NATO ADVANCED RESEARCH WORKSHOP

The Nature of Time:

Geometry, Physics and Perception

Book of Abstracts

of the talks to be presented at the workshop

Rosolino Buccheri and Metod Saniga

Co-Directors of the ARW

May 21–24, 2002 / Tatranská Lomnica / Slovak Republic

March 21, 2002

Session 1 – Perception of Time

May 21, 2002 – Tuesday morning. Chairman: Stuart Hameroff

Anna **EISLER (**Key Speaker)

Department of Psychology, Stockholm University, 106 91 Stockholm, Sweden

**Time perception: Biological, psychological and cultural considerations. **Psychological (subjective) time is the feeling of how time is now passing, how much time seems to have gone by. Our inner clocks, most often circadian, are postulated as basic to our sense of internal time. Light seems to be the most prominent zeitgeber, or time giver of biological rhythms. Most blind people respond to the same circadian rhythm as sighted people, presumably because social cues convey sufficient time-of-day information. The relation between psychological (subjective, perceived) time and the universal objective (physical, clock) time depends not only on the biological time sense, but also on learning, cognitive ability, experience, physical and social environment, personality, culture, age, and so on. Disruption of psychological time is a central feature of many kinds of psychopathology, for instance in certain individuals with organic brain lesions, in schizophrenics, depressive patients, etc. From this point of view disruption of psychological time, or of the time sense, influences behavior and leads to impairing of the sense of identity, thereby giving rise to the feeling of depersonalization. Some results from my empirical research are presented in terms of biological, psychological, neuropsychological, developmental, and cultural factors.

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Harald** ATMANSPACHER**

Institut fuer Grenzgebiete der Psychologie und Psychohygiene e.V., Dept. of Theory and Data Analysis,

Wilhelmstr. 3a, D-79098 Freiburg, Germany

**Parametrization and sequentialization of events in perception. **The perception of temporally distant events has been studied for a long time. A surprising feature in some of these studies is the existence of a window of temporal distances in which individual events can be distinguished but their sequence cannot be assigned properly. The extension of this elementary “now” for temporal perception is of the order of some ten milliseconds. Another feature for which a lot of evidence has been collected is the chaotic nature of particular brain processes in many contexts. Chaotic systems have positive dynamical entropy, implying both limited predictability and a specific type of temporal non locality for such systems. It will be explored whether these characteristics can be used to conceptualize the cognitive capacities, to distinguish and sequentialize events in time.

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Simon **GRONDIN**

Laval University, Ecole de Psychologie, Quebec, Que., G1K 7P4, Canada

**Using Weber's law for studying psychological time***. Psychophysics*, a discipline of psychology, aims to describe the relationship between physical quantities and the perception of these quantities. One of the classical laws of psychophysics, called "Weber's law", states that the minimum difference (difference threshold: D
f
) necessary for discriminating between two stimuli increases as a function of the magnitude (f
) of these stimuli. This law can be used for studying psychological time. Several types of violations of Weber’s law occur when the stimulus under investigation is time. These violations question the assumption that there is a single timekeeping mechanism, or a so-called *internal clock*. For a single duration range, f
, a wide variety of discrimination performances (D
f
estimates) can be observed. One of the critical factors that causes this variety is the structure of the intervals to be discriminated, i.e., whether they are filled or empty, or marked by auditory, visual, tactile, or bimodal stimuli. A *Generalized form of Weber’s law* provides a reasonable explanation for the diversity of discrimination performances. However, there is another form of violation of Weber’s law that is more difficult to account for. For intervals in the vicinity of 1.2 s, the Weber fraction (D
f
/f
) becomes larger as physical time gets longer. This observation applies in various discrimination conditions, as well as to the production of a series of intervals. In the latter case, it is the coefficient of variation (equivalent to the Weber fraction) that increases with the length of the intervals to be produced. These disruptions of the Weber function might be compensated by using another timing strategy, i.e., by segmenting the intervals to be timed with, for instance, explicit counting of numbers. The point where there is a disruption in the Weber function, or where explicit counting becomes a useful strategy, is argued to have critical meaning with regard to the limitations of the information processing system used by humans.

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John Joseph **SANFEY**

39 London Rd., Shardlow, Derby, DE72 2GR, UK

**Time, life and the perception of process**.** **Einstein regarded the subjective 'now' as completely beyond scientific enquiry. Subjectivity in general is seen by most scientists as unnecessary for a complete description of the universe. Here I show by a simple logical argument that these views are mistaken: that every description of objective reality must contain a hidden framework that reflects the function of human perception, a framework defined as that which in principle is unobservable because of the 'subjective now' paradox. The argument is this: The 'subjective now' paradox arises because change is both constant and causally determined; everything is process. 'Now' should not exist since no duration is brief enough to exclude change and the beginning of a duration is gone by its end. But 'now' certainly does exist, in consciousness if not in physics. Next: the perception of any change must assume some unobservable framework that remains constant in relation to that change: unobservable in principle, because change is continuous. During conscious perception, the framework is the working mind of the observer witnessing throughout the change. In empirically valid scientific theories, the same framework must also exist otherwise that theory would not describe something empirically real, i.e. observable. In other words, the structure of descriptions of objective reality must reflect and describe the process of empirical observation i.e. must describe human perception. This really should not surprise us. After all, the whole of objective science is simply that inter-subjective agreement on invariance we all experience. The exact form of the hidden perceptual framework in physical theory is somewhat arbitrary. For instance, the choice of using fields rather than alternative strategies allowing backward causation is not empirically based, but arbitrary. The 'hypothesis of duality' proposing that loop quantum gravity and string theories are two ways of describing the same thing exemplifies this. Every description of 'objective reality' must use some arbitrary framework that overcomes the paradox of three incompatible principles: the constancy of process, the principle of causality, and the empirical certainty of being. The framework allows knowledge of the past to have causal influence in the present. The way this knowledge operates illustrates the function of consciousness and the framework itself provides a useful, axiomatic basis for defining life and consciousness. Life exists whenever knowledge of the past influences the behaviour of a causally defined physical event. Consciousness exists whenever such knowledge is globally available across a whole system. The experience of being conscious is the experience of being an unconscious yet highly active field of knowledge in which the world lights up. Every physical concept is entangled with consciousness via the 'perceptual framework' consisting of that which is unobservable in principle because of the 'observation of process' or 'subjectve now' paradox. Our understanding of time and space is confounded by the organisational strategies demanded by the framework. If these principles hold true, then time in particular has an intimate relationship to conscious perception. Whenever knowledge of the non-immediate influences physical behaviour, consciousness or its equivalent framework in physical theory, is operating.

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Rumiana **NIKOLAEVA**

Bulgarian Academy of Science, Institute for Nuclear Research and Nuclear Energy,

Theoretical Nuclear Physics Group, 72 Tzaregradsko Shousse Blvd, 1784, Sofia, Bulgaria

, ,

**Time in the cognitive process of humans. **In this paper an attempt is made to model the process of information and the organization of the brain function based on Discrete-time dynamics' principles and principles, underpinning the running of the Universe, as they are unfold in G. Jaroszkiewicz's works (1, 2). The brain is considered as an observer of the Universe, which himself is a part of this Universe. What is the role of time in the perceiving process, in the process of consciousness and in the logistics of information is deiscussed. The organization of the process of cognition in time of normal people is compared with the organization of the same of handicapped children. References: 1) Jaroszkiewizc G and Norton K, Principles of discrete time mechanics: I-Particle systems, J.Phys.A: Math.Gen., 9(7): 3115, May 1997; 2) Jaroszkiewicz G, The running of the Universe and the quantum structure of time, quant-ph/0105013, May 2001.

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May 21, 2002 – Tuesday afternoon. Chairman: Anna Eisler

Giovanni B. **VICARIO** (Key Speaker)

Pedagogical Faculty, University of Udine, via Antonini 8, I-33100 Udine, Italy

**Temporal displacement. **Given a sequence of very brief heterogeneous stimuli, say a-b-c, often occurs that the succession of percepts is different, say A-C-B. The phenomenon, observed by astronomers since the early 19^{th} century, was named by Wundt (1893) Zeitverschiebung (temporal displacement). At first such mislocalizations were charged to the “different velocity” of sensations, because visual latency is 10 times higher than auditory one, but Wundt demonstrated that the “attention” directed to whatever item of the sequence makes it to be perceived in advance. Benussi (1913) opposed the attentional hypothesis of Wundt: such brief sequences are perceived as temporal Gestalten, and displacements are due to the Auffälligkeit (salience) of some item in respect of the others. The problem was taken over again by Rubin (1949), who offered evidence that displacements occur even in the same sensory modality (audition, making use of three noises, two identical and one different), and explained the phenomenon by facilitation and inhibition processes in neural paths. In psycholinguistic domain, Ladefoged and Broadbent (1960) reported that a very brief noise, inserted in a spoken sentence, is heard here and there, for the most in the agogical pauses. Vicario (1963) connected Benussi’s ideas with Rubin’s methodology: using triplets of tones, demonstrated (a) that displacements occur when the whole sequence is shorter than 1 sec, and (b) that its probability grows with the tonal distance between the central item and the lateral ones. Fraisse (1967), the famous psychologist of time, pointed out that is difficult to compare sequences of stimuli with succession of percepts, because in the sequences we have aut simultaneity aut sequence, where in perception we have also impression of non-simultaneity (without true succession) and of non-succession (without true simultaneity). In fact, the displaced elements seem to float in a temporal elsewhere, or on a parallel line of events. In the effort to nail down the percepts to the chronometry of stimuli, Vicario (1999) devised an experiment where the temporal position of the displaced element was estimated after a perceptual task, or calculated by means of a simple motor reaction task. Results showed that the reaction task locates stimuli almost exactly, where huge displacements are found in estimations based on the perceptual task. The consequent hypothesis is that the rules of physical time of neural processes (that govern reaction task) are not extendable to phenomenal time (where other rules are at work). The conclusion fits the scheme of Fraser (1987) of the growing number of the properties of time as grows the complexity of phenomena at issue. About to which time we have to assign the character of reality – the physical or the phenomenal one – there are some comments on a letter of Newton (1670) and on a passage of Russell (1948).

