The Power Of Closed Timelike Curves John Smolin

Outline Closed Timelike Curves Grandfather Paradox Deutsch model State distinguishing Computational power The linearity

References Stockum, Proc. Roy. Soc. Edinburgh A, 57: 135 (1937) Godel, Rev. Mod. Phys.

First law of time travel Whenever anyone gets a time machine, the first thing

Deutsch Model Swap Pure state evolves to mixed state This is nonunitary and nonlinear!

State Distinguishing Brun, Harrington, Wilde

Can send information back in time Big deal: We have a time machine But

Breaks BB 84 Cryptography A generalization can distinguish arbitrarily many states. --Allows encoding infinite

Aaronson-Watrous-Fortnow BQPCTC=PSAPCE BQPPCTC ? =BQPQPOLY

Weinberg-Polchinski Nonlinear extension which maps smoothly to regular QM Can distinguish nonorthogonal states “EPR-Phone”

The Principle of Universal Inclusion The evolution of a nonlinearly evolving system may depend

Objections It works for every input state/I made a firm decision Fine but boring

Slides: 30

Download presentation

The Power? Of Closed Timelike Curves John Smolin joint work with Charles Bennett Debbie Leung Graeme Smith

Outline Closed Timelike Curves Grandfather Paradox Deutsch model State distinguishing Computational power The linearity trap and the principle of universal inclusion

Closed Timelike Curves

References Stockum, Proc. Roy. Soc. Edinburgh A, 57: 135 (1937) Godel, Rev. Mod. Phys. , 21: 447 (1949) Morris, Thorne and Yurtsever, PRL 61, 1446 (1988) Gott, PRL 66, 1126 (1991) Deser, Jackiw and 't. Hooft, PRL 68, 267 (1992) Hawking, Phys. Rev. D 46, 603 (1992) Ori, PRL 95, 021101 (2005) Deutsch, Phys. Rev. D 44, 3197 (1991)

First law of time travel Whenever anyone gets a time machine, the first thing they do is go back in time and kill their grandfather.

Deutsch's Model

Fixing the Paradox

Deutsch Model Swap Pure state evolves to mixed state This is nonunitary and nonlinear! SWAP

Two Universes Unitarity restored!

State Distinguishing Brun, Harrington, Wilde

Communicate Faster Than Light

Can send information back in time Big deal: We have a time machine But we're sending it from after the CTC ends!

Breaks BB 84 Cryptography A generalization can distinguish arbitrarily many states. --Allows encoding infinite classical information in one qubit!

Definition of state discrimination

Circuit with Referee

No CTCs need apply

The Linearity Trap

A CTC-assisted Computer

Aaronson-Watrous-Fortnow BQPCTC=PSAPCE BQPPCTC ? =BQPQPOLY

Weinberg-Polchinski Nonlinear extension which maps smoothly to regular QM Can distinguish nonorthogonal states “EPR-Phone” “Everett Phone”? ?

The Principle of Universal Inclusion The evolution of a nonlinearly evolving system may depend on parts of the universe with which is does not interact. In regular quantum mechanics this holds: CTCs give: Confusing point: You might get the right rho anyway

Objections It works for every input state/I made a firm decision Fine but boring model---No free will Same density matrix is not the same as the same mixture. Clintonian arguments—what the meaning of “is” is. We are restricting to theories that reduce to QM away from the nonlinear region