Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30
Lecture 42: Time Travel
- 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?
- 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
According to General Relativity:
- 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 is in charge of Mission Control.
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.
Planet of the Warthogs
As measured by Dick's accelerated clock:
- 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.
- After a nuclear war, humans have been replaced by sentient warthogs as
the dominant species.
The trip described is physically possible, but technologically
infeasible for our culture:
- 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...
Acceleration makes a clock run more slowly, but it still runs
To travel to the past, you have to run your clock backwards:
- Requires faster-than-light travel
- This is physically impossible according to Relativity.
A wormhole is a tunnel of spacetime that connect two widely
- 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.
A Foot in the Door...
If any radiation or ordinary matter enters a wormhole, it hastens
- Normal matter or light has "positive energy density"
- 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
- It could be used to hold open the walls of the wormhole, allowing you
to pass through.
The Cosmic Shortcut
With exotic matter, you [or at least some extremely advanced
civilization] might be able to use wormholes for space & time
- Consider a wormhole, with one mouth at Earth and the other at Vega.
- The distance from Earth to Vega is 26 light years through
- 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 & Jane share a 1-meter wormhole:
- 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
The Time Machine
When Dick returns to Earth:
- He asks Jane through the wormhole what time it is. She says: "September
- He then pops the hatch and asks a passing warthog what time it is. He
says: "Grunt grunt snuffle snort" [Translation: "September 57428,
- Dick crawls through the wormhole, back to Earth, September 2044.
- Jane could also use the wormhole in reverse to visit September 57428
by way of the starship.
The "Grandfather Paradox"
Dick and Jane grow up, get married (to other people), and have kids.
- Jane's son grows up to becomes 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?
- This sort of thing obviously doesn't bother James Cameron or
Captain Kirk one little bit.
- It does, however, give Stephen Hawking the screaming willies.
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":
- 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
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:
- 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
- In Universe 2: a cyborg enters a wormhole in 2015 and
vanishes. Dick & Jane's father lived to be 85 and had 10
Wormholes connect the alternative universes.
Even seemingly fanciful scenarios as exotic matter and quantum wormholes
serve useful purposes in science:
- 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
- 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?
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
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.