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The Transformation to the third Quantum Dimension (Bohr-distance)



The Transformation to the third Quantum Dimension (Bohr-distance)

When you are inter­ested in physics you must read “Unbe­liev­able”!

We demon­strated that with /​2 point-​volumes we can cre­ate a per­fect “cir­cle” with 864 tri­an­gles OAB. Point O (fig­ure 4) is the cen­ter of the cre­ated Comp­ton quan­tum cir­cle (Rc). Between O and Rc the quan­tum space is imper­fect. The “bulbs” with radius QD can­not fill up spher­i­cal space homogeneously.

The “per­fect” geom­e­try is cre­ated at Rc. For the observer in O it is not pos­si­ble to observe per­fect cir­cles all around (no per­fect bulb pos­si­ble when space is filled with point-​volumes).

The ori­en­ta­tion of the two pos­si­ble cir­cles Rc is not fixed.

With the “per­fect” two-​dimensional cir­cle Rc we are able to cre­ate a per­fect bulb shell tun­nel with diam­e­ter Rc at the dis­tance *Rc; the Bohr-​distance.

Fig­ure 6. Comp­ton cir­cles cre­at­ing the 3rd quan­tum dimension.

With /​2 cir­cles Rc (two cir­cles each) we are able, in con­junc­tion with the cre­ation of the Compton-​circle, to cre­ate two “per­fect” bulb shell tun­nels with radius Rc at the Bohr-​distance; the begin­ning of the 3rd quan­tum dimension.

The ratio between the dis­tances Rb and Rc should be .

We have observed that the ratio between the Bohr-​radius and the Compton-​radius is:

(14)

The Bohr/​Compton dis­tance ratio appears to be 10.8674 times larger than the ratio Rc/​QD or the Rydberg/​Bohr ratio.

We must how­ever not for­get that the sit­u­a­tion at 2-​QD is not the same as the 1-​QD level or the 3-​QD level. We have seen that a math­e­mat­i­cal cor­rec­tion from 1-​QD to 2-​QD with the fac­tor 2pi was nec­es­sary. We now com­pare the 3rd dimen­sion of the Bohr-​bulb with 2nd dimen­sion of the Compton-​plate. A math­e­mat­i­cal cor­rec­tion is necessary.

The fac­tor 10.8674 is the cor­rec­tion fac­tor from the 2-​QD to the 3-​QD. From the 1st to the 2nd QD the cor­rec­tion fac­tor is 2π. This trans­for­ma­tion explains the ori­gin of the math­e­mat­i­cal nat­ural con­stant π. Is it a coin­ci­dence that the other math­e­mat­i­cal nat­ural con­stant e can be found in 10.8674, because and the dif­fer­ence is there­fore only 0.05%? **

So both math­e­mat­i­cal nat­ural con­stants may well orig­i­nate from the dimen­sion trans­fer from the point-​volume to three-​dimensional space.

After the dimen­sion cor­rec­tion we have also the ratio Rb/​Rc=.

The total math­e­mat­i­cal cor­rec­tion from the point-​volume (1st dimen­sion) to our 3rd dimen­sion is: .

(** When we cor­rect for neglect­ing the fac­tor (1+Me/Mp)=1.0005446, when equa­tion 5a was derived from 5, the devi­a­tion fac­tor with 4*e is less than 2.10^−5)

Next chap­ter: The 12 Ion­iza­tion Lev­els of the Atom

When you are interested in physics you must read “Unbelievable“!

We demonstrated that with /2 point-volumes we can create a perfect “circle” with 864 triangles OAB. Point O (figure 4) is the center of the created Compton quantum circle (Rc).  Between and Rc the quantum space is imperfect. The “bulbs” with radius QD cannot fill up spherical space homogeneously.

The “perfect” geometry is created at Rc. For the observer in O it is not possible to observe perfect circles all around (no perfect bulb possible when space is filled with point-volumes).

The orientation of the two possible circles Rc is not fixed.

With the “perfect” two-dimensional circle Rc we are able to create a perfect bulb shell tunnel with diameter Rc at the distance *Rc; the Bohr-distance.

Figure 6.  Compton circles creating the 3rd  quantum dimension.

With /2 circles Rc (two circles each) we are able, in conjunction with the creation of the Compton-circle, to create two “perfect” bulb shell tunnels with radius Rc at the Bohr-distance; the beginning of the 3rd quantum dimension.

The ratio between the distances Rb and Rc should be .

We have observed that the ratio between the Bohr-radius and the Compton-radius is:

 (14)

The Bohr/Compton distance ratio appears to be 10.8674 times larger than the ratio Rc/QD or the Rydberg/Bohr ratio.

We must however not forget that the situation at 2-QD is not the same as the 1-QD level or the 3-QD level. We have seen that a mathematical correction from 1-QD to 2-QD with the factor 2pi was necessary. We now compare the 3rd dimension of the Bohr-bulb with 2nd dimension of the Compton-plate. A mathematical correction is necessary.

The factor 10.8674 is the correction factor from the 2-QD to the 3-QD. From the 1st to the 2nd QD the correction factor is 2π. This transformation explains the origin of the mathematical natural constant π. Is it a coincidence that the other mathematical natural constant e can be found in 10.8674, because  and the difference is therefore only 0.05%?  **

So both mathematical natural constants may well originate from the dimension transfer from the point-volume to three-dimensional space.

After the dimension correction we have also the ratio Rb/Rc=.

The total mathematical correction from the point-volume (1st dimension) to our 3rd dimension is: .

(** When we correct for neglecting the factor (1+Me/Mp)=1.0005446, when equation 5a was derived from 5, the deviation factor with 4*e is less than 2.10^-5)

Next chapter: The 12 Ionization Levels of the Atom

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