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Hannes **EISLER**

Department of Psychology, Stockholm University, S-106 91 Stockholm, Sweden

**The parallel-clock model: A tool for quantification of experienced duration. **Subjective, psychological, experienced time (duration) practically never agrees with clock time. Psychophysics, instead of regarding this as error, constructs subjective scales and relates these to the physical scales. For almost all modalities the psychophysical function proved to be a power function, in its simplest form Y
= KF
b
, where Y
denotes subjective, F
physical magnitude, and the exponent b
is characteristic for the pertinent modality. The exponent is, e.g., about .6 for loudness (vs. sound pressure), 1.5 for heaviness, and .9 for time (durations in the second range). One common psychophysical method is to ask an observer to halve or double a sensation. From the empirically found linearity between set ratios and standards the power function can be derived mathematically. However, psychophysical scaling experiments are based on observers' conception of numbers, like 1/2 or 2, the epistemological status of which is not quite clear. The parallel-clock model provides an elegant solution of this problem. It builds on __duration reproduction__, that is, a standard of a certain duration is indicated by, e.g., noise, and after a short pause (a silent interval) the noise resumes and is terminated by the observer when s/he experiences that the noise after the pause has lasted as long as the standard duration. The reproduced duration is a linear function of the standard duration, entailing a power function for subjective time, too. According to the parallel-clock model the total subjective duration Y
t (standard + reproduction, that is, the duration from the onset of the standard to the offset of the reproduction) is accumulated in one sensory register ("internal clock"), and the subjective counterpart of the reproduction Y
r in another. The observer experiences the two durations to be of the same length when the difference between the total subjective duration Y
t and the subjective duration of the reproduction Y
r equals the subjective duration of the reproduction (Y
t - Y
r = Y
r). Accordingly, the subjective reproduced duration is half of the subjective total duration. In this way the for scaling necessary number (here 1/2) is introduced by__ means of the model__ rather than by the observer. The parallel-clock model, which thus makes quantification of subjective duration possible, was tested empirically both in humans and rats. After a detailed mathematical description certain applications of the model on experimental data will be mentioned.

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Georg **FRANCK**

Vienna University of Technology, Dept. of Computer Aided Planning and Architecture

Treitelstrasse 3/272, A-1040 Vienna, Austria

**Presence and time**. Until today, no conclusive description of the now and the passage of time is available. The paper conjectures that this is due to not clearly distinguishing between real change and temporal change. Real change is what kinetics and dynamics are about. Temporal change is the process by which one time slice of space-time after another is raised to presence. To be present means to exist in the now. In the context of space-time, the now is ignored, change thus reduced to real change. In order to describe temporal change, a conceptual framework is needed that accounts both for the dimension of distance in time and for the degree of freedom that the existence of the now makes use of. In a two-dimensional framework, the persistence and progression of the now, the speed at which time passes, and the change that the regions of past and future are subject to can be described by means of geometry.

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Dimiter G. **CHAKALOV**

IT consultant, Postal address: Box 13, Dragalevtsy, BG-1415 Sofia, Bulgaria

**Two modes of time: Biocausality. **What could be the most economical solution to the mind-brain problem, which will not contradict any fact from brain science, psychology, and physics? As far as physics is concerned, the task boils down to the nature of time. Hence two ideas are proposed: (i) a new kind of physical reality, resembling Platonic ideas, presented with two modes of time, and (ii) a new kind of retarded causality, called biocausality, in a putative universal time arrow being the physical basis of the psychological time arrow. Possible implications for solving the problem of Lorentz invariant nonlocality are outlined, with links to author's web site "Physics of Human Intention".

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Institute of Psychology, Jagiellonian University, Poland

**Time and the problem of consciousness**. The main topic of my presentation is a proposal of how to include a temporal perspective into the domain of consciousness studies, and to view consciousness not as a representation of some external events in the brain, but rather an outcome of an interaction between the brain and its environment. In the first part I propose a description of the phenomenal experiences – i.e. qualia - in the physical terms. It is based on two assumptions. The first is that there is an objective arrow of time. It means that every physical event in the universe, apart of its physical properties, has also the property of uniqueness, that is, it happens only once. According to the second assumption, for every phenomenal experience we can point at a neural event with which it is accompanied. Such a physical event - correlated with phenomenal experience - I call a C-event. Thus, the proposal of the description of qualia in physical terms is therefore as follows: the phenomenal aspect of a conscious experience is the property of uniqueness of its C-event. In the second part – relying on a definition of consciousness as a ‘subjective present’ – I try to point in the human brain at the neural processes which can be candidates for the C- events. The focus will be on the neural processes underlying putative phenomena associated with the ‘subjective now’, such as simultaneity, the origin of the qualitative differences in sensory modalities and temporal perception.

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Stuart **HAMEROFF**

Departments of Anesthesiology and Psychology, Center for Consciousness Studies

The University of Arizona, Tucson, Arizona, USA

**Consciousness, time and events in quantum spacetime. **Two peculiar features of time perception are 1) the subjective feeling of the "forward flow" of time, and 2) experimental evidence (e.g. Libet, Bierman/Radin, Damasio) for apparent "backwards time" referral of conscious information in the brain. The nature of consciousness is unknown, however to accommodate its enigmatic features mechanisms involving quantum state reductions have been proposed. In particular the Penrose-Hameroff model of "Orchestrated objective reduction (Orch OR)" suggests that consciousness depends on quantum computations in microtubule protein polymers within the brain's neurons. In the Orch OR model, microtubule quantum computations reach threshold for "self-collapse" due to Penrose objective reduction (OR) which derives from instability in quantum superposition/spacetime separations at the Planck scale (quantum spacetime). "Orchestrated" by

biological feedback from neuronal membranes/synapses, each Orch OR event selects (noncomputably, according to Penrose) a particular Planck scale configuration which gives rise to a particular conscious experience. Sequences of Orch OR events (equivalent philosophically to Whitehead's

"occasions of experience") give rise to our familiar stream of consciousness, and the subjective feeling of forward flow of time. As the intervals between quantum state reductions are time indeterminate (or,

alternatively each reduction results in "Aharonov "dual vector" time arrows) apparent backwards time referral in consciousness is also accommodated. Recent findings support microtubule quantum coherent superposition at brain temperature.

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Session 2 – Mathematical Approaches to the Concept of Time

May 22, 2002 – Wednesday morning. Chairman: Jonathan D.H. Smith

Metod **SANIGA **(Key Speaker)

International Solvay Institutes for Physics and Chemistry, Université Libre de Bruxelles, Campus Plaine,

CP – 231, Boulevard du Triomphe, 1050 Brussels, Belgium

&

Astronomical Institute, Slovak Academy of Sciences, SK-05960 Tatranská Lomnica,

Slovak Republic

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**Geometry of time and dimensionality of space**. One of the most distinguished features of our algebraic geometrical, pencil concept of space-time is the fact that spatial dimensions and time stand, as far as their intrinsic structure is concerned, on completely different footings: the former being represented by pencils of *lines*, the latter by a pencil of *conics*. As a consequence, we argue that even at the classical (macroscopic) level there exists a much more intricate and profound coupling between space and time than that dictated by (general) relativity theory. It is surmised that this coupling can be furnished by so-called Cremona (or birational) transformations between two projective spaces of three dimensions, being fully embodied in the structure of configurations of their *fundamental* elements. We review properties of some of the simplest Cremona transformations and show that the corresponding “fundamental” space-times exhibit an intimate connection between the extrinsic geometry of time dimension and the dimensionality of space. Moreover, these Cremonian space-times seem to provide us with a promising conceptual basis for the possible reconciliation between two extreme concepts of (space-)time, viz. physical and psychological. Some speculative remarks in this respect are made.

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Mohammed S. **El NASCHIE (**Key Speaker)** **

Cobham, Surrey, KT11 2FQ, U.K.

**On the Cantorian space-time and the exact mass spectrum of the Standard model. **It is argued that the observed (macroscopic) dimensionality of space-time (4) results on statistical averaging of an originally infinite dimensional, transfinite fractal set called the Cantorian space, and its signature (3+1) reflects the fact that, under a special assumption, the effective topological dimension of this space amounts to 3 (spatial degrees of freedom), while its averaged Hausdorff dimension is 4.236067971 (including thus also the time dimension). It is further demonstrated that if this concept is combined with four dimensional fusion algebra, noncommutative geometry and capped group topology, one is able to determine the entire mass spectrum of the standard model, including quarks: all the so obtained results are found to be in an astonishing agreement with the current experimental data found in the literature.

