Quantum Theory of Gravity - "QTG"

 

Author: Rolf Arturo Blankschein Guthmann          E-Mail: rolfguthmann@uol.com.br

 

Porto Alegre,  May / 2002

    

 

 

5. The gravitational potential of the hydrogen atom.

                The General Theory of Relativity states that atoms and electromagnetic waves vibrate or oscillate differently in locations with different gravitational potentials. In other words, a “clock” in a region of low gravitational potential, close to a large mass, will mark time more slowly than a clock located further from this mass, in a region of high gravitational potential.

                Let us imagine a truly minimal universe consisting of a single hydrogen atom, so as to determine to what extent the classical gravity of its mass affects the time of its orbiting electron. The proton nucleus is the center of mass and the gravitational source of the system. The first step is to calculate the gravitational potential in the electron cloud:

               

                Where:  ΦElectroncloud  is the gravitational potential in the electron cloud [m2/s2],

                        KGravitational   is the Universal Gravitational Constant, = 6.672590 x 10-11 m3/(Kg.s2), and

                        mo Proton   is the rest mass of the proton = 1.6726231 x 10-27 kg.

 

                Substituting the relativistic form of the atomic radius (from equation 13) into equation 23 and using the velocity of the electron from equation 14, we get:

               

                Solving equation 24, the ΦElectroncloud  result is:

               

                An object in uniform circular motion or in rotation – in this case, an electron in electrostatic suspension in a hydrogen atom – is also under constant acceleration. Within the volume of this atom, from the reference point of the electron, we have a region of higher gravitational potential at the center and a lower gravitational potential in the electron cloud. We therefore have a behavior that is inverse to that of a body in a real gravitational orbit. In order to determine the change of gravitational potential to which the electron is subject, we must calculate the following:

               

                 Where:  ΔΦH-atom  is the change in gravitational potential in the system [m2/s2],

                        ΦNucleus   is the gravitational potential at the nucleus [m2/s2], and

                        ΦElectron   is the gravitational potential at the electron [m2/s2].

 

                We can now determine the gravitational potentials:

               


                The change in gravitational potential in the system is therefore:

               

 

                Here we have two different circumstances that influence the time of the electron: the first is the mass of the nucleus, which places the electron under the influence of a gravitational potential, and the second is the inertia generated by the circular motion or centripetal acceleration, as seen in chapter 3, where the temporal dilation was determined according to the postulates of the General and Special Theories of Relativity. We must now determine the real velocity of the electron that will compensate for the circumstances introduced by the logic of relativity. From what we have seen, this value must logically be larger than those obtained in equation 14.

                Adopting the gravitational potential in the electron cloud from the classical formulation above as being the change in gravitational potential in this system, we have:

                ΦElectroncloud   =   ΔΦH-atom   =   ΔΦElectroncloud

 

                From equation 25, we have:

               
:
                The velocity of the electron is therefore υ1electron, as follows:

               


                Solving, we find:

               

 
                We can call this the “the velocity of the electron modulated only by the classical gravity of the mass of the proton”. The  ±  sign indicates that the motion of the electron can be in either direction. The difference between the velocities υ1electron and υelectron is small:

                

 

                We can obtain the same result calculating in another manner, using the central forces:

               

 

                The complete formula is as follows:

               

 

                Substituting the relativistic mass and radius of the electron (equations 12 and 13) and the new velocity (υ2electron) into equation 28, we have:

               

 

                Solving for υ2electron, we have:

               

                 According to equation 30 the difference is:

               

                Hence  υ1electron  =  υ2electron   >  υelectron, demonstrating that the velocity of the electron in the electron cloud of a single hydrogen atom is increased as a result of the classically defined gravity of the nucleus.

 

 

 

 

Next Chapter:   6. The gravity of the hydrogen atom.

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