11

Emergence of Relativistic Space-Emergence of Relativistic Space-Time in a Computational Universe Time in a Computational Universe

Michael Nicolaidis Michael Nicolaidis TIMA LaboratoryTIMA Laboratory

22

OutlineOutline -- Motivation: paradoxes and fracture of physics Motivation: paradoxes and fracture of physics

-- Special relativity versus computation rules Special relativity versus computation rules (interaction laws)(interaction laws)

-- Space-time structure in special relativity Space-time structure in special relativity

-- Implications of the relativistic space-time structure Implications of the relativistic space-time structure

-- Treatment of Special Relativity: the approach Treatment of Special Relativity: the approach

-- Condition for the emergence of relativistic space Condition for the emergence of relativistic space timetime

-- Illustration examples Illustration examples

-- Proof Generalization Proof Generalization

-- Perspectives Perspectives

33

Paradoxes, Metaphysics, Fracture of Paradoxes, Metaphysics, Fracture of PhysicsPhysics

A dilemma: A dilemma: - - In a 3D world it exists a division of events into past, present, In a 3D world it exists a division of events into past, present, and future. Which is not consistent with relativity. and future. Which is not consistent with relativity. - In the alternative view – a 4D space-time world – there is (i) - In the alternative view – a 4D space-time world – there is (i) no objective time flow (all events of spacetime are equally no objective time flow (all events of spacetime are equally existent), (ii) absolute determinism (at the macro scale), and existent), (ii) absolute determinism (at the macro scale), and (iii) no free will. These consequences make most physicists (iii) no free will. These consequences make most physicists and philosophers agree that this world view is undoubtedly and philosophers agree that this world view is undoubtedly wrong. wrong. But so far, no one has succeeded in formulating a view that But so far, no one has succeeded in formulating a view that avoids the above dilemma and is compatible with relativity.avoids the above dilemma and is compatible with relativity.

From theFrom the foundation text foundation text of International Conference on the of International Conference on the Nature and Ontology of Space-timeNature and Ontology of Space-time

44

Paradoxes, Metaphysics, Fracture of Paradoxes, Metaphysics, Fracture of PhysicsPhysics

MetaphysicsMetaphysics:: structure of space-time structure of space-time length contraction of length contraction of objects (by which objects (by which metaphysicalmetaphysical meanmean space constraints space constraints objects to contract). objects to contract). Idem for time dilatation effects on processes.Idem for time dilatation effects on processes.

Fracture of physics:Fracture of physics: since space, time and elementary objects since space, time and elementary objects are primary ingredients of the universe, two theories are are primary ingredients of the universe, two theories are necessary to describe the world (structure of space-time, necessary to describe the world (structure of space-time, behavior of particles)behavior of particles)

Is there a vision which eliminates these paradoxes and Is there a vision which eliminates these paradoxes and unifies the physics ?unifies the physics ?

55

Space-time versus computation Space-time versus computation (interaction) laws(interaction) laws

Space and timeSpace and time are engendered by the evolution of the states are engendered by the evolution of the states of the elementary particles composing the universe.of the elementary particles composing the universe.

The rules of computation (interaction laws)The rules of computation (interaction laws) determine the determine the evolution of these states.evolution of these states.

The interaction laws should determine the structure of The interaction laws should determine the structure of space-time. But how ?space-time. But how ?

Unifying approach since a complete theory of interactions Unifying approach since a complete theory of interactions could describe everything (relativity becomes a by-product).could describe everything (relativity becomes a by-product).

66

Space-time structure in special Space-time structure in special relativityrelativity

Space-time structure defined by Space-time structure defined by Lorentz transformationsLorentz transformations

S

0

S : u = v//x

x

x’

t’

t

),tvx(x v zz ,yy

x

c

vtt v 2

77

Implications of the relativistic Implications of the relativistic space-time structurespace-time structure

Implications Implications : :

S

0

S

Desynchronization:Desynchronization: t2 - t1 =x v

v/c2

t’

xt

x’

x

t’ t’

t2t1

Length contraction:Length contraction: x = x’/v

Time dilatation:Time dilatation: t =v

t’22 /1

1

cvv

t’

t

88

Treatment of Special Relativity:Treatment of Special Relativity:the approachthe approach

• Space and time are engendered by the evolution of the Space and time are engendered by the evolution of the states of elementary particles. states of elementary particles.