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Sergey **MAYBUROV**

P.N.Lebedev Inst. of Physics, Russian Academy of Sciences, Leninsky Prospect 53

Moscow 117924, Russia

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**Fuzzy space-time geometry and approaches to quantization. **Fuzzy ordered sets (Fosets) studied as possible basic structure of quantum space-time and phase space (PS) [1]. It differs from Classical space-time manifold structure which is ordered set of points X, so for any points pair a,b strong order relation R: a<b (or b<a ) holds corresponding to verity values V=0 or 1. Foset M permit generalized or fuzzy order relations R between its elements - fuzzy points a,b, so that R set mapped to real V=w(a,b); 0<w<1; for example V about .5 means a,b are approximately equal. Thus relative to ordered coordinates axe X fuzzy point b characterized by positive function w(x) which describe b principal position uncertainty dx [1]. We suppose that {x,p} phase space has fuzzy geometry and particle m is fuzzy point which state |m} described by positive distributions w(x),w'(p),..., w"(q) for arbitrary observable Q. They aren't independent, but obey to constraints of the kind C(w,w')=0 induced by fuzzy structures fundamental smearing (SFS) [1]. It results in uncertainty relations dxdp>k where k is free parameter. Due to SFS state |m} evolution effectively reduced to linear equation for complex function f(x,t) generating all w"(q) - analog of quantum wave function. Fuzzy mechanics reproduces the main quantum effects starting from Fuzzy Geometry axioms and is shown to have common basis with Aharonov's Quantum Reference Frames Theory [2]. Relativistic fuzzy space-time stidied and its relation to Noncommutative Geometry regarded. Possible applications to gravity quantization discussed [3]. References: (1) H.Bandmeyer, S.Gottwald 'Einfuerung in Fuzzy-Methoden' (Academie Verlag,Berlin,1993), (2) Y.Aharonov, T.Kaufherr Phys.Rev. D30, 368 (1984), (3) S.Mayburov Proc. VII Marcell Grossman conference (Jerusalem,1997) (World Scientific, Singapore,1998).

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Eugene **TOKAREV**

B. E. Ukrecolan, Kharkiv National University, 33-81 Iskrinskaya str., 61005, Kharkiv-5, Ukraine

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**An algebraic point of view on the Time**. For studying the **Time** as an algebraic structure (=as a model for the set of axioms that are fulfilled for the Time in the manner of we it understand) the first step is to chose elements of the set which will be considered as a mathematical (or, rather, logical or set theoretical) support of the Time. If for elements of this set will be chosen “moments of time” this may leads to a lot of difficulties (apparently described in other communications). Let us choose as primary elements (i.e. as those elements, which need no definitions) ** events. **On the set of all events may be defined a partial order “<” if we assume that, for a pair of events -

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Matej **PAVSIC**

Jozef Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia

**Clifford algebra, geometry and physics**. The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much reacher than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists not only of points, but also of 1-loops, 2-loops, etc.. They are associated with multivectors which are the wedge product of the basis vectors, the generators of Clifford algebra. Within C-space we can perform the so called polydimensional rotations which reshuffle the multivectors, e.g., a bivector into a vector, etc.. A consequence of such a polydimensional rotation is that the signature can change: it is relative to a chosen set of basis vectors. Another important consequence is that the well known unconstrained Stueckelberg theory is embedded within the constrained theory based on C-space. The essence of the Stueckelberg theory is the existence of an evolution parameter which is invariant under the Lorentz transformations. The latter parameter is interpreted as being the true time - associated with our perception of the passage of time.

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May 22, 2002 – Wednesday afternoon. Chairman: Mohammed S. El Naschie

Jonathan D. H. **SMITH** (Key Speaker)

Department of Mathematics, Iowa State University, Ames, IA 50011, U.S.A.

**Time in biology and physics**. It has long been recognised that an important aspect of the evolution of biological systems is their ability to create their own internal environments. Various recent studies are indicating the extent to which the emergence of internal time parameters, more or less independent of universal time, is an essential corollary of this development. In answer to Schrödinger's question "What is life?" one may then identify biological systems as systems complex enough to encompass parts functioning according to their own independent space and time parameters. By contrast, purely physical systems are those systems that are fully coupled to universal time. Studied from this new perspective, the nature of physics changes. Rather than assuming the existence of a given underlying spacetime subject to universal laws, one has to explain the observed linking of the space and time parameters of the components of a physical system. The classic example of the coupling of time parameters in the components of a complex system, due to Wiener, is the exact synchronisation of the turbines generating electricity in a power grid. The establishment of the common time takes place through electron exchange. In analogous fashion, the specification of the spacetime in mechanics is achieved through graviton exchange, thus accounting for the coincidence of gravitational and inertial mass.

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Vito **Di Gesu’ (**Key Speaker)** **

Department of Mathematics, University of Palermo, Italy

**Q-computing: A way to break complexity**. This presentation will introduce the issues of quantum computing (q-computing) [1] in both the computational complexity of NP-hard problems [2] and their experimental setting. At this end, a review of the existing q-computer design will be given. The notion of interval function will be also introduced to discuss an extension of the concept of cellular q-computation [3]. A generalization of a space-time graphical representation of causality will be given. The new computational paradigm is represented by a Discrete Space Time Graphs (DSTG) [4] and it is a starting point for the discussion of reversibility and causality in both quantum and parallel computing. Several concrete examples of computation are given in the framework of the generalized space-time graphs. A new concept of interval function will introduce that has a strong relation with discrete space-time graphical representations of causal processes in dynamics. Potential applications to conventional distributed and parallel computing systems will be investigated. The interval function formalism can be further developed to represent quantum computing and non conventional models of computation. Quantum algorithms represented by DSTG are more expressive, easily readable, and contain timing information crucial to synchronize parallel processes. Recent technological development will allow the realization of nanoscale quantum computation [5]. For example, quantum cellular automata will become more important for the simulation of physical systems such as quantum lattice gases [6]. The hope is that interval functions and DSTG will provide an useful computational paradigm for discussing and designing new devices based on quantum computation. References: [1] R.P. Feyman, “Feyman Lectures on Computation”, ABP, Perseus book, 1996. [2] P.W. Shor, “Algorithms for Quantum Computation: Discrete Logarithm and Factoring”, in Proceedings of the 35th Annual Symposium on the Foundation of Computer Science}, S.Goldwasser ed., IEEE, Los Alamos, CA, 1994, SIAM J. Comp., Vol.26, 1997.

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Carlos **CASTRO**

Center for Theoretical Studies of Physical Systems, Clark Atlanta University, Atlanta, Georgia 30314, USA

The programs of the Extended relativity theory in C-spaces.

An outline of the Extended Relativity Theory is presented. Such theory is an extension of Einstein's Special-General Relativity and Nottale's Scale Relativity theories where all dimensions ( all p-branes ) and spacetime signatures are on equal footing. It is based on two fundamental observer-independent invariants , the speed of light and the minimum Planck scale. We will derive, among other things, the string and p-brane generalized Heisenberg uncertainty relations ; the logarithmic corrections to the black hole area-entropy relation and show how higher-derivative gravity with torsion and the kappa-deformed Poincare theories of gravity can be obtained explicitly from this Extended Relativity theory formulated in C-spaces ( Clifford Manifolds ). We conclude with a discussion on why quantum spacetime is infinite-dimensional ( at the Planck scale ) and why four is the average dimension of our world.

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Vladimir **ARISTOV**

Computing Center of the Russian Academy of Sciences, 119991, Vavilova str. 40, Moscow, Russia,

**Development of the relative statistical space-time concept. **According to the relative (relational) principle to construct the model of physical space implies constructing the model of an instrument for fundamental measurements, namely, a clock. In the model [1,2] the main equation is postulated. In this equation an increment of time is expressed through a sum of increments of coordinates of all particles of the system under consideration. This statistical relationship reflects important properties of motion realized in a clock (its uniform, uninterrupted and one-directed character). The standard relativistic equation of motion are derived from the main equation. Time and space are in fact connected immediately in the postulated equation, but it is emphasized that the unit of time is measured in terms of the unit of space, of course, with the appropriate factor equal to the speed of light appearing in the main equation. In the present paper we discuss how to develop this relative statistical approach in some ways. Geometry of time is complicated: the moment of time is now characterized not only by a point in the time axis but by the point in 3-N dimensional configuration space (N is number of particles of the system). And not only metric properties of time ("the time as a process") can be considered but "the time as a state". The irreversibility of time itself can be defined now, because the recurrence of the moment of time is treated as the recurrence of the point in the configuration space to the same position (the probability of this event is very small if N is large). The introduction of entropy is discussed. The generalization is also related to obtaining the quantum effects in the model. For this purpose a model of the physical space is constructed, i.e. the relative discrete statistical model of rods (the idea of this method is described in the preprint [3]). A rod is considered as a part of uniform matter constituted by particles (atoms). The measurement of length is determined by the operation of bringing the object under measurement against the particles on the straight line of a rod. The problem of definition of a straight line in a discrete media is resolved by a definition of geometry on graphs, where the straight line between two points (vertices of a graph) is defined as a line of a minimum length. The length of a line is measured by the number of particles of this line (one can express this value by the mass with the appropriate factor, which is a combination of the fundamental constants). There is the minimal length equal to a mass of an atom. The straight line may not be unique. The non-Eucledian geometry is studied (formalism analogous to the Hilbert axiomatic is used). The transition to the Eucledian geometry is performed when the length of a straight line tends to infinity, in so doing calculation of all possible straight lines with the appropriate statistics causes the unique straight line. (It is of interest that this mathematical apparatus is formally similar to the apparatus of fractal geometry of quantum paths, see, e.g., a review [4]). For small distances a non-unique straight line implies that the trajectory of a free particle is also non-unique, therefore one can treat it as indeterminism of the quantum theory. Taking into account the main equation for time one conclude that there is minimum time interval (the ratio of the minimum length to the light speed). Thus the limitations for measurements of position and momentum yield Heisenberg's uncertainty relation.

