Lecture 40: Science Fact or
Science Fiction?
Time Travel
Key Ideas
Travel into the future:
Permitted by General
Relativity
Relativistic
starships or strong gravitation
Travel back to the past
Might be possible
with stable wormholes
The Grandfather Paradox
HawkingÕs Chronology
Protection Conjecture
Into the futureÉ.
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
Special and General Relativity
Accelerated Clocks
According to General
Relativity
Accelerated
clocks run at a slower rate than a
clock moving with uniform velocity
Choice of accelerated
reference frames:
Starship accelerated
to relativistic (near-light) speeds
Close proximity to a
very strongly gravitating body (e.g. black holes)
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 DickÕs
accelerated clock:
Round trip
(including 1 year of study) takes ~42 years
He return at age
22+42=64 years old
Meanwhile back on Earth:
DickÕs trip takes
~52,000 yrs
Jane died long, long
ago
After
a nuclear war, humans have been replaced by sentient warthogs as the dominant
species
Advantages to taking Astro
162
Dick was smart and took Astro
162
Dick knew about accelerating
clocks running slow, and so he could conclude ÒAh, thereÕs been a nuclear war
and humans have been replaced by warthogsÓ.
Unlike Charlton Heston in Planet
of the Apes
Starship Party-poopers
The trip described is
physically possible, but technologically infeasible for our culture:
1 g for 10 years
accelerates the ship to 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 (about an asteroid 2km
across of fuel mass)
Back to the PastÉ
Acceleration makes a clock
run more slowly, but it still runs forward.
To travel to the past, you
have to run your clock backwards.
Requires
faster-than-light travel
This is physically
impossible according to classical Relativity
Wormholes
Tunnel of spacetime that
connect two widely separated points:
Like a black hole
with no singularity
Two singularities
join across ÒhyperspaceÓ and annihilate each other
Wormhole grows in
size then starts to contract
Pinches off into 2
singularities again
Allowed by GR, but they donÕt
last very long
A Foot in the Door É
If any radiation or ordinary
matter enters a wormhole, it hastens the pinch-off.
Normal matter or
light has Òpositive energyÓ
If
you try to fly into a wormhole, it will slam shut in your face and you will
die.
Exotic Matter might have
Ònegative energyÓ
Could
hold open the walls of the wormhole, allowing you to pass through.
The Cosmic Shortcut
With exotic matter, you can
use wormholes for space & time travel:
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.
Way to build a type of
time machine
Journey to the Galactic
Center II
Dick & Jane share a
1-meter wormhole.
Dick carries one end
on the starship.
Jane keeps the other
end on Earth.
As Dick travels, they talk
via the wormhole:
It
stays 1-meter long, so they agree on the time when talking through the
wormhole.
Neither
is accelerated relative to each other.
Dick leaves in 2006 on his
42-year journey
The Time Machine
Dick returns to Earth:
He asks Jane through
the wormhole what time it is.
She says ÒSeptember
2048Ó
Dick pops the hatch and asks
a passing warthog what time it is:
The warthog says
ÒGrunt grunt snuffle snortÓ
==ÓSeptember57428,
monkey-boyÓ
Dick crawls through the
wormhole back to Earth where it is September 2048.
The ÒGrandfather ParadoxÓ
Dick and Jane grow up, get
married (to other people), and have kids.
JaneÕs
son becomes an evil psychopathic genius who invents a way to manipulate
wormholes using exotic matter in 2015.
One
day in 1920, a wormhole opens in to a small Midwestern town, a heavily armed
cyborg with an Austrian accent pops out and murders the small child who would
have become Dick & JaneÕs father.
If their father never reaches
maturity, and D&J are never born, how can Jane's future son create the
wormhole and cyborg that kills his grandfather as a child?
This
sort of thing obviously doesnÕt bother James Cameron or Captain Kirk one little
bit.
It
does, however, give Stephen Hawking the screaming willies.
HawkingÕs discontent, or
The ÒChronology Protection
ConjectureÓ
The
laws of General Relativity permit the construction of classical time machines
(e.g. wormholes using exotic matter)
The
laws of Quantum Gravity, however, must forbid the construction of time machines (quantum
fluctuations circulate through & destroy them)
ÒKeeps the world safe for
historiansÓ
Alternative Histories
Hypothesis
A way of avoiding Chronology
Protection:
In
Universe 1: a cyborg pops out of a wormhole in 1920 and kills Dick &
JaneÕs father as a child; Dick & Jane are never born.
In
Universe 2: a cyborg enters a wormhole in 2015 and vanishes. Dick &
JaneÕs father lives to be 85 and has 10 grandchildren.
The wormholes connect the two
alternate universes.
Silliness aside
Even seemingly fanciful
scenarios as exotic matter and quantum wormholes serve useful purposes in
science:
Lead
to deeper investigation of otherwise neglected corners of our ideas of space,
time and gravity.
Can
illuminate problems or limitations of our ideas (classical vs. quantum
approaches)
It
can even lead to surprising results.
You never know where an
idea will leadÉ.