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The Quantum Distance and the Second Quantum Dimension (Compton-radius)



The Quantum Distance and the Second Quantum Dimension (Compton-radius)

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

The Planck-​radius is the small­est known dis­tance so we assume that the quan­tum dis­tance is:

(12)

We have seen that the ratio between the clas­si­cal radius of the elec­tron, the Comp­ton radius (Rc), and QD is the same as the ratio between the rydberg-​distance Rr and the Bohr-​distance. Is this a coin­ci­dence or not?

We assume the ratio has the inte­ger value of:

In fig­ure 3 the quan­tum num­bers 6 and 12 already give some sym­me­try. First we will con­cen­trate on the quan­tum num­ber and show that with this num­ber we can cre­ate “homo­ge­neous” space.

In fig­ure 4 schemat­i­cally the Compton-​radius is the radius of the drawn circle.

Fig­ure 4. The quan­tum dis­tance transformation.

Cal­cu­la­tion gives 25 min­utes for the angle α (=Alpha=Fine Struc­ture Constant=2π/864***) in fig­ure 4. In 360 degrees there are exact 864 angles of 25 min­utes. The perime­ter of the “cir­cle” in fig­ure 4, the sum of all 864 straight lines AB=2*QD, is:

The perime­ter of the cre­ated cir­cle is Rc (864 angles α of 25’=360 degrees) while the perime­ter of a cir­cle in the macro-​world is 2πRc !

This result is remark­able. How can Rc be 2πRc at the same time?

When we want to com­pare the quan­tum perime­ter with the macro-​world perime­ter the cor­rec­tion fac­tor is 2π.

The straight line AB, the basis of tri­an­gle OAB, is 2*QD. The sur­face of one tri­an­gle OAB is:

The total sur­face of one side with 864 tri­an­gles is: .

The sur­face of both sides of the cre­ated “cir­cle” has tri­an­gles with a total sur­face .

The “macro-​world” sur­face of two cir­cles with radius Rc is Oc=2πRc^2, so with the sur­face there is also a “trans­la­tion” fac­tor of 2π for the trans­for­ma­tion from the QD to Rc level.

Fig­ure 5. Illus­tra­tion of the imper­fect Quan­tum Space at the Compton-​distance.

At the Compton-​level Rc, /​2 point-​volumes cre­ate a “per­fect” cir­cle for observers in O (fig­ure 4). The observer in O can observe no more than two, right angled “per­fect” cir­cles, at the same time at dis­tance Rc. Because there is no restric­tion for the angle of obser­va­tion of the two “per­fect” cir­cles, one should be able to observe the cir­cles in “any” direc­tion, but not at the same time (the point-​volumes cre­ate at Rc the 2-​dimensional quan­tum space).

The quan­tum bulbs at Rc (fig­ure 5) touch each other in such a way that they can form with /​2 QD-​bulbs a “per­fect” cir­cle around O; all QD-​bulbs of cir­cle Rc are “in touch”. One can observe that the QD-​bulbs up and down Rc (fig­ure 5) do not have closed perime­ters because “curved” 3-​dimensional space around a charge can­not be filled con­tin­u­ously with bulbs. Inho­mo­gene­ity is unavoidable.

Next chap­ter: The Trans­for­ma­tion to the third Quan­tum Dimen­sion (Bohr-​distance)

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

The Planck-radius is the smallest known distance so we assume that the quantum distance is: 

  (12)

We have seen that the ratio between the classical radius of the electron, the Compton radius (Rc), and QD is the same as the ratio between the rydberg-distance Rr and the Bohr-distance. Is this a coincidence or not?

We assume the ratio has the integer value of:

In figure 3 the quantum numbers 6 and 12 already give some symmetry. First we will concentrate on the quantum number  and show that with this number we can create “homogeneous” space.

In figure 4 schematically the Compton-radius is the radius of the drawn circle.

                  

Figure 4. The quantum distance transformation.

Calculation gives 25 minutes for the angle α (=Alpha=Fine Structure Constant=2π/864***) in figure 4. In 360 degrees there are exact 864 angles of 25 minutes. The perimeter of the “circle” in figure 4, the sum of all 864 straight lines AB=2*QD, is:

The perimeter of the created circle is Rc (864 angles α of 25’=360 degrees) while the perimeter of a circle in the macro-world is 2πRc !

This result is remarkable. How can Rc be 2πRc at the same time?

When we want to compare the quantum perimeter with the macro-world perimeter the correction factor is 2π.

The straight line AB, the basis of triangle OAB, is 2*QD. The surface of one triangle OAB is:

The total surface of one side with 864 triangles is: .

The surface of both sides of the created “circle” has  triangles with a total surface .

The “macro-world” surface of two circles with radius Rc is Oc=2πRc^2, so with the surface there is also a “translation” factor of 2π for the transformation from the QD to Rc level.

Figure 5. Illustration of the imperfect Quantum Space at the Compton-distance.

At the Compton-level Rc/2 point-volumes create a “perfect” circle for observers in O (figure 4). The observer in O can observe no more than two, right angled “perfect” circles, at the same time at distance Rc.  Because there is no restriction for the angle of observation of the two “perfect” circles, one should be able to observe the circles in “any” direction, but not at the same time (the point-volumes create at Rc the 2-dimensional quantum space).

The quantum bulbs at Rc (figure 5) touch each other in such a way that they can form with /2 QD-bulbs a “perfect” circle around O; all QD-bulbs of circle Rc are “in touch”. One can observe that the QD-bulbs up and down Rc (figure 5) do not have closed perimeters because “curved” 3-dimensional space around a charge cannot be filled continuously with bulbs. Inhomogeneity is unavoidable.

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

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