Arrow of time

The main topic of this paper is a description of the generation of entropy at the end of the inflationary era. As a generalization of the present standard model of the Universe dominated by pressureless dust and a Lorentz invariant vacuum energy (LIVE), we first present a flat Friedmann universe model, where the dust is replaced with an ideal gas. It is shown that the pressure of the gas is inversely proportional to the fifth power of the scale factor and that the entropy in a comoving volume does not change during the expansion. We then review different measures of gravitational entropy related to the Weyl curvature conjecture and calculate the time evolution of two proposed measures of gravitational entropy in a LIVE-dominated Bianchi type I universe, and a Lemaitre-Bondi-Tolman universe with LIVE. Finally, we elaborate upon a model of energy transition from vacuum energy to radiation energy, that of Bonanno and Reuter, and calculate the time evolution of the entropies of vacuum energy and radiation energy. We also calculate the evolution of the maximal entropy according to some recipes and demonstrate how a gap between the maximal entropy and the actual entropy opens up at the end of the inflationary era.

The interface between classical physics and quantum physics is explained from the point of view of Quantum Information Theory (Feynman Processes), based on the qubit model. The interpretation depends on a hefty sacrifice: the classical determinism or the arrow of time. As a benefit, the wave-particle duality naturally emerges from the qubit model, as the root of creation and annihilation of possibilities (quantum logic). A few key experiments are briefly reviewed from the above perspective: quantum erasure, delayed-choice and wave-particle correlation. The CPT-Theorem is interpreted in the framework of categories with duality and a timeless interpretation of the Feynman Processes is proposed. A connection between the fine-structure constant and algebraic number theory is suggested.

This is an excerpt from the Pictorial Compendium of The Secret Doctrine
Volume IV, The Nature of Everything.

Follow me down the rabbit hole into the magical world of the Nature of Everything. It is like nothing you have ever imagined! It is filled with wonder and awe! The Universe is all of time and Space and its contents. It includes planets, moons, minor planets, stars, galaxies, the contents of intergalactic space, and all matter and energy.

Why does time reversal involve two operations, a temporal reflection and the operation of complex conjugation in quantum mechanics? Why is it that time reversal preserves position and reverses momentum and spin? This puzzle of time reversal in quantum mechanics has been with us since Wigner's first presentation. In this paper, I show that the standard account of time reversal in quantum mechanics can be derived from the natural requirement that time reversal reverses velocities by analyzing the continuity equation.

In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition (the Past Hypothesis) to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a natural initial condition. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix (a mixed state) that represents something objective. This stands in sharp contrast to Wave Function Realism, the thesis that the quantum universe is described by a wave function (a pure state) that represents something objective. Second, I suggest that the Past Hypothesis is sufficient to determine a natural density matrix, which is also simple and unique. This is achieved by what I call the Initial Projection Hypothesis: the initial density matrix of the universe is the normalized projection onto the special low-dimensional Hilbert space. Third, because the initial quantum state is unique and simple, we have a strong case for the Nomological Thesis: the initial quantum state of the universe is on a par with laws of nature. This new package of ideas has several interesting implications, including on the harmony between statistical mechanics and quantum mechanics, the dynamic unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement.

Erwin Schrödinger holds a prominent place in the history of science primarily due to his crucial role in the development of quantum physics. What is perhaps lesser known are his insights into subject-object duality, consciousness and mind. He documented himself that these were influenced by the Upanishads, a collection of ancient Hindu spiritual texts. Central to his thoughts in this area is that Mind is only One and there is no separation between subject and object. This chapter aims to bridge Schrödinger’s view on One Mind with the teachings of Dōgen, a twelfth century Zen master. This bridge is formed by addressing the question of how time relates to One Mind, and subject-object duality. Schrödinger describes the experience of One Mind to be like a timeless now, whereas subject-object duality involves a linear continuum of time. We show how these differing positions are unified in the notion of ‘absolute present’, which was put forward in the philosophy of Nishida Kitarō (1871–1945). In addition, we argue that it is in this notion of absolute present that the views of Schrödinger, Dōgen and Nishida meet.

