The Nature of Time The Nature of Time TravelTravel

Xiaolong Shawn LiuXiaolong Shawn LiuDinna RamlanDinna RamlanDavid SimonsDavid Simons

OverviewOverview IntroductionIntroduction Worm HolesWorm Holes ParadoxesParadoxes FeasibilityFeasibility

IntroductionIntroduction In many science fiction books/movies one can In many science fiction books/movies one can

often find the story of people traveling backward often find the story of people traveling backward or forward in timeor forward in time

Who among us has not seen “Back to the Who among us has not seen “Back to the Future”Future”

What is really allowed if one were to take into What is really allowed if one were to take into account the laws of physics? Is it allowed?account the laws of physics? Is it allowed?

How Would We Do It?How Would We Do It? Special Relativity Theories by EinsteinSpecial Relativity Theories by Einstein

Time slows down if you go really really really really Time slows down if you go really really really really really fast (e.g. >95% the speed of light)really fast (e.g. >95% the speed of light)

But…mass at these speeds becomes infiniteBut…mass at these speeds becomes infinite This still doesn’t get you backwards in timeThis still doesn’t get you backwards in time

In 1935, Albert Einstein and Nathan Rose In 1935, Albert Einstein and Nathan Rose realized that general relativity allowed the realized that general relativity allowed the existence of “bridges,” originally called existence of “bridges,” originally called Einstein-Rosen bridges but are now called Einstein-Rosen bridges but are now called wormholes. Will this work???wormholes. Will this work???

Definition of a WormholeDefinition of a Wormhole A geometry of 4-dimensional space time in which A geometry of 4-dimensional space time in which

two regions of the universe are connected by a two regions of the universe are connected by a narrow throatnarrow throat

They are hypothetical connections between a They are hypothetical connections between a black hole and a white holeblack hole and a white hole

Wormholes Cont…Wormholes Cont… Black HoleBlack Hole: :

everything (and I do everything (and I do mean everything) is mean everything) is sucked into a black sucked into a black hole with an hole with an inescapable inescapable gravitational forcegravitational force

White HoleWhite Hole: this will : this will take a little more take a little more explaining…explaining…

White Holes Cont…White Holes Cont… Theoretical opposite of a black holeTheoretical opposite of a black hole Not impossible to escape but impossible to reachNot impossible to escape but impossible to reach Repels everything (including massive particles Repels everything (including massive particles

and photons) and nothing can ever enter themand photons) and nothing can ever enter them

We have not yet We have not yet observed observed oneone

Wormholes Cont…Wormholes Cont… They can provide relatively easy means of They can provide relatively easy means of

traveling distant regions of space or even traveling distant regions of space or even backwards in timebackwards in time

By journeying through a wormhole, you could By journeying through a wormhole, you could travel between two regions faster than a normal travel between two regions faster than a normal beam of light would be able to in normal space beam of light would be able to in normal space timetime

Challenges to Transverse Challenges to Transverse WormholesWormholes

Worm holes are not static structuresWorm holes are not static structures It’s a shape that expands from zero It’s a shape that expands from zero

throat radius and then back to zerothroat radius and then back to zero Even light won’tEven light won’t

make it through make it through in time in time

Challenges Cont…Challenges Cont… Travel through one may be extremely Travel through one may be extremely

challenging because any object thrown in would challenging because any object thrown in would pull the wormhole together through gravitypull the wormhole together through gravity

We would need matter with negative energy We would need matter with negative energy density (the magnitude of the tension of the density (the magnitude of the tension of the matter must be greater than the energy density matter must be greater than the energy density of the matter itself) to stabilize the openingof the matter itself) to stabilize the opening

““Exotic matter” is required (we have not yet Exotic matter” is required (we have not yet found it yet but is not unproven under the laws of found it yet but is not unproven under the laws of physics)physics)

Implications of Traveling Implications of Traveling Through a WormholeThrough a Wormhole

One of the wormhole One of the wormhole mouths is placed in Tech mouths is placed in Tech and another mouth is and another mouth is placed at Norris placed at Norris

Shawn and David get in Shawn and David get in the time machine, travel the time machine, travel away from the earth at away from the earth at 5:00 pm 6/4/03 at nearly 5:00 pm 6/4/03 at nearly the speed of light from the speed of light from TechTech

Dinna stays in Norris, Dinna stays in Norris, waiting for them to returnwaiting for them to return

Implications Cont…Implications Cont… Shawn and David return Shawn and David return

after 12 hours of their after 12 hours of their time but Dinna has gone time but Dinna has gone through 10 years of her through 10 years of her life (life (Twin ParadoxTwin Paradox))

From the mouth at Tech, From the mouth at Tech, Dinna can see her Dinna can see her younger self at Norris. younger self at Norris.

