Comments on Indeterminism and Undecidability

Abstract

In a recent paper \cite{Landsman1}, it has been claimed that the outcomes of a quantum coin toss which is idealized as an infinite binary sequence is {\it 1-random}. We also defend the correctness of this claim and assert that the outcomes of quantum measurements can be considered as an infinite {\it 1-random} or {\it 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 \cite{Landsman1}. Furthermore, we speculate a logical-axiomatic study of nature which we believe can intrinsically provide quantum mechanical probabilities based on {\it 1(n)-randomness}.

A dynamical approach to relativity: Desynchronization of clocks in rigid acceleration and gravitational redshift

“…Our second motivation that the acceleration should be discrete near the Planck scale is based on the algorithmic information theoretical explanation of nature. There are proposals that the universe and everything in it could be encoded as a long (perhaps infinite) string of 0s and 1s, and that the apparent laws of nature could be explained by the evolution of this long string of bits [44,45]. If such claims are true, the smallest change in the particle's state must be described with at least 1 bit of information; states evolve discontinuously at the most fundamental level.…”

“…Of course, there are various possibilities for the existence of a universal time. For example, if the evolution of the universe is given by an incomputable 1(n)-random sequence, the universe will choose its own destiny of its own free will[45].Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 26 May 2023 doi:10.20944/preprints202202.0216.v3…”