Readers are advised that an up-to-date discussion of the author's fundamental thesis (’The Idea’), on the origin, operation, and destiny of the World, is now found at the top of the main page under the rubric, Thematic Evolution and Prospect of 'The Idea.'

A substantial part of our work attempts to construct an adequate Theory of the Face. See 'The Soul of Life' (below) and other studies on the page, some of which remain in draft and others merely projected. (Five papers on this difficult subject are planned.)

Progressive and substantial concretion of the thesis has been recently demonstrated through focused studies (2018-2020), whose URLs are conveniently grouped below:

'The Spirit of War'
https://www.academia.edu/36536128/The_Spirit_of_War

'Carlyle and the Idea'
(https://www.academia.edu/37362600/Carlyle_and_the_Idea)

'The Last Day (Illustrated Essay)'
(https://www.academia.edu/41144933/The_Last_Day_Illustrated_Essay_)

'How the German Spirit Died (A History)'
(https://www.academia.edu/41745763/How_the_German_Spirit_Died_A_History_)

'How the Human Spirit Died (Meta-Analysis)'
(https://www.academia.edu/41985864/How_the_Human_Spirit_Died_Meta-Analysis_)

'Three Malefactors of the Communist Idea (Meta-Analytical Note)'
(https://www.academia.edu/42052811/Three_Malefactors_of_the_Communist_Idea_Meta-Analytical_Note_)

Our gradual (and still incomplete) conceptualization of absolute cosmogony, cosmology, and eschatology in its modern (often microphysical) aspects, which has arisen quite organically over several years of detailed study, may be briefly encapsulated and characterized (A-T) for the reader as follows:

A. The Idea is the fundamental reality of the World, whose existence was clearly intuited (as “hypodoche”) by Plato, operationally defined by Boehme (first as “das Rad Gottes” and subsequently as “Eternal Nature”), organically articulated by Hegel (as “the Idea”), and finally discovered to be the locus of proto-being and foundation of living motion by means of 20th century microphysics (and accurately named by it “the color vacuum”). The electron is its projection into the finite. Field theory is its "physical" basis.

B. This definition of “substance” as a completely immaterial and literally infinite, self-related, hebdomadic-triadic system of actuality within the Idea at the fundament or basis of reality constitutes the greatest discovery of the human mind which, before the end of the 21st century, upon full comprehension, will completely revolutionize religion and therefore geopolitics, as well as pedagogy, paleontology, and biophysics.  The seat of the animating principle in organisms can now be described and explained.

C. Briefly, the research for this book involves the cosmology, cosmogony, and eschatology (destiny) of the world as the finite projection of the Eternal Idea. The Idea itself was created by the Triune Absolute Spirit as a finite-infinite field to manifest, reward, and punish moral, aesthetic, and intellectual performances in a Living Matrix.

D. Through the vast and distributed powers of its microphysical basis, the Idea as the created conduit of Absolute Power has autonomously generated a pseudo-history in geology and astronomy. The powers of Light and Darkness guided by Eternal Life deep within the fundament sustain the finite living motion of which we are aware through biology and empower conscious awareness in animals. Biopsychological functioning and all positive intellectual achievement in Mankind have their roots in the Idea.

E. Moreover, though unseen, the silent workings of a vast cosmological Absolute Hebdomad (deduced through study of the Idea in the 17th century) mercifully overarch and limit the Inchoate Life of the Sinister Itself--a Cosmic Disruptor also previously unsuspected that is responsible for the nocturnal Dream Life of animals. Is this a conceptual solution to the mysterious phenomena of telepathy and clairvoyance?

F. Biological and psychic life thus have always been suspended between two great cosmological powers representing a generalized War Between Infinite and Finite Life that began with King Lucifer, and which in its present form continually tests, through Contention, War, and Worldly Contrariety, the whole of Living Being as it follows a tortured and fateful course between Life and Death according to the much-lamented plan chosen by the Mind ("Gemüt") of Adam.

G. Finally, the hidden existence of the Idea necessarily implies a universal negative unity as the ideal origin of all gravitational and inertial phenomena, offering to science a solution at last to storied and continuing, completely beguiling conundrums (e.g., "Dark Matter" and "Dark Energy") involving the ultimate structure of the cosmos.

