Related papers: On Buckingham's $\Pi$-Theorem
We formulate a quantum theory of the Universe based on Bayesian probability. In this theory, the probability of the Universe is not a frequency probability, which can be obtained by observing experimental results several times, but is a…
We apply dimensional analysis with Buckinghams "Pi" theorem to estimate the volume of wood in a tree stem, given the tree's height and diameter. We use Meyer's (1953) data on 31 cherry trees from the Allegheny National forest as the main…
Quantum experiments yield random data. We show that the most efficient way to store this empirical information by a finite number of bits is by means of the vector of square roots of observed relative frequencies. This vector has the unique…
The theory of quantum mechanics is examined using non-standard real numbers, called quantum real numbers (qr-numbers), that are constructed from standard Hilbert space entities. Our goal is to resolve some of the paradoxical features of the…
The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture…
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
In the present report the author presents a simple and systematically defined formula for the fine structure constant based only on the number $\pi$. The difference between the suggested value and the currently known experimental one is…
It is shown that the basic equations of quantum theory can be obtained from a straightforward application of logical inference to experiments for which there is uncertainty about individual events and for which the frequencies of the…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
Quantum theory is usually formulated in terms of abstract mathematical postulates, involving Hilbert spaces, state vectors, and unitary operators. In this work, we show that the full formalism of quantum theory can instead be derived from…
The principle which allows to construct new physical theories on the basis of classical mechanics by reduction of the number of its axiom without engaging new postulates is formulated. The arising incompleteness of theory manifests itself…
Measurement is an important scientific activity. In most of science, including classical physics, is may be understood as a way of finding out about the physical world and representing the results numerically. No-go theorems show that…
The mathematical formulation of Quantum Mechanics is derived from purely operational axioms based on a general definition of "experiment" as a set of transformations. The main ingredient of the mathematical construction is the postulated…
The relevance of the Planck scale to a theory of quantum gravity has become a worryingly little examined assumption that goes unchallenged in the majority of research in this area. However, in all scientific honesty, the significance of…
Quantum theory is a mathematical formalism to compute probabilities for outcomes happenning in physical experiments. These outcomes constitute events happening in space-time. One of these events represents the fact that a system located in…
A Bayesian approach is developed to determine quantum mechanical potentials from empirical data. Bayesian methods, combining empirical measurements and "a priori" information, provide flexible tools for such empirical learning problems. The…
Amplitudes are the major logical object in Quantum Theory. Despite this fact they presents no physical reality and in consequence only observables can be experimetally checked. We discuss the possibility of a theory of Quantum Probabilities…
Bell's theorem is a fundamental result in quantum mechanics: it discriminates between quantum mechanics and all theories where probabilities in measurement results arise from the ignorance of pre-existing local properties. We give an…
The familiar theories of physics have the feature that the application of the theory to make predictions in specific circumstances can be done by means of an algorithm. We propose a more precise formulation of this feature --- one based on…
The PBR theorem gives insight into how quantum mechanics describes a physical system. This paper explores PBRs' general result and shows that it does not disallow the ensemble interpretation of quantum mechanics and maintains, as it must,…