Abstract
In this paper, a very simple novel model is presented concerning the unified field theory (“theory of everything”). In the scope of this novel theory, it is assumed that matter, space and time are quantized. It is assumed that the space is subdivided into cubic elementary cells (space quanta), and in each of its eight corners a Delta potential is positioned. That means the Delta potentials are equidistantly arranged, so that the Delta potentials are forming a lattice similar to a crystal lattice in solid state physics. The novel theory is analogue to the Kronig-Penney model well-known in solid state physics: a crystal lattice comprises Delta potentials arranged equidistantly to one another, so the lattice space can be considered as being quantized by an array of equally spaced Delta potentials or the lattice space is divided into cubic elementary cells (space quanta). But instead of electrons, material quanta are inserted into the cubic elementary cells or space quanta. So the material quanta are not freely vibrating (unbound state), but are vibrating in a bound state with discrete energy levels separated by an energy gap. This is due to the presence of the array of Delta potentials. In the frame of this novel theory the Schr?dinger Equation for the Kronig-Penney-Model is not solved by differentiation, but the Schr?dinger Equation is integrated yielding the formula , by whose discussion the existence of an energy gap is revealed. This energy gap is responsible if the material quantum occurs as light quantum (photon) or mass quantum.
Highlights
In the frame of the unified field theory research (“theory of everything”), there exist two theories competing one another: the first one is called the string theory and the second one is called the loop quantum gravity theory.According to the string theory the universe consists of freely vibrating objects called strings with the dimension in the order of Planck length [1]-[10]
The novel theory is analogue to the Kronig-Penney model well-known in solid state physics: a crystal lattice comprises Delta potentials arranged equidistantly to one another, so the lattice space can be considered as being quantized by an array of spaced Delta potentials or the lattice space is divided into cubic elementary cells
The novel theory is analogue to the Kronig-Penney model well-known in the solid state physics [22] [23] [24]: The equidistantly spaced positively charged atom cores are represented as Delta potentials, a crystal lattice is contemplated which contains Delta potentials arranged equidistantly to one another, so the lattice space can be considered as being quantized by an array of spaced Delta potentials or the lattice space is divided into cubic elementary cells
Summary
In the frame of the unified field theory research (“theory of everything”), there exist two theories competing one another: the first one is called the string theory and the second one is called the loop quantum gravity theory. A further development of this theory is called Superstring theory [12]. According to the loop quantum gravity theory, the space and time is quantized, while the space is structured by a very fine network of woven finite loops [16] [17] [18] [19] [20]. D. Vaid has tried to combine both well-recognized theories the string theory and the loop quantum gravity theory into a common theory, so both theories are not competing one another but are completing one another [21]
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