References: (1) V.V.Aristov. Statistical model of clocks in a physical theory. Physics-Doclady (Doclady of Russian Acad.Sci.), 1994, Vol.39, No.1, pp.45-59, (2) Aristov V.V. Relative statistical model of clocks and physical properties of time. in: On the way to understanding the time phenomenon: the constructions of time in nature science. World Scientific, Singapore, 1995, p.26-45, (3) V.V.Aristov. Statistical mechanics and a model of description of space-time. Communications in applied mathematics. Computing Center of the Russian Academy of Sciences, Moscow, 1999, 22p. (4) Kroger H. Fractal geometry in quantum mechanics, field theory and spin systems. Physics Reports, 2000, V.323, p.81-181.

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Michel **PLANAT**

Laboratoire de Physique et Métrologie des Oscillateurs 32 Avenue de l'Observatoire,

25044 Besançon Cedex, France

**Time measurements, 1/f noise of the oscillators and algebraic numbers**. Any measurement of the time period of an oscillator versus a reference one thanks to a non linear detector shows generic arithmetical features [1-4]: * the beat period measurement behaves as a diophantine approximator for the ratio n of periods of input oscillators [1], * there is an attempt of the oscillators to phase-lock: this creates amplitude and frequency fluctuations of the beat signal with a 1/f power spectrum [4]. These time measurements have been interpreted in the frame of algebraic number theory: the candidate instantaneous coupling coefficient is an arithmetical function a(n;pi,qi) at time n and resolution i of the harmonic n"pi/qi. Its prototype connects to prime number theory [4]: in such a case a(n) is the generalized von Mangoldt function, the average coupling coefficient between times from n=1 to t is about 1/f(qi) (with f(qi) the Euler function), and the error term e(t) shows a 1/f power spectrum. At the fundamental 1/1 the fluctuation e(t) is related to the non trivial zeros of Riemann zeta function z(s)=å1/ns which are located on the critical line s=1/2; at the harmonic pi/qi it is related to the non trivial zeros of Dirichlet function L(s,k)= åk(n)/ ns, with the character k(n mod qi). In such a frame the 1/f noise thus relates to Riemann hypothesis. Time measurements of electronic devices also show a generic 1/f noise. The arithmetical dynamics can be applied to a perfect gas of fermions of mass m in a box of size L. Replacing time t by the number p of energy quanta dE=h2/8mL2, the degeneracy of energy levels (and the density of states) is essentially the class number h(-p) in the field QÖ-p; it is the source of the 1/f power spectrum [5].

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Luciano **BOI**

École des Hautes Études en Sciences Sociales, Centre de Mathématiques, 54, Boulevard Raspail,

F-75006 Paris, France

**A sketch of a multidimensional geometrical representation of time and time perception.** The aim of this talk is to sketch the essential features of a geometric model suited to represent the multidimensional and polycyclical nature of psychological and maybe physical time upon which rest partly our perception of the world. We borrow the fundamental ideas of this model from the mathematical theory of superstrings and from the theory of Calabi-Yau spaces. The central idea is that the space-time structure of the Universe may have both extended dimensions and curled-up dimensions. This is an astounding suggestion made in 1919 by the polish mathematician Theodor Kaluza, and refined some years later by Oskar Klein. This means that our spatial universe has dimensions that are large, extended, and easily visible, namely the three spatial dimensions of common experience, but that may also have additional spatial dimensions that are tightly curled up into a very tiny space. For instance, circular loops may exist at every point in the familiar extended dimensions. It is worthy of note that the circular dimension is not merely a circular bump within the familiar extended dimensions; rather, the circular dimension is a *new* dimension, one that exists at every point in the familiar extended dimensions; it is a new and independent direction in which some being, if it were small enough, could move. In the 1979s, it has been showed that one may generalise the Kaluza-Klein theory to higher-dimensional theories with numerous curled-up spatial directions. These extra dimensions are curled up into the surface of a sphere. Of course, beyond proposing a different number of extra dimensions, one can also imagine other shapes for the extra dimensions, for instance, the shape of a torus. And also more complicated possibilities can be imagined in which there are three, four, five, essentially any number of extra spatial dimensions, curled up into a wide spectrum of exotic shapes. In fact, the extra dimensions or the curled-up dimensions, which seems very profoundly to influence basic physical properties of the universe, look like a class of six-dimensional geometrical shapes known as *Calabi-Yau spaces*. Roughly, we have to imagine replacing each of the spheres–which represented two curled-up dimensions–with Calabi-Yau space. That is, at every point in the three familiar extended dimensions, string theory claims that there are six hitherto unexpected dimensions, tightly curled up into one of these rather complicated-looking shapes. These dimensions are an integral and ubiquitous part of the space’s structure; they exist everywhere. For instance, if you sweep your hand in a large arc, you are moving not only through the three extended dimensions, but also through these curled-up dimensions. Of course, because the curled-up dimensions are very small, as you move your hand you circumnavigate them an enormous number of times, repeatedly returning to your starting point. Now, given the requirement of numerous extra dimensions, is it possible that some are additional *time* dimensions, as opposed to additional space dimensions? We all have an understanding of what it means for the universe to have multiple space dimensions, since we live in a word in which we constantly deal with a plurality–three. But what would it mean to have multiple times? Would one align with time as we presently experience it psychologically while the other would somehow be “different?” It gets even hard to accept when you think about a curled-up time dimension. Nevertheless, we may think of time not solely as a dimension we can traverse in only one direction with absolute inevitability, never being able to return to an instant after it has passed. At any rate, it might be that curled-up time dimensions have vastly different properties from the familiar, vast time dimension that we imagine reaching back to the creation of the universe and forward to the present moment. But, in contrast to extra spatial dimensions, new and previously unknown time dimensions would clearly require an even more profound change of our intuition. It seems to us that the intriguing possibility of new time dimensions could well play a role in future developments of our conceptions of physical reality and of living beings. Starting from these mathematical objects, the talk will be aimed to sketch a geometrical model notably of psychological time which cannot be conceived like a linear and one-dimensional concept any more, but rather as a multidimensional and polycyclical one.

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Session 3 – Physicist’s View of Time

May 23, 2002 – Thursday morning. Chairman: George Jaroszkiewicz

Mark **STUCKEY** (Key Speaker)

Department of Physics, Elizabethtown College, Elizabethtown, PA 17022, USA

**Time via pre-geometric foundations of quantum mechanics. **A notion of time is presented that is intimated by a discrete, 'bottom up', graphical approach to pregeometry. This formalism produces a graph per a metric induced over a uniform space. The uniform space is generated by a low-order, discrete topological group. Extrapolation to large-order sets may be accomplished by fractal embedding.

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Sisir **ROY **(Key Speaker)

Physics and Applied mathematics Unit, Indian Statistical Institute, Calcutta, India

**Planck scale physics, pregeometry and the notion of time. **There exists a certain suspicion among the scientific community that the nature may be discrete or rather behaves discretely on the Planck scale. But it is far from being evident what this vague metaphor actually means or how it should be implemented into a concrete and systematic inquiry concerning physics and mathematics in the Planck regime. There are basically two overall attitudes towards this kind of discreteness at Planck regime. In one approach one starts from continuum concepts and then try to detect or create modes of discrete behaviour on very fine scales. for example string theory or loop quantum gravity or more recent version Spin Network are the promising candidates. This is called top down approach. In the second approach one can think the physical space-time as emergent phenomena starting from a kind of pregeometry of a web of overlapping fuzzy lumps which interact with each other. The individual lumps are understood as certain closely entangles subgraphs(cliques) in a dynamically evolving network which, in a certain approximation can be visualised as time dependent random graphs. The general goal of this approach is to find a better adapted geometric environment for the description of microphysics. This approach is known as Bottom up approach. In this lecture we will elaborate this second approach. In this framework the concept of time might be said to emerge (called order parameter manifold) on large scale dynamics. Here the word “emergence” is used in the non-temporal, philosophical sense of, roughly, reduction. The standard ideas of time and more generally spacetime, might be not fundamental to reality but instead “emergent” as an approximately valid concept on sufficiently large scales.

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Robert **KIEHN**

Physics Department, University of Houston, Houston, Texas, USA

Current Address: 69 Chemin Saint Donat, 84380 Mazan, France

**A topological perspective of the arrow of time and thermodynamic irreversibility.** Exterior differential forms, unlike tensor fields, are well behaved with respect to C1 differentiable, but not invertable, maps, such as those used to describe projections. Relative to these non-homeomorphic maps that induce topological change, a logical arrow of time is generated, for the functional coefficients of the exterior differential forms may be retrodicted from data on the final state, but not predicted from data on the initial state. It follows that Cartan's methods of exterior differential forms can be used to study continuous topological evolution, and thermodynamic irreversibility. The methods are applied to those physical systems that can be described by a 1-form of Action, A, and to processes that admit description in terms of a vector field, V. Cartan's evolutionary formula uses the Lie derivative with respect to the vector field, V, acting on the 1-form of Action, A, to create an evolutionary 1-form Q. These dynamical equations of topological evolution formally establish the long sought for connection between mechanics and the first law of thermodynamics. They can be used to demonstrate that thermodynamic irreversibility is an artifact of Pfaff topological dimension of at least 4.* *

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Avshalom C. **ELITZUR**

Unit of Interdisciplinary Studies Bar-Ilan University, 52900 Ramat-Gan, Israel

**Quantum-mechanical and thermodynamic clues in search of a deeper concept of time. **The concept of time has undergone a major revolution in special and general relativity, but at the same time it became alienated from our ordinary experience. We experience events differently in time and in space. In space, we can observe sequences of events in whatever order, e.g., from left to right or *vice versa*, whereas in time we experience them only from past to future. In space, we can remain at the same place, whereas in time we seem to “move” from one moment to the next. Relativity, however, has undermined this account of time. In the Einstein-Minkowski spacetime, all events – past, present and future – have the same degree of existence, time’s passage being a mere illusion. In this lecture I bring evidence from two different realms of physics that indicate that the present account of time in physics is insufficient. From the viewpoint of quantum mechanics, we have shown (Elitzur, Dolev & Zeilinger, 2001) that the famous EPR experiment can be turned upside down in time. That is, two particles can manifest non-local influence not only if they share a common origin in the past but also if they are about to interact in the *future*. In another thought-experiment (Dolev & Elitzur, 2001), we have shown that a wave function that interacts with a row of atoms sometimes seems to interact only with the middle atom, while leaving the others unaffected. These and other results indicate that, at least at the quantum level, time remains very poorly understood. Another work of ours (Elitzur & Dolev, 1999) proves that, if a single genuinely random event occurs in a closed system, then, *regardless of that system’s initial conditions*, an arrow of time is bound to emerge in it, and this arrow accords with that of the rest of the universe, from which the closed system is supposed to be shielded. Hence, if Hawking’s information-erasure hypothesis is correct, time’s arrow is intrinsic, much in accord with Prigogine’s unorthodox claim. Based on these surprising results, I propose a tentative model of time that tries to integrate the insights of relativity on the one hand, and everyday conscious experience on the other hand, into a more comprehensive scheme.

