Related papers: Uncertainty, incompleteness, chance, and design
Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known…
The paper starts with the proposal that the cause of the apparent insolubility of the free-will problem are several popular but strongly metaphysical notions and hypotheses. To reduce the metaphysics, some ideas are borrowed from physics. A…
Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. Indeed, representatives of each class can be found…
The unexpected discoveries at the beginning of the century, particularly thanks to Heisenberg, Bohr, and Godel, has driven the science to drastic changes, opening new, extraordinary, and infinite research fields. After this, many scientists…
Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg's uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum…
Heisenberg's uncertainty principle states that the position and momentum of a particle cannot be sharply determined simultaneously. Standard-deviation and entropic formulations capture the spread of the probability distribution but say…
In two articles, the authors claim that the Heisenberg uncertainty principle limits the precision of simultaneous measurements of the position and velocity of a particle and refer to experimental evidence that supports their claim. It is…
Quantum theory is indeterministic, but not completely so. When a system is in a pure state there are properties it possesses with certainty, known as actual properties. The actual properties of a quantum system (in a pure state) fully…
We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest…
This is an article written in a popular science style, in which I will explain: (1) the famous Heisenberg uncertainty principle, expressing the experimental incompatibility of certain properties of micro-physical entities; (2) the Compton…
The violation of Bell inequalities seems to establish an important fact about the world: that it is non-local. However, this result relies on the assumption of the statistical independence of the measurement settings with respect to…
Einstein, Podolsky and Rosen (EPR) argued that the quantum-mechanical probabilistic description of physical reality had to be incomplete, in order to avoid an instantaneous action between distant measurements. This suggested the need for…
A new mathematics, the constructive one, characterizes a singular limit as undecidable. Hence, a singular limit between two theories actually represents a difference between two different kinds of mathematics. This particular situation…
The issue of asymmetric uncertainties resulting from fits, nonlinear propagation and systematic effects is reviewed. It is shown that, in all cases, whenever a published result is given with asymmetric uncertainties, the value of the…
According to Heisenberg's uncertainty relation, there is an ultimate limit to how precisely we may predict the outcome of position and momentum measurements on a quantum system. We show that this limit may be violated by an arbitrarily…
The fundamental physical theories that interpret and explain behaviour of matter in nature are dependent on several unobservables and insensibles in their construction. While a rigorous natural philosophy cannot take them for granted, there…
Chaitin's work, in its depth and breadth, encompasses many areas of scientific and philosophical interest. It helped establish the accepted mathematical concept of randomness, which in turn is the basis of tools that I have developed to…
I investigate the question whether G\"odel's undecidability theorems play a crucial role in the search for a unified theory of physics. I conclude that unless the structure of space-time is fundamentally discrete we can never decide whether…
This article examines the subtle relationship between chaos and randomness, two concepts that, although they refer to seemingly unpredictable phenomenon, are based on fundamentally different principles. Chaos manifests in deterministic…
Probability theory is far from being the most general mathematical theory of uncertainty. A number of arguments point at its inability to describe second-order ('Knightian') uncertainty. In response, a wide array of theories of uncertainty…