1 A Numerical Philosophy of the Universe and the Fundamental Nature of Computer Science Michael Nicolaidis TIMA Laboratory

2 Outline - Motivation - Vision - Emergence of relativistic space-time - Representation of quantum mechanics by stochastic computations

3 Outline

4 Space-Time During millenniums, we considered that the world was made of objects immerged in a space and evolving with the progress of a time  Objects, space and time would be the primary ingredients that engender our world. This representation reflects a perception of the world that we realize through our sensorial and mental structures. In this harmonious perception: - space would be immutable and identical for all observers, only objects evolve with time. - each object occupies a precise position in space at any given time.

5 Metaphysics, Paradoxes, Logic Antinomies, Fracture of Physics Relativity and quantum mechanics conserved this vision but disrupted its harmonious perception by introducing various paradoxes: A dilemma: - In a 3D world it exists a division of events into past, present, and future, but it is not consistent with relativity. - In the alternative view – time is a 4th dimension – there is (i) no objective time flow (all events of space-time are equally existent), (ii) absolute determinism (at the macro scale), and (iii) no free will. These consequences make most physicists and philosophers agree that this world view is undoubtedly wrong. But so far, no one has succeeded in formulating a view that avoids the above dilemma and is compatible with relativity. From the foundation text of International Conference on the Nature and Ontology of Space-time

6 Metaphysics, Paradoxes, Logic Antinomies, Fracture of Physics Metaphysics: structure of space-time  length contraction of objects (by which metaphysical mean space constraints objects to contract). Idem for time dilatation effects on the pace of processes. Logic antinomy: in the state of quantum superposition, an object at a given instant can be at several positions (following certain probabilities) Paradox: an action on a particle can influence instantaneously the state of another particle, and at any distance (entangled particles). Space looses its essence: separate objects. Fracture of physics: since space, time and elementary objects are primary ingredients of the universe, two theories are necessary to describe the world (structure of space-time, behavior of particles).  Is there a vision which eliminates these paradoxes and unifies the physics ?

7 Outline - Motivation - Vision - Emergence of relativistic space-time - Representation of quantum mechanics by stochastic computations

8 Insert your pin code Objects and Behaviors

9 Objects and Observers (external to the observable) Observer external to the observed object: he can have access on information concerning the nature of the object producing the observed behavior.

10 Objects and Interactions The next state of an object is determined by its present state and by informations coming from the objects with which it interacts. Since interactions may only reflect the behavior of the objects  the state of an object can only reflect the behavior of other objects: can not contain information concerning their profound nature

11 Observers being part of the observable (the Universe and its structures)

12 Observers being part of the Universe Ultimate limit of our knowledge: as we are observers being part of the Universe, we can have access on information concerning the behavior of elementary particles, but not concerning the profound nature of the objects producing this behavior.  Particles: meta-objects producing a behavior through the process of evolution of their state (like a computation)  Universe: engendered by a meta-system composed of these meta-objects  We can, at our convenience, associate to this meta- system any structure (or architecture), as far as it produces the behavior of the Universe that we observe.

13 A Universe engendered by a process Illustration: (meta)cellular network  Each cell is a meta-object that engenders the behavior of an elementary particle.  Comports a set of state variables which determine: particle kind, its position, its speed, etc.  Changes its state at the pace of a meta-time: - present state of the cell + present state of the cells in interaction + computation rules = next state - computation rules = laws of interactions  Local interactions : only between particles whose position variables have close values.

14 A Universe engendered by a process Meta-Cellular-Network:  The position variable of a cell determines the position of the particle.  The set of all position variables determines the form of space.  Communication (interaction) between particles having close positions  Value of Position Variable: - frequency of modulation to emit its state - frequency of demodulation to receive states of close particles c’ c Universe b a a’ b’

15 A Universe engendered by a process  If the rules computing the cell states are identical to the laws which govern the evolution of the state of the particles in the universe, the state of these cells will evolve/move "identically" with the particles of the universe and will create the similar structures.  If some observers emerge in this universe, an image of a world similar to our will be formed in their mental structures. p p’

16 Emergence of time Let us imagine a world in which: -certain times the zebras are incomparably faster than the lions and certain times it is the opposite, -a car being at several km from a person suddenly covers this distance in a fraction of a second and crushes him, -the earth carries out hundreds of revolutions around the sun without your biological age being increased, while several generations of other people already passed, and suddenly you age of a hundred years in a fraction of a second......, - a world in which there is no stable correlation between the paces of evolution of the various processes. In such a world the notion of time has no meaning. Let us imagine a world in which: - certain times the zebras are incomparably faster than the lions and certain times it is the opposite, - a car being at several km from a person suddenly covers this distance in a fraction of a second and crushes him, - the earth carries out hundreds of revolutions around the sun without your biological age being increased, while several generations of other people already passed, and suddenly you age of a hundred years in a fraction of a second......, - a world in which there is no stable correlation between the paces of evolution of the various processes. In such a world the notion of time has no meaning.

17 Emergence of time On the other hand: In a system where the relationship between the paces of evolution of any two processes is the same each time they take place, we can speak about time, since: -we can choose a process as reference for measuring time, and - after having observed once the correspondence between the events of the reference process and the events of another process, we can: - we can choose a process as reference for measuring time, and - after having observed once the correspondence between the events of the reference process and the events of another process, we can: use the reference process to predict the instant (event of the reference process) in which each event of the second process occurs. use the reference process to predict the instant (event of the reference process) in which each event of the second process occurs. measure the duration of a process, by observing the events of the reference process in which starts and finishes the process under measurement. measure the duration of a process, by observing the events of the reference process in which starts and finishes the process under measurement.

