Related papers: Reply to a "Comment on 'Physics without determinis…
This paper argues for the following three theses: (1) There is a clear reason to prefer physical theories with deterministic dynamical equations: such theories are maximally rich in information and usually also maximally simple. (2) There…
We formalise the self-referential definition of physical laws using monotone operators on a lattice of theories, resolving the pathologies of naive set-theoretic formulations. By invoking Tarski fixed point theorem, we identify physical…
This paper forms part of a wider campaign: to deny pointillisme. That is the doctrine that a physical theory's fundamental quantities are defined at points of space or of spacetime, and represent intrinsic properties of such points or…
A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's…
I review some recent advances in foundational research at Pavia QUIT group. The general idea is that there is only Quantum Theory without quantization rules, and the whole Physics---including space-time and relativity--is emergent from the…
The paper has heuristic character. The conceptual frame, based on the assumption of quantum uncertainty only, has been formerly introduced in two papers [S. Tosto, Il Nuovo Cimento B, vol. 111, n.2, 1996 and S. Tosto, Il Nuovo Cimento D,…
In the present article we use the quantum formalism to describe the process of choice under rational ignorance. We consider as a basic task a question or an issue where the only answers are 0 and 1. We show that under rational ignorance the…
I point out a radical indeterminism in potential-based formulations of Newtonian gravity once we drop the condition that the potential vanishes at infinity (as is necessary, and indeed celebrated, in cosmological applications). This…
An out of the box intellectual path exploring the foundations of quantum mechanics is discussed in some detail, in order to clarify why a possibly different way to look at the relevant fundamental questions can be identified and can support…
There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…
Dynamical system techniques are extremely useful to study cosmology. It turns out that in most of the cases, we deal with finite isolated fixed points corresponding to a given cosmological epoch. However, it is equally important to analyse…
In two papers we noted that in common practice many algebraic constructions are defined only `up to isomorphism' rather than explicitly. We mentioned some questions raised by this fact, and we gave some partial answers. The present paper…
The standard presentation of the principles of quantum mechanics is critically reviewed both from the experimental/operational point and with respect to the request of mathematical consistency and logical economy. A simpler and more…
I contrast two possible attitudes towards a given branch of physics: as inferential (i.e., as concerned with an agent's ability to make predictions given finite information), and as dynamical (i.e., as concerned with the dynamical equations…
Does the notion of a quantum randomized or nondeterministic algorithm make sense, and if so, does quantum randomness or nondeterminism add power? Although reasonable quantum random sources do not add computational power, the discussion of…
Recently there has been a great deal of interest in tabletop experiments intended to exhibit the quantum nature of gravity by demonstrating that it can induce entanglement. We argue that these experiments also provide new information about…
We reconstruct quantum theory starting from the premise that, as Asher Peres remarked, "Unperformed experiments have no results." The tools of modern quantum information theory, and in particular the symmetric informationally complete (SIC)…
A unified conceptual foundation of classical and quantum physics is given, free of undefined terms. Ensembles are defined by extending the `probability via expectation' approach of Whittle to noncommuting quantities. This approach carries…
Baroque questions of set-theoretic foundations are widely assumed to be irrelevant to physics. In this article, I demonstrate that this assumption is incorrect. I show that the fundamental physical question of whether a theory is…
We introduce PHYSICS, a comprehensive benchmark for university-level physics problem solving. It contains 1297 expert-annotated problems covering six core areas: classical mechanics, quantum mechanics, thermodynamics and statistical…