We are looking at comparison of two action integrals and we identify the Lagrangian multiplier as setting up a constraint equation (on cosmological expansion). This is a direct result of the fourth equation of our man...We are looking at comparison of two action integrals and we identify the Lagrangian multiplier as setting up a constraint equation (on cosmological expansion). This is a direct result of the fourth equation of our manuscript which unconventionally compares the action integral of General relativity with the second derived action integral, which then permits Equation (5), which is a bound on the Cosmological constant. What we have done is to replace the Hamber Quantum gravity reference-based action integral with a result from John Klauder’s “Enhanced Quantization”. In doing so, with Padamabhan’s treatment of the inflaton, we then initiate an explicit bound upon the cosmological constant. The other approximation is to use the inflaton results and conflate them with John Klauder’s Action principle for a way, if we have the idea of a potential well, generalized by Klauder, with a wall of space time in the Pre Planckian-regime to ask what bounds the Cosmological constant prior to inflation, and to get an upper bound on the mass of a graviton. We conclude with a redo of a multiverse version of the Penrose cyclic conformal cosmology. Our objective is to show how a value of the rest mass of the heavy graviton is invariant from cycle to cycle. All this is possible due to Equation (4). And we compare all these with results of Reference [1] in the conclusion, while showing its relevance to early universe production of black holes, and the volume of space producing 100 black holes of value about 10^2 times Planck Mass. Initially evaluated in a space-time of about 10^3 Planck length, in spherical length, we assume a starting entropy of about 1000 initially.展开更多
The equations for energy, momentum, frequency, wavelength and also Schr?dinger equation of the electromagnetic wave in the atom are derived using the model of atom by analogy with the transmission line. The action con...The equations for energy, momentum, frequency, wavelength and also Schr?dinger equation of the electromagnetic wave in the atom are derived using the model of atom by analogy with the transmission line. The action constant A0 = (μ0/ε0)1/2s02e2 is a key term in the above mentioned equations. Besides the other well-known quantities, the only one unknown quantity in the last expression is a structural constant s0. Therefore, this article is dedicated to the calculation of the structural constant of the atoms on the basis of the above mentioned model. The structural constant of the atoms s0 = 8.277 56 shows up as a link between macroscopic and atomic world. After calculating this constant we get the theory of atoms based on Maxwell’s and Lorentz equations only. This theory does not require Planck constant h, which once was introduced empirically. Replacement for h is the action constant A0, which is here theoretically derived, while the replacement for fine structure constant α is 1/(2s02). In this way, the structural constant s0 replaces both constants, h and α. This paper also defines the stationary states of atoms and shows that the maximal atomic number is equal to 2s02 = 137.036, i.e., as integer should be Zmax=137. The presented model of the atoms covers three of the four fundamental interactions, namely the electromagnetic, weak and strong interactions.展开更多
文摘We are looking at comparison of two action integrals and we identify the Lagrangian multiplier as setting up a constraint equation (on cosmological expansion). This is a direct result of the fourth equation of our manuscript which unconventionally compares the action integral of General relativity with the second derived action integral, which then permits Equation (5), which is a bound on the Cosmological constant. What we have done is to replace the Hamber Quantum gravity reference-based action integral with a result from John Klauder’s “Enhanced Quantization”. In doing so, with Padamabhan’s treatment of the inflaton, we then initiate an explicit bound upon the cosmological constant. The other approximation is to use the inflaton results and conflate them with John Klauder’s Action principle for a way, if we have the idea of a potential well, generalized by Klauder, with a wall of space time in the Pre Planckian-regime to ask what bounds the Cosmological constant prior to inflation, and to get an upper bound on the mass of a graviton. We conclude with a redo of a multiverse version of the Penrose cyclic conformal cosmology. Our objective is to show how a value of the rest mass of the heavy graviton is invariant from cycle to cycle. All this is possible due to Equation (4). And we compare all these with results of Reference [1] in the conclusion, while showing its relevance to early universe production of black holes, and the volume of space producing 100 black holes of value about 10^2 times Planck Mass. Initially evaluated in a space-time of about 10^3 Planck length, in spherical length, we assume a starting entropy of about 1000 initially.
文摘The equations for energy, momentum, frequency, wavelength and also Schr?dinger equation of the electromagnetic wave in the atom are derived using the model of atom by analogy with the transmission line. The action constant A0 = (μ0/ε0)1/2s02e2 is a key term in the above mentioned equations. Besides the other well-known quantities, the only one unknown quantity in the last expression is a structural constant s0. Therefore, this article is dedicated to the calculation of the structural constant of the atoms on the basis of the above mentioned model. The structural constant of the atoms s0 = 8.277 56 shows up as a link between macroscopic and atomic world. After calculating this constant we get the theory of atoms based on Maxwell’s and Lorentz equations only. This theory does not require Planck constant h, which once was introduced empirically. Replacement for h is the action constant A0, which is here theoretically derived, while the replacement for fine structure constant α is 1/(2s02). In this way, the structural constant s0 replaces both constants, h and α. This paper also defines the stationary states of atoms and shows that the maximal atomic number is equal to 2s02 = 137.036, i.e., as integer should be Zmax=137. The presented model of the atoms covers three of the four fundamental interactions, namely the electromagnetic, weak and strong interactions.
