Quantum systems and traversable wormholes Carlos Sabn ComFuturo - PowerPoint PPT Presentation

Quantum systems and traversable wormholes Carlos Sabín ComFuturo Researcher IFF, CSIC

“Of all thought experiments, perhaps the most helpful are those that push the laws of physics in the most extreme ways” (Kip S. Thorne, Proceedings 13th Conference GR and Gravitation 1993 ) Quantum simulators as tools to explore the frontiers of theoretical physics .

A brief history of wormholes ER bridges =wormholes in Schwarzschild spacetime � � 1 � � � ds 2 ¼ � 1 � 2 m 1 � 2 m dt 2 þ dr 2 r r þ r 2 ð d h 2 þ sin 2 h d / 2 Þ ; CQ" C4

A brief history of wormholes ER bridges =wormholes in Schwarzschild spacetime � � 1 � � � ds 2 ¼ � 1 � 2 m 1 � 2 m dt 2 þ dr 2 r r þ r 2 ð d h 2 þ sin 2 h d / 2 Þ ; CQ" C4

A brief history of wormholes ER bridges =wormholes in Schwarzschild spacetime � � 1 � � � ds 2 ¼ � 1 � 2 m 1 � 2 m dt 2 þ dr 2 CQ" C4 r r þ r 2 ð d h 2 þ sin 2 h d / 2 Þ ;

A brief history of wormholes ER bridges =wormholes in Schwarzschild spacetime � � 1 � � � ds 2 ¼ � 1 � 2 m 1 � 2 m dt 2 þ dr 2 CQ" C4 r r þ r 2 ð d h 2 þ sin 2 h d / 2 Þ ; OCTOB ER 15, 1962 P H YSI CAL 128, NUMBER R EVI EW VOLUME 2 Space-Time and Multiply Connected Causality ER bridges = non- traversable wormholes ROBERT W. FULLER Collmbia %eve York, Pew VoJ'I; Ps&pin Physical Laboratories, University, JOHN A. VVHEKLKRt Rem Jersey Palmer Physical Laboratory, Princeton Princeton, University, (Received May 16, 1962) Kruskal time evolution of embeddings of space like surfaces in Schwarzschild metric (Am. J. Phys 80, 203 (2012))

A brief history of wormholes Traversable wormholes! But… “negative energy”

A brief history of wormholes Traversable wormholes! But… “negative energy”

A brief history of wormholes Traversable wormholes! But… “negative energy” And… How to turn the wormhole into a time machine

And… How to turn the wormhole into a time machine Relative motion of wormhole mouths Acceleration twin paradox effect for external observers but not through the wormhole! Carolee goes to a distant star with one mouth and comes back Carolee's proper time: 12 hours Kip´s proper time: 10 years But same time through the wormhole When she´s back, if Kip traverses the wormhole from her mouth to his, he accesses his own past

And… How to turn the wormhole into a time machine Relative motion of wormhole mouths Acceleration twin paradox effect for external observers but not through the wormhole! GEDANKEN Carolee goes to a distant star with one mouth and comes back Carolee's proper time: 12 hours Kip´s proper time: 10 years But same time through the wormhole When she´s back, if Kip traverses the wormhole from her mouth to his, he accesses his own past

And… How to turn the wormhole into a time machine Relative motion of wormhole mouths Acceleration twin paradox effect for external observers but not through the wormhole! Carolee goes to a distant star with one mouth and comes back Carolee's proper time: 12 hours Kip´s proper time: 10 years But same time through the wormhole When she´s back, if Kip traverses the wormhole from her mouth to his, he accesses his own past

N E K N A D E G PHYSICAL REVIEW 0 VOLUME 46, NUMBER 2 15 JULY protection conjecture Chronology S. W. Hawking Department of Applied Mathematics University of Cambridge, and Theoretical Physics, CB3 9E8; Uni ted It ingdom Silver Street, Cambridge {Received 23 September 1991) It has been to warp spacetime that an advanced have the technology so civilization might it appears to prevent a time tions, one from creating It seems there is a chronology machine. protection agen- of closed cy, which the timelike prevents appearance curves and so makes the universe safe for historians. Kim and Thorne [5] have considered the expectation Do quantum effects prevent CTCs?

