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Galaxy NGC4414 from HST Astronomy 162:
Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30

Lecture 42: Time Travel

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...

We are traveling into the future right now without trying very hard.

Can we get there faster?

This is permitted by classical General Relativity

Accelerated Clocks

According to General Relativity:

Choice of accelerated reference frames:

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

A Journey to the Galactic Center

Jane is 20, Dick is 22.

Jane is in charge of Mission Control.

Dick flies to the Galactic Center 8 kpc away:

Planet of the Warthogs

As measured by Dick's accelerated clock:

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

Starship Party-poopers

The trip described is physically possible, but technologically infeasible for our culture:

Back to the Past...

Acceleration makes a clock run more slowly, but it still runs forward.

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


A wormhole is a tunnel of spacetime that connect two widely separated points.

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

A Foot in the Door...

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

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

The Cosmic Shortcut

With exotic matter, you [or at least some extremely advanced civilization] might be able to use wormholes for space & time travel:

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 & Jane share a 1-meter wormhole:

As Dick travels, they talk via the wormhole:

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

The Time Machine

When Dick returns to Earth:

The "Grandfather Paradox"

Dick and Jane grow up, get married (to other people), and have kids. The Paradox:

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"

As a way to avoid the obvious absurdity of the Grandfather paradox, Stephen Hawking has proposed the "Chronology Protection Conjecture":

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

Another way out, preserving the wormhole with exotic matter time machine, is the "Alternative Histories Hypothesis".

This is a cheap way of avoiding Chronology Protection:

Wormholes connect the alternative universes.

Silliness aside...

Even seemingly fanciful scenarios as exotic matter and quantum wormholes serve useful purposes in science:
If you would like to read more about some of these ideas, which are being taken more seriously than you might imagine, I strongly recommend Black Holes & Time Warps; Einstein's Outrageous Legacy, by Caltech astrophysicist Kip Thorne. Kip's book is wonderfully written and engaging (he was also one of the most gifted teachers I had at Caltech).

My thanks to Prof. Barbara Ryden who allowed me to adapt her own lecture on this topic for this class.

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Updated: 2006 March 5
Copyright Richard W. Pogge, All Rights Reserved.