Related papers: Indeterminism and Randomness Through Physics
At any time, there are areas of science where we are standing at the frontier of knowledge, and can wonder whether we have reached a fundamental limit to human understanding. What is ultimately possible in physics? I will argue here that it…
Before we combine actions and probabilities two very obvious questions should be asked. Firstly, what does "the probability of an action" mean? Secondly, how does probability interact with nondeterminism? Neither question has a single…
We introduce an approach to the foundations of physics that is more in line with the foundations of mathematics. The idea is to examine current theories and find a set of starting physical assumptions that are sufficient to rederive them,…
The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements,…
Randomness is viewed through an analogy between a physical quantity, density of gas, and a mathematical construct -- probability density. Boltzmann's deduction of equilibrium distribution of ideal gas placed in an external potential field…
Heisenberg's reciprocal relation between position measurement error and momentum disturbance is rigorously proven under the assumption that those error and disturbance are independent of the state of the measured object. A generalization of…
The certainty principle (2005) allowed to conceptualize from the more fundamental grounds both the Heisenberg uncertainty principle (1927) and the Mandelshtam-Tamm relation (1945). In this review I give detailed explanation and discussion…
Appeals to randomness in various number-theoretic constructions appear regularly in modern scientific publications. Such famous names as V.I. Arnold, M. Katz, Ya.G. Sinai, and T. Tao are just a few examples. Unfortunately, all of these…
Quantum uncertainty is described here in two guises: indeterminacy with its concomitant indeterminism of measurement outcomes, and fuzziness, or unsharpness. Both features were long seen as obstructions of experimental possibilities that…
The physical nature of numerous of the nonlinear phenomena in optics is explained by inequality of forward and reversed optical transitions, that corresponds to a principle of time invariance violation in electromagnetic interactions. The…
The following three sections and appendices are taken from my thesis "The Foundations of Inference and its Application to Fundamental Physics" from 2021, in which I construct a theory of entropic inference from first principles. The…
A simple experiment using radioactive decay is proposed to test the possibility of a determinsistic, but chaotic, origin of quantum mechanical randomness.
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a…
Quantum theory is widely regarded as fundamentally indeterministic, yet classical frameworks can also exhibit indeterminism once infinite information is abandoned. At the same time, relativity is usually taken to forbid superluminal…
These lecture notes cover classical undecidability results in number theory, Hilbert's 10th problem and recent developments around it, also for rings other than the integers. It also contains a sketch of the authors result that the integers…
A physical system is determined by a finite set of initial conditions and "laws" represented by equations. The system is computable if we can solve the equations in all instances using a "finite body of mathematical knowledge". In this…
Along with weaving together observations, experiments, and theoretical constructs into a coherent mesh of understanding of the world around us, physics over its past five centuries has continuously refined the base concepts on which the…
This expository paper advocates an approach to physics in which ``typicality" is identified with a suitable form of algorithmic randomness. To this end various theorems from mathematics and physics are reviewed. Their original versions…
We survey the Kolmogorov's approach to the notion of randomness through the Kolmogorov complexity theory. The original motivation of Kolmogorov was to give up a quantitative definition of information. In this theory, an object is randomness…
Rejoinder to ``The 2005 Neyman Lecture: Dynamic Indeterminism in Science'' [arXiv:0808.0620]