H. By tracing the Idea's manifold determinations of physical, biological, and psychic being, then, the present study seeks to explicate the final, and heretofore unsuspected, links in the fabled Great Chain of Being for the edification of Mankind. Inherently opposing it, pathetically and even insanely, is guileless materialism.

I. The war of materialism against idealism eventually culminated in the death of the German Spirit (1918). The main intellectual cause of German spiritual morbidity, however, is traceable to events within the Reformation (1517-1546). This did not prevent a period of optimism within Prussian education and science (1800-1840).

J. The theft of Silesia (1946) was an intentionally demoralizing spiritual crime against Germany with major consequences for the spiritual life of the world. The German Spirit's whole turbulent career constituted a vacillation on renunciation of self-will, and this latter always was the essential content of the Absolute Mind in Germany.

K. Germany's fatal spiritual debility can be considered to be a world "contagion" that spread centrifugally from the center of Europe to the whole Human Race which, therefore, is itself now in the throes of an analogous spiritual death, self-contemplation, and deliverance from the finite. The Zero-Hour is imminent.

L. Each of the Six Days (in Moses) is now fundamentally understood to mean a thousand-year period. Thus, Creation has all along been continuous and--after 6,000 years--will soon be completed (the argument proposes a means to confirm or deny the asserted beginning of 3,970 B.C.). Thus, the Day of Rest (for the Community of Heaven) will soon arrive for the self-elect of Mankind.

M. This tortured path was, of course, divinely foreseen but nevertheless represents an accommodative posture which was not at first understood. The Creator's response achieves a wise and just outcome despite the wreck and pain arising from myopic creatural assertion and pathetic gratification, as recounted in the mosaic story of old.

N. In fact, Talmudic commentators reached this conclusion in the 2nd or 3rd century A.D.--amending (in 'Sanhedrin 97a') the original mosaic interpretation of once-and-for-all Creation in favor of Continuous Creation with a clear Limit or End, specified as 6,000 years (each "day of creation," as mentioned above, being 1,000 years).

O. Thus, Moses (properly cogitated) was right but his dicta were for a long period taken wrongly--perforce leading the Christians astray through an accident of church history that remains a stumbling block up to the present day. See the author's 'The Last Day (Illustrated Essay).'

P. We know from modern physics that the "physical" world at the fundament is sustained by completely immaterial field relations that never cease, or else creation-in-process would not maintain itself. The creative motion is mathematically and physically infinite but disguises its own infinity--the chief insight, credited to Dirac, supporting Absolute Physics.

Q. Hence, it is now clear that the Creation--continuous since the beginning--is approaching its End and Goal. The Last Day is thus imminent and will arrive within the present decade, according to the wisest Christian view, this actually having been announced four centuries ago in German idealism.

R. The Eternal Word's role has always been to Shine Divinely (inwardly) in the gloom and darkness of the outward finite (the "Field of the Reprehensible") for salvation's sake (see 'Carlyle and the Idea'). It is this that Jesus of Nazareth spoke of, and it is this his followers embody, when they speak of the "true bread from heaven," etc..

S. This is why Christians can claim that the finalized ("Third") Temple of God is already in existence and is composed of living stones (minus the winnowed Condemned and Damned) whose essence will endure forever in God.

T. Our thesis is only now emerging in its final form. This is because the horizon of knowledge keeps receding as the true depth is revealed--the world is a set of nested dolls and the innermost doll is God, who is unknowably deep (but friendly, since we are Him in disguise when we abandon our finite wills).

