Time Travel Paradoxes&

Some Fun With Time Machines

Why Do We Want to Travel in Time?

Time Travel Paradoxes

• The Grandfather Paradox

• Time Machine Paradox

• Breakfast Creation Paradox

• Statue Creation Paradox

• Knowledge Creation Paradox

The Grandfather Paradox

January, 1914. Grandfather Carlos is born.

January, 1948. Father Carlito is conceived.

September, 1948. Father Carlito is born.

June, 1980. Son Carl is born.

April, 2000. Carl enters time machine.

Carl travels back in time to October, 1940.

October, 1940. Carl murders Carlos!!

But, if Carlos iskilled by Carl,

Carl is never born! Carl cannot kill Carlos if Carl is never born … ??

The Time Machine Paradox

July, 2030. Sue Smart discovers theprinciple of the time machine.

Sue takes 10 years to build a time machine.

July, 2040. The time machine is now finished.

Sue hesitates. She waits a few months beforeusing the time machine.

September, 2040. Sue enters the time machine.

Sue travels to the future.

October, 3040. Sue arrives in the future.

Sue explores the future. Discoversa depressing world of mutants.

November, 3040. Sue says, “I want to go back.” Returns to the time machine.

Sue travels back in time to August, 2040.

August, 2040. Sue destroys(both!) time machines!

If the time machine is destroyed, Sue cannot

travel to the futurenor return to destroy

the time machine …??

The Breakfast Creation Paradox

7:30 am. Wake up.

Lie in bed thinking how nice it would be to have breakfast.

7:45 am. Decide: “Later I’ll preparebreakfast, travel back to the past, thenset breakfast before myself one minutefrom now.”

8:30 am. Get out of bed.

9:00 am. Step into time machine with breakfast.

Prepare breakfast.

Travel to the pastwith breakfast

7:46 am. Serve yourself breakfast!

Travel tothe future

9:00:01 am. Return after serving breakfast.Clean dishes.

What causes theappearance of

breakfast? Thoughtsand intentions

alone?

From: Cosmic Wormholesby Paul Halpern

The Statue Creation Paradox

April, 2050. Our hero, Rocky Bronze,enters the time machine.

Rockytravelsto thefuture.

May 1, 2092. Rocky arrives in the future.

Rocky discovers a statue of himself erectedto honor the first time traveler.Date on base: July 20, 2050

May 3, 2092. At night Rocky loads the statueinto the time machine. Then he leaves forthe past.

Rocky takesthe statue backto provideevidence ofhis time journey.

June 2, 2050. Rocky returns. He rolls outthe statue, and is given a hero’s welcome.

July 20, 2050. The statue of Rocky Bronzeis erected to honor the first time traveler.

August 10, 2080. Rocky dies.

Question:When was thestatue made??

?

From: Find The Sculptorby Sam mines

The Knowledge Creation Paradox

March 10, 2014. Time traveler, Ned Copy,leaves for the future.

Nedtravelsto thefuture.

February 10, 3021. Ned arrives in the future.

February 15, 3021. Ned finds famous paper onhalting aging. The paper, titled: “Immortality”, was published in the journal Nature in September, 2015. The author is Ann Young.

Nedcopiesthe paper.

February 16, 3021. Ned gets in the timemachine with the copy. He leaves for the past.

Nedreturnsto thepast.

March 11, 2014. Ned returns with a copyof the paper.

April 6, 2014. Ned finds senior RMWCbiology major, Ann Young.

Ned shows Ann the paper. She learns thetheory.

September, 2015. Ann publishes the paper“Immortality” in the journal Nature.

Where did theknowledge

come from???

?

Idea from: About Timeby Paul Davies

Closed Causal Loops

• Zoltan Tries to Shoot Himself

• Anne Goes to Work

• How to Get Rich With a Time Machine

Zoltan Tries to Shoot Himself

September, 2005. Young Zoltan is ahappy, carefree, right-handed rascal.

October, 2005. A scruffy bearded strangerfires several shots at Zoltan. Zoltan is hitin the right elbow.

December, 2005. Zoltan’s elbow woundhas caused severe damage and destroyedmuch of his natural coordination.

January, 2009. Zoltan becomes depressedabout his clumsiness. He grows a beard.

February, 2010. Zoltan is now so depressedthat he wishes he never survived the shooting.He decides to travel back in a time machineand shoot himself.

Zoltan travelsback in timewith a gun andan aching elbow.

Zoltan tries to kill hisprevious self, but his

defective elbow preventsaccurate aiming!

A policemanshoots and killsthe beardedZoltan.

Why doesn’t Zoltan just shoothimself now? Well, … never mind!

Anne Goes to Work

8:30:00 AM. Ann is walking to work. Sheapproaches the open door of a time machineon the side of the path ahead.

8:30:57. Ann passes a stone marker bythe side of the path. The time machine dooris just ahead on her right.

8:31:00. Anne suddenly emerges froma time machine. She is enraged tofind an identical replica of herselfwalking along the path just in frontof her! This occurs just a few stepsbeyond the stone marker.

Ann walks along towards the timemachine unconcerned.

Anne walksalong behindAnn fuming!

