## 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:

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 *2**π**Rc* !

This result is remarkable. How can *Rc *be *2**π**Rc* 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

**, is 2*QD. The surface of one triangle**

*OAB**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=2**π**Rc^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)**