budapest, september 10, 2012relativistic computingpage: 1

RELATIVISTIC COMPUTING

by Péter Németi (joint work with Hajnal Andréka, István Németi and Gergely Székely)

Budapest, September 10, 2012Relativistic Computing Page: 1

THE IDEA

Church Thesis was formulated in Newtonian worldview

Turing Machine concept incorporates “ABSOLUTE TIME”

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G. R. you can MANIPULATE TIME (just like space)

after Black Hole Physics breaking the Turing Barrier becomes conceivable

PLAN OF TALK

Black hole computing

Wormhole computing (astrophysicist Igor Novikov)

Comparison, realisticity issues

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GRAVITY CAUSES SLOW TIME

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G. R. Gravity causes slow time

New physics brings in new horizons, new possibilities and breaks old barriers.

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GRAVITATIONAL TIME DILATION IN EVERYDAY LIFE

+45 μs/day because of gravity-7 μs/day because of the speed of sat.

approx. 4 km/s (14400 km/h)

Relativistic Correction: 38 μs/day approx. 10 km/day

GPSGlobal Positioning System

COMPUTING BEYOND THE TURING BARRIER

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We want to use the GR effect that gravity causes slow time to decide an arbitrary recursively enumerable set.

We will show the idea in two levels of abstraction.1. In Cartoon-like pictures2. The same idea in spacetime diagrams

SPEEDING UP TIME USING GRAVITY

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SPEEDING UP TIME USING GRAVITY

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SPEEDING UP TIME USING GRAVITY

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SECOND LEVEL: SPACETIME DIAGRAMS

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Let us see in more mathematical detailhow this fairy tale can be implementedin terms of GR spacetime diagrams.

ORDINARY BLACK HOLE – COMPUTER’S VIEW

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ORDINARY BLACK HOLE – PROGRAMMER’S VIEW

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ROTATING BLACK HOLE

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Malament-Hogarth event!

Etesi-Nemeti paper: computationsInfinite space inside

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WORRIES – ONE BY ONE

1. Blue shift (communication)2. Evaporation of BH3. Strong Cosmic Censor Hypothesis4. Instability of Cauchy Horizon5. Blue shift (cosmic, distant galaxies)6. Unlimited tape7. Predictability, Repeatability, Radiation from

singularity8. Decay of protons9. Heat Death

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Cauchy horizon

outer event horizon

worldline of programmer

worldline of computer

photon signal communication messenger communication

already solved in [ND], Fig.5, sec.5.3.2, p.133

WORRIES: 1. COMMUNICATION BLUE SHIFT

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WORRIES: 2. EVAPORATION OF BH Shielding (only gradually) CMB Apostolos’ book, p.146 Evaporation is only hypothetical Penrose 2004, p.848:

“… BH evaporation is an entirely theoretical … might be that Nature has other ideas for future of BH’s.”

Papers: Nikolic, H., Black holes radiate but do not evaporate.

arXiv:hep-th/0402145v3, Aug 2005. Helfer,A. D., Do black holes radiate? arXiv:gr-qc/0304042v1, Apr 2003.

Therefore since we are using a huge BH for hypercomputing, Hawking radiation should cause no problem.

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WORRIES: 3. – 4. – 5.

3. Strong Cosmic Censor 4. Instability of Cauchy Horizon 5. Blue shift (cosmic, distant galaxies)

- Expansion of Universe forever

- Asymptotically de Sitter background implies stability

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FOREVER EXPANDING UNIVERSE

worldlines of galaxies

photon geodesicsphoton geodesics

worldlines of galaxies

t

cosmological event horizon

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KERR-NEWMANN WORMHOLE IN FOREVER EXPANDING UNIVERSE

r = 0 singularityr = 0

I+I+ BH interior distant galaxies

(Olbers paradox)

worldline of computer

1

23

1: Inner event horizon(Cauchy horizon)

2: Outer event horizon

3: Cosmological eventhorizon

Kerr-Newmann-deSitter space-time

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WORRIES: 3. – 4. – 5.

Papers for “fall of censor”: Joshi, P.S., Do naked singularities break the

rules of physics? Scientific American, January 2009.

Chambers, C. M., The Cauchy horizon in black hole-de Sitter spacetimes. arXiv:gr-qc/9709025v1, Sep 1997.

German,W.S., Moss, I.A., Cauchy horizon stability and cosmic censorship. arXiv:gr-qc/0103080v1, Mar 2001.

Lobo, F.X. N., Exotic solutions in general relativity: traversable wormholes and “warp drive” spacetimes. arXiv:0710.4474v1 Oct 2007.

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WORRIES: 3. – 4. – 5.

Weak Energy Condition is not LAW: Barcelo, C., Visser, M., Twilight for the

energy conditions?, Int. J. Mod. Phys. C 11 (2002), 1553. arXiv:gr-qc/0205066.

Cosmology accelerated expansion, dark energy

Wormholes’ boom implies new kinds of MH-regions

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WORRIES: 6. – 7. – 8.

