Recently, the author of this paper and his research team have extended the orthodox quantum theory of atoms in molecules (QTAIM) to a novel paradigm called the two-component QTAIM (TC-QTAIM). This extended framework enables one to incorporate nuclear dynamics into the AIM analysis as well as performing AIM analysis of the exotic species; positronic and muonic species are a few examples. In present paper, this framework has been reviewed, providing some computational examples with particular emphasis on origins and applications, in (...) a non-technical language. The main questions, enigmas and basic ideas that finally yielded the TC-QTAIM are considered in chronological order to help the reader comprehend the intuition behind the math. Finally, it is demonstrated that the TC-QTAIM and its more refined versions are able to tackle problems inaccessible to the orthodox QTAIM. (shrink)

We observe that Schrödinger’s equation may be written as two real coupled Hamilton–Jacobi (HJ)-like equations, each involving a quantum potential. Developing our established programme of representing the quantum state through exact free-standing deterministic trajectory models, it is shown how quantum evolution may be treated as the autonomous propagation of two coupled congruences. The wavefunction at a point is derived from two action functions, each generated by a single trajectory. The model shows that conservation as expressed through a continuity equation is (...) not a necessary component of a trajectory theory of state. Probability is determined by the difference in the action functions, not by the congruence densities. The theory also illustrates how time-reversal symmetry may be implemented through the collective behaviour of elements that individually disobey the conventional transformation (T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{T}$$\end{document}) of displacement (scalar) and velocity (reversal). We prove that an integral curve of the linear superposition of two vectors can be derived algebraically from the integral curves of one of the constituent vectors labelled by integral curves associated with the other constituent. A corollary establishes relations between displacement functions in diverse trajectory models, including where the functions obey different symmetry transformations. This is illustrated by showing that a (T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{T}$$\end{document}-obeying) de Broglie-Bohm trajectory is a sequence of points on the (non-T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{T}$$\end{document}) HJ trajectories, and vice versa. (shrink)

We construct a local \-epistemic hidden-variable model of Bell correlations by a retrocausal adaptation of the originally superdeterministic model given by Brans. In our model, for a pair of particles the joint quantum state \\rangle \) as determined by preparation is epistemic. The model also assigns to the pair of particles a factorisable joint quantum state \\rangle \) which is different from the prepared quantum state \\rangle \) and has an ontic status. The ontic state of a single particle consists (...) of two parts. First, a single particle ontic quantum state \|i\rangle \), where \\) is a 3-space wavepacket and \ is a spin eigenstate of the future measurement setting. Second, a particle position in 3-space \\), which evolves via a de Broglie–Bohm type guidance equation with the 3-space wavepacket \\) acting as a local pilot wave. The joint ontic quantum state \\rangle \) fixes the measurement outcomes deterministically whereas the prepared quantum state \\rangle \) determines the distribution of the \\rangle \)’s over an ensemble. Both \\rangle \) and \\rangle \) evolve via the Schrodinger equation. Our model exactly reproduces the Bell correlations for any pair of measurement settings. We also consider ‘non-equilibrium’ extensions of the model with an arbitrary distribution of hidden variables. We show that, in non-equilibrium, the model generally violates no-signalling constraints while remaining local with respect to both ontology and interaction between particles. We argue that our model shares some structural similarities with the modal class of interpretations of quantum mechanics. (shrink)

In the same way as the quantum no-cloning theorem and quantum key distribution in two preceding papers, entanglement-assisted quantum teleportation and Grover’s search algorithm are generalized by transferring them to an abstract setting, including usual quantum mechanics as a special case. This again shows that a much more general and abstract access to these quantum mechanical features is possible than commonly thought. A non-classical extension of conditional probability and, particularly, a very special type of state-independent conditional probability are used instead (...) of Hilbert spaces and wavefunctions. (shrink)

The notion of non-equilibrium, in the sense of a particle distribution other than rho equal psi squared, is imported into Nelson’s stochastic mechanics, and described in terms of effective wavefunctions obeying non-linear equations. These techniques are applied to the discussion of non-locality in non-linear Schroedinger equations.

We present a technique for the analysis of pattern formation by a class of models for the formation of ocular dominance stripes in the striate cortex of some mammals. The method, which employs the adiabatic approximation to derive a set of ordinary differential equations for patterning modes, has been successfully applied to reaction-diffusion models for striped patterns [1]. Models of ocular dominance stripes have been studied [2,3] by computation, or by linearization of the model equations. These techniques do not (...) provide a rationale for the origin of the stripes. We show here that stripe formation is a non-linear property of the models. Our analysis indicates that stripe selection is closely linked to a property in the dynamics of the models which arises from a symmetry between ipsilateral and contralateral synapses to the visual cortex of a given hemisphere. (shrink)