We address four physics opportunities. First, suggest new elementary particles and forces. Second, explain phenomena such as dark matter. Third, augment and unite physics theories and models. Fourth, point to opportunities for further research.
We use models based on solutions to equations featuring isotropic pairs of isotropic quantum harmonic oscillators.
First, we show solutions that match the known elementary particles. We propose that other solutions correlate with elementary particles that people have yet to detect and with dark energy forces leading to three known eras - early acceleration, subsequent deceleration, and current acceleration - pertaining to the rate of expansion of the universe.
Second, we extend solutions to encompass known conservation-law symmetries. Extended solutions correlate with known kinematics. We suggest that extended solutions describe dark matter, explain ratios of density of dark matter to density of ordinary matter, correlate with dark energy density, and explain other phenomena.
Third, we propose that our work unites, suggests details regarding, extends, suggests complements to, and suggests limits regarding aspects of traditional physics theory. Those aspects include classical physics, special relativity, general relativity, quantum mechanics, the elementary particle Standard Model, the cosmology timeline, and galaxy evolution scenarios. The work provides possible insight regarding foundation of physics topics.
Fourth, we suggest opportunities for people. We suggest opportunities for observational, experimental, and theoretical physics research. We suggest quantum field theory that features few interaction vertices, sums of few terms as alternatives to conditionally convergent sums of infinite numbers of terms, and no needs to deal with some infinities. We point to possible opportunities to further develop and apply modeling and math we use.

In this paper, we use a large-scale dynamical systems perspective to provide a system-theoretic foundation for thermodynamics. Specifically, using a state space formulation, we develop a nonlinear compartmental dynamical system model characterized by energy conservation laws that is consistent with basic thermodynamic principles. In addition, we establish the existence of a unique, continuously differentiable global entropy function for our large-scale dynamical system, and using Lyapunov stability theory we show that the proposed thermodynamic model has convergent trajectories to Lyapunov stable equilibria determined by the system initial energies. Finally, using the system entropy, we establish the absence of Poincaré recurrence for our thermodynamic model and develop a clear connection between irreversibility, the second law of thermodynamics, and the entropic arrow of time.

En este trabajo trataremos el problema de la asimetría temporal o flecha del tiempo. Para esto, analizaremos parte del trabajo de Huw Price respecto al origen de la asimetría temporal en la física y expondremos como a partir de este se desprende un fuerte componente antrópico. Tomando en consideración esto, mostraremos cómo el trabajo de George Lakoff y Mark Johnson en el área de la cognición corporeizada logra capturar algunos puntos relevantes de la construcción del concepto de tiempo mencionados por Price. Finalmente, esto permitirá argumentar que no parece lícito atribuirle asimetría al tiempo en el microuniverso, ya que esta es una característica que le atribuimos al tiempo a partir de nuestra experiencia en el mundo y no tenemos acceso directo a los eventos del mundo microfísico.

Abstract
In this paper we discuss the problem of time asymmetry or the arrow of time. For this, we analyze some part of the work of Huw Price about the origin of time asymmetry in physics and expose how this shows a strong anthropic component. Considering this, we show how the work of George Lakoff and Mark Johnson in the area of embodied cognition captures some highlights of the construction of the concept of time mentioned by Price. Finally, this will allow us to argue against the atribution of time asymmetry in the micro-universe, because this is a feature that we attribute to the time based on our experience in the world and we have no direct access to the microphysical world events.

If our universe underwent inflation, its entropy during the inflationary phase was substantially lower than it is today. Because a low-entropy state is less likely to be chosen randomly than a high-entropy one, inflation is unlikely to arise through randomlychosen initial conditions. To resolve this puzzle, we examine the notion of a natural state for the universe, and argue that it is a nearly-empty spacetime. If empty space has a small vacuum energy, however, inflation can begin spontaneously in this background. This scenario explains why a universe like ours is likely to have begun via a period of inflation, and also provides an origin for the cosmological arrow of time.

We suggest that spontaneous eternal inflation can provide a natural explanation for the thermodynamic arrow of time, and discuss the underlying assumptions and consequences of this view. In the absence of inflation, we argue that systems coupled to gravity usually evolve asymptotically to the vacuum, which is the only natural state in a thermodynamic sense. In the presence of a small positive vacuum energy and an appropriate inflaton field, the de Sitter vacuum is unstable to the spontaneous onset of inflation at a higher energy scale. Starting from de Sitter, inflation can increase the total entropy of the universe without bound, creating universes similar to ours in the process. An important consequence of this picture is that inflation occurs asymptotically both forwards and backwards in time, implying a universe that is (statistically) time-symmetric on ultra-large scales.

