[Fis] WHY ?

[Prof. Dr. Thomas Görnitz]

Dear Eric, dear FIS,
an AQI has SU(2) and U(1) as its symmetry group.

SU(2) as its maximum homogeneous space is geometrically an S3, the  
three-dimensional “surface” of a four-dimensional sphere. (This is one  
dimension more than S2, the surface of a three-dimensional sphere,  
e.g. the Earth.)

Why the space in which everything that exists is located is exactly  
three-dimensional was a question that remained unanswered in physics  
for a long time. I found Weizsäcker's idea that the  
three-dimensionality of space is a logical result of the fundamental  
structure of the quantized binary alternative to be the first  
suggestion that I could consider physically meaningful.
This S3, a continuum, is the set of all states of an AQI that can be  
reached with SU(2) from the unit element.
However, the set of all points that can actually be found in a given  
state of an AQI is not evenly distributed over S3.

In order to determine the distribution of possible factual results for  
a given quantum state, one must move on to representing the state by a  
function over the position space. The quantum-theoretical description  
of the possibilities is thus achieved by the transition from the base  
space to the power set.
The states of an AQI form a two-dimensional irreducible partial  
representation of the regular representation of SU(2). Their state  
space is the space of all square-integrable functions over this S3:  
L2(S3).

The functions of the two-dimensional irreducible representation are  
functions on S3 with only one zero area. (A one-dimensional analogy  
would be sine and cosine, which also have only one node with their  
wavelength 2π.)

If there are many AQIs, then the product representation of the  
two-dimensional representations must be formed. The space of this  
tensor product can be reduced to irreducible representations, which  
can be higher-dimensional. In such representations, functions with  
shorter wavelengths then appear.
While the points in space form a continuum, those areas that can still  
occur so frequently with a finite number N of AQIs in the cosmos that  
the assumption of their actual occurrence does not become nonsensical  
depend on this number N.

Wavelengths whose occurrence is so rare that the possibility of their  
actual occurrence can be ignored are therefore not taken into account  
for physical reasons. An example calculation in the cited articles  
shows that the smallest acceptable length, i.e., the Planck length, is  
of the order of magnitude R/2√N. Here, R is the radius of curvature of  
cosmic space and N is the number of AQIs in the cosmos at the relevant  
point in time.

There is a current preprint on this topic (which I am still working on):
https://urldefense.com/v3/__https://www.researchgate.net/publication/392264415_Contributions_of_quantum_theory_to_cosmology_Questions_and_answers__;!!D9dNQwwGXtA!UnorKR9l9qX7eq5GVytCP3r7flcvnSCehQLnaTwIz1Mp-qCFftEfwtTi5EpWdqVCyWgh0ctVtTgS9XyQeNlJFySk2as1Ig$ 

and two published papers
·Görnitz T, Schomäcker U (2018) The Structures of Interactions: How to  
Explain the Gauge Groups U(1), SU(2) and SU(3). Found Sci 23, 51–73  
https://urldefense.com/v3/__https://doi.org/10.1007/s10699-016-9507-6__;!!D9dNQwwGXtA!UnorKR9l9qX7eq5GVytCP3r7flcvnSCehQLnaTwIz1Mp-qCFftEfwtTi5EpWdqVCyWgh0ctVtTgS9XyQeNlJFyTroulf6Q$ 

·Görnitz T, Schomäcker U (2021) Quantumbit Cosmology explains Effects  
of Rotation Curves of Galaxies, Foundations of Science,  
https://urldefense.com/v3/__https://doi.org/10.1007/s10699-021-09808-y__;!!D9dNQwwGXtA!UnorKR9l9qX7eq5GVytCP3r7flcvnSCehQLnaTwIz1Mp-qCFftEfwtTi5EpWdqVCyWgh0ctVtTgS9XyQeNlJFySoa9aJTg$ 

All the best
Thomas



Quoting Eric Werner <eric.werner at oarf.org>:

> Dear Thomas, please explain a bit more. How  you are using group  
> theory here to generate possibilities? Are you using Mathematics as  
> a metaphor?
>
> “Space and time begin as a consequence of group theory from a single  
> quantum of action, a single AQI. Possibilities generate new  
> possibilities, causing the number of AQIs to grow”
>
> Eric
>
> Sent from my iPhone
>
>> On Jun 14, 2025, at 18:53, Prof. Dr. Thomas Görnitz  
>> <goernitz at em.uni-frankfurt.de> wrote:
>>
>> Space and time begin as a consequence of group theory from a single  
>> quantum of action, a single AQI. Possibilities generate new  
>> possibilities, causing the number of AQIs to grow



Prof. Dr. Thomas Görnitz
Fellow of the INTERNATIONAL ACADEMY OF INFORMATION STUDIES

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Fachbereich Physik
J. W. Goethe-Universität Frankfurt/Main