Transcript Nicolaidis-PhilNum.B..

A Numerical Philosophy of the Universe
and the Fundamental Nature of Computer Science
Michael Nicolaidis
TIMA Laboratory
1
Outline
- Motivation
- Vision
- Emergence of relativistic space-time
- Representation of quantum mechanics by stochastic
computations
2
Outline
- Motivation
- Vision
- Emergence of relativistic space-time
- Representation of quantum mechanics by stochastic
computations
3
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.
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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
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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 ?
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Outline
- Motivation
- Vision
- Emergence of relativistic space-time
- Representation of quantum mechanics by stochastic
computations
7
Objects and Behaviors
Insert your
pin code
8
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.
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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
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Observers being part of the observable
(the Universe and its structures)
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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 metasystem any structure (or architecture), as far as it produces
the behavior of the Universe that we observe.
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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.
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A Universe engendered by a process
a’
Universe
a
b’
b
c’
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
c
- frequency of demodulation to
receive states of close particles
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A Universe engendered by a process
p’
p
 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.
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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.
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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:
• 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.
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Emergence of time
In a universe engendered by the evolution of the states of a set of metaobjects 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’
Universe
a
b’
b
c
A
c’
B
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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.
a’
Universe
a
b
c
A
b’
c’
B
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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?
a’
a’
Universe
a
b
Universe
a
b’
c’
b’
b
c’
c
c
T
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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 th 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.
th
T1
T2
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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)
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Emergence of Relativistic Space-Time in
a Computational Universe
Next talk
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Outline
- Motivation
- Vision
- Emergence of relativistic space-time
- Representation of quantum mechanics by stochastic
computations
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Quantum Mecanics
(state superposition)
particle
A:
Observable A
State superposition
1, 2 ,..., n ,...
p1, p2 ,..., pn ,...
Measurement of physical
observable
 i  {1, 2, …, n}
operator
observable
of
a
physical
y1, y2, yn eigen-vectors of A
1, 2, …, n: eigen-values of A
p1= |c1|2, p2 = |c2|2, …, pn = |cn|2
ci
= ‹yi|y› (inner product of yi
and y).
y = solution of Schrödinger’s
equation
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Computations over stochastic signals:
theorem of existence
Probability density
function
Probability density
function
s(w)
p(g)
w
g
Theorem:  p(g)  f(_): p(f(w)) = p(g), discreet and continue spectrum
w
g
wi
gi
g  f ( w )  [  s(b)db ], F(g)   p(a)da    F1 : by int ervals
Input signal
w
s(w)
f(_)
g=f(w)
p(g)
Output signal
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State superposition  deterministic transformation
of a stochastic variables
Interaction with
environnement
Wave function y
+ Rules Algebra Operators
=> statistical distributions :
P( r )
P( p )
E1, E2, …, En
pe1, pe2, …, pen
Compute functions
fr, fp, fe, fs


wr
wp
we
ws
fr(wr)
fp(wp)
fe(we)
fs(ws)
r
p
E
s
s1, s2
ps1, ps2
• The particle realizes a state
superposition determined by
S.E.
• Measurement of physical
observable
 i  {1, 2, …, n}
• 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
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g = f(w) corresponding to the current value of w.
State superposition  deterministic
transformation of a stochastic variable
Observable A
State superposition
1, 2 ,..., n ,...
p1, p2 ,..., pn ,...

ww
s(w)
f(_)
g=f(w)
p(g)
• 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.
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Entangled Particles
Particle 2
Particle 1
Creation of entangled states
Particle 2
Particle 1
1, 2 ,..., n ,...
1, 2 ,..., n ,...
p1, p2 ,..., pn ,...
p1, p2 ,..., pn ,...
Measure = i
spin = sx


Measure = f(i)
spin = - sx
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
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Entangled Particles versus Computing
Meta-objects: an example
Particle i: IDi
Particle j: IDj
Compute functions
fa, fp, fe, fs
Compute functions
fa, fp, fe, fs
fa(wa)
fa(wa)
signals
wa
EVi=IDJ
signals a
signals
wa
signals a
EVj=IDi
• 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-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.
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- idem for particle j