Incompleteness: Gödel and Einstein

The thesis is:

Einstein, Podolsky and Rosen’s argument (1935, Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?) is another interpretation of the famous Gödel incompleteness argument (1931, Über formal unentscheidbare Sätze der Principia mathematica und verwandter Systeme I) in terms of quantum mechanics. The close friendship between the Princeton refugees Einstein and Gödel might address that fact. However the outlines of a common set-theory structure interpretable in both ways are much more essential concerning the incompleteness (or openness) of infinity: 

An arbitrary infinite countable set “A” and another set “B” so that their intersection is empty are given. One constitutes their union “C”, which will be an infinite set whatever B is. Utilizing the axiom of choice, a one-to-one mapping “f ” exists. One designates the image of B into A through f by “B(f)” so that B(f) is a true subset of A. If the axiom of choice holds, there is always an internal and equivalent image as B(f) for any external set as B. Thus, if one accepts that B(f) coincides with B, whether an element b of B belongs or not to A is an undecidable problem as far as b(f) coincides with b. However if the axiom of choice is not valid, one cannot guarantee that f exists and should display how a constructive analog of “f” can be built. If one shows how f to be constructed at least in one case, this will be a constructive proof of undecidablity as what Gödel’s is. 

The EPR argument interprets the same structure: There is an initial quantum system Q, which is divided to two other systems P and S moving with some relative speed to each other in space-time. For Q, P, and S are quantum systems and they are represented by three infinite-dimensional Hilbert spaces, the EPR argument can be bared to the following set-theory core: There is an initial infinity Q, which is divided into two infinities P and S, each of which suggests an external viewpoint to the other. So each of the two pairs (P, Q) and (Q, P) models the above structure and can serve to demonstrate the “incompleteness of quantum mechanics”, which produces that description of reality. However the cause is the paradoxical properties of infinity rather than the description of quantum mechanics once forced to introduce infinity in itself.

@
@

The presentation as a PowerPointPowerPoint, a PDF, or a video; furthermore as slides @ EasyChair

The paper (in Bulgarian) as a PDF or embeded: Гьодел и Айнщайн: непълнотата