The wormhole forms a The wormhole forms a “loop”“loop”

CausalityCausality

Law of identity applied to actionLaw of identity applied to action

The relationship between causes and The relationship between causes and effectseffects

Events must be in the order of causes then Events must be in the order of causes then follow by effectsfollow by effects

ParadoxParadox A statement that is seemingly A statement that is seemingly

contradictory or opposed to common contradictory or opposed to common sense and yet is perhaps true (from sense and yet is perhaps true (from Merriam-Webster Dictionary)Merriam-Webster Dictionary)

Violates the law of causalityViolates the law of causality Argument that time traveling is impossibleArgument that time traveling is impossible Can be broken down into: matricide Can be broken down into: matricide

paradox, Polchinski paradox, and the free-paradox, Polchinski paradox, and the free-lunch paradoxlunch paradox

Matricide ParadoxMatricide Paradox Also known as grandfather paradoxAlso known as grandfather paradox A time traveler goes back in time to kill his young A time traveler goes back in time to kill his young

grandfathergrandfather His success means that he could never have His success means that he could never have

existed in the first placeexisted in the first place

Polchinski ParadoxPolchinski Paradox Also known as billiard ball Also known as billiard ball

paradoxparadox Utilizes time travel to Utilizes time travel to

prevent time travel from prevent time travel from occurringoccurring

Ball is launched from the Ball is launched from the right hole and gets out right hole and gets out from the left before it from the left before it enters the right holeenters the right hole

It “collides” with itself to It “collides” with itself to “deflect” himself so that it “deflect” himself so that it misses the time machinemisses the time machine

Free-Lunch ParadoxFree-Lunch Paradox Leonardo da Vinci travels Leonardo da Vinci travels

back in time to meet his back in time to meet his younger self and gives him younger self and gives him the portrait of Mona Lisathe portrait of Mona Lisa

Young Leonardo gets a free Young Leonardo gets a free lunch without putting any lunch without putting any effort in drawing the portraiteffort in drawing the portrait

Where is the origin of the Where is the origin of the portrait?portrait?

Resolution to ParadoxesResolution to Paradoxes

Parallel universe or multi-verseParallel universe or multi-verse

Chronology protection conjectureChronology protection conjecture

Entanglement theoryEntanglement theory

Parallel Universe or Multi-verseParallel Universe or Multi-verse

Theory by Dr. Hugh Everett, IIITheory by Dr. Hugh Everett, III Wormholes do not necessarily connect to Wormholes do not necessarily connect to

our own universeour own universe Consider the wave function as real objectConsider the wave function as real object Specifying the state of one system leads to a unique Specifying the state of one system leads to a unique

specification of the state of the other subsystems specification of the state of the other subsystems Each system only observing one of the possible results Each system only observing one of the possible results

of a measurement and unaware of the other results of a measurement and unaware of the other results All outcomes exist simultaneously but do not interact All outcomes exist simultaneously but do not interact

with each otherwith each other Each universe is mutually unobservable but are equally Each universe is mutually unobservable but are equally

real worldsreal worlds

Chronology Protection Chronology Protection ConjectureConjecture

Theory by Stephen HawkingTheory by Stephen Hawking The law of physics conspire to The law of physics conspire to

prevent time travel by prevent time travel by macroscopic objectsmacroscopic objects

Universe will react in such a way Universe will react in such a way as to destroy the time machine as to destroy the time machine that tries to get into the wormholethat tries to get into the wormhole

When someone tries to kill his When someone tries to kill his young grandfather, he misses his young grandfather, he misses his shot and only hits his shot and only hits his grandfather’s leggrandfather’s leg

