Download Wormhole Physics - In Classical and Quantum Theories of Gravity

Wormhole Physics
Quantum Wormhole Physics
Summary
Wormhole Physics
In Classical and Quantum Theories of Gravity
S. Al Saleh
A. Mahrousseh
L.A. Al Asfar
Department of Physics and Astronomey ,King Saud University
The 100th Anniversary of General Relativity.
The 30th of November, 2015
Wormhole Physics
Quantum Wormhole Physics
Outline
Wormhole Physics
Introduction
What are Wormholes?
Can Einstein Rosen Bridges Allow Spacetime Travel ?
Traversable wormholes
Wormhole and Time Travel
Quantum Wormhole Physics
Preliminaries
Mathematical and Physical Results
Summary
Wormhole Physics
Quantum Wormhole Physics
Outline
Wormhole Physics
Introduction
What are Wormholes?
Can Einstein Rosen Bridges Allow Spacetime Travel ?
Traversable wormholes
Wormhole and Time Travel
Quantum Wormhole Physics
Preliminaries
Mathematical and Physical Results
Summary
Wormhole Physics
Quantum Wormhole Physics
Summary
Introduction
• Einstein’s Theory of general relativity is one of the most
magnificent achievements humanity had ever encountered. It
demonstrates the marriage between matter and background
geometry. Matter and spacetime had became one!
G µν = κT µν
(1)
• These equations (1) were published a 100 years from today
[3]. Are known as the Einstein Field Equations.Although They
are not the only equations for gravity. But they are the only
tested ones.[10].
Wormhole Physics
Quantum Wormhole Physics
Summary
Introduction
Many solutions to (1) were found, a lot of them were very
interesting and related to observations. But one solution was so
strange that Einstein himself was very skeptical about. This
solution is called the Schwazchild solution It predicted the
existence of Black holes a very dense object having an enormous
gravity even spacetime will not make sense because of it! Later, in
1935 Einstein and Rosen [4] studied the extension of Schwarzchild
solution to predict an even stranger object, knows as
Einstein-Rosen Bridge. Or what is known as a Wormhole.
Wormhole Physics
Quantum Wormhole Physics
r =0
III
=
=
u
∞
i+
J+
Summary
u
0
i0
II
I
v
=
0
−
IV
u
=
∞
J−
i−
r =0
Figure: Penrose diagram of the maximally- extended Schwarzchild
solution, demonstrating two universes with an Einstein-Rosen Bridge .
Wormhole Physics
Quantum Wormhole Physics
Outline
Wormhole Physics
Introduction
What are Wormholes?
Can Einstein Rosen Bridges Allow Spacetime Travel ?
Traversable wormholes
Wormhole and Time Travel
Quantum Wormhole Physics
Preliminaries
Mathematical and Physical Results
Summary
Wormhole Physics
Quantum Wormhole Physics
Definition of a Wormhole
• We can start with a mathematical definition of a wormhole,
Definition ( Einstein-Rosen Bridge)
A compact region of Minkowskian spacetime Ω is homeomorphic
to R × Σ. Where Σ having non-trivial topology and boundary
∂Σ ' S 2 . All hyper surfaces Σ are spacelike/ The region Ω is
called a Wormhole / Einstein-Rosen Bridge .
Summary
Wormhole Physics
Quantum Wormhole Physics
Summary
Definition of a Wormhole
• We can start with a mathematical definition of a wormhole,
Definition ( Einstein-Rosen Bridge)
A compact region of Minkowskian spacetime Ω is homeomorphic
to R × Σ. Where Σ having non-trivial topology and boundary
∂Σ ' S 2 . All hyper surfaces Σ are spacelike/ The region Ω is
called a Wormhole / Einstein-Rosen Bridge .
• Despite the abstractness of this definition. It contain a lot of
insight of the physics and geometry of a wormhole. This
definition describes exactly what one pictures a wormhole to
”look like”
Wormhole Physics
Quantum Wormhole Physics
The picture that approximate what the previous definition
describes:
Summary
Wormhole Physics
Quantum Wormhole Physics
Summary
• It is not required to have two separate spaces connected by an
ER bridge. We can imagine such topologies forming with a
single space. It is similar to folding a paper and making a
”shortcut” route between two distant points.
• This will make our spacetime multiply connected!
Wormhole Physics
Quantum Wormhole Physics
Outline
Wormhole Physics
Introduction
What are Wormholes?
Can Einstein Rosen Bridges Allow Spacetime Travel ?
Traversable wormholes
Wormhole and Time Travel
Quantum Wormhole Physics
Preliminaries
Mathematical and Physical Results
Summary
Wormhole Physics
Quantum Wormhole Physics
Summary
Schwazchild Wormholes
• A paper by Wheeler and Fuller had shown that ER bridges
resulting from Schwazchild solutions are unstable. They will
pinch off very quickly at the speed of light. and Not allowing
any information to pass through the other side [6].
Wormhole Physics
Quantum Wormhole Physics
Summary
Schwazchild Wormholes
• A paper by Wheeler and Fuller had shown that ER bridges
resulting from Schwazchild solutions are unstable. They will
pinch off very quickly at the speed of light. and Not allowing
any information to pass through the other side [6].
