of the nuclear force. Similarly, we can say that a weak charge and a gravitational charge are the sources of the weak and gravitational forces, respectively. The statement “charge is the source of the force” is not determine the nature of charge, i. e., it is not a definition of charge, and it is only represent the status. Thus, still we have the question: What is the charge for any kind of well-known four forces? Any particle is a collection of energy. A part of this energy gives the measured mass of the particle and the other part makes the field of the particle. This field may be represents electromagnetic, strong, weak or gravitational force, or may be represents a combination of some or all of these forces. Thus, sometimes a part of energy makes electromagnetic force (field), sometimes makes strong force (nuclear force) and so on. Therefore, we can suggest that a part of energy with a certain configuration gives some kind of force, and another part of energy with another configuration gives another kind of force and so on. Then, we can define the charge of some kind of force as an (eigen) configuration of this part of energy making the field of the force. I.e., we can say that the charge is a part of energy with specific (eigen) configuration. This configuration is responsible of all properties of the considered kind of force, even the generation of the particle of the field. With this definition of the charge we can understand, not only the electric charge, but also the