18 Emergence of time In a universe engendered by the evolution of the states of a set of meta- objects composing a meta-system, there is emergence of time if: - the laws governing the evolution of the states of the meta-objects are invariant (independent of the values of the position variables, and constant throughout the evolution of the meta-system),  In the engendered universe, the correspondence between the events of two processes will be always the same. A B c’ c Universe b a a’ b’

19 Destruction of time in case of lost of laws’ invariability In a universe engendered by the evolution of the states of a set of meta-objects composing a meta-system, there is emergence of time only if: - the laws governing the evolution of the states of the meta-objects are invariable  otherwise the correspondence between the events of two processes will vary arbitrarily. c’ c Universe b a a’ b’ A B

20 Time and Meta-time Meta-time: the emergence of time presupposes that the state of the meta-objects (cells of the meta-network) evolves. For example, new values of state variables are computed at each step of a meta-clock.  Does it means that time is a simple translation of this meta-time? c’ c Universe b a a’ b’ c’ c Universe b a a’ b’ T

21 Independence between time and meta-time The period T of the meta-clock takes two different values T1 and T2 in two different cycles of computation: - the same interval t h of time corresponds to two different intervals T1 and T2 of meta-time. - freezing, decelerating, or accelerating the meta-clock does not have any effect on the time of the universe.  Time is not a category having an autonomous existence, independent of the laws of the universe, because it is not a translation of meta-time.  Time is determined by the relations between the paces of processes, thus by the laws which govern the evolution of the universe. It is a byproduct of the evolution of the state of the particles governed by these laws. thth T1 T2

22 Nature and Emergence of Time  time, like everything else in the universe, cannot not exist without change: an engine of change (meta-clock or meta-time) is mandatory  time does not have a per se existence (it is not a translation of a preexisting meta-time).  time is determined by the laws which govern the evolution of the state of the particles (or of the universe): - qualitatively: the invariance of the laws is the necessary and sufficient condition for its existence - quantitatively: it is determined by the ratios of the paces of the evolution of the processes. These ratios are determined in their turn by the laws governing the evolution of the state of the particles (or of the universe)

23 Emergence of Relativistic Space-Time in a Computational Universe Next talk

24 Outline - Motivation - Vision - Emergence of relativistic space-time - Representation of quantum mechanics by stochastic computations

25 Quantum Mecanics (state superposition) Observable A State superposition particle A: operator of a physical observable  1,  2,  n eigen-vectors of A 1, 2, …, n : eigen-values of A p 1 = | c 1 | 2, p 2 = | c 2 | 2, …, p n = | c n | 2 c i = ‹  i |  › (inner product of  i and  ).  = solution of Schrödinger’s equation Measurement of physical observable  i  { 1, 2, …, n }

26 Computations over stochastic signals: theorem of existence f(_) g=f(w) w Probability density function s(w) Probability density function p(g) s(w) p(g) Theorem:  p(g)  f(_): p(f(w)) = p(g), discreet and continue spectrum Input signal Output signal wg

27 State superposition  deterministic transformation of a stochastic variables particle = meta-object performing two computations: - compute deterministic functions f(_) according to previous slide: to give the statistical distributions of observables defined by QM. - transform stochastic states w into stochastic states g, by means of functions f(_). A measurement of a physical observable: value g = f(w) corresponding to the current value of w. The particle realizes a state superposition determined by S.E. Measurement of physical observable  i  { 1, 2, …, n }   Wave function  + Rules Algebra Operators => statistical distributions : P( r ) P( p ) E 1, E 2, …, E n p e1, p e2, …, p en s 1, s 2 p s1, p s2 Interaction with environnement w r r w p p w e E w s s f r (w r ) f p (w p ) f e (w e ) f s (w s ) Compute functions f r, f p, f e, f s

28 State superposition  deterministic transformation of a stochastic variable Observable A State superposition Elimination of the logical antinomy: in state of superposition an object can be at the same time in several positions following certain probabilities. But this interpretation is incompatible with the vision of the particles immerged in a true space (veritable position not computable).  The position must be a state variable.  w f(_) g=f(w) s(w) p(g ) w

29 Entangled Particles Particle 1 Particle 2 Measure = i  Measure = f( i ) spin = s x  spin = - s x Creation of entangled states Particle 1 Particle 2 How the result of a measurement on particle 1 can determine instantaneously the result of measurement on the very distant particle 2? => Paradox in a veritable space

30 Entangled Particles versus Computing Meta-objects: an example Compute functions f a, f p, f e, f s Particle j: ID j signals w a signals  EV j =ID i f a (w a ) signals w a signals  EV i =ID J f a (w a ) Particle i: ID i Compute functions f a, f p, f e, f s Each computing meta-object: ID number and entanglement variable EV During entanglement between particles i and j meta-object i sets EVi = IDj. Idem for particle j. At each computation step: - meta-objectj emits its state at frequency = IDj - meta-objecti uses demodulation frequency = EVi (= IDj). It receives state of particle j. - meta-objecti receives at each computation step the state of particle j and can adapt its state immediately. - idem for particle j At each computation step: - meta-object j emits its state at frequency = IDj - meta-object i uses demodulation frequency = EVi (= IDj). It receives state of particle j. - meta-object i receives at each computation step the state of particle j and can adapt its state immediately. - idem for particle j