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Paola Anne **ZIZZI**

Department of Astronomy, Padua University, Vicolo dell' Osservatorio, 2, 35122, Padova, Italy

**Events in quantum spacetime**. The very concept of event should be revised in the context of quantum spacetime. In fact, the concept of event as a point in a four-dimensional smooth manifold is lost once spacetime is assumed to be discrete, and quantized in Planck units. If the minimum length is assumed to be the Planck length, and the minimum time interval is assumed to be the Planck time, it follows that an event in quantum spacetime is an extended object. This extended object is in fact a virtual Planckian black hole, for which the time-energy uncertainty relation is saturated. Moreover, the virtual black hole, is a carrier of virtual information, (which can be transformed into real information once the quantum fluctuations of the metric are taken into account). This is due to the fact that the horizon area of the Planckian black hole encodes one bit of information, because of the holographic principle. In summary, an event in quantum spacetime, is an extended object, endowed with energy and information.

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Tomas **KOPF**

Mathematical Institute of the Silesian University at Opava ,Bezrucovo nam. 13, 74601 Opava,

Czech Republic

**Spacetime: A classical concept in a quantum world. **The physics underlying our world appears to be of quantum nature. Thus, an explanation is needed for the approximate appearance of the classical spacetime we observe. The talk will focus on what can be said on this problem on the basis of quantum field theory on curved spacetime, i.e., without the knowledge of a fundamental theory of quantum gravity but within reach of experimentally verified facts.

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Ivan I. **SHEVCHENKO**

Pulkovo Observatory, Russian Academy of Sciences, Pulkovskoje ave. 65-1, St.Petersburg 196140, Russia

,

**Conformal time in cosmology**. Conformal time (called also arc time) is an objective measure of the age of the Universe. Among the closed Friedmann models with the cosmological constant, the asymptotic model of the first kind (the A1 model) is the only one in which the Universe has infinite conformal lifetime. Therefore this model provides unique conditions for information networking on the global distance scale, and is most preferable from the viewpoint of a variant of the strong anthropic principle [1]. The A1 model has analogs among cosmological models with a scalar field, in the sense that they imply infinite conformal lifetime of the Universe. Scenarios of dynamical evolution in such models are considered and discussed. Models are selected which are consistent with the currently observed values of the normalized density parameters. Reference [1] Shevchenko, I.I. On verification of the asymptotic model of the first kind. Astrophys. Space Sci 202 (1993) 45-56.

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May 23, 2002 – Thursday afternoon. Chairman: Mark Stuckey

Ilya **PRIGOGINE** (Key Speaker)

International Solvay Institutes for Physics and Chemistry, Université Libre de Bruxelles, Campus Plaine,

CP – 231, Boulevard du Triomphe, 1050 Brussels, Belgium

**Quantum mechanics for dissipative systems. **(Abstract not yet available)

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Giuseppe **VITIELLO**

Dipartimento di Fisica "E.R.Caianiello", INFM and INFN Salerno, Universita' di Salerno

84100 Salerno, Italy

**The arrow of time in quantum theories**. In principle there is no room for dissipative systems in Quantum Mechanics since the formalism of Quantum Mechanics is based on conserving probabilities. The description of time-irreversible evolution (the arrow of time) is therefore ruled out by definition in Quantum Mechanics. In Quantum Field Theory it is, however, possible to describe time-irreversible evolution by resorting to the existence of infinitely many unitarily inequivalent representations of the canonical commutation relations (ccr). In this paper we review such a result by discussing the canonical quantization of the damped harmonic oscillator (dho), a prototype of dissipative systems. We show that the set of states of the system splits into unitarily inequivalent representations of the ccr. The irreversibility of time evolution is expressed as tunnelling among the unitarily inequivalent representations. Canonical quantization is shown to lead to time dependent SU(1,1) coherent states. We derive the exact action for the dho in the path integral formalism of the quantum Brownian motion developed by Schwinger and by Feynman and Vernon. The doubling of the phase-space degrees of freedom for dissipative systems is related to quantum noise effects. Finally, we shortly comment on the role of dissipation in the quantum model of the brain and on the occurrence that the cosmological arrow of time, the thermodynamical one and the biological one point into the same direction.

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Serguei M. **KOROTAEV**

Geoelectromagnetic Research Institute, Russian Academy of Sciences. GEMRI, PO Box 30,

Troitsk, Moscow Region 142190, Russia

**Experimental verification of transaction of the dissipative processes through the active properties of time.** The concept of the active properties of time, originated from the acceptance of its fundamental asymmetry, was suggested by N.A. Kozyrev. According to this concept , developed in Kozyrev's causal mechanics, time has, except the passive property of duration, some active ones (course, density), which involve interaction or more exactly, transaction of any dissipative processes. In spite of extensive series of the experiments performed by N.A. Kozyrev, causal mechanics met a contradictory reaction because of weak formalization of the theory and doubt about the rigor of the experiments. Recently the basic statements of causal mechanics have been strictly formulated. A formal definition of causality was suggested, which allowed on the other hand, strictly to formulate Kozyrev's axioms and on the other hand, to develop the method of causal analysis. The last one has found utility in various experimental applications. The association of causal mechanics with quantum nonlocality in the strong macroscopic limit and action-at-a-distance electrodynamics has been revealed. Equation of macroscopic nonlocality expresses transaction through active properties of time. It predicts existence of correlations of any dissipative processes with symmetrical retardation and advancement. At such approach asymmetry of time is expressed as asymmetry of efficiency of the retarded and advanced Wheeler-Feynman fields absorption. Due to less efficiency of advanced field absorption by an intermediate screening medium, the level advanced correlation must be higher than retarded one. Lastly advanced correlations can be observed only for the noncontrolled source processes. For verification of the described hypothesis the GEMRI setup had been devised. The setup included two types of the detectors of macroscopic nonlocal correlations based on different probe processes. Exhaustive steps have been taken to control all local noise-forming factors and to protect the detectors against them. The long-term experiment on observation of nonlocal correlations caused by some large-scale non-controlled (natural) geophysical and astrophysical has been performed. Namely as the source processes the synoptic, geomagnetic, ionospheric and solar activity were studied. Synchronous measurements by two remote setups (including one more type of the detector, devised by A.N. Morozov, Centre of Applied Physics, Bauman Moscow State Technical University) were invoked in data processing. In addition series of the experiments with well-controlled (artifical) source processes has been fulfilled. Natural time variations in period range 1 minute -1 year recorded by all detectors turned our to be correlated and by nonlocal influence of the external large-scale processes. Nonlocal character of transaction was proved by violation of the macroscopic analogs of Bell-type inequalities. For all kinds of the studied natural source processes advanced reaction of the probe processes was reliably detected. Level of advanced correlations proved to be essentially higher than retarded ones. As a result of interference of the signal and idler apparent instantaneous reaction can be also observed. Among the studied source processes the most strong nonlocal influence on the probe processes was revealed for the solar and synoptic activity. On the other hand, a comparatively low-power process of geomagnetic activity was more convenient for quantitative interpretation. By contrast the experiments with the controlled artifical source processes revealed only retarded reaction of the detector. Thus experiments on macroscopic nonlocality have shown violation of strong causality and persisting of weak causality. However taking into account heuristic character of tested model representation, development of the theory combining the ideas of causal mechanics, quantum nonlocality and action-at-a-distance electrodynamics is burning.

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Vladimir **DZHUNUSHALIEV**

Kyrgyz-Russian Slavic University, Physics Department, Mcr. Asanbai, d.25, kv.24,

Bishkek, 720060, Kyrgyzstan

**Time at the origin of Universe: Fluctuation between two possibilities. **It is supposed that in quantum gravity such non-differentiable quantity as metric signature can fluctuate (see, Ref's [1], [2]). In this case we can consider quantum fluctuations between Euclidean and Lorentzian metrics. It means that the time at the origin of Universe can fluctuate between two possibilities: Euclidean and Lorentzian direction of the time. It leads to the fact that physical laws can fluctuate and as a result we have a quantum birth of the non-singular Universe with frozen extra dimensions and filled with instanton-like field. The probability for such quantum fluctuations is connected with an algorithmical complexity of the Einstein equations.

