Comments on indeterminism and undecidability

TL;DR

This paper discusses the claim that quantum measurement outcomes can be modeled as infinite 1-random sequences, defending and critiquing the argument while exploring the potential for a logical-axiomatic foundation for quantum probabilities.

Contribution

It provides a critical commentary on the claim that quantum outcomes are 1-random sequences and explores a logical-axiomatic approach to quantum probabilities.

Findings

Supports the claim that quantum outcomes can be 1-random sequences

Offers critiques and positive comments on previous arguments

Speculates on a logical-axiomatic basis for quantum probabilities

Abstract

In a recent paper [1], it has been claimed that the outcomes of a quantum coin toss which is idealized as an infinite binary sequence is 1-random. We also defend the correctness of this claim and assert that the outcomes of quantum measurements can be considered as an infinite 1-random or n-random sequence. In this brief note we present our comments on this claim. We have mostly positive but also some negative comments on the arguments of the paper [1]. Furthermore, we speculate a logical-axiomatic study of nature which we believe can intrinsically provide quantum mechanical probabilities based on 1(n)-randomness.