The Cosmic Atom & Quantum Friedmann Equations

Posted By: AlenMiler
The Cosmic Atom & Quantum Friedmann Equations

The Cosmic Atom & Quantum Friedmann Equations: The Quantum States of Friedmann–Lemaître–Robertson–Walker (FLRW) Universes and the 4 Friedmann equations by Norbert Schwarzer
English | 22 Jun. 2017 | ASIN: B07354DZFK | 24 Pages | PDF | 1.07 MB

By taking the line element of any Einstein-compatible metric and quantizing it, thereby applying the method of the intelligent zero, we receive metric Dirac, Klein-Gordon and Schrödinger equations.
One might therefore consider the new equations as the Dirac-, Klein-Gordon- or Schrödinger-forms of the General Theory of Relativity.
A separation approach applied to the complete quantized Friedmann metric leading to a metric Klein-Gordon equation gives an interesting spatial part leading to atom-like solutions and quantization of space and – subsequently - time.
Thus, applying the new METRIC or Einstein-Field-compatible Klein-Gordon equation to Friedmann–Lemaître–Robertson–Walker (FLRW) universes gives solutions similar to the boding states of a hydrogen atom, with the difference of a rather complicated time-dependency. This dependency results from the scale parameter a[t] classically building the two independent Friedmann equations. Now an additional equation has to be added to the two classical ones, which is accounting for the quantum effects of the universe. This gives three Friedmann equations instead of two and four independent functions instead of three, because in addition to the classical scale function a[t], the density and the pressure we get another function accounting for the quantum wiggle f[t]. Thus, on first sight the system remains under-determined, but at closer inspection we find that there are actually two independent quantum equations, namely one of metric Klein-Gordon and one of metric Dirac character. Subsequently we result at 4 independent Friedmann Equations (two of which are the new Quantum Friedmann Equations) and 4 time-dependent functions to be determined by the 4 equations. As an example the hyper-spherical universe is been considered and it is found that the usual singularities at the “big bang” and at the “big crunch” moments will be substituted by rather sharp but nevertheless smooth minima transition areas. The cosmological density and pressure functions are directly obtained from assumptions about the potential quantum states the universe is in. There is no need for the adding in of assumptions about certain matter compositions, like the “radiation-“ or “matter-dominated” cosmos. It the new picture this comes out automatically from the cosmological quantum states in connection with the classical Friedmann equations.