There is a widespread view in the artificial life community that life is not so much about materiality but about organization. However, one of the favourite candidate theories that explain what this organization should be like has an ambivalent position with respect to materiality. This is the theory or autopoiesis (Maturana and Varela, 1980, Autopoiesis and cognition, D. Reidel). Accordingly, autopoiesis is the self-production of a unity in the domain of processes of material construction, transformation and destruction. The identity of the living system, in this view, is sustained in its form in spite (or rather because) of its material flux.

The elementary physics battle-tested principles of Lorentz invariance, Einstein equivalence principle and the boson commutation and fermion anti-commutation rules of quantum field theory explain gravitationally repulsive dark energy as virtual bosons and gravitationally attractive dark ...

We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and theoretical reasons, and a probabilistic description involving the observers is required. The criterion of maximum von Neumann entropy is then used for making reasonable inferences. It means that no spurious information is introduced besides the known data. Its outcomes can be given a direct justification based on the principle of indifference of Laplace. We introduce the concept of relevant entropy associated with some set of relevant variables; it characterizes the information that is missing at the microscopic level when only these variables are known. For equilibrium problems, the relevant variables are the conserved ones, and the Second Law is recovered as a second step of the inference process. For non-equilibrium problems, the increase of the relevant entropy expresses an irretrievable loss of information from the relevant variables towards the irrelevant ones. Two examples illustrate the flexibility of the choice of relevant variables and the multiplicity of the associated entropies: the thermodynamic entropy (satisfying the Clausius-Duhem inequality) and the Boltzmann entropy (satisfying the H-theorem). The identification of entropy with missing information is also supported by the paradox of Maxwell's demon. Spin-echo experiments show that irreversibility itself is not an absolute concept: use of hidden information may overcome the arrow of time.

The first and main claim of this paper is that physics cannot provide, empirical evidence for the objectivity (mind-independence) of absolute becoming, for the simple reason that it must presuppose it, at least to the extent that a classical (i.e., non-quantum) spacetime theory presupposes a priori an ontology of events. However, the fact that a theory of absolute becoming must be situated in the abstract realm of metaphysics does not make becoming completely irrelevant for physics, since my second claim will consist in showing that relational becoming, once appropriately defined and understood, properly belongs to the tangled set of issues usually referred to with the label "the arrow of time".

In previous work, we showed that the answer to the question posed in the title cannot be found within an equilibrium setting. The inclusion of {\em dynamical} backreaction effects from massive long wavelength modes on the initial DeSitter patches results in gravitational instabilities that cleanse the phase space of inflationary initial conditions of all regions except those allowing high energy inflation. This interplay between the matter and gravitational degrees of freedom explains why ergodicity is broken and why the Universe starts in an out-of equlibrium state with low entropy. Here we argue that this reduction of the phase space of inflationary initial conditions implies that an inflationary universe is incompatible with holography inspired proposals such as causal patch physics and D (N)-bounds. We also discuss why chaotic or eternal inflation may not resolve the puzzle of the initial conditions and of the arrow of time.

Globalization is the most general feature of the historical period education will experience in this century. There has been a marked acceleration in political and intellectual consideration of the inextricable set of social, technological, economic and cultural phenomena that define it. It has been abruptly submitted to analysis, at the same time as Internet has in just a few years

Application of New Cybernetics in Physics describes the application of new cybernetics to physical problems and the resolution of basic physical paradoxes by considering external observer influence. This aids the reader in solving problems that were solved incorrectly or have not been solved. Three groups of problems of the new cybernetics are considered in the book: ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- (a) Systems that can be calculated based on known physics of subsystems. This includes the external observer influence calculated from basic physical laws (ideal dynamics) and dynamics of a physical system influenced even by low noise. ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- (b) Emergent systems. This includes external noise from the observer by using the black box model (complex dynamics), external noise from the observer by using the observer’s intuition (unpredictable dynamics), defining boundaries of application of scientific methods for system behavior prediction, and the role of the observer’s intuition for unpredictable systems. ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- (c) Methods for solution of basic physical paradoxes by using methods of the new cybernetics: the entropy increase paradox, Schrödinger’s cat paradox (wave package reduction in quantum mechanics), the black holes information paradox, and the time wormholes grandfather paradox. All of the above paradoxes have the same resolution based on the principles of new cybernetics. Indeed, even a small interaction of an observer with an observed system results in their time arrows’ alignment (synchronization) and results in the paradox resolution and appearance of the universal time arrow. ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- • Provides solutions to the basic physical paradoxes and demonstrates their practical actuality for modern physics ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- • Describes a wide class of molecular physics and kinetic problems to present semi-analytical and semi-qualitative calculations of solvation, flame propagation, and high-molecular formation ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- • Demonstrates the effectiveness in application to complex molecular systems and other many-component objects ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- • Includes numerous illustrations to support the text

