Abstract
In this work first we show that the three main formulations of physics, namely, Newton’s second law of motion, Maxwell field equations of electromagnetism and Einstein field equations of gravitation can be formulated in similar covariant forms so that the formulations differ only by the nature of the geometrical objects that represent the corresponding physical entities. We show that Newton’s law can be represented by a scalar, the electromagnetic field by a symmetric affine connection or a dual vector, and the gravitational field by a symmetric metric tensor. Then with the covariant formulation for the gravitational field we can derive differential equations that can be used to construct the spacetime structures for short-lived and stable quantum particles. We show that geometric objects, such as the Ricci scalare curvature and Gaussian curvature, exhibit probabilistic characteristics. In particular, we also show that Schrodinger wavefunctions can be used to construct spacetime structures for the quantum states of a quantum system, such as the hydrogen atom. Even though our discussions in this work are focused on the microscopic objects, the results obtained can be applied equally to the macroscopic phenomena.
Highlights
In classical physics, particle is a general term that refers to a localized object that can be used to model physical theories
In this work we show that quantum particles that are formed from the microscopic spacetime structures can be regarded as elementary particles in three-dimensional Euclidean space and can be assumed to possess the geometric and topological structure of a differentiable manifold, and a physical theory can be formulated as the dynamics of its spacetime structures
We have shown in this work that physical formulations in classical physics that include Newton’s second law of motion, the field equations of the electromagnetic field and the field equations of the gravitational field can be formulated in a general covariant form so that the formulations differ only by the nature of the geometrical objects that represent the corresponding physical entities
Summary
Particle is a general term that refers to a localized object that can be used to model physical theories. The concept of the classical particle is still retained even though in the realm of quantum mechanics a quantum particle exhibits the phenomenon of matter wave, which, if not being probabilistically interpreted, is a physical occurrence due to an extended medium rather than a single physical object occupying a single position at a particular time in space. This epistemological problem raises the question of whether the concept of particle as a localized object is adequate for modeling physical theories or physical theories should be based on the model of a particle as an extended object.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
