Foundations of the Quaternion Quantum Mechanics

We show that quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of the elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing the physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra, we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems, allowing exposing its falsity.

Foundations of the Quaternion Quantum Mechanics

We show that the quaternion quantum mechanics has well-founded mathematical roots and can be derived from the model of elastic continuum by French mathematician Augustin Cauchy, i.e., it can be regarded as representing physical reality of elastic continuum. Starting from the Cauchy theory (classical balance equations for isotropic Cauchy-elastic material) and using the Hamilton quaternion algebra we present a rigorous derivation of the quaternion form of the non- and relativistic wave equations. The family of the wave equations and the Poisson equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic continuum. This is the most general kind of quantum mechanics possessing the same kind of calculus of assertions as conventional quantum mechanics. The problem of the Schrödinger equation, where imaginary ‘i’ should emerge, is solved. This interpretation is a serious attempt to describe the ontology of quantum mechanics, and demonstrates that, besides Bohmian mechanics, the complete ontological interpretations of quantum theory exists. The model can be generalized and falsified. To ensure this theory to be true, we specified problems allowing exposing its falsity.

The Rotating Snakes Illusion Is a Straightforward Consequence of Nonlinearity in Arrays of Standard Motion Detectors

The Rotating Snakes illusion is a motion illusion based on repeating, asymmetric luminance patterns. Recently, we found certain gray-value conditions where a weak illusory motion occurs in the opposite direction. Of the four models for explaining the illusion, one also explains the unexpected perceived opposite direction.We here present a simple new model, without free parameters, based on an array of standard correlation-type motion detectors with a subsequent nonlinearity (e.g., saturation) before summing the detector outputs. The model predicts (a) the pattern-appearance motion illusion for steady fixation, (b) an illusion under the real-world situation of saccades across or near the pattern (pattern shift), (c) a relative maximum of illusory motion for the same gray values where it is found psychophysically, and (d) the opposite illusion for certain luminance values. We submit that the new model’s sparseness of assumptions justifies adding a fifth model to explain this illusion.

Quaternions and Cauchy Classical Theory of Elasticity

Developed by French mathematician Augustin-Louis Cauchy, the classical theory of elasticity is the starting point to show the value and the physical reality of quaternions. The classical balance equations for the isotropic, elastic crystal, demonstrate the usefulness of quaternions. The family of wave equations and the diffusion equation are a straightforward consequence of the quaternion representation of the Cauchy model of the elastic solid. Using the quaternion algebra, we present the derivation of the quaternion form of the multiple wave equations. The fundamental consequences of all derived equations and relations for physics, chemistry, and future prospects are presented.

The Rotating Snake Illusion is a straightforward consequence of non-linearity in arrays of standard motion detectors

The Rotating Snakes illusion is a motion illusion based on repeating, asymmetric luminance patterns. Recently, we found certain grey-value conditions where a weak, illusory motion occurs in the opposite direction. Of the four models for explaining the illusion, one (Backus and Oruç, 2005) also explains the unexpected perceived opposite direction. We here present a simple new model, without free parameters, based on an array of standard correlation-type motion detectors with a subsequent non-linearity (e.g., saturation) before summing the detector outputs. The model predicts (1) the pattern-appearance motion illusion for steady fixation, (2) an illusion under the real-world situation of saccades across or near the pattern (pattern shift), (3) a relative maximum of illusory motion for the same grey values where it is found psychophysically, and (4) the inverse illusion for certain luminance values. We submit that the model’s sparseness of assumptions justifies adding a fifth model to explain this illusion.

Nonasymptotic bounds for the quadratic risk of the Grenander estimator

There is an enormous literature on the so-called Grenander estimator, which is merely the nonparametric maximum likelihood estimator of a nonincreasing probability density on [0, 1] (see, for instance, Grenander (1981)), but unfortunately, there is no nonasymptotic (i.e. for arbitrary finite sample size n) explicit upper bound for the quadratic risk of the Grenander estimator readily applicable in practice by statisticians. In this paper, we establish, for the first time, a simple explicit upper bound 2n−1/2 for the latter quadratic risk. It turns out to be a straightforward consequence of an inequality valid with probability one and bounding from above the integrated squared error of the Grenander estimator by the Kolmogorov–Smirnov statistic.

Landauer Principle and General Relativity

We endeavour to illustrate the physical relevance of the Landauer principle applying it to different important issues concerning the theory of gravitation. We shall first analyze, in the context of general relativity, the consequences derived from the fact, implied by Landauer principle, that information has mass. Next, we shall analyze the role played by the Landauer principle in order to understand why different congruences of observers provide very different physical descriptions of the same space-time. Finally, we shall apply the Landauer principle to the problem of gravitational radiation. We shall see that the fact that gravitational radiation is an irreversible process entailing dissipation, is a straightforward consequence of the Landauer principle and of the fact that gravitational radiation conveys information. An expression measuring the part of radiated energy that corresponds to the radiated information and an expression defining the total number of bits erased in that process, shall be obtained, as well as an explicit expression linking the latter to the Bondi news function.

Process Reliabilism, Prime Numbers and the Generality Problem

This paper aims to show that Selim Berker’s widely discussed prime number case is merely an instance of the well-known generality problem for process reliabilism and thus arguably not as interesting a case as one might have thought. Initially, Berker’s case is introduced and interpreted. Then the most recent response to the case from the literature is presented. Eventually, it is argued that Berker’s case is nothing but a straightforward consequence of the generality problem, i.e., the problematic aspect of the case for process reliabilism (if any) is already captured by the generality problem.

Quantified Boolean Formulas: Call the Plumber!

In this tool paper we describe a variation of Nintendo’s Super Mario World dubbed Super Formula World that creates its game maps based on an input quantified Boolean formula. Thus in Super Formula World, Mario, the plumber not only saves his girlfriend princess Peach, but also acts as a QBF solver as a side. The game is implemented in Java and platform independent. Our implementation rests on abstract frameworks by Aloupis et al. that allow the analysis of the computational complexity of a variety of famous video games. In particular it is a straightforward consequence of these results to provide a reduction from QSAT to Super Mario World. By specifying this reduction in a precise way we obtain the core engine of Super Formula World. Similarly Super Formula World implements a reduction from SAT to Super Mario Bros., yielding significantly simpler game worlds.

Disorder dissected (ii): the inversion of the social order

This chapter studies Shakespeare's treatment of the Cade rebellion in one of his Henry VI plays. The play presents Cade's rebellion as a straightforward consequence of Henry's non-rule and of the noble factionalism and succession disputes that that non-rule enabled. Certainly, in one of the soliloquies that mark York out as the play's leading Machiavel, he expounds his double-sided plan to seize the political initiative and the crown. The play also leaves readers in doubt that elite political manoeuvres lay behind Cade's insurrection. On this view, the roots of popular revolt must lie, not in the agency of subaltern political actors, be they plebeian or female, but rather in the dereliction of duty of their social superiors and natural rulers, and thus in the machinations of court politics.