Application of New Cybernetics in Physics. Available from:

All laws of physics are time-invariant. Quantum mechanical experiments show time reversibility in micro-scale conditions. Everyday experience demonstrates that time flows only from past to future and never back. This conundrum of physics has not been solved until now. The article discloses an explanation of nature of time based on the statement that time itself does not exist. Time is one characteristic of movement as such.

In this paper we address the problem of the arrow of time from a cosmological point of view, rejecting the traditional entropic approach that defines the future direction of time as the direction of the entropy increase: from our perspective, the arrow of time has a global origin and it is an intrinsic, geometrical feature of space-time. Time orientability and existence of a cosmic time are necessary conditions for defining an arrow of time, which is manifested globally as the time-asymmetry of the universe as a whole, and locally as a time-asymmetric energy flux. We also consider arrows of time of different origins (quantum, electromagnetic, thermodynamic, etc.) showing that they can be non-conventionally defined only if the geometrical arrow is previously defined.

In the first part of this four-part paper, the framework of a unified deterministic theory of fields and particles is presented. The model is based on a single set of field equations, Einstein's vacuum equations for a higher-dimensional metric space. The extra space is not compactified, for example by assuming a spherical topology with very high extra-space curvature, the metric being represented as a perturbation superimposed on a flat-space background metric. It is proposed that the equations contain nonlinear soliton-type solutions, termed metrons, which are strongly localized in physical space, while carrying far fields which are independent of or periodic with respect to extra space and time. The solutions are generated through the mutual interaction between an inhomogeneous mean field (e.g. a gravitational or electromagnetic field), which acts as a wave guide, and a wave field, which is periodic in extra (harmonic) space and is trapped in the wave guide. The modetrapping mechanism is demonstrated for a simplified Lagrangian which reproduces the basic nonlinear properties of the gravitational Lagrangian while suppressing its tensor complexities. The more difficult task of computing metron solutions for the higher-dimensional gravitational system is not attempted in this paper.

Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions initially, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the arrow of time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the baker's map.

We suggest that spontaneous eternal inflation can provide a natural explanation for the thermodynamic arrow of time, and discuss the underlying assumptions and consequences of this view. In the absence of inflation, we argue that systems coupled to gravity usually evolve asymptotically to the vacuum, which is the only natural state in a thermodynamic sense. In the presence of a small positive vacuum energy and an appropriate inflaton field, the de Sitter vacuum is unstable to the spontaneous onset of inflation at a higher energy scale. Starting from de Sitter, inflation can increase the total entropy of the universe without bound, creating universes similar to ours in the process. An important consequence of this picture is that inflation occurs asymptotically both forwards and backwards in time, implying a universe that is (statistically) time-symmetric on ultra-large scales.

Thermodynamics is the paradigm example in physics of a time-asymmetric theory, but the origin of the asymmetry lies deeper than the second law. A primordial arrow can be defined by the way of the equilibration principle (“minus first law”). By appealing to this arrow, the nature of the well-known ambiguity in Caratheodory’s 1909 version of the second law becomes clear. Following Caratheodory’s seminal work, formulations of thermodynamics have gained ground that highlight the role of the binary relation of adiabatic accessibility between equilibrium states, the most prominent recent example being the important 1999 axiomatization due to Lieb and Yngvason. This formulation can be shown to contain an ambiguity strictly analogous to that in Caratheodory’s treatment.