Entanglement TheoryEntanglement Theory Your grandfather is represented as a pure Your grandfather is represented as a pure

quantum state vectorquantum state vector All the men at that time are All the men at that time are

“indistinguishable”“indistinguishable” Characterized by their “entanglement” with Characterized by their “entanglement” with

each othereach other You cannot recognize your grandfather to You cannot recognize your grandfather to

kill himkill him

Feasibility OverviewFeasibility Overview Transversable wormholes permitted Transversable wormholes permitted

wormholes can be “time machines”wormholes can be “time machines” Event Horizon forbiddenEvent Horizon forbidden Wormholes often require violation of Wormholes often require violation of

“Weak Energy Condition”“Weak Energy Condition” Alternative: Cosmic Strings?Alternative: Cosmic Strings? String Theory: Hope for the FutureString Theory: Hope for the Future

Requirement: No Event HorizonRequirement: No Event Horizon Virtual Particles that enter Wormhole could trigger Virtual Particles that enter Wormhole could trigger

infinite energy density infinite energy density Destruction! Destruction! This is an event horizon, just like a black holeThis is an event horizon, just like a black hole

TerminologyTerminology Weak energy condition: The idea that the Weak energy condition: The idea that the

mass (energy) density in any one frame mass (energy) density in any one frame would always be at least equal to or would always be at least equal to or greater than zero is called the "weak greater than zero is called the "weak energy condition.”energy condition.”

Averaged Null Energy Conditions (ANEC) Averaged Null Energy Conditions (ANEC) synonym for Weak Energy Condition synonym for Weak Energy Condition (WEC)(WEC)

Quantum Mechanics RestrictionsQuantum Mechanics Restrictions

Quantum Mechanics allows for Negative Quantum Mechanics allows for Negative Energy Density!Energy Density!

Quantum Fluctuations make this possibleQuantum Fluctuations make this possible Wormholes also require Negative Mass, Wormholes also require Negative Mass,

similar to Negative similar to Negative Energy (E = McEnergy (E = Mc22))

See right for See right for wormhole examplewormhole example

Violations of Averaged Null Violations of Averaged Null Energy ConditionsEnergy Conditions

How much “exotic matter” is required?How much “exotic matter” is required? We know Quantum Mechanics allows We know Quantum Mechanics allows

somesome energy condition violations energy condition violations 2 Possibilities: Do we need 2 Possibilities: Do we need

Infinitesimal ANEC violations? Infinitesimal ANEC violations? Large WEC (weak energy condition) Large WEC (weak energy condition)

violations?violations?

Energy Density Theory ResultsEnergy Density Theory Results

Only small amounts of ANEC (Averaged Only small amounts of ANEC (Averaged Null Energy Conditions) needed!Null Energy Conditions) needed!

May 2003 Physical Review Letter: Visser, May 2003 Physical Review Letter: Visser, Kar, and DadhichKar, and Dadhich

Requires proper geometry choice: Static Requires proper geometry choice: Static spherically symmetric space-times spherically symmetric space-times

Special circumstance of theory supports Special circumstance of theory supports idea of time travelidea of time travel

Further Research: Cosmic Further Research: Cosmic StringsStrings

Cosmic Strings are under enormous pressure & Cosmic Strings are under enormous pressure & tension, cross section smaller than an atomtension, cross section smaller than an atom

Extremely fast acceleration: accelerate the sun Extremely fast acceleration: accelerate the sun from 0 to 60 miles per hour in 1/30 of a secondfrom 0 to 60 miles per hour in 1/30 of a second

The disproportional orientation of the universe The disproportional orientation of the universe makes the existence of these strings makes the existence of these strings highly highly possiblepossible

Cosmic String Theory ResultsCosmic String Theory Results Interesting case: “Closed Time-like Curves” Interesting case: “Closed Time-like Curves”

produced by pairs of moving cosmic stringsproduced by pairs of moving cosmic strings Research: Gott, 1991 Exact Solutions to Research: Gott, 1991 Exact Solutions to

Einstein’s Field Equations for cosmic stringsEinstein’s Field Equations for cosmic strings ““Closed Time-like Curves” physics-speak for Closed Time-like Curves” physics-speak for

time travel, produced with cosmic string speeds time travel, produced with cosmic string speeds greater than a certain threshold speedgreater than a certain threshold speed

Research shows in nature these speeds “should Research shows in nature these speeds “should be possible!”be possible!”

