The Nature of Time Travel

1. The Nature of Time Travel Xiaolong Shawn Liu Dinna Ramlan David Simons

2. Overview • Introduction • Worm Holes • Paradoxes • Feasibility

3. Introduction • In many science fiction books/movies one can often find the story of people traveling backward or forward in time • Who among us has not seen “Back to the Future” • What is really allowed if one were to take into account the laws of physics? Is it allowed?

4. How Would We Do It? • Special Relativity Theories by Einstein • Time slows down if you go really really really really really fast (e.g. >95% the speed of light) • But…mass at these speeds becomes infinite • This still doesn’t get you backwards in time • In 1935, Albert Einstein and Nathan Rose realized that general relativity allowed the existence of “bridges,” originally called Einstein-Rosen bridges but are now called wormholes. Will this work???

5. Definition of a Wormhole • A geometry of 4-dimensional space time in which two regions of the universe are connected by a narrow throat • They are hypothetical connections between a black hole and a white hole

6. Wormholes Cont… • Black Hole: everything (and I do mean everything) is sucked into a black hole with an inescapable gravitational force • White Hole: this will take a little more explaining…

7. White Holes Cont… • Theoretical opposite of a black hole • Not impossible to escape but impossible to reach • Repels everything (including massive particles and photons) and nothing can ever enter them • We have not yet observed one

8. Wormholes Cont… • They can provide relatively easy means of traveling distant regions of space or even backwards in time • By journeying through a wormhole, you could travel between two regions faster than a normal beam of light would be able to in normal space time

9. Challenges to Transverse Wormholes • Worm holes are not static structures • It’s a shape that expands from zero throat radius and then back to zero • Even light won’t make it through in time

10. Challenges Cont… • Travel through one may be extremely challenging because any object thrown in would pull the wormhole together through gravity • We would need matter with negative energy density (the magnitude of the tension of the matter must be greater than the energy density of the matter itself) to stabilize the opening • “Exotic matter” is required (we have not yet found it yet but is not unproven under the laws of physics)

11. Implications of Traveling Through a Wormhole • One of the wormhole mouths is placed in Tech and another mouth is placed at Norris • Shawn and David get in the time machine, travel away from the earth at 5:00 pm 6/4/03 at nearly the speed of light from Tech • Dinna stays in Norris, waiting for them to return

12. Implications Cont… • Shawn and David return after 12 hours of their time but Dinna has gone through 10 years of her life (Twin Paradox) • From the mouth at Tech, Dinna can see her younger self at Norris. • The wormhole forms a “loop”

13. Causality • Law of identity applied to action • The relationship between causes and effects • Events must be in the order of causes then follow by effects

14. Paradox • A statement that is seemingly contradictory or opposed to common sense and yet is perhaps true (from Merriam-Webster Dictionary) • Violates the law of causality • Argument that time traveling is impossible • Can be broken down into: matricide paradox, Polchinski paradox, and the free-lunch paradox

15. Matricide Paradox • Also known as grandfather paradox • A time traveler goes back in time to kill his young grandfather • His success means that he could never have existed in the first place

16. Polchinski Paradox • Also known as billiard ball paradox • Utilizes time travel to prevent time travel from occurring • Ball is launched from the right hole and gets out from the left before it enters the right hole • It “collides” with itself to “deflect” himself so that it misses the time machine

17. Free-Lunch Paradox • Leonardo da Vinci travels back in time to meet his younger self and gives him the portrait of Mona Lisa • Young Leonardo gets a free lunch without putting any effort in drawing the portrait • Where is the origin of the portrait?

18. Resolution to Paradoxes • Parallel universe or multi-verse • Chronology protection conjecture • Entanglement theory

19. Parallel Universe or Multi-verse • Theory by Dr. Hugh Everett, III • Wormholes do not necessarily connect to our own universe • Consider the wave function as real object • Specifying the state of one system leads to a unique specification of the state of the other subsystems • Each system only observing one of the possible results of a measurement and unaware of the other results • All outcomes exist simultaneously but do not interact with each other • Each universe is mutually unobservable but are equally real worlds

20. Chronology Protection Conjecture • Theory by Stephen Hawking • The law of physics conspire to prevent time travel by macroscopic objects • Universe will react in such a way as to destroy the time machine that tries to get into the wormhole • When someone tries to kill his young grandfather, he misses his shot and only hits his grandfather’s leg

