Complex joint probabilities as expressions of determinism in quantum mechanics

The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have non-zero mutual overlap. Transformations to a new basis set are then expressed in terms of complex conditional probabilities that describe the fundamental relation between precise statements about the three different observables. Since such transformations merely change the representation of the quantum state, these conditional probabilities provide a state-independent definition of the deterministic relation between the outcomes of different quantum measurements. In this paper, it is shown how classical reality emerges as an approximation to the fundamental laws of quantum determinism expressed by complex conditional probabilities. The quantum mechanical origin of phase spaces and trajectories is identified and implications for the interpretation of quantum measurements are considered. It is argued that the transformation laws of quantum determinism provide a fundamental description of the measurement dependence of empirical reality.Comment: 12 pages, including 1 figure, updated introduction includes references to the historical background of complex joint probabilities and to related work by Lars M. Johanse

A Cross-Recurrence Analysis of the Pupil Size Fluctuations in Steady Scotopic Conditions

Pupil size fluctuations during stationary scotopic conditions may convey information about the cortical state activity at rest. An important link between neuronal network state modulation and pupil fluctuations is the cholinergic and noradrenergic neuromodulatory tone, which is active at cortical level and in the peripheral terminals of the autonomic nervous system (ANS). This work aimed at studying the low- and high-frequency coupled oscillators in the autonomic spectrum (0–0.45 Hz) which, reportedly, drive the spontaneous pupillary fluctuations. To assess the interaction between the oscillators, we focused on the patterns of their trajectories in the phase-space. Firstly, the frequency spectrum of the pupil signal was determined by empirical mode decomposition. Secondly, cross-recurrence quantification analysis was used to unfold the non-linear dynamics. The global and local patterns of recurrence of the trajectories were estimated by two parameters: determinism and entropy. An elliptic region in the entropy-determinism plane (95% prediction area) yielded health-related values of entropy and determinism. We hypothesize that the data points inside the ellipse would likely represent balanced activity in the ANS. Interestingly, the Epworth Sleepiness Scale scores scaled up along with the entropy and determinism parameters. Although other non-linear methods like Short Time Fourier Transform and wavelets are usually applied for analyzing the pupillary oscillations, they rely on strong assumptions like the stationarity of the signal or the a priori knowledge of the shape of the single basis wave. Instead, the cross-recurrence analysis of the non-linear dynamics of the pupil size oscillations is an adaptable diagnostic tool for identifying the different weight of the autonomic nervous system components in the modulation of pupil size changes at rest in non-luminance conditions

Quantum Information Dynamics and Open World Science

One of the fundamental insights of quantum mechanics is that complete knowledge of the state of a quantum system is not possible. Such incomplete knowledge of a physical system is the norm rather than the exception. This is becoming increasingly apparent as we apply scientific methods to increasingly complex situations. Empirically intensive disciplines in the biological, human, and geosciences all operate in situations where valid conclusions must be drawn, but deductive completeness is impossible. This paper argues that such situations are emerging examples of {it Open World} Science. In this paradigm, scientific models are known to be acting with incomplete information. Open World models acknowledge their incompleteness, and respond positively when new information becomes available. Many methods for creating Open World models have been explored analytically in quantitative disciplines such as statistics, and the increasingly mature area of machine learning. This paper examines the role of quantum theory and quantum logic in the underpinnings of Open World models, examining the importance of structural features of such as non-commutativity, degrees of similarity, induction, and the impact of observation. Quantum mechanics is not a problem around the edges of classical theory, but is rather a secure bridgehead in the world of science to come

Deterministic Dynamics and Chaos: Epistemology and Interdisciplinary Methodology

We analyze, from a theoretical viewpoint, the bidirectional interdisciplinary relation between mathematics and psychology, focused on the mathematical theory of deterministic dynamical systems, and in particular, on the theory of chaos. On one hand, there is the direct classic relation: the application of mathematics to psychology. On the other hand, we propose the converse relation which consists in the formulation of new abstract mathematical problems appearing from processes and structures under research of psychology. The bidirectional multidisciplinary relation from-to pure mathematics, largely holds with the "hard" sciences, typically physics and astronomy. But it is rather new, from the social and human sciences, towards pure mathematics