Multiverse scenarios in cosmology assume that other universes exist "beyond" our own universe. They are an exciting challenge both for empirical and theoretical research as well as for philosophy of science. They could be necessary to understand why the big bang occurred, why (some of) the laws of nature and the values of certain physical constants are the way they are, and why there is an arrow of time. This essay clarifies competing notions of "universe" and "multiverse"; it proposes a classification of different multiverse types according to various aspects how the universes are or are not separated from each other; it reviews the main reasons for assuming the existence of other universes: empirical evidence, theoretical explanation, and philosophical arguments; and, finally, it argues that some attempts to criticize multiverse scenarios as "unscientific", insisting on a narrow understanding of falsification, is neither appropriate nor convincing from a philosophy of science point of view.

We review the possibility that metallicity could provide a diagnostic for the age of a galaxy, hence that the most metal-poor star forming galaxies in the local universe may be genuinely young. Indeed, observational evidence for "downsizing" shows the average age of the stars in a galaxy to decrease with decreasing mass and metallicity. However, we conclude both from observational and theoretical viewpoints that metallicity is not an arrow of time.

This is an introductory set of lecture notes on quantum cosmology, given in 1995 to an audience with interests ranging from astronomy to particle physics. Topics covered: 1. Introduction: 1.1 Quantum cosmology and quantum gravity; 1.2 A brief history of quantum cosmology. 2. Hamiltonian formulation of general relativity: 2.1 The 3+1 decomposition; 2.2 The action. 3. Quantisation: 3.1 Superspace; 3.2 Canonical quantisation; 3.3 Path integral quantisation; 3.4 Minisuperspace; 3.5 The WKB approximation; 3.6 Probability measures; 3.7 Minisuperspace for the Friedmann universe with massive scalar field. 4. Boundary Conditions: 4.1 The no-boundary proposal; 4.2 The tunneling proposal. 5. The predictions of quantum cosmology: 5.1 The period of inflation; 5.2 The origin of density perturbations; 5.3 The arrow of time.

In several previous papers we have argued for a global and non-entropic approach to the problem of the arrow of time, according to which the "arrow" is only a metaphorical way of expressing the geometrical time-asymmetry of the universe. We have also shown that, under definite conditions, this global time-asymmetry can be transferred to local contexts as an energy flow that points to the same temporal direction all over the spacetime. The aim of this paper is to complete the global and non-entropic program by showing that our approach is able to account for irreversible local phenomena, which have been traditionally considered as the physical origin of the arrow of time. *

One of the most intriguing discoveries during the last decade of developmental neurobiology is the fact that both in the developing and adult nervous system neural stem cells often turn out to have a glial identity: Radial glia generates neurons in the developing telencephalon of fish, birds and mammals and astro/radial glial stem cells in specialized neurogenic zones give rise

Quantum mechanics in the Rigged Hilbert Space formulation describes quasistationary phenomena mathematically rigorously in terms of Gamow vectors. We show that these vectors exhibit microphysical irreversibility, related to an intrinsic quantum mechanical arrow of time, which states that preparation of a state has to precede the registration of an observable in this state. Moreover, the Rigged Hilbert Space formalism allows

The interface between classical physics and quantum physics is explained from the point of view of quantum information theory (Feynman Processes). The interpretation depends on a hefty sacrifice: the classical determinism or the arrow of time. The wave-particle duality steams from the qubit model, as the root of creation and annihilation of possibilities. A few key experiments are briefly reviewed from the above perspective: quantum erasure, delayed-choice and wave-particle correlation. The CPT-Theorem is interpreted in the framework of categories with duality and a timeless interpretation of the Feynman Processes is proposed. A connection between the fine-structure constant and algebraic number theory is suggested.

The purpose of this article is to provide an alternative, strictly geometric, interpretation for the observed phenomenon of time. This Geometric Model of Time (GMT) is consistent with both Theories of Relativity but goes beyond cur- rent explanations for the nature of and the apparent one-directness of time - the so-called Arrow of Time. Key elements of the model are: 1. Our physical space (not space-time) is a 4-dimensional phenomenon. The notion of a dimension of time that is distinct from space is not necessary for a complete description of our universe. All dimensions are identical and symmetrical. No one dimension can be singled out to be universally or uniquely labeled as "time" or be otherwise unique. 2. All physical objects in our universe are endowed with an axiomatic vectorial property we call velocity. The scalar value of this property (speed) is invariable and identical for all objects and is labeled as c (speed of light). 3. The experience of time as we know i...