Related papers: X-probability and Irreversibility Paradox
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
The observed general time-asymmetric behavior of macroscopic systems -- embodied in the second law of thermodynamics -- arises naturally from time-symmetric microscopic laws due to the great disparity between macro and micro-scales. More…
We study the probability that a random polynomial with integer coefficients is reducible when factored over the rational numbers. Using computer-generated data, we investigate a number of different models, including both monic and non-monic…
Simpson's Paradox is a well-known phenomenon in statistical science, where the relationship between the response variable $X$ and a certain explanatory factor of interest $A$ reverses when an additional factor $B_1$ is considered. This…
Many of the conceptual problems students have in understanding quantum mechanics arise from the way probabilities are introduced in standard (textbook) quantum theory through the use of measurements. Introducing consistent microscopic…
For decades, researchers have sought to understand how the irreversibility of the surrounding world emerges from the seemingly time symmetric, fundamental laws of physics. Quantum mechanics conjectured a clue that final irreversibility is…
If no optimal propositional proof system exists, we (and independently Pudl\'ak) prove that ruling out length $t$ proofs of any unprovable sentence is hard. This mapping from unprovable to hard-to-prove sentences powerfully translates facts…
A model of correlated particles described by a generalized probability theory is suggested whose dynamics is subject to a non-linear version of Schr\"odinger equation. Such equations arise in many different contexts, most notably in the…
We implement several non-binary logic systems using the spin dynamics of nuclear spins in nuclear magnetic resonance (NMR). The NMR system is a suitable test system because of its high degree of experimental control; findings from NMR…
It was argued [1] that there can be no extension of quantum mechanics with improved predictive power on a measurement freely chosen, independently of any event that is not in its future light cone. The assumption of measurement choice was…
Max Born's statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. While the latter always result from an…
Here we give a necessary and sufficient condition for the convergence to a random max infinitely divisible law from that of a random maximum. We then discuss random max-stable laws, their domain of max-attraction and the associated extremal…
In most circumstances, probability sampling is the only way to ensure unbiased inference about population quantities where a complete census is not possible. As we enter the era of 'big data', however, nonprobability samples, whose sampling…
The transition probability of a spin driven by a rotating magnetic field is reformulated. This work shows that, once projection onto the measurement basis is properly accounted for, the laboratory measured probability is governed by both…
Zurek claims to have derived Born's rule noncircularly in the context of an ontological no-collapse interpretation of quantum states, without any "deus ex machina imposition of the symptoms of classicality." After a brief review of Zurek's…
In reverse mathematics, is is possible to have a curious situation where we know that an implication does not reverse, but appear to have no information on on how to weaken the assumption while preserving the conclusion. A main cause of…
Mass-superselection rule (MSR) states that in the non-relativistic quantum theory superpositions of states with different masses are unphysical. While MSR features even in textbooks, its validity, physical content and consequences remain…
The dynamical equation of hybrid systems, being the combination of Schr\"odinger and Liouville equations, produces noncausal evolution when the initial state of interacting quantum and classical mechanical systems is as it is demanded in…
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…
Recent results suggest that quantum mechanical phenomena may be interpreted as a failure of standard probability theory and may be described by a Bayesian complex probability theory.