Electromagnetic and gravitational fields

Awkward questions about the electromagnetic and gravitational fields of infinitely many particles in the vacuum remain unanswered. Also, the Dirac theory, amended by the hole proposition is certainly not a one-particle theory, and hence not a relativistic generalization of Schrodinger s equation. 

Keywords Klein-Gordon equation Maxwell s equation Complex symmetry Jordan blocks Special and general relativity Electromagnetic and gravitational fields Schwarzschild radius... 

Addition of ideal points at infinity results in the definition of jvdimensional projective space by n - -1 homogeneous coordinates, which remains valid on multiplication by an arbitrary gauge factor, the fundamental operation in field theory and wave mechanics. This property disappears on mapping to affine space where it is the subject of a special assumption. The unification of the electromagnetic and gravitational fields appears naturally only in projective space. 

The problem is that this superposition principle is the basis of many theories, for instance electromagnetic and gravitational field theories. The string theory has a large part of its elanental assumptions based on it too. One of the most used properties of the wave function in qnantum mechanics is precisely its linearity. 

The previous statement is based on the results of reformulating the theory of general relativity in projective space, as a model of unified electromagnetic and gravitational fields [30]. On transformation of the electromagnetic part into tangent space, the relationship between 3D and 4D potentials is of the form [31]... 

Fields and particles. In classical physics, electromagnetic or gravitational fields are vectors of mntnal inflnence between charges or masses. The notion of force expresses the action of a field on these quantities. 

Gravitooptical and near-field traps are based on a combined use of electromagnetic and gravitational forces. 

Forces, such as the gravitational force, are transmitted by means of quantities that scientists call fields. All matter is influenced by forces carried by gravitational fields. Electrically charged particles are influenced by forces carried by electromagnetic fields. The gravitational and electromagnetic fields are not matter, but they have energy. 

The concept of potential energy in mechanics is one example of a scalar field, defined by a simple number that represents a single function of space and time. Other examples include the displacement of a string or a membrane from equilibrium the density, pressure and temperature of a fluid electromagnetic, electrochemical, gravitational and chemical potentials. All of these fields have the property of invariance under a transformation of space coordinates. The numerical value of the field at a point is the same, no matter how or in what form the coordinates of the point are expressed. 

The concept of a gauge field and the notion of gauge invariance originated with a premature suggestion by Weyl [42] how to accommodate electromagnetic variables, in addition to the gravitational field, as geometric features of a differential manifold. 

If 0(3) electromagnetism [denoted e.m. in Eq. (640)] and gravitation are both to be seen as phenomena of curved spacetime, then both fields are derived ultimately from the same Riemann curvature tensor as follows ... 

A distinction must be made between gravitational effects for which the presence of material in the field does not change the intensity of the field, and the electrostatic and magnetic effects for which the presence of material within the field does alter the intensity. A complete treatment of electrostatic and magnetic effects would require a discussion of electromagnetic theory and the use of Maxwell s equations. However, we wish only to illustrate the thermodynamic effects of electric and magnetic fields. We therefore accept the results of a complete treatment and apply the results to simple systems. 

There is no reason why the previous result should not be valid for all holistic systems, which accordingly are predicted to exclude the electromagnetic field6. It may well be the case for protons, and perhaps for atomic nuclei, but clearly not for atoms, in which case the electronic energy is determined by coulombic interaction. Another intriguing possibility is that the gravitational field may disappear at short range for the same reason. 

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