• Their structure (e.g. length contraction, time dilation), Their structure (e.g. length contraction, time dilation), reflects the reflects the impact of the lawsimpact of the laws governing the evolution of governing the evolution of particles on the particles on the dimensionsdimensions of the objects, their of the objects, their distancesdistances, , their their movementmovement, and the , and the pacepace ofof their their evolutionevolution..

The computation laws governing the evolution of particles The computation laws governing the evolution of particles determinedetermine the space-time structure.structure.

99

Treatment of Special Relativity: Treatment of Special Relativity: the the approachapproach

Goal:Goal: Determine the conditions which imply that the space-Determine the conditions which imply that the space-time engendered by the computation of the states of a set of time engendered by the computation of the states of a set of particles (a computational universe) is in conformity with particles (a computational universe) is in conformity with special relativity. special relativity.

Idea 1:Idea 1: The intensity of the interactions (computation rules) The intensity of the interactions (computation rules) change with the speed of the particleschange with the speed of the particles

modification of the modification of the distances of equilibriumdistances of equilibrium of the particles of the particles composing an object (composing an object (length contractionlength contraction) and of the ) and of the pace of pace of evolutionevolution of a set of particles engendering a process ( of a set of particles engendering a process (time time dilationdilation).).

it is not a veritable structure of space-time that forces the it is not a veritable structure of space-time that forces the objects to modify their dimensions and the processes to objects to modify their dimensions and the processes to modify their pace of evolution (by which means?)modify their pace of evolution (by which means?)

Idea 2:Idea 2: The accelerations induced by the particle interactions The accelerations induced by the particle interactions must be in conformity with special relativity.must be in conformity with special relativity.

ConditionCondition which engenders a space-time conform to Lorentz which engenders a space-time conform to Lorentz transformations. transformations.

u1 = 0 u2 = 0 u1 = v u2 = v

1010

Treatment of Special Relativity: Treatment of Special Relativity: "privileged" reference frame"privileged" reference frame

Start with apparent relativistic “no-sense”: Start with apparent relativistic “no-sense”:

• A particle determines only one value for its position variable A particle determines only one value for its position variable and for its speed variableand for its speed variable

the variables of position computed by the meta-objects the variables of position computed by the meta-objects

define by default a (privileged) reference frame: Sdefine by default a (privileged) reference frame: S00

• But relativity does not admit privileged reference frames. But relativity does not admit privileged reference frames.

Admit such a reference frame in order to develop the Admit such a reference frame in order to develop the approach. approach.

Then, show that for any observer being part of the universe, Then, show that for any observer being part of the universe,

SS00 is not distinguishable from any other inertial frame. is not distinguishable from any other inertial frame.

1111

S

0

r=(rx, ry, rz)u2=(ux2, uy2,

uz2)

a2=(ax2, ay2, az2)

u1=(ux1, uy1, uz1)

Special Relativity : the conditionSpecial Relativity : the condition (Relativistic Constraint of Accelerations) (Relativistic Constraint of Accelerations)

Introduce an inertial frame: the values of position variables of particles determined by the computation are considered as positions in an inertial frame S0

The accelerations induced by the interactions* must change when the speed of particles changes.

RCA describes the impact of speed change on the accelerations

*interactions propagated at speed c are considered: interaction takes its source at a past position of particle 1 (t = c.r)

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Special Relativity : the conditionSpecial Relativity : the condition (Relativistic Constraint of Accelerations)(Relativistic Constraint of Accelerations)

S

0

r’=(rx/v, ry,

rz)

21x

1z2

1x

1y2

1x

1x1

/u1

/u,

/u1

/u,

/u1

u'u

cvcvcv

v vv

22x

2z2

2x

2y2

2x

2x2

/u1

/u,

/u1

/u,

/u1

u'u

cvcvcv

v vv

22 /1

1

cvv

1313

Special Relativity :Special Relativity : the condition the condition (RCA)(RCA)

32x2

2v

2x2

2z22

x22

v

2zz2

)c/uv1(

)a/cuv( -

)c/uv1(

a'a

r=(rx/v, ry,

rz)

,)c/uv1(

)a/cuv( -

)c/uv1(

a'a

32x2

2v

2x2

2y22

x22

v

2yy2

32x2

3v

x2x2

)c/uv1(

a'a

1414

Emergence of relativistic space-timeEmergence of relativistic space-time

ShowShow thatthat RCA implies: RCA implies:

1.1. In S In S00, the dimensions of objects, the distances , the dimensions of objects, the distances between objects and the pace of evolution of processes between objects and the pace of evolution of processes that are in movement, undergo the Lorentz contraction that are in movement, undergo the Lorentz contraction of lengths time dilation.of lengths time dilation.