In this work, a neo-classical relativistic mechanics theory is presented where the spin of an electron is an inherent part of its world space-time path as a point particle. The fourth-order equation of motion corresponds to the same covariant Lagrangian function in proper time as in special relativity except for an additional spin energy term. The theory provides a hidden-variable model of the electron where the dynamic variables give a complete description of its motion, giving a classical mechanics explanation of (...) the electron’s spin, its dipole moments, and Schrödinger’s zitterbewegung, These features are also described mathematically by quantum mechanics theory, of course, but without any physical picture of an underlying reality. The total motion of the electron can be decomposed into a sum of a local spin motion about a point and a global motion of this point, called here the spin center. The global motion is sub-luminal and described by Newton’s Second Law in proper time, the time for a clock fixed at the spin center, while the total motion occurs at the speed of light c, consistent with the eigenvalues of Dirac’s velocity operators having magnitude c. The local spin motion is an inherent perpetual motion, which for a free electron is periodic at the ultra-high zitterbewegung frequency and its path is circular in a spin-center reference frame. In an electro-magnetic field, this spin motion generates magnetic and electric dipole energies through the Lorentz force on the electron’s point charge. The electric dipole energy corresponds to the spin-orbit coupling term involving the electric field that appears in the corrected Pauli non-relativistic Hamiltonian, which has long been used to explain the doublet structure of the spectral lines of the excited hydrogen atom. Pauli’s spin-orbit term is usually derived, however, from his magnetic dipole energy term, including also the effect of Thomas precession, which halves this energy. The magnetic dipole energy from Pauli’s and Dirac’s theory is twice that in the neo-classical theory, a discrepancy that has not been resolved. By defining a spin tensor as the angular momentum of the electron’s total motion about its spin center, the fundamental equations of motion can be re-written in an identical form to those of the Barut–Zanghi electron theory. This allows the equations of motion to be expressed in an equivalent form involving operators applied to a state function of proper time satisfying a neo-classical Dirac–Schrödinger spinor equation. This state function produces the dynamic variables from the same operators as in Dirac’s theory for the electron but without any probability implications. It leads to a neo-classical wave function that satisfies Dirac’s relativistic wave equation for the free electron by applying the Lorentz transformation to express proper time in the state function in terms of an observer’s space-time coordinates, showing that there is a close connection between the neo-classical theory and quantum mechanics theory for the electron’s dynamics. (shrink)

A recently proposed approach to relativistic quantum mechanics is applied to the problem of a particle in a quadratic potential. The methods, both exact and approximate, allow one to obtain eigenstate energy levels and wavefunctions, using conventional numerical eigensolvers applied to Schrödinger-like equations. Results are obtained over a nine-order-of-magnitude variation of system parameters, ranging from the non-relativistic to the ultrarelativistic limits. Various trends are analyzed and discussed—some of which might have been easily predicted, others which may be a bit (...) more surprising. (shrink)

We emphasize that the pressure related work appearing in a general relativistic first law of thermodynamics should involve proper volume element rather than coordinate volume element. This point is highlighted by considering both local energy momentum conservation equation as well as particle number conservation equation. It is also emphasized that we are considering here a non-singular fluid governed by purely classical general relativity. Therefore, we are not considering here any semi-classical or quantum gravity which apparently suggests thermodynamical properties even for (...) a (singular) black hole. Having made such a clarification, we formulate a global first law of thermodynamics for an adiabatically evolving spherical perfect fluid. It may be verified that such a global first law of thermodynamics, for a non-singular fluid, has not been formulated earlier. (shrink)

In this article, we analyze the third of three papers, in which Einstein presented his quantum theory of the ideal gas of 1924–1925. Although it failed to attract the attention of Einstein’s contemporaries and although also today very few commentators refer to it, we argue for its significance in the context of Einstein’s quantum researches. It contains an attempt to extend and exhaust the characterization of the monatomic ideal gas without appealing to combinatorics. Its ambiguities illustrate Einstein’s confusion with his (...) initial success in extending Bose’s results and in realizing the consequences of what later came to be called Bose–Einstein statistics. We discuss Einstein’s motivation for writing a non-combinatorial paper, partly in response to criticism by his friend Ehrenfest, and we paraphrase its content. Its arguments are based on Einstein’s belief in the complete analogy between the thermodynamics of light quanta and of material particles and invoke considerations of adiabatic transformations as well as of dimensional analysis. These techniques were well known to Einstein from earlier work on Wien’s displacement law, Planck’s radiation theory and the specific heat of solids. We also investigate the possible role of Ehrenfest in the gestation of the theory. (shrink)