6. Unlimited tape information ≠ energy 

7. Predictability Repeatability Radiation from singularity

New orbit for programmer  8. Decay of protons

Small enough particles do not decay (electron, positron, neutrino)

9. Heat Death

PART II: WORMHOLE COMPUTING

We reviewed BH computing, now comes WH computing.

This is another kind of thought-experiment, based on a different GR space-time

Both have advantages and disadvantages. WH computing: can compute more complex problems, is smaller, no need for Noahs Ark

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AB

WORMHOLE (AS SPACE-STRUCTURE)

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A

BLong path (outside)

Short path (inside)unfold

AB

WORMHOLE IN SPACETIME DIAGRAM

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Short path (inside)

AB

t

Long path (outside)

ORDINARY BLACK HOLE – PROGRAMMER’S VIEW

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MANIPULATING TIME...

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t

1

1

2

3

4

5

6

2

3

B Ar

r = 0

Signal outside WHFrom A to B

Signal inside WHFrom B to A

Event horizon of BH

MANIPULATING TIME...

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t

1

1

2

3

4

5

6

2

3

B Ar

r = 0

Signal outside WHFrom A to B

Signal inside WHFrom B to A

Event horizon of BH

INDUCING A TIME SHIFT

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t

2

4

6

8

10

12

B Ar

Signal outside WHFrom A to B

Signal inside WHFrom B to A

1

3

5

7

9

11

2

4

6

8

1

3

5

7

9

BlackHole disappears

BlackHole appears

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Designing the wormhole computer

Task is: decide for any recursive set S whether S is finite or infinite.

S is specified by fixing a number theoretic 0 -formula Φ(x)

S x : Φ(x)

We will check whether there is a greatest x with Φ(x).

ENTITIES OF THE WH COMPUTER Ca – Turing machine (TM) at mouth A (see its

program later) Ma – Mirror at mouth A (acts either as a mirror or a

prism) Mirror: reflects signals coming from the wormhole towards

Mb outside the wormhole

Prism: filters red light, reflects green towards Mb

Cb – TM at mouth B (see its program later) Mb – Mirror at mouth B

Reflects light signals coming from Cb or Ma into the

wormhole towards Ma

Pr – Programmer (checks incoming signals on Ma till TMH) Red and Green light means there are finitely many x such

that Φ(x) Only Red light means there are infinitely many x such that

Φ(x) No signals means there is no x such that Φ(x)

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Σ2 THOUGHT EXPERIMENT

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Wait TMH time

Φ(x) & Flash

Infinite many x Φ(x)

Finite many x

Φ(x)

Pr Ca Ma Mb Cb

Wormhole time gap

(Malament-Hogard event)

Inside WHOutside WH

PROGRAM OF CB

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X := 0

Φ(x)?Message to Mb

(red light)Y

Flash to Ca

X := X+1

N

Wait TMH time Pr Ca Ma Mb Cb

PROGRAM OF CA

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F := 0

Ma := Prism

Red light till TMH? F := 1Y

Wait till TMH

Ma := Mirror

Wait for Flash from Cb

Ma := Mirror N

F = 1

Message to Ma

(green light)

True

HALT

False

Pr Ca Ma Mb Cb

WORMHOLES CAN COMPUTE MORE

How much more? Beyond-Turing complexity issues: Jiri

Wiedermann, Philip Welch, Marek Suchenek, Mark Hogarth

BH decidable problems are all

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WORMHOLES CAN COMPUTE MORE

Theorem (P. Welch): BH can compute all problems if and only if one can create a computer which able to receive an arbitrary large (but finite) amount of information.

WH can decide all problems.

Question: can WH decide all n problems by using perhaps n WH-s?

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COMPARISON BETWEEN BH AND WH COMPUTING

BHs observedBlue shift problem:

BHs are focusing lenses

No time travel

We need big BHs

Programmer travels

BH can compute

less

WHs not yet

observedWHs are defocusing

lenses (no bs roblem)

Time travel

WHs may be small

No need for Noahs

Ark

WH can compute

more

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THE WAY TO GET THROUGH THE TURING BARRIER

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THE END

OR THE FUTURE ? …

1.ST QUESTION

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Physics General Relativity

Cosmic censor

conjectureExotic Matter

Closed time-like curves

Malament-Hogart Spacetimes

Cosmology

SingularitiesRELATIVISTICCOMPUTING

QUESTIONS…You can read more on Istvan Nemeti’s homepage:

http://www.renyi.hu/~nemeti/

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PEOPLE, HISTORY

History of relativistic computing

1987 - start:Andréka & Németi Univ. Ames USA Lecture Notes

1992 - Independent start:Hogarth (Cambridge)

Other authors:Pitowsky (Israel), Shagrir (Israel), Earman (Pittsburgh), Norton

(Pittsburgh), Malament (USA), Etesi (Hungary, Dept. Phys.), Dávid (Hungary, Dept. Phys.), Tipler, Barrow, Jiří Wiedermann, Philip Welch, Marek Suchenek, Chris Wüthrich, B. Gyenis (Pittsburgh)

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