2.2. The relations between the measurements of the The relations between the measurements of the dimensions of objects, of the distances between objects dimensions of objects, of the distances between objects and of the paces of evolution of processes, carried out in and of the paces of evolution of processes, carried out in various inertial reference frames, conform the Lorentz various inertial reference frames, conform the Lorentz transformations.transformations.

1515S

0

u1 = 0

Length Contraction ExampleLength Contraction Example

0rm

gg

rm

qqk

23k

v

21t

23t

v

21

0rm

qq

rm

ggk

1

21t

1

21

u2 = 0

u1 = v//x u2 = v//x

)kt(

o gg

qql

21

21

0rm

gg

rm

qqk

23k

v

21t

23t

v

21

0rm

qq

rm

ggk

2

21t

2

21

kt

21

21

v gg

qq1

1616

S

0

u1 = 0 u2 = 0 u1 = v//x u2 = v//x

u2 = 0

u2 = 0

u2 = v//x

u2 = v//x

For the above object and laws, length contraction conforms special relativity on all directions

Length Contraction ExampleLength Contraction Example

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Frame S

u = v//x

Frame S0

u = 0

Motionless clock: P1 interacts with P2 at rest in S0 (law g1g2/m2l02)

it carries out a circular trajectory of ray l0 around P2, as checked

by the length reference l0.

Moving clock : P1 under the same interaction performs a trajectory around particle P2 which is in rest in S (S: u=v). The clock is the same, since the new trajectory is also circular and of

ray l0 for the observer of S, as checked by his length reference l0.

Time Dilatation: we find T’ = Tv.

Time Dilatation ExampleTime Dilatation Example

P1 P1P2 P2

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Synchronization of distant clocks Synchronization of distant clocks in Sin S

• From M launchFrom M launch towards H1 and H2 two objects having speed towards H1 and H2 two objects having speed = c (photons) = c (photons)

clocks synchronized at S have a desynchronization inclocks synchronized at S have a desynchronization in SS00

equal toequal to t = t = vvvl/cvl/c22. .

• Lengths at rest inLengths at rest in S S contraction in S contraction in S00

• Time intervals measured in the same position of S Time intervals measured in the same position of S

dilatation in Sdilatation in S00

• Relation of desynchronizationRelation of desynchronization

Lorentz TransformationsLorentz Transformations S : u = v//xM

l

H1 H2

1919

Synchronization using moving clocksSynchronization using moving clocks

What about if we don’t know in advance particles with What about if we don’t know in advance particles with invariant speed?invariant speed?

Launch towards H1 and H2 two objects having equal speeds Launch towards H1 and H2 two objects having equal speeds in S.in S.

• But how to measure their speeds in S without synchronized But how to measure their speeds in S without synchronized clocks?clocks?

Idea:Idea: launch two identical clocks towards H1 and H2. launch two identical clocks towards H1 and H2.

Check if they indicate identical times when they cross Check if they indicate identical times when they cross equidistantly distributed positions. equidistantly distributed positions.

Same desynchronization relation Same desynchronization relation

Important equations to seek laws that could produce non-Important equations to seek laws that could produce non-Lorentzian “relativistic” space-timeLorentzian “relativistic” space-time

H1 H2

llll llll

2020

GeneralizationGeneralization

Illustrations for simple objects and processes and simple Illustrations for simple objects and processes and simple interaction laws are given. But we need a general proof.interaction laws are given. But we need a general proof.

Prove length contraction for any object (any # and type of Prove length contraction for any object (any # and type of particles, in any repartition in space, at rest or moving around particles, in any repartition in space, at rest or moving around their positions of equilibrium ...) their positions of equilibrium ...)

Prove time dilation for any process. Prove time dilation for any process.