Cosmic String Cont…Cosmic String Cont…

Advanced Civilization could accelerate Advanced Civilization could accelerate separate strings to high speeds by towing separate strings to high speeds by towing with massive rocketswith massive rockets

SomeSome Closed Time-like Curves (CTC) do Closed Time-like Curves (CTC) do not violate Weak Energy Conditions not violate Weak Energy Conditions even ‘easier’ for CTC to actually happen!even ‘easier’ for CTC to actually happen!

String TheoryString Theory If successful, will unite General Relativity and If successful, will unite General Relativity and

Quantum TheoryQuantum Theory Includes 4 dimensions we’re currently familiar Includes 4 dimensions we’re currently familiar

with, + 6 very small dimensionswith, + 6 very small dimensions Implications not completely known yetImplications not completely known yet

ReferencesReferences ““Black Holes and Time Warps” by Kip S. Thorne, 1994, W.W. Black Holes and Time Warps” by Kip S. Thorne, 1994, W.W.

Norton & Company.Norton & Company. Time Trips, Black Holes and Relativity website Time Trips, Black Holes and Relativity website

http://www.geocities.com/CapeCanaveral/Hall/5803/index.htmlhttp://www.geocities.com/CapeCanaveral/Hall/5803/index.html The “big” time travel The “big” time travel

http://www.anu.edu.au/Physics/courses/A07/studentsites/studentsitehttp://www.anu.edu.au/Physics/courses/A07/studentsites/studentsites2001/The_Big/s2001/The_Big/

Time travel homepage Time travel homepage http://www.anu.edu.au/Physics/courses/A07/studentsites/studentsitehttp://www.anu.edu.au/Physics/courses/A07/studentsites/studentsites2001/Benz_Group/s2001/Benz_Group/

The Everett Interpretation The Everett Interpretation http://www.hedweb.com/manworld.htm#believeshttp://www.hedweb.com/manworld.htm#believes

Wikipedia, the free encyclopedia http://www.wikipedia.orgWikipedia, the free encyclopedia http://www.wikipedia.org

ReferencesReferences ““The Universe in a Nutshell” by Stephen Hawking, 2001, Bantam The Universe in a Nutshell” by Stephen Hawking, 2001, Bantam

Books.Books. Public Lectures from Website of Stephen Hawking: Public Lectures from Website of Stephen Hawking: http://http://

www.hawking.org.uk/lectures/lindex.htmlwww.hawking.org.uk/lectures/lindex.html Definition of Weak Energy Condition: Definition of Weak Energy Condition:

http://www.aip.org/enews/physnews/1998/split/pnu398-2.htmhttp://www.aip.org/enews/physnews/1998/split/pnu398-2.htm Morris, Thorne, and Yurtsever. Morris, Thorne, and Yurtsever. Wormholes, Time Machines, and the Wormholes, Time Machines, and the

Weak Energy ConditionWeak Energy Condition. Vol 61, Number 13, 26 September 1988 . Vol 61, Number 13, 26 September 1988 http://http://prl.aps.orgprl.aps.org//

Gott, Richard. Gott, Richard. Closed Timelike Curves Produced by Pairs of Moving Closed Timelike Curves Produced by Pairs of Moving Cosmic Strings: Exact SolutionsCosmic Strings: Exact Solutions. Vol 66, Number 9, 4 March 1991. . Vol 66, Number 9, 4 March 1991. http://prl.aps.org/ http://prl.aps.org/

String Theory Overview: http://superstringtheory.comString Theory Overview: http://superstringtheory.com Visser, Kar, and Dadhich. Visser, Kar, and Dadhich. Traversable Wormholes with Arbitrarily Traversable Wormholes with Arbitrarily

Small Energy Condition ViolationsSmall Energy Condition Violations, Volume 90, Number 20, 23 May , Volume 90, Number 20, 23 May 2003. http://prl.aps.org/ 2003. http://prl.aps.org/

Thank You!!!Thank You!!!