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Alexander A. **CHERNITSKII**

St.-Petersburg Electrotechnical University, Alexander Friedmann Laboratory for Theoretical Physics

(St. Petersburg) Prof. Popov str. 5, 197376 St. Petersburg, Russia

**Global causality in space-time universe. **Because we believe for an unified mathematical representation of the material space-time universe, we must consider it as a solution for some mathematical model. Must this model be simple or complicated? Is this solution complicated or simple? The materialistic or physical point of view is that we have the very complicated world solution but we aspire to find that simplest and more general mathematical model, the solution of which is the material universe. In this connection we can consider an unified local field model. But on the other hand we have the experimental indication for existence of nonlocal correlations between space separate events (Aspect type experiments for testing of Bell inequality). We show that such nonlocality agree with the local field model for matter, because though the model is local the world solution is nonlocal in character. In this framework the quantum description and the classical one must be the levels for investigation of the world solution. Corresponding arguments is stated in the article by A.A. Chernitskii "Concept of unified local field theory and nonlocality of matter", ** http://arXiv.org/pdf/quant-ph/0102101**.

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Francisco **LOBO**

Departamento de Física da Faculdade de Ciências da Universidade de Lisboa, Campo Grande

Ed. C8, Piso 6, P-1749-016 Lisboa, Portugal

**Time, closed timelike curves and causality**. Time is an essential parameter both in the Special Theory of Relativity as in General Relativity. In Newtonian physics, time flows at a constant rate, the same for all observers. But, it necessarily flows at different rates, for different observers, in Special Relativity, e.g., as in the twin paradox, and in General Relativity, e.g., as in different spacetime points in a gravitational potential. Through the Special Theory of Relativity, time became intimately related with space, giving rise to the notion of spacetime, in which both parameters cannot be considered as separate entities. As time is incorporated into the proper structure of the fabric of spacetime, it is interesting to note that General Relativity is contaminated with non-trivial geometries which generate closed timelike curves. A closed timelike curve allows time travel, in the sense that an observer which travels on a trajectory in spacetime along this curve, returns to an event which coincides with the departure. This fact apparently violates causality, producing time travel paradoxes. The notion of causality is fundamental in the construction of physical theories, therefore time travel and it's associated paradoxes have to be treated with great caution. We shall treat all these questions in detail, in particular the solutions of the Einstein Field Equations that generate closed timelike curves and their associated paradoxes. With this in view, we hope to contribute, through the prism of a relativist, some insight into the nature of Time.

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Be'la **LUKA'CS**

Central Research Institute for Physics, H-1525 Bp.114. Pf. 49, Budapest, Hungary

**Acausal motions in orthodox and higher dimensional general relativity. **Most physicists believe that mainstream physics does not have causality problems. However it is not true. Causality violation is quite frequent in General Relativity, even in its simplest form. Assume that we POSTULATE that motions have to be timelike. This condition automatically guarantees causality in SPECIAL Relativity. However in General Relativity it is not true. The emerging "causality violations" are various, some may be trivial but some others probably inherent in the present theory. The Kerr spacetime has closed timelike orbits. The problem is the unicity theorem for black holes restricting the possible black hole spacetimes just to Kerr. A multiplicity of spacetimes, solutions of the Einstein equations, are acausal too. They are ruled out via the Principle of Cosmic Censorship, or simply by Causality. The problem is that they are Principles which, so far, failed to be possible to be incorporated into the gravitational equations. Therefore they can be used only if we are strongly convinced that "acausality" does not exist. If not, General Relativity offewrs explicite possibilities to elaborate model acausality situations. Higher dimensional spacetimews are commonplace in General Relativity, only some arguments are needed not to see them macroscopically. The simplest argument for n>3 SPACELIKE dimensions is compactification on microscopic scales. An example is 4+1 dimensional Kaluza, which, however, yields Gravity + Electrodynamics only if we permit spacelike motions in 5 dimensions (Gegenberg & Kundstatter, 1985), which, then would open a door for acausality. Alternative possibility is that the fifth dimension, if exists, is not connected with Electromagnetism but something else (e.g. Strangeness) while Electromagnetism cannot be geometrised. However if the extra dimension is timelike (so 3+2 instead of 4+1), the resulting theory is inherently acausal. If experiences/enperiments required, General Relativity might be able to describe such a World.

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May 24, 2002 – Friday morning. Chairman: Giuseppe Vitiello

George **JAROSZKIEWICZ** (Key Speaker)

School of Mathematical Sciences, University of Nottingham, Nottingham, UK

**Analysis of the relationship between real and imaginary time in physics. **An outstanding problem in modern theoretical and mathematical physics concerning the nature of time and its interpretation is the need in various fundamental particle/field theories to go to imaginary time. There are several important contexts in which this situation arises. Historically, one of the earliest and most important was in 1908, when Minkowski suggested that if the time co-ordinate *ct* was replaced by (-1)^{1/2}*w* then the Lorentzian signature metric of special relativity *ds ^{2} = -c^{2}dt^{2} +dx^{2} +dy^{2} +dz^{2}* would take on the Euclidean signature form

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Jonathan **EAKINS**

School of Mathematics, University of Nottingham, University Park, Nottingham, England

**Quantum cellular automata, A 'Stages' view of time, and the EPR paradox**. I shall introduce the concept of a generalised quantum cellular automaton, and show how space and time may arise as emergent concepts. Such a network can be applied to situations occurring in mathematical physics. The example of an EPR type problem will be given, both to elaborate on how these models can be used, and to highlight the inherent conflict between the roles of time in relativity and quantum theory: viz, how the non-local correlations of quantum measurement 'classically' imply a signal propagating faster than the speed of light. Finally, I shall propose a new approach: that is modelling the evolution of a quantum system in terms of stages instead of a linear time. This alternative construction may resolve the apparent conflict, and yet still preserve the results of standard quantum theory over the Bell inequalities. Additionally, this research emphasises important questions concerning not only the types of operator we are allowed to use in quantum mechanics, but also how the appearance of factorisable and entangled states leads, respectively, to semi-classical and quantum systems. To this end, the Universe is envisaged to be a giant quantum machine consisting of systems, sub-systems, sub-sub-systems (etc) of states generating a multitude of possible operators, which in turn generate the next set of possible systems of physical reality.

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Dmitrii B. **KUCHER**

Institute International Solomon University, Lenin Avenue 47, 61103 Kharkov, Ukraine

**Self-organization in discrete systems with Fermi-type memory. **We research a new class of model self-organizing ensembles that simulate the integrity of macroscopic systems using the integrated memory and conditions of the "excluded volume" (so-called Fermi-Memory Systems, FMS). The evolution of such ensemble includes calls to subprograms of choice and algorithmic clinch passing. We show that different types of self-organization correspond to different statistics of events of algorithmic clinch and choice.

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Huba Laszlo **SZÖCS**

Kodolanyi J. University College, Dept. of Mathematics and Statistics, Szabadságharcos str. 59,

H-8000 Székesfehérvár, Hungary

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**On possibility of quantization of space and time**. In my paper I am refferring to idea of Endre Rákosi, one-time Transylvanian physicist, regarding the problem of quantization of space, energy and time. His paper, as well " The unhomogeneous theory of space" was published in 1970 in Annals "Aluta" of Muzeum from Sepsiszentgyörgy-Sfintu Gheorghe with very small spread in the World. Understanding his ideas were revised, completed and interpreted by the Author of present paper.We underline that the problem of quantization of space and special of the time are very-very moderne problems, which appeared in the literature of foundations of physics just in late 10-20 years, as Planck-lenght, Planck-time and so on.In this way our people is ahead of his time. Also the axioms of this theory are the following: 1.The matter is quantized; 2.The space is quantized; 3.Not a space-quanta is empty; 4.The space is not filled continuous by matter; 5.One space-quanta can contain only one matter-quanta and in this case the space-quanta is filled. Definition D1: A matter-quanta is homogeneous if fill only a single space-quanta. In the contrary case it is unhomogeneous. Definition D2: A part of space is homogeneous if its all space-quantas are homogeneous. Definition D3: We consider as smallest unity of time in which the light cover a space quanta. The diameter of one space-quanta being 6.3.10 ^{- 20} cm it results that __the time -quanta T__ is equal to 2.1 10 ^{- 30} s. One elementary physicaly phenomenon it occurs not more than one time-quanta. For the claryfying the essence of time we make a theorethical experience.Also we referr to the Sagnac - experience (rotating disc with mirrors) .One light - signal going from point A of circumference will be back into A after time T = 2 p
R / c , R being the radius of disc and the c the velocity of light.But what will be the result if the disc it rotats with the velocity v (precisely: the linear velocity of circumference) and the signal propagates in sense of sense of rotation of the disc ? We have in this case T ' = 2 p
R / (c-v) .What will be happen if the velocity of disc tends to the velocity of light ? In this case we obtain lim T ' = lim [2 p
R / (c-v)] = ¥
if v ®
c .Also the light-signal will be back in the site of his source after a infinite time because the velocity of referred system is equal to the velocity of reference system. An another interpretation of time can be the following: for all phenomenon which we analyse in function of time it is valuable the relativistic effect.So we can establish the following: I. All moving systems have theirs proper-time T_{ p} referring to the light as a reference frame.II.The difference of velocities of two moving systems can be calculate function of time-difference between the systems and inversely.III.In case if we admit that the systems are moving with the velocity of light the time as referred factor vanish.

