The book A Search for the Finite Physics makes fundamental changes in two theoretical fields, the theory of the electro-magnetic (E-M) fields, also known as Maxwell's equations; and in the theory of general relativity. In both theories the basic form of the Lagrangians from which field equations are derived, are radically changed.
As a consequence of these changes, the solutions to these modified field equations yield particle-like and charge-like clusters entirely free of singularities. This enables one to make full use of various formal expressions for densities of energy, linear momentum, and angular momentum without restrictions on their global quantities beyond quantization. Normally, such densities are also full of singularities.
The theory of the electro-magnetic fields is further developed beyond its Maxwell's boundary in that the magnetic components are allowed to have monopole solutions whose charges and forms take on independent values.
To make the modified EM theory agree with the conventional Maxwell's equations as well as with its empirical legacy asymptotic or reality, conditions are applied to each component separately. Thus, the electric components should take on the form of e/r where e is the electric charge and r is the radial distance.
The magnetic components or monopoles have not made their appearance yet and are not observable. To make them unobservable we require that they asymptotically vanish as 1/r2. This condition accomplishes a number of highly desirable results.
- The magnetic components become unobservable as is required by the reality conditions
- Their range of action becomes short
- Their charge and form remain independent from other components and
- Their contribution to the angular momentum density makes the latter integrable.
The last several characteristics are such that the modified EM theory is capable of accomodating the strong interaction theory and that the magnetic components are good candidates to form the basis for quarks.
From the numerical results obtained so far it is reasonable to hope that the entire zoo of elementary particles can be derived from first principles using this theory.
The general theory of relativity was constructed by retaining the traditional approach toward the differential variables yielding field equations that are likewise full of singularities. The main reason to modify the GR theory is to get rid of singularities and the accompanying complications arising with them.
The reason was significatly reinforced by the analysis of the differential equations underlying GR where it was found that the solutions to the GR field equations do not follow any physical model or cause but can be generated entirely arbitrarily having nothing to do with physics or any models of physical reality.
A method is developed, presented and illustrated where it is shown how such arbitrary solutions can be generated.
In contrast to this, a new gravitational theory is proposed which is based on the wave geneerator rather than on an arbitrary geometric constraint. It is formulated in the flat spacetime but can be expressed entirely in general covariant terms. It does possess both local densities for energy, linear momentum and angular momentum resulting in the corresponding global characteristics.
The new formulation of the gravitational theory shows that one is able not only to eliminate singularities but, with some effort, it is possible to arrange the behavior of the gravitational field in such a way that the metric signature is preserved throughout the entire range.
An important feature of the new gravitational field is that for certain arrangements of parameters the field assumes extreme values reminiscent of singular point. |