MIP*= RE: What Could This Mean Physically?

Abstract

This article was inspired by the article by Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen having a rather concise title "MIP*=RE". This article states that the problems solvable by using recursively enumerable languages (RE) is equal to the class of problems solved multiple-interrogator-prover allowing quantum entanglement between provers (MIP*). Quantum entanglement would play an essential role in quantum computation. Also the implications for physics are highly non-trivial. Connes imbedding problem asking whether all infinite-D matrices can always be approximated by finite-D matrices has a negative solution.Therefore MIP*= RE does not hold true for hyperfinite factors of type II₁ (HFFs) central in quantum TGD. Also the Tirelson problem finds a solution. The measurements of commuting observers performed by two observers are equivalent to the measurements of tensor products of observables only in finite-D case and for HFFs. That quantum entanglement would not have any role in HFFs is in conflict with intuition.