Todd Thompson
Department of Astronomy
The Ohio State University

Key Ideas

Travel into the future:

Permitted by General Relativity

Relativistic starships or strong gravitation

Travel back to the past:

Possible if wormholes exist

The Grandfather Paradox

Hawking's Chronology Protection Conjecture

Into the future...

Can we get there faster?

• What if you want to celebrate new years in 3000?
• Simple: slow your clock down relative to the clocks around you.

This is permitted by classical General Relativity

Accelerated Clocks

• Accelerated clocks run at a slower rate than a clock moving with a uniform velocity.
• Example: on-board clocks on GPS satellites tick faster on orbit than they did on the ground before launch

Choice of accelerated reference frames:

• Starship accelerated to relativistic (near-light) speeds
• Close proximity to a very strongly gravitating body (e.g., black holes)

We can explore these possibilities with a few simple thought experiments.

A Journey to the Galactic Center

Jane is 20, Dick is 22.

Jane stays on Earth.

Dick flies to the Galactic Center 8 kpc away:

• Accelerates at 1g half way, then
• Decelerates at 1g rest of the way.
• Studies the Galactic Center for 1 year, then
• Returns to Earth by the same route.

The Future

• Round trip (including 1 year of exploring) takes about 42 yrs
• He is 22+42 = 64 years old on his return.

Meanwhile back on Earth, as measured by Jane's clock:

• Dick's round trip takes about 56,000 years
• Jane died long long ago.

Requirements of Starship

• 1 g for 10 years accelerates the ship close to the speed of light
• The energy requirements are enormous.
• Even a hypothetical matter-antimatter drive (~10% efficient) requires 1.5x10¹³ metric tons of fuel mass for each 1000 MT of payload (this fuel mass is equivalent to an asteroid ~2km across).

Back to the Past...

To travel to the past, you have to run your clock backwards:

• Requires faster-than-light travel
• This is physically impossible according to Relativity.

Wormholes

• Like a black hole with no singularity.
• Two singularities join across "hyperspace" and annihilate each other.
• Wormhole grows in size then starts to contract
• Pinches off into 2 singularities again

Wormholes are formally allowed by General Relativity, but they don't last very long.

If any radiation or ordinary matter enters a wormhole, it hastens the pinch-off:

• Normal matter or light has "positive energy density" (increases local gravity).
• If you try to fly into a wormhole, it will slam shut in your face and you will die.

Exotic Matter might have "negative energy density" in some frames of reference:

• It could be used to hold open the walls of the wormhole, allowing you to pass through.

The Cosmic Shortcut

• Consider a wormhole, with one mouth at Earth and the other at Vega.
• The distance from Earth to Vega is 26 light years through ordinary space.
• The distance through the wormhole might be only 1 km.

This gives you a way to get around (in a way) the vast distances separating objects in space.

A wormhole and exotic matter provide a way to make a type of time machine.

A Journey to the Galactic Center II

• Dick carries one end on his starship.
• Jane keeps the other end on Earth.

As Dick travels, they talk via the wormhole:

• Since it stays 1-meter long, they agree on the time when talking through the wormhole.
• Neither is accelerated relative to each other.

Dick leaves in 2002 & undertakes his 42 year journey to the Galactic Center.

The "Grandfather Paradox"

• Jane's son grows up to become an evil psychopathic genius who invents a way to manipulate wormholes using exotic matter in 2015.
• One day in 1920, a wormhole opens into a small midwestern town, & a huge, heavily-armed cyborg pops out and murders a small child who would have grown up to become Dick & Jane's father.

If their father never reaches maturity, and Dick & Jane are never born, then how can Jane's future son create the wormhole and cyborg that kills his grandfather as a child?

Hawking's "Chronology Protection Conjecture"

• The laws of General Relativity permit the construction of classical time machines (e.g., wormholes using exotic matter)

• However, the laws of Quantum Gravity forbid the construction of such time machines (quantum fluctuations circulate through & destroy them)

It thus "keeps the world safe for historians"

In other words, the appearance of the Grandfather paradox in classical General Relativity gives us a hint as to one of the properties a Quantum Theory of Gravity might have. Since we do not yet have such a theory, having such hints is most useful.

Alternative Histories Hypothesis

This is a cheap way of avoiding Chronology Protection:

• In Universe 1: a cyborg pops out of a wormhole in 1920 and blows away Dick & Jane's father as a child, and Dick & Jane are never born.

• In Universe 2: a cyborg enters a wormhole in 2015 and vanishes. Dick & Jane's father lived to be 85 and had 10 grandchildren.

Wormholes connect the alternative universes.

Silliness aside...

• They help lead us to deeper investigations of otherwise neglected corners of our ideas of space, time, and gravity. There is no reason to believe we have exhausted the possibilities inherent in General Relativity.

• Can illuminate problems or limitations of our ideas (e.g., classical vs. quantum approaches).

• It can even lead to surprising results. Black holes were one such surprising result of classical General Relativity, are there others?

My thanks to Prof. Barbara Ryden and Prof. Rick Pogge who allowed me to adapt their lectures on this topic for this class.