General proof for all laws obeying the RCA, in order to cover General proof for all laws obeying the RCA, in order to cover all possible interactions (existing or imagined).all possible interactions (existing or imagined).

• Such demonstration is impossible by means of analytical Such demonstration is impossible by means of analytical expression of the evolution of all possible objects and expression of the evolution of all possible objects and processes (complexity + inapplicable if we don’t know the processes (complexity + inapplicable if we don’t know the exact expression of interaction laws). exact expression of interaction laws).

2121

GeneralizationGeneralization

ApproachApproach

We consider that the observers of S and We consider that the observers of S and SS00 decide arbitrarily decide arbitrarily

to:to:

• synchronize their clocks in a way that verify the relation synchronize their clocks in a way that verify the relation t t

= = vvvl/cvl/c22. .

• use as length references objects which verify the relation use as length references objects which verify the relation of length contractionof length contraction

• use as time references, processes which verify the use as time references, processes which verify the relation of time dilationrelation of time dilation

We We show that all measurements conform Lorentz show that all measurements conform Lorentz transformationstransformations

Arbitrary choicesArbitrary choices of measurement means of measurement means imply Lorentz imply Lorentz transformations !?transformations !?

2222

GeneralizationGeneralization

These arbitrary choices will not engender by miracle a These arbitrary choices will not engender by miracle a relativistic space-time. The results of measurements will not relativistic space-time. The results of measurements will not be coherent if the laws of interactions are arbitrary: be coherent if the laws of interactions are arbitrary:

• the objects selected as length references n S and S0 will the objects selected as length references n S and S0 will not be identical. Idem for processes used as time referencenot be identical. Idem for processes used as time reference

• measurements of the same object or processes carried measurements of the same object or processes carried

out in S andout in S and S S00 will give different resultswill give different results

But we now dispose in S and But we now dispose in S and SS00 a tool (Lorentz a tool (Lorentz

transformations) which we will use to show that these choices transformations) which we will use to show that these choices are coherent.are coherent.

2323

GeneralizationGeneralization

We show that We show that ifif the laws of interactions the laws of interactions verify RCAverify RCA, then, , then, these these arbitrary choices imply identical resultsarbitrary choices imply identical results when we when we

measure the same objects and processes measure the same objects and processes in S and in S and SS00. .

the the resultsresults of measurements are of measurements are coherentcoherent. .

the the arbitrary choicearbitrary choice ofof length and time length and time referencesreferences becomes becomes coherentcoherent: use of the same object and of the same process as : use of the same object and of the same process as

length reference and time reference in S and in length reference and time reference in S and in SS00. .

space-time verifies the transformations of Lorentz. space-time verifies the transformations of Lorentz.

all all laws of interactionlaws of interaction which verify RCA which verify RCA engenderengender a a space-space-timetime conformconform to to special relativityspecial relativity..

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GeneralizationGeneralization

We show that: We show that:

• RCARCA defines the defines the largest familylargest family of laws of laws thatthat engenderengender a a space-timespace-time conformconform to to special relativityspecial relativity. .

• All laws compatible with relativity verify RCA. All laws compatible with relativity verify RCA.

For stochastic laws (quantum laws of interactions): For stochastic laws (quantum laws of interactions):

• RCA applies to the average values on the macroscopic scale. RCA applies to the average values on the macroscopic scale.

• Develop stochastic form of RCA on the quantum scale. Develop stochastic form of RCA on the quantum scale.

Fusion of special relativity with the quantum laws of Fusion of special relativity with the quantum laws of interactions that are compatible with relativity interactions that are compatible with relativity (electromagnetic, weak and strong). (electromagnetic, weak and strong).

Idem for the gravitation, if current efforts lead in quantum Idem for the gravitation, if current efforts lead in quantum law of gravitation.law of gravitation.

2525

PerspectivesPerspectives

Pieces of physics already treated under the vision of Pieces of physics already treated under the vision of Computational Universes (special relativity, quantum systems)Computational Universes (special relativity, quantum systems)

Further treatments needed for:Further treatments needed for:

• General RelativityGeneral Relativity

• Quantum theories of interactionsQuantum theories of interactions

• Gravitational interactionGravitational interaction

Discreet space and time.Discreet space and time.

Meaning and emergence of conscience in Computational Meaning and emergence of conscience in Computational UniversesUniverses

…………..