"It is possible to create in our immediate environment any
configuration of matter that the laws of physics permit locally,
without reference to what the rest of the universe may be doing" (Deutch).
(this is really "free will" principle).
Most of time machines violate AP.
Deutch considers Everetts multi-universe interpretation of
quantum mechanics as a remedy.
Billiard ball experiment/crisis
Any (thought) experiment that involves a classical ball entering a time
machine (typically a wormhole TM) so that at the exit
("at previous times") it collides with its entering copy.
It is the Grandpa Paradox reduced to classical mechanics (no free will
involved), used to test theories in the presence of time machines.
Introduced by J. Polchinski as a "pool-ball crisis."
Black hole
A solution of Einstein equations, first obtained (to Einstein's surprise)
by Schwarzschild 1917, that correspond to a heavy collapsing body.
The existence of black holes was predicted already by Rev. John Michell
in 1783 within the Newtonian physics.
S. Chandrasekhar (Nobel prize 19??) established that stars of
1.4 solar mass are doomed to form a BH rather than end up as white dwarves.
Centers of galaxies are believed to host big BHs.
The "mathematical" black holes (i.e., solutions to field equations)
come in a few flavors:
Schwarzschild BH.
Formed by a nonrotating matter.
Possesses an event horizon and a singularity.
No direct interest for TM.
Kerr BH.
Formed by a rotating matter.
Possesses a ring singularity.
Of direct interest for time travelers since it permits close timelike curves
(trough the ring).
Reissner-Nordstrom BH.
Formed by a non rotating but electrically charged matter.
When collapsing, such arrangement forms a Cauchy horizon
Formation of closed timelike curves is uncertain.
Casimir effect
Two metal plates placed extremely close to each other will induce
attracting force due to fluctuational quantum nature of vacuum.
Can be understood as a repulsive Casimir energy of the vacuum
outside the enclosed region and therefore
mentioned as a source of negative energy needed for
construction some of the TMs (like traversable wormhole or warp drive).
Cauchy horizon
A boundary of a region of space-time beyond which the prediction of motion
cannot be extended. Often coincides with the chronology horizon.
Chronology horizon
A boundary of a region of space-time which admits close timelike curves.
Often coincides with the Cauchy horizon, and previously (wrongly) identified.
Chronology protection conjecture
Term introduced by Stephen Hawking (1991).
It states that solutions to GTG that permit time-like closed curves
are physically meaningless.
In other words: our world does not permit time machines.
Strongly advocated by Hawking:
"the universe is save for historians"
but based purely on his 'common sense':
"where are the hordes of tourists from the future?"
This argument is obviously in disagreement with the principle that one
cannot travel to times before the machine was constructed.
A specification of Niven's Law well-known among S-F fans.
Chronology violating spacetime
A spacetime that admits closed time-like curves, i.e. curves that could
represent an actual "observer."
The first CVS was proposed by Kurt Goedel, after he befriended Einstein
and his theory (1917).
Closed causal curve paradox
Self conceiving. Something out of nothing. Two types:
1) matter; 2) information
Closed timelike curve
A closed curve in spacetime that is permitted by a particular
spacetime as a trajectory of an object.
Only st with a timemachine permits a ctc.
Cosmological constant (Lambda)
Proposed by Einstein in 1917 to save his theory.
Equation Curv= 4pi T +Lambda*g would allow for a static universe,
which Einstein believed to be our universe.
In 1940 Hubbell showed otherwise.
Einstein judged his introduction of Lambda as his "greatest mistake."
Einstein-Rosen bridge
The formal (older) name of a wormhole.
Exotic matter
A hypothetical matter that has negative energy
and exerts repulsive gravitational force.
Important in construction of many time machines,
including one based on traversable worm hole.
Introduced by K. Thorne.
F-locality condition
Proposed by Kay as a mathematical implementation of a philosophical
bias related to the equivalence principle,
(called also "GH-equivalence principle"),
which is often used to build a generalization of quantum field
theory to nonglobally hyperbolic spacetimes.
Friedman-Paastatiou-Simon theorem
(for frie scalar field), the unitarity of quantum mechanics
follows from the fact that classical evolution preserves
Klein-Gordon inner product.
(recall that quantum mechanics at the presence of time machine is non-unitary).
Goedel universe (time machine)
Hypothetical universe that admits time travel into past. It is infinite,
static (not expanding), rotating, with nonzero cosmological constant
(our is expanding).
Goedel was among first fascinated by the possible physical basis of time travel.
In his invited essay on Einstein's work (1949),
introduced "grandpa paradox."
Gott time machine
Two cosmic strings that pass each other with the velocity near c
produce time-like close curves, hence may be considered as a TM.
Good sides: no cosmological cosmological constant, exotic matter, etc
(besides the controversy of existing of the cosmic strings).
Bad sides: no way to construct one. Use it only if you encounter one!
Grandpa paradox
Killing your ancestors long before you are conceived.