8:31:05. Anne pushes Ann into the timemachine on the right side of the path. The time machine has been preset to senda time traveler back 5 seconds.

Startled Anntravels backin time. Shequicklychanges hername to Anne.

8:31:08. Anne continues walkingon to work along the path!

Idea from: Cosmic Wormholesby Paul Halpern

Albert Einstein, in his later years, was unable to figureout why, if he was so smart and so famous, he wasn’t rich.

How to Get Rich With a Time Machineand Get Four Times More Out of Life

December 27, 2007. Scrooge #1 has $1,000

10:00 am, January 2, 2008. Scrooge #1 deposits $1,000 into bank account #13.

10:00 am, January 2, 2009. Scrooge #1 withdraws $1,000 from bank account #13.He leaves the interest in the account.

January 3, 2009. Scrooge #1 gets into a time machine with $1,000.

Scrooge #1travelsback intime.

BecomesScrooge #2.

11:00 am, Jan. 2, 2008.Scrooge #2 deposits

$1,000 in account #13.

12:00 am, Jan. 2, 2008.Scrooge #3 deposits

$1,000 in account #13.

1:00 pm,Jan. 2, 2008.Scrooge #4

deposits $1,000in account #13.

Four simultaneous versions of Scroogeexist. Each has deposited $1,000 inaccount #13. Interest accumulates on $4,000.The Scrooges can eat 4 bowls of chocolatechip ice cream at once!

9:30 am, Jan. 2, 2009. Scrooge #2 withdraws $1,000from account #13.

9:00 am, Jan. 2, 2009. Scrooge #3 withdraws $1,000from account #13.

Scrooge #2travels back

in time.Becomes

Scrooge #3.

Scrooge #3travels back

in time.Becomes

Scrooge #4.

Jan. 4, 2009. Scrooge #4 closes the account. He now has the original $1,000 plus the interest earned on $4,000 for one year.

Thinking About Time Machines

What Do TheyLook Like?

How does time progress within the time machine when the machine is traveling through time?

NOV 10 08:31:05 : :

The time traveler’s own digitalclock advances normally.

The clock showing progression of timeoutside the time machine exhibits

rapidly changing digits. Often, they change so rapidly they are blurred!

Question: How much time does a time traveler spend in each epoch as he travels through time?

What happens at the boundary of the time machine?

Normal TimeTime“flies”

Time“flies” Normal Time

Magnified wallof time machine

Normal Time? OrTime continuouslychanging ratewithin the wall?

Magnified wallof time machine

Someatomsin thewall ofthe timemachinewheretime isnormal.

Some atomsoutside thetime machinewhere time“flies” forwardor backward

Do these atoms interact?They’re right next to

each other?

If you roll down the window and stick your headout of the time machine, what happens?

After the time machine leaves the present what is left in its place?

One nanosecond beforethe time machine beginsto travel:

The material constituents of thetime machine occupy space andprevent surrounding matter fromoccupying the same space.

One nanosecond after thetime machine begins traveling:

The material constituents of the timemachine are no longer present. Is amomentary perfect vacuum left behind?Does a sudden implosion result?

Perfect vacuum?

How to create a perfect vacuum with a time machine:

A time machinetightly enclosed insome larger container.

When the timemachine leavesa perfect vacuumis left within thecontainer.

When the time machine arrives at its temporaldestination, does it displace matter already there?

What if the time machine arrivesin the midst of a nuclear explosion?

What if the time machine arrives inthe middle of a dinosaur’s gut?

Does the mass (or charge) of a traveling time machine have gravitational or electric effects on the epochs

through which the time machine travels?

Time machine just passing through exerts a gravitational pull on some dominoscausing them to fall over!

Question: Could “missing mass” be caused by the gravitational effects of multitudes of time traveling masses passing through our epoch?

What happens if one time machine is nested inside another?

Time machine #1 travelsforward in time.

Time machine #2travels back in time.

If the forward and backwardtime travel rates of the two time

machines are equal, will timemachine #2 remain in the “present”

surrounded by a region (green)which moves toward the future?

Is there a “velocity addition law” for time travel rates?

Time machine #2travels forward in

time at rate R2.

Time machine #1 travelsforward in time at rate R1.

Does the rate of forward time travel fortime machine #2 (relative to the “present”)

equal R1 + R2 ?

Is there an upper limit on the rate oftime travel as there is for travel

through space?

What do we mean by a time travel rate anyway?

Rate of travel through space ~ Velocity ~ in meters/second

Rate of travel through time ~ ???????? ~ in seconds/second

This measures how many seconds of time outside the time machineelapse during one second of time within the time machine. But a“second per second” has no units!!??

Understanding by analogy?

The slope of a hill ~ Gradient ~ is measured in meters/meter

The fractional change of length ~ Strain ~ is measured in meters/meter

But ...

The idea of a time gradient would require more than one time dimension!!!

The idea of a time strain requires time to expand or compress???

What happens when time machines collide?

Time machine #1 travelsforward in time.

Time machine #2 travelsback in time.

?

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?

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Is there some intermediate timetravel rate in this collision region?

Do the left and right halves ofthe time travelers travel at

different rates??

Are they smeared out in time?

Does spatial location change during the journey through time?

The End