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Session 4 – Borderline Research on Time

May 24, 2002 – Friday morning. Chairman: Attila Grandpierre

Rosolino **BUCCHERI** (Key Speaker)

Consiglio Nazionale delle Ricerche

Istituto di Astrofosica Spaziale e Fisica Cosmica, Via Ugo La Malfa 153, Palermo,Italy

**Intelligibility of nature, endo-physical paradigm and the relationship between time of perception and time of physics.** We, the human beings, aim at fully understanding the world where we live and at obtaining the maximum possible control on it. The process of pursuing the intelligibility of the nature occurs in the *subjective time* of all individual elements of the human societies who communicate to each other their single achievements in knowledge, based on their points of view in direct or indirect relation to the rest of the interacting universe. Intercommunication between individuals has the result of mediating among single points of view and tends to construct a “common view”, generally referred as “objective” within human societies. The *physical time* and the *scientific theories* are important examples of these constructed “common views”. During the last centuries this process of intercommunication has been made extremely efficient by Science and by its use of Mathematics as the rigorous, and universally accepted language of description for all observed phenomena. *Subjectivity* and *relativity* remain nevertheless the most relevant characteristics of the process of understanding the nature which occurs in the *subjective time* of each individual but is coded in the *physical time*, a “common view” of the former. Subjective and relational views (such as those aspects intrinsic to Quantum and Relativity theories) may find a more natural place in a Science where theories are built within an endo-physical framework where the “intelligibility of nature” acquires a radically different meaning from that implied by the classical physics with the determinism and the block universe. Not a single unified theory of everything and a laplacian a-temporal possibility to “see” simultaneously past, present and future but a limited set of theories, each valid within certain approximation limits, concurring to an high level of knowledge and control on the nature and leaving consistent room to unpredictability of the future and the individual feeling of the free will. Within the endo-physical paradigm, trying a mathematical description of the subjective time is no more anathema but a way to link it, at least qualitatively, to an “external” *physical time*, representative of an unpredictable change.

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György **DARVAS**

Institute for Research Organisation of the Hungarian Academy of Sciences, Eötvös Loránd University, Department of History and Philosophy of Sciences,International Society for the Interdisciplinary Study of Symmetry (ISIS-Symmetry), P.O. Box 994, Budapest, H-1245 Hungary

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**Potential and actual time concepts. Different approaches to time in philosophy and physics. **The approach of philosophy to time differs from that of physics. If one disregards these differences, will use the same term for differently perceived phenomena and may make false conclusions. In general, physics operates with actual time concepts, while philosophy, generally applies time as a potential form of existence. The two can be brought in accordance, although one should respect the limits, how far can use this or that time concept in the realm of the other discipline. I will investigate the temporal sequence on an example, along the ontological appearance of a phenomenon, namely the sequence of *symmetry breaking* in the evolution of matter. This process starts at the physical appearance of matter and continues in the organic forms of being up to the development of human mind. This special outlook beyond physics throws a new light on the comparison between the particular time concept applied by physics and the general time concept of philosophy applicable to all the three fundamental ontological levels. Fist I will formulate general laws of symmetry breaking. Then I will investigate what role can time play in defining and arranging ontological levels along broken symmetries.

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Franz-Guenter **WINKLER**

Stumpergasse 63/11, A-1060 Vienna, Austria

**Inside versus outside views of space-time. **The most fascinating of the riddles of time is the passage of time. An investigation into the passage of time, however, is not part of natural science. In this contribution, we suggest an approach to the phenomena of time which also tackles the passage of time. The basis for our investigation is a fundamental distinction between two views. In the final analysis, every observation has to be regarded as an inside operation in the sense that both the observer and the thing observed, as well as the act of observation are part of the physical universe. The associated inside view deals with phenomena that are produced by the system containing the observer, the thing observed, and the act of observation. Abstracting from the observer and the act of observation leads to the construction of an outside view. Taking a perfect outside view would mean to observe from a god-like perspective, without physical operation. It can be regarded as the classical ideal of natural science to construct a consistent outside view of the world. However, the physical treatment of time does not provide a satisfying outside view. Even the standard interpretation of relativity theory does not fulfill the criteria of an outside view. It is possible, though, to formulate an appropriate outside view of the space-time continuum that treats the time dimension exactly the same as the spatial dimensions in the framework of a thoroughly Euclidean geometry. The complete integration of space and time, which - from the inside - are so highly distinct dimensions, in one geometry opens room for an alternative account on time as it is perceived by inside observers. In contrast to the dominating scientific world view, we suggest a radical holistic approach which regards the universe as one indivisible space-time object of infinite complexity. What we usually perceive as objects existing by their own right are sub-structures of the whole that show some autonomy, but cannot be fully separated from the whole. The most important tool for the analysis of the space-time whole is a concept of complexity, which is introduced as a combined measure of continuity (non-locality) and discontinuity (locality) along different dimensions and on different levels of abstraction. By its use, a duality between two types of space-time structure can be formulated: Discontinuity in space is correlated with continuity in time, and continuity in space is correlated with discontinuity in time. The best example for the first combination is the causal object, which is local in space and non-local in time. Whenever a system produces collective behavior which is present in all its parts, we talk of non-locality in space. According to the suggested duality, the temporal evolution is discontinuous (e.g. phase transitions) and no longer predictable. For the inside observer, non-locality means the experienced quality of identification. The time dimension, which from the outside view is overwhelmingly continuous, is perceived as so different from space, because it is the dimension along which we are identical with ourselves. This, of course, does not imply that there is no experienced identification in space. There is always a mixture of both aspects of the duality on different levels of description. Our approach to space and time allows to formulate a very general question: What are the possible relations between space-time structures in different (space-time) locations? Beside the two extremes "no relation" and "structural identity" standing behind discontinuity and continuity there are two more relations worth mentioning: Two structures may differ in complexity, which makes a sequence of increasingly complex structures possible, and more complex structures may contain less complex structures. On the basis of the first relation, the asymmetry of time can be understood as increasing complexity along one dimension. The second relation allowing recursive containment of space-time structures can explain the passage of time, as it appears to inside observers, from the a-temporal outside view. In every time location, the inside observer contains a history of recursive containments of "earlier" space-time structures.

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Alexander P. **LEVICH**

Biology Faculty of M.V. Lomonosov Moscow State University, Moscow 119899. Russia

**Paradigms of natural science and substantial temporology**. A number of problems of natural science require temporal comprehension. Among them there are:

- the origin of the "course" of time and the formation mechanism, the creation of changes and the appearance of novelty in the World;

- the contradiction between the Second Law of thermodynamics and the absence of any traces of degradation in the Universe;

- the contradiction between the time reversibility in the equations of physics and the evident irreversibility in the world of real processes;

- the absence of formal methods enabling one to derive rather than guess the basic equations of science;

- scientific forecasting;

- measurement and control of systems' proper time.

We advocate the viewpoint that the temporal comprehension of the problems makes it necessary to abandon the existing scientific paradigm. A brief review of the temporal concepts of the 20th century reveals a changing tendency in the views that dominate in the scientific community. Namely: one can speak of natural references of time, and the time phenomenon is becoming a competent object of natural science rather than philosophy only. The time of natural systems is no longer a primary, undefinable notion, it has a structure and can be an object of theoretical modelling. A further development of such concepts as time, space, matter, motion and interaction in the conceptual basis of natural science apparently lacks certain new essences, and such essences are most likely to appear in the framework of the substantial approach. Standard processes used for measuring the variability of systems, i.e., clocks can be of quite various nature. Different clocks may turn out to lack comparable uniformity, and the descriptions of the laws of nature obtained with their aid may be irreducible to each other. A radical resolution of the problems of the time course and irreversibility seems to require that the existence of isolated systems should be denied, which leads to the concept of an open World, possibly becoming more and more complex. The temporal outlook on the problems of natural science requires that an explicit construction, or model of time should be created. We suggest, as an example of one of the possible constructions, the generating flows hypothesis. The substance of these flows belongs to the depth levels of the structure of matter and maybe cannot be identified by the presently existing experimental technologies. Our Universe is not isolated with respect to the generating flows, and therefore it turns out to be free of the thermal death bugaboo. The generating flows create the World variability. They represent the natural reference of the "course" of time. The formation phenomenon becomes a reformulation of the generating flows hypothesis. Time turns out to be reversible or irreversible to the same extent to which reversible or irreversible are the generating flows. It is suggested to identify matter in the form of fermionic particles with sources and drains of the generating flow substance. The charges and interactions of inanimate and living matter are determined by the flows' dynamical characteristics in their sources and drains. It is convenient to introduce the substitutional clocks in order to measure the variability created by the generating flows. According to such clocks, duration is expressed by the number of element substitutions at different levels of the hierarchic structure of the system. Owing to the substitutional time construction, there emerges a conceptual framework for modelling and discussing such properties of time as its multicomponent nature, system specificity, course non-uniformity, discreteness, non-additivity and the existence of extratemporal events. One also obtains prerequisites for deriving the equations of substitutional motion.

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Boris **DICHEV**

Consultant Petroleum Reservoirs Mathematical Modeling,

Jk Iztok, block 43A, app. 19, 1373 Sofia, Bulgaria

**Theory of time: Probability, origin of matter and nature of time. **The Paper includes a systematic introduction of the notion about the Probability as an independent coordinate and the basic assumptions and boundary of validity of the Theory of Time. The Origin of Mater and Concept of Time are explained as a part of the notion about the 4-Dimensional World as subset of the 5-Dimensional World. The unification theory of T. Kaluza is discussed and it is shown that the Probability could be the missing 5th dimension in his model. The theories and methods developed by I. Prigogine are significantly used. Several Application Areas are analyzed and described using the Method of Theory of Time: a) Gravity and Dark Matter explanation, b) Origin of Hydrocarbons in the source rocks, c) Explanation of the role of the Homeopathic remedies, d) Model of the Human Thinking, e) Model of the Society Behavior. A vision for the future development of the Theory of Time is presented.