It has been shown that quantum mechanics in its orthodox interpretation violates four different formulations of causality principle endowed with empirical meaning. The present work aims to highlight how even a realistic non-standard interpretation of the theory conflicts with causality in its Cartesian formulation of the principle of the non-inferiority of causes over effects. Such an interpretation, which attributes some form of weak physical reality to the wave function (called empty wave, regarded as a zero-energy wave-like phenomenon), is a sort (...) of precursor of the more recent so-called wavefunction realism. We also discuss a more radical realistic interpretation according to which physical properties can also be assigned to non-metaphysical relative nothing, seen as the simple absence of a particle such as a photon, but not of its corresponding state (no-photon), which is considered real. By interpreting the wave function collapse as a consequence of an interaction with empty waves or of a detection of the no-photon, we will highlight how more real physical effects can derive from lower causes, including relative nothing. Finally, we will show how these interpretations, while violating Cartesian causality in its two variants, do not seem to affect the validity of the principle of a rational explanation that nothing can derive from (absolute) nothing, which does not seem satisfied by the orthodox interpretation. (shrink)

QUALITY AND QUANTITY are fairly generally regarded as complementary terms, although the profound reason for their comple- mentarism is often far from being understood, this reason lying in the 'polar' correspondence referred to toward ...

The Reign of Quantity gives a concise but comprehensive view of the present state of affairs in the world, as it appears from the point of view of the 'ancient wisdom', formerly common both to the East and to the West, but now almost entirely lost sight of. The author indicates with his fabled clarity and directness the precise nature of the modern deviation, and devotes special attention to the development of modern philosophy and science, and to the part played (...) by them, with their accompanying notions of progress and evolution, in the formation of the industrial and democratic society which we now regard as 'normal'. Guénon sees history as a descent from Form (or Quality) toward Matter (or Quantity); but after the Reign of Quantity-modern materialism and the 'rise of the masses'-Guénon predicts a reign of 'inverted quality' just before the end of the age: the triumph of the 'counter-initiation', the kingdom of Antichrist. This text is considered the magnum opus among Guénon's texts of civilizational criticism, as is Symbols of Sacred Science among his studies on symbols and cosmology, and Man and His Becoming according to the Vedanta among his more purely metaphysical works. (shrink)

A study of the constitution and development of the human being from the metaphysical point of view, with special reference to Vedantic doctrine.

Publié pour la première fois en 1945, ce texte oppose aux religions historiques la tradition unique et originelle de la connaissance ésotérique. Le monde moderne est décrit comme une monstruosité qui ne reconnaît aucune transcendance et privilégie le règne de la contingence, du quantitatif et de l'individualisme.

Description: Contents: Preface 1. General Remarks on the Vedanta 2. Fundamental Distinction Between The Self and the Ego 3. The Vital Centre of the Human Being, Seat of Brahma 4. Purusha and Prakriti 5. Purusha Unaffected by Individual Modifications 6. The Degrees of Individual Manifestation 7. Buddhi or the Higher Intellect 8. Manas or the Inward Sense : The Ten External Faculties of Sensation and Action 9. The Envelopes of the Self ; The Five Vayus or Vital Functions 10. The (...) Essential Unity and Identity of the Self in all the States of the Being 11. The Different Conditions of Atma in the Human Being 12. The Waking State or the Condition of Vaishwanara 13. The Dream State or the Condition of Taijasa 14. The State of Deep Sleep or the Condition of Prajna 15. The Unconditioned State of Atma 16. The Symbolical Representation of Atma and its Conditions by the Sacred Monosyllable Om 17. The Posthumous Evolution of the Human Being 18. The Reabsorption of the Individual Faculties 19. Differences in the Posthumous Conditions According to the Degrees of Knowledge 20. The Coronal Artery and the Solar Ray 21. The Divine Journey of the Being on the Path of Liberation 22. Final Deliverance 23. Videha-mukti and Jivana-mukti 24. The Spiritual State of the Yogi : The Supreme Identity. (shrink)

Buddhist concepts of personal life and responsibilities.

The concluding chapter lays down the essential conditions for any genuine understanding between East and West, which can only come through the work of those who have attained, at least in some degree, to the realization of 'wisdom uncreate' ...

The objective of this study is twofold: to examine the patterns that govern social reporting with reference to an Islamic framework and to identify the moral legitimacy factors that influence them. We select 146 publicly listed Sharia‐compliant companies and classify the disclosures in their annual reports according to an Islamic framework that categorises items as either Required, Expected or Desired to indicate the degree of importance each item carries from an Islamic perspective. Based on this framework, we then analyse moral (...) legitimacy factors, specifically the type of Sharia screening body and the proportion of Muslims in the population, that may influence the prioritisation of the different categories of social reporting. We find that disclosures that fall into the Required category of our framework—especially those that relate to companies’ involvement in “haram” activities (activities not permissible in Islam)—are still few among the companies studied. Our research also reveals that both moral legitimacy factors under investigation influence the three categories of social reporting, although in different ways. This research contributes to the existing literature by empirically examining how organisations prioritise their disclosure of virtues and the moral legitimacy factors that influence that prioritisation. (shrink)