21. Entanglement Theory • Your grandfather is represented as a pure quantum state vector • All the men at that time are “indistinguishable” • Characterized by their “entanglement” with each other • You cannot recognize your grandfather to kill him

22. Feasibility Overview • Transversable wormholes permitted  wormholes can be “time machines” • Event Horizon forbidden • Wormholes often require violation of “Weak Energy Condition” • Alternative: Cosmic Strings? • String Theory: Hope for the Future

23. Requirement: No Event Horizon • Virtual Particles that enter Wormhole could trigger infinite energy density  Destruction! • This is an event horizon, just like a black hole

24. Terminology • Weak energy condition: The idea that the mass (energy) density in any one frame would always be at least equal to or greater than zero is called the "weak energy condition.” • Averaged Null Energy Conditions (ANEC) synonym for Weak Energy Condition (WEC)

25. Quantum Mechanics Restrictions • Quantum Mechanics allows for Negative Energy Density! • Quantum Fluctuations make this possible • Wormholes also require Negative Mass, similar to Negative Energy (E = Mc2) • See right for wormhole example

26. Violations of Averaged Null Energy Conditions • How much “exotic matter” is required? • We know Quantum Mechanics allows some energy condition violations • 2 Possibilities: Do we need • Infinitesimal ANEC violations? • Large WEC (weak energy condition) violations?

27. Energy Density Theory Results • Only small amounts of ANEC (Averaged Null Energy Conditions) needed! • May 2003 Physical Review Letter: Visser, Kar, and Dadhich • Requires proper geometry choice: Static spherically symmetric space-times • Special circumstance of theory supports idea of time travel

28. Further Research: Cosmic Strings • Cosmic Strings are under enormous pressure & tension, cross section smaller than an atom • Extremely fast acceleration: accelerate the sun from 0 to 60 miles per hour in 1/30 of a second • The disproportional orientation of the universe makes the existence of these strings highly possible

29. Cosmic String Theory Results • Interesting case: “Closed Time-like Curves” produced by pairs of moving cosmic strings • Research: Gott, 1991 Exact Solutions to Einstein’s Field Equations for cosmic strings • “Closed Time-like Curves” physics-speak for time travel, produced with cosmic string speeds greater than a certain threshold speed • Research shows in nature these speeds “should be possible!”

30. Cosmic String Cont… • Advanced Civilization could accelerate separate strings to high speeds by towing with massive rockets • Some Closed Time-like Curves (CTC) do not violate Weak Energy Conditions  even ‘easier’ for CTC to actually happen!

31. String Theory • If successful, will unite General Relativity and Quantum Theory • Includes 4 dimensions we’re currently familiar with, + 6 very small dimensions • Implications not completely known yet

32. References • “Black Holes and Time Warps” by Kip S. Thorne, 1994, W.W. Norton & Company. • Time Trips, Black Holes and Relativity website http://www.geocities.com/CapeCanaveral/Hall/5803/index.html • The “big” time travel http://www.anu.edu.au/Physics/courses/A07/studentsites/studentsites2001/The_Big/ • Time travel homepage http://www.anu.edu.au/Physics/courses/A07/studentsites/studentsites2001/Benz_Group/ • The Everett Interpretation http://www.hedweb.com/manworld.htm#believes • Wikipedia, the free encyclopedia http://www.wikipedia.org

33. References • “The Universe in a Nutshell” by Stephen Hawking, 2001, Bantam Books. • Public Lectures from Website of Stephen Hawking: http://www.hawking.org.uk/lectures/lindex.html • Definition of Weak Energy Condition: http://www.aip.org/enews/physnews/1998/split/pnu398-2.htm • Morris, Thorne, and Yurtsever. Wormholes, Time Machines, and the Weak Energy Condition. Vol 61, Number 13, 26 September 1988 http://prl.aps.org/ • Gott, Richard. Closed Timelike Curves Produced by Pairs of Moving Cosmic Strings: Exact Solutions. Vol 66, Number 9, 4 March 1991. http://prl.aps.org/ • String Theory Overview: http://superstringtheory.com • Visser, Kar, and Dadhich. Traversable Wormholes with Arbitrarily Small Energy Condition Violations, Volume 90, Number 20, 23 May 2003. http://prl.aps.org/

34. Thank You!!!