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

ds2 ¼ 1 2m r

• dt2 þ

1 2m r

• 1

dr2 þ r2ðdh2 þ sin2 hd/2Þ;

C4

CQ"

A brief history of wormholes

ER bridges =wormholes in Schwarzschild spacetime

ds2 ¼ 1 2m r

• dt2 þ

1 2m r

• 1

dr2 þ r2ðdh2 þ sin2 hd/2Þ;

C4

CQ"

A brief history of wormholes

ER bridges =wormholes in Schwarzschild spacetime

ds2 ¼ 1 2m r

• dt2 þ

1 2m r

• 1

dr2 þ r2ðdh2 þ sin2 hd/2Þ;

C4

CQ"

A brief history of wormholes

ER bridges =wormholes in Schwarzschild spacetime

ds2 ¼ 1 2m r

• dt2 þ

1 2m r

• 1

dr2 þ r2ðdh2 þ sin2 hd/2Þ;

C4

CQ"

P H YSI CAL R EVI EW

VOLUME

128, NUMBER

OCTOB ER 15, 1962

Causality and Multiply

Connected

Space-Time

ROBERT W. FULLER

Ps&pin Physical

Laboratories, Collmbia

University,

%eve York, Pew VoJ'I; JOHN A. VVHEKLKRt

Palmer Physical Laboratory, Princeton

University,

Princeton, Rem Jersey (Received May 16, 1962)

ER bridges = non- traversable wormholes

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”

Traversable wormholes! But… “negative energy”

A brief history of wormholes

Traversable wormholes! But… “negative energy”

A brief history of wormholes

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 Kip´s proper time: 10 years Carolee's proper time: 12 hours 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 Kip´s proper time: 10 years Carolee's proper time: 12 hours 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

GEDANKEN

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 Kip´s proper time: 10 years Carolee's proper time: 12 hours 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

G E D A N K E N

PHYSICAL REVIEW 0 VOLUME 46, NUMBER 2

Chronology

protection conjecture

15 JULY

S.W. Hawking

Department ofApplied Mathematics and Theoretical Physics,

University of Cambridge,

Silver Street, Cambridge

CB39E8; Uni ted It ingdom

{Received 23 September

1991)

It has been

that an advanced civilization

might have the technology

to warp spacetime

so

tions,

it appears

to prevent

• ne from

creating

a time

machine.

It seems there is a chronology

protection

agen-

cy, which

prevents

the appearance

• f closed

timelike 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

Chronology

protection conjecture

15 JULY

S.W. Hawking

Department ofApplied Mathematics and Theoretical Physics,

University of Cambridge,

Silver Street, Cambridge

CB39E8; Uni ted It ingdom

{Received 23 September

1991)

It has been

that an advanced civilization

might have the technology

to warp spacetime

so

tions,

it appears

to prevent

• ne from

creating

a time

machine.

It seems there is a chronology

protection

agen-

cy, which

prevents

the appearance

• f closed

timelike curves and so makes the universe safe for historians.

Kim and Thorne

[5] have considered

the expectation

Do quantum effects prevent CTCs?

l → ∞ l → −∞ l = 0

the redshift function Φ(r) functions of the radius r only

the shape function b(r) There is a value

• f

at

Then, the proper radial distance to [15] l = ± R r

b0 dr0(1 b(r0)/r0)1/2,

Universes or regions within the same

Proper radial distance

functions of the radius r only which b (r = b0) = r = b0, the wormhole’s throat. Then,

Throat

l → ∞ l → −∞ l = 0

massless wormhole

that Φ(r) = 0

• rmhole will

and 1+1 D

ds2 = c2 dt2 + 1 1 b(r)

r

dr2

Conformal invariance of K-G equation in 1+1 D

ds2 = c2 (1 b(r) r ) dt2 + dr2

Effective speed of light:

c2(r) = c2 (1 b(r) r ),

c2(r) = c2 (1 b(r) r ),

Effective speed of light: SQUID array embedded in a superconducting transmission line Quantum simulation

c2(φext) = c2 cos πφext φ0

External magnetic flux

C.S. PRD 94, 081501 (2016)

a) b) l → ∞ l → −∞ l → ∞ l → −∞ l = 0 l = 0

φext(r) = φ0 π arccos(1 b(r) r ).

c2(r) = c2 (1 b(r) r ),

c2(φext) = c2 cos πφext φ0

C.S. PRD 94, 081501 (2016)

a) b) l → ∞ l → −∞ l → ∞ l → −∞ l = 0 l = 0

φext(r) = φ0 π arccos(1 b(r) r ).

Example: b(r) = b2

r ,

Ellis 1973, Morris-Thorne 1988

• 1.0
• 0.5

0.0 0.5 1.0 0.0 0.1 0.2 0.3 0.4 0.5

x(mm) ϕext π ϕ0

C.S. PRD 94, 081501 (2016) |x|=r-b0

for b0 = 0.1 mm consistent with the idea

ds2 = c2 e2Φ(r)(1 + g(t) l F(l) cos θ)2dt2 + 1 1 b(r)

r

dr2 + r2(dθ2 + sin2 θdφ2),

a) b) l → ∞ l → −∞ l → ∞ l → −∞ l = 0 l = 0

Time machine Acceleration

where g(t) to 1 in the Form factor

and F(l) is Again, we

φext(r, t) = φ0 π arccos(1 b(r) r )(1 + g(t) l F(l))2,

Interval of constant acceleration

and also F(l) = l/l0 = 0, g = c2/(20 l0) Outside this region the flux

mouth trajectory. and l0 = 0.2 mm, a few SQUIDs,

• 0.10
• 0.05

0.00 0.05 0.10 0.20 0.25 0.30 0.35 0.40 0.45 0.50

x(mm) ϕext π ϕ0

C.S. PRD 94, 081501 (2016)

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? Quantum metrology techniques Estimation of the throat size of a distant wormhole

C.S.Sci. Rep. 7, 716 (2017)

Alternative to gravitational lensing schemes Space-based laser interferometry (LISA)

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)