Related papers: The certainty principle (review)
This is the logical foundation for for Relativity Theory, Probability Theory, and for Quantum Theory. Contents is the following: 1 Introduction. 2 Classical logic. 3 Time and space. 3.1 Recorders. 3.2 Time. 3.3 Space. 3.4 Relativity. 4.…
It is shown that the phenomenon of irreversibility in many-body and few-body systems can be explained and described within the framework of the concept of direct (not instantaneous) interaction of particles without using probabilistic…
Probability theory as a physical theory is, in a sense, the most general physics theory available, more encompassing than relativity theory and quantum mechanics, which comply with probability theory. Taking this simple fact seriously, I…
The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite $N$ quantum observables. We…
Time is one of the undisputed foundations of our life in the real world. Here it is argued that inside small isolated quantum systems, time does not pass as we are used to, and it is primarily in this sense that quantum objects enjoy only…
The celebrated Heisenberg Uncertainty Principle \Delta x \Delta p\ge \hbar/2 can allow measurement accuracies less than \Delta x or \Delta p. Classical analog of this is known as sub-Fourier sensitivity. We illustrate this phenomenon in a…
In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the Clifford-Fourier transform on $\mathbb{R}^m$.
A concise review of various mathematical formulations of the uncertainty relations in quantum mechanics discovered since 1927 is given. Besides the traditional Heisenberg inequality, the modifications made by Schr\"odinger and Robertson, as…
We expand on a recent development by Hardy, in which quantum mechanics is derived from classical probability theory supplemented by a single new axiom, Hardy's Axiom 5. Our scenario involves a `pretend world' with a `pretend' Heisenberg who…
This note shows that Heisenberg's choice for a wave function in his original paper on the uncertainty principle is simply a renormalized characteristic function of a stable distribution with certain restrictions on the parameters. Relaxing…
Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…
Bohr and Heisenberg suggested that the thermodynamical quantities of temperature and energy are complementary in the same way as position and momentum in quantum mechanics. Roughly speaking, their idea was that a definite temperature can be…
A universal formulation of uncertainty relations for quantum measurements is presented with additional focus on the representability of quantum observables by classical observables over a given state. Owing to the simplicity and operational…
Birnbaum's theorem, that the sufficiency and conditionality principles entail the likelihood principle, has engendered a great deal of controversy and discussion since the publication of the result in 1962. In particular, many have raised…
The purpose of this article is to formulate a number of probabilistic hidden-variable theorems, to provide proofs in some cases, and counterexamples to some conjectured relationships. The first theorem is the fundamental one. It asserts the…
Despite its enormous empirical success, the formalism of quantum theory still raises fundamental questions: why is nature described in terms of complex Hilbert spaces, and what modifications of it could we reasonably expect to find in some…
Motivated by the Generalized Uncertainty Principle, covariance, and a minimum measurable time, we propose a deformation of the Heisenberg algebra and show that this leads to corrections to all quantum mechanical systems. We also demonstrate…
This thesis investigates the connection between quantum theory, thermodynamics and information theory. Theories with structure similar to that of quantum theory are considered, mathematically described by the framework of "Generalized…
Heisenberg's breakthrough in his July 1925 paper that set in motion the development of Quantum Mechanics through subsequent papers by Born, Jordan, Heisenberg and also Dirac (from 1925 to 1927) is reexamined through a modern lens. In this…