CENSORED PHYSICAL REVIEW 0 VOLUME 46, NUMBER 2 15 JULY protection conjecture Chronology S. W. Hawking Department of Applied Mathematics University of Cambridge, and Theoretical Physics, CB3 9E8; Uni ted It ingdom Silver Street, Cambridge {Received 23 September 1991) It has been to warp spacetime that an advanced have the technology so civilization might it appears to prevent a time tions, one from creating It seems there is a chronology machine. protection agen- of closed cy, which the timelike prevents appearance curves and so makes the universe safe for historians. Kim and Thorne [5] have considered the expectation Do quantum effects prevent CTCs?

l → ∞ functions of the radius r only the redshift function Φ ( r ) functions of the radius r only which b ( r = b 0 ) = r = b 0 , the shape function b ( r ) l = 0 Throat There is a value of at the wormhole’s throat. Then, Proper radial distance Then, the proper radial distance to R r b 0 dr 0 (1 � b ( r 0 ) /r 0 ) � 1 / 2 , [15] l = ± Universes or regions within the same l → −∞

and 1+1 D massless wormhole that Φ ( r ) = 0 l → ∞ ormhole will 1 ds 2 = � c 2 dt 2 + dr 2 1 � b ( r ) r l = 0 Conformal invariance of K-G equation in 1+1 D ds 2 = � c 2 (1 � b ( r ) r ) dt 2 + dr 2 Effective speed of light: l → −∞ c 2 ( r ) = c 2 (1 � b ( r ) r ) ,

c 2 ( r ) = c 2 (1 � b ( r ) Effective speed of light: r ) , Quantum simulation SQUID array embedded in a superconducting transmission line c 2 ( φ ext ) = c 2 cos πφ ext φ 0 External magnetic flux C.S. PRD 94, 081501 (2016)

c 2 ( r ) = c 2 (1 � b ( r ) a) l → ∞ r ) , l = 0 π arccos(1 � b ( r ) φ ext ( r ) = φ 0 r ) . l → −∞ b) l = 0 c 2 ( φ ext ) = c 2 cos πφ ext φ 0 l → −∞ l → ∞ C.S. PRD 94, 081501 (2016)

π arccos(1 � b ( r ) φ ext ( r ) = φ 0 r ) . a) l → ∞ Example: b ( r ) = b 2 0 Ellis 1973, Morris-Thorne 1988 r , l = 0 0.5 l → −∞ 0.4 0.3 ϕ ext b) π ϕ 0 0.2 l = 0 0.1 0.0 - 1.0 - 0.5 0.0 0.5 1.0 l → −∞ l → ∞ for b 0 = 0 . 1 mm x ( mm ) consistent with the idea |x|=r-b 0 C.S. PRD 94, 081501 (2016)

Time machine 1 ds 2 = � c 2 e 2 Φ ( r ) (1 + g ( t ) l F ( l ) cos θ ) 2 dt 2 + dr 2 1 � b ( r ) r a) l → ∞ + r 2 ( d θ 2 + sin 2 θ d φ 2 ) , Form factor Acceleration and F ( l ) is where g ( t ) l = 0 Again, we to 1 in the π arccos(1 � b ( r ) φ ext ( r, t ) = φ 0 r )(1 + g ( t ) l F ( l )) 2 , l → −∞ Interval of constant acceleration 0.50 b) 0.45 l = 0 0.40 ϕ ext 0.35 π ϕ 0 0.30 and also F ( l ) = l/l 0 l → −∞ l → ∞ 0.25 mouth trajectory. = 0 , g = c 2 / (20 l 0 ) 0.20 and l 0 = 0 . 2 mm , Outside this region the flux C.S. PRD 94, 081501 (2016) - 0.10 - 0.05 0.00 0.05 0.10 a few SQUIDs, x ( mm )

Effective CTCs in this simulated Universe? The impedance of the array might grow large and generate quantum fluctuations of the superconducting phase Effective chronology protection? Killer paradox, from “Into S. Hawking´s universe” C.S. PRD 94, 081501 (2016)

Quantum detection? Space-based laser interferometry (LISA) Quantum metrology techniques Estimation of the throat size of a distant wormhole Alternative to gravitational lensing schemes C.S.Sci. Rep. 7, 716 (2017)

Conclusions We have introduced an analogue quantum simulator of a 1+1 D wormhole spacetime and shown how to turn it into a time machine. An analogue chronology-protection mechanism emerges naturally in this superconducting setup. The detection of a real wormhole might be in principle possible with space-based laser interferometers.

Do not go gentle into that good night, Old age should burn and rave at close of day; Rage, rage against the dying of the light. Though wise men at their end know dark is right, Because their words had forked no lightning they Do not go gentle into that good night. Good men, the last wave by, crying how bright Their frail deeds might have danced in a green bay, Rage, rage against the dying of the light. Wild men who caught and sang the sun in flight, And learn, too late, they grieved it on its way, Do not go gentle into that good night. Grave men, near death, who see with blinding sight Blind eyes could blaze like meteors and be gay, Rage, rage against the dying of the light. And you, my father, there on the sad height, Curse, bless, me now with your fierce tears, I pray. Do not go gentle into that good night. Rage, rage against the dying of the light. (Dylan Thomas)