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May 24, 2002 – Friday afternoon. Chairman: Rosolino Buccheri

Attila **GRANDPIERRE** (Key Speaker)

Konkoly Observatory of the Hungarian Academy of Sciences,

H1525Budapest, P. O. Box 67, Budapest, Hungary

**The dynamic of time and timelessness: Philosophy, physics and prospects for our life**. Besides the conceptions of endo-physical (internal, mental) and exo-physical (physical) views, I call the attention to the ultimate (exo-cosmic) view. The exo-physical view seems to have a twofold character, as it requires the ignorance of human (and, in general, internal) view, and regards itself as an "outer view". At the same time, it is a naturalistic view bound to the internal (and finite) relations of the "material world as a whole". Apparently, while it expresses an unnatural, non-realisable view, it ignores the connection to the source of genuine activity of the material world. The ultimate (or exo-cosmic) view regards the Universe-as-a-whole from the point of logical comprehension attempting to reach an overall view. The ultimate view is closely related to the three ultimate principles: that of physics, biology and spirit. The Universe defined as an all-inclusive notion is time-inclusive, too. In this view time is an internal part of the Universe, and the Universe-as-a-whole is living behind the temporal (but not atemporal) realms, in timelessness. In this view, space and time may be approached as being partial constituents of the internal, mental life of the Universe. The realm of "material time" (of the 3+1 dimensions) is governed by the laws of physics. Physics is based on the ultimate principle of least action (or Hamilton principle). Based on the results of Saniga (Saniga, 1998, 1999), the here developed ultimate view suggests that the "physics" of these higher dimensions should be biology, and the governing laws of its behavior are related to the ultimate principle of life (Bauer, 1935). Biological laws are related to physical phenomena as governing agents, and the (almost) closed system of physics can be directed mostly from higher dimensions. The intricateness and enormous complexity of biological organisation is possible mostly from a position of transparency available above the material 3+1 dimensions. The timeless character of the ultimate view of the Universe seems to be closely related to the timeless character of mental emotions and thoughts. The existence of cumulative traditions points to the possibility that timeless existents (e.g. thoughts) may develop their own organisational (timelike) dimension. An ultimate cosmology is suggested in which pre-material existents of life initiate the realisation of the material world and evolving toward the realisation of the ultimate principle of spirit. A possibility is found to be realisable in which the eternal Universe "evolves" in the "time of eternity". Some consequences of the ultimate picture will be touched like the meaning and destination of Universe and life. A possibility of a quantitative estimation for the origin of self-consciousness is shown. Ultimate perspectives of mankind with consequences on our personal lives are indicated.

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Zachary **JACOBSON**

Carleton University, Cognitive Science Program, Government of Canada, Canada

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**Time from quantum uncertainty-information vanishes and entropy appears: Further questions and possible empirical tests. **I have suggested previously that time, or least time’s arrow, arises from the repeated collapse of quantum mechanical uncertainties in positions and momenta into specific and precise values of one molecule under impact from another. [That suggestion is] that chaos, information and entropy come together to yield irreversible time. Rather than consider the small, quantum world building up to form the everyday world, [this perspective] examines the everyday world impacting on the quantum realm. Trajectories in the larger world, get smaller and smaller in chaotic mixing--as cigarette smoke disperses into still air. [But trajectories are undefined in the quantum realm; this suggestion holds that] trajectories convert to entropy when they become small relative to the cloud of quantum uncertainty associated with the molecules they impact upon. [Such a] view accounts for time's arrow and the development of entropy… Jacobson, *report from the Palermo meeting, 1999*

This notion raises several avenues for subsequent investigation:

- Can the model make testable predictions? Viz.,

- Friction-free systems would not to exhibit time’s arrow, under this theory.
- Indeed, a “hard” interpretation of the theory would hold that, in testing this, the apparatus not to even

exhibit time as a duration running in either direction.

Can either of these possibilities be tested empirically, in a superconducting circuit or a quantum computer?

- The exact nature of the collapse of the wave equation becomes interesting. Originally, that “collapse of probabilities” was considered ineffable, a sardonic half-guess to keep the rest of the quantum story from seeming even more strange than it already did. But under the above hypothesis it becomes an even-more-interesting area for study and experiment.
- Does the same relation hold for other complementary pairings of measurable quantities under Quantum Mechanics?

- Can this model of time’s arrow deal with some of the other deep problems surrounding the nature of time? Viz., Time seems to go in the same direction for all entities visible to us, at least all complex entities. Time appears to proceed in parallel to all entities visible, at least locally. Only one instant seems to exist [at least for each entity] that is separate from past and future. Is there a spin-off from this relation between the quantum and classical world into the information and economic sciences? Many [not all!] theorists posit that information is identically the negative of entropy. Does this mean that the loss of trajectory predictability at the point of quantum collapse is tantamount to a loss of information from a communications channel [as in classic Information Theory]? This paper will ask which of these avenues are most likely to reward further study.

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Menas **KAFATOS**

Center for Earth Observing & Space Research(CEOSR), School of Computational Sciences (SCS)

George Mason University, fairfax, VA 22030, USA

**Physical processes, consciousness and the nature of time**. The nature of time is intimately related to the issue of consciousness. As such, one may inquire as to their connection through physical theory views of the universe. Two seemingly opposing principles are usually considered by the scientific community to explain life, mind, consciousness and the quantum nature of the universe, which involves evolution in time: Either current structural science is sufficient to explain all nature comprising of life, mind and consciousness; or it is not sufficient and incomplete for such explanation. In the structural belief system itself, since any structural information processing is submitted to the Turing-Church thesis and computation can be realized by structural physical process, then the modelling of the biological cell, mind and consciousness would be expected to be in principle possible on digital computers as biological structures are derived from physical laws. It is, therefore, necessary to consider quantum like processes as associated with the structural information processing among the different cortical areas of the brain. To be successful in this approach, one needs to assign the geometrical properties to the anatomical level of brain so that one can describe such a process. We have shown that it is possible to assign a kind of statistical geometric notion to the cortical areas of the brain and also define the concept of filters similar to filters used in quantum mechanics. This helps us to find an integrating principle operative in different areas as well in different levels of brain activities. However, a set of principles is necessary to describe all levels of brain activities i.e. including consciousness. An integrative approach has been proposed using the language of category theory which includes a generalized concept of time.

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Richard L. **AMOROSO**

Noetic Advanced Studies Institute, 120 Village Square MS 49, Orinda, CA 94563-2502, USA

**The physical cosmology of time: A topological quantum field theory of origins in higher dimensional geometry.** Recently "the nature of time" has begun to generate significant interest among scientists. In this paper a theory is introduced for the origin of time in the geometry of a specific Higher Dimensional Topological Quantum Field Theory (TQFT) that arises from the author's continuing work in developing a model of a continuous state conscious universe (CSCU). Historicaly a debate has continues as to wether space is ultimately 'relational' or 'absolute'; where classically Newton proposed a form of Euclidian absolute space and more recently Einstein has demonstrated that spacetime is relational. According to the CSCU model there is a 'new' kind of 11(12)D higher dimensional absolute space to which conventional 3(4)D Einstein - Minkowski/ Riemann spacetime gives correspondence. That is, a Bohr type complementarity exists between Absolute and Relational space. The spacetime of 'our' higher order phenomenological reality is shown through the vehicle of a TQFT to arise in a continuous manner in the transformation of the topology.

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A. F. **KRACKLAUER**

Bauhau University, Weimar, Germany

**Time contortions in modern physics. **Modern physics, Quantum Mechanics and both Special and General Relativity, seem to have introduced several exotic effects that can be designated as ``time contortions." These include: `Advanced Interaction, the positron as a `back flowing' electron, closed time loops, `twin paradox,' nonlocality and retrocausality.' In my presentation, I will review the theories that support these effects with an eye to identifying exactly what assumptions lead to the conclusion that such effects are to be considered seriously. Following this analysis, I will describe certain small changes in the reasoning behind these theories that permit similarly small changes in these theories such that these effects are banished. It will be shown that these small changes does not conflict with the great quantity of positive understanding that modern physics has otherwise achieved. The level of my presentation is at that of Rindler (SR) and Ballintine (QM).

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Christos C.** EVANGELIOU**

Department of Philosophy, Towson University, Towson, MD 21204, USA

**The Aristotelian relation of time to motion and to soul.** “What is time?” Aristotle raises this ontological question in the *Physiscs *and endeavors to provide an answer that will grasp the elusive entity of *chronos (*time*). *He maintains that what distinguishes the natural beings and sets them apart from the artificial, man-made things, is the fact that they have “within themselves” the capacity to move and to change in various ways, which are determined by the categories of *ousia, *quantity, quality, and place (*topos*). *Chronos* (time), like *topos* (place) and like *kinesis* (motion), with which it is ontologically connected, is considered by Aristotle as a “continuous magnitude,” which is characterized, like the other continua, by divisibility *ad infinitum*. This study will focus on two aspects of Aristotle’s analysis of time: (1) its connection with motion as it is found in his technical definition of time that conceives of it as “the number” (arithmos) and “the measure” (metron) of motion; and (2) its relation to the *psyche *(the soul), which appears to be responsible for “the measuring” and “the counting” of motions and, thus, for the coming into being and the *genesis *of *chronos *at the human level as a psychological phenomenon with ontological pretensions. I will attempt to show that time, because of its necessary connections with natural motions and anthropic psychology, cannot apply or affect in any way the activities of such special *ousiai *(substances) as the “human intellect*” *in its purity as “active *nous,” *and the Divine Intellect (*Nous*) in its a-temporal and eternally *homo-ousian* and unchanging activity: As a *Noesis* of *Noesis*! So, at the end, even on this theme Aristotle remained a student of Plato, who had connected time to the Cosmic Soul and conceived of it as “an image of eternity,” in relation to the Divine *Nous* and the “*Kosmos Noetos*.”

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Closure of the Workshop by George Jaroszkiewicz