Previously known as a "matricide paradox," renamed by gender-sensitive
authors who seem to be unaware of the old adage that "only mother is certain."
Kay, Radzikowski, and Wald theorem
Implies that time machines with compactly generated Cauchy horizons
are incompatible with the F-locality condition.
cited by some in support of the "chronology protection conjecture,"
but other claim that the F-locality
condition must be modified or abandoned.
Lense-Thiring effect
Discovered in 1918 by Joseph Lense and Hans Thiring.
Rotation of matter may lead to closed time-like curves.
Such time machines as Goedel universe, Kerr black hole,
Tipler's rotating cylinder are examples of Lense-Thiring effect in action.
Actually, one may add Gott's time machine, for a couple of cosmic strings
passing each other has a rather enormous angular momentum as a system.
MF-locality condition
Proposed by Krasnikov. Replacing the F-locality
condition with the MF-locality condition leads to theories
consistent with both locality and the existence
of time machines.
Niven's law
If a universe permits time travel,
then no time machine will be invented in that universe.
Introduced by a hard S-F writer Larry Niven.
It is a strong version of Sophoclean principle.
It became in Stephen Hawking's writing a
chronology protection conjecture after a specification.
Newman-Unti-Tamburino universe
(also called somewhat sarcastically a NUT universe)
A solution to Einstein equations.
A black hole resides in space, a trip around it would lead a traveler
to a new sheet of space (like in spiral staircase, similarly to Riemann surfaces)
The NUT universe is a time machine as it permits closed timelike curves.
Novikov consistency conjecture
(principle of self-consistency)
"You cannot change recorded history,"
"there is only one history of the universe."
Closed timelike curves exist, but physics laws must somehow
prevent time travel paradoxes.
Considered most often in the context of quantum mechanics and
its interpretations.
Ori-Soen time machine
A time machine with asymptotically flat space-time and a toroidal
region of altered geometry.
Does not require exotic matter,
as it does not violate the weak energy condition.
Quantum time machine
As suggested by Aharomov, quantum mechanics admits
in the microscale a rapid jumps to the future or the past.
Unpredictability makes this principle rather useless as
a controlled machine for time travel.
Self-consistency principle
Local solutions to the equations of physics may be realized in the real
universe only if they can be extended to global solutions.
Sophoclean mechanism
Knowing the future does not help to change it, for the knowledge is
inscribed into the whole narration of the world.
Well, nature abhors paradoxes and has her ways to prevent them
(heart attack of the potential killer of his own ancestors inside the TM,
confused personalities, etc.
Strong Energy Condition
Assumption that gravitational forces are always attractive (and not repulsive).
Antimatter is believed to obey SEC.
A matter that would violate SEC is nicknamed "exotic matter."
and is required to build a stable traversable wormhole.
Strong cosmic censorship
Solutions to Einstein's field theory must be of global hyperbolicity.
(advocated by R. Penrose).
This would imply existence of global time function and hence exclude
closed timelike curves (time travel).
Time bomb paradox
A (thought) experiment of throwing a time bomb into a time machine
with its detonating mechanism set so that it will destroy its entering copy.
It is to show that removing free-will (see Billiard experiment)
does not reduce the Grandpa paradox.
Time machine
A region of space-time that permits a close time-like curves
("nonchronological region").
Also, a nickname of any spacetime that permits close timelike curves.
Called also a "chronology violating spacetime."
Traversable wormhole
A wormhole with the tidal forces small enough to allow a save passage
of a potential traveler. Typically, tidal forces would tear a traveler
into pieces.
Tourists from the future argument
"Where are the hordes of tourists from the future?"
This argument (forwarded among others by S. Hawking)
against the possible exisdtence of time machines
has obvious holes:
one cannot travel to times before the machine was constructed!
Van Stokum time machine
A time machine based on an infinite rotating cylinder.
Walking around such a cylinder can lead to a close timelike curve.
Based on Lense-Thiring effect. Ordinary matter used,
however of incredible density.
A 100 km long cigar of radius could be a good physical
implementation of TRS, it would require matter 10^8 times more dense
than the nuclear matter.
Warp drive
A region of space that "moves" with respect to the rest of space with
arbitrary velocity. Discovered as a solution to GFT by Alcubierre (1994)
and proposed as a time machine by Everett (1996).
It requires exotic matter, like wormhole time machine, but forms
a new family of time machines that do not change the ST topology.
Weak energy condition
Condition that mass-energy density should be nonnegative for any observer.
Once almost a "law of physics." Construction of a stable wormhole
(and wormhole time machine) must violate WEC.
Casimir effect, observed in nature, does too, giving some hopes for WTM.
Wormhole time machine
A wormhole (Einstein-Rosen bridge) whose mouths reside in the same
universe, but have a time difference between them
(due to motion of--, or presence of a massive body at-- one of them).
A single wormhole makes a closed space into S1 x S2.