• In other words, the ”bridge” connecting the two black holes
will keep getting longer and longer at the speed of light. Such
that no particle entering one side is able to cross the other
one.
Wormhole Physics
Quantum Wormhole Physics
Wormholes In Einstien-Cartan Theory
• General Relativity is not the only theory of gravitation.
Einstein-Cartan theory is an alternative one. It is a
modification of EFE’s by including how spin couples to the
geometry of spacetime via changing its torsion.
Summary
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Quantum Wormhole Physics
Wormholes In Einstien-Cartan Theory
• General Relativity is not the only theory of gravitation.
Einstein-Cartan theory is an alternative one. It is a
modification of EFE’s by including how spin couples to the
geometry of spacetime via changing its torsion.
• In this theory, the gravitational singularity formed by a
collapsing matter of the blackhole cannot form due to the
coupling of spin of the fermions. Instead, the collapsing
matter bounces back and forms an Einstein-Rosen Bridge as
well. Hence, every black hole in Einstein -Cartan theory is a
wormhole.[15]
Summary
Wormhole Physics
Quantum Wormhole Physics
Outline
Wormhole Physics
Introduction
What are Wormholes?
Can Einstein Rosen Bridges Allow Spacetime Travel ?
Traversable wormholes
Wormhole and Time Travel
Quantum Wormhole Physics
Preliminaries
Mathematical and Physical Results
Summary
Wormhole Physics
Quantum Wormhole Physics
Summary
Traversable wormholes
A Traversable wormhole is a wormhole that allow matter and
information to cross from one mouth to the other one.
Figure: Image of a simulated traversable wormhole that connects the
square in front of the physical institutes of University of Tbingen with the
sand dunes near Boulogne sur Mer in the north of France. Here the
gravito-optical effects are ignored.
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Summary
Examples of Traversable Wormholes
• Traversable wormholes seem not to exist naturally. As there is
no known natural cosmological process that allows them to
form (unlike black holes)
Wormhole Physics
Quantum Wormhole Physics
Summary
Examples of Traversable Wormholes
• Traversable wormholes seem not to exist naturally. As there is
no known natural cosmological process that allows them to
form (unlike black holes)
• However, semi-classical theories of gravity that predicts more
than 3+1 D of spacetime such as Gauss Bonnet gravity[12][7]
predict the existence of trasversable wormholes with ordinary
matter or even without matter!
Wormhole Physics
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Summary
Examples of Traversable Wormholes
• Traversable wormholes seem not to exist naturally. As there is
no known natural cosmological process that allows them to
form (unlike black holes)
• However, semi-classical theories of gravity that predicts more
than 3+1 D of spacetime such as Gauss Bonnet gravity[12][7]
predict the existence of trasversable wormholes with ordinary
matter or even without matter!
• Moreover, Brane cosmology theories allow traversable
wormholes open by cosmic strings of negatives mass . [15]
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Summary
Examples of Wormholes
• In General Relativity however, it is required to have wormholes
made from exotic matter to be stable and allow
transportation. Such wormholes are knows are Morris-Torn
wormholes [18] [14]
Wormhole Physics
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Summary
Examples of Wormholes
• In General Relativity however, it is required to have wormholes
made from exotic matter to be stable and allow
transportation. Such wormholes are knows are Morris-Torn
wormholes [18] [14]
• Wormholes do not only connect two distinct spacelike points
in one universe. They could link distinct ”times” or spacetime
points in multiverse. For example, if the spacetime is multiply
connected at the quantum information inside a blackhole
could ” leak out ” to other universes by going into a
wormhole.
Wormhole Physics
Quantum Wormhole Physics
Outline
Wormhole Physics
Introduction
What are Wormholes?
Can Einstein Rosen Bridges Allow Spacetime Travel ?
Traversable wormholes
Wormhole and Time Travel
Quantum Wormhole Physics
Preliminaries
Mathematical and Physical Results
Summary
Wormhole Physics
Quantum Wormhole Physics
Summary
The Concept of Causality
Closed timelike curves:
In a future-directed Lorentzian spacetime. A closed timelike curve
( CTC) is a world line of a particle that allows it to ”return” to
the starting timelike point. In other words, the future of that
particle lies in its past !
Wormhole Physics
Quantum Wormhole Physics
Summary
The Concept of Causality
Causality
Causality is a relation between two events. The first is called the
”cause” while the second is called the ”effect”. Causality requires
the cause proceeds the effect. Also due to relativity, they are
timelike or null like separated ( the effect lies in the light cone of
the other). CTC’s seems to classically violate causality.
Wormhole Physics
Quantum Wormhole Physics
Summary
The Concept of Causality
Causality
Causality is a relation between two events. The first is called the
”cause” while the second is called the ”effect”. Causality requires
the cause proceeds the effect. Also due to relativity, they are
timelike or null like separated ( the effect lies in the light cone of
the other). CTC’s seems to classically violate causality.
Causal relation between events (points on the spacetime manifold)
are equivalence relations. They are mathematical rules for the
points in the spacetime allows preservation of causality ( which is
rather a logical entity.)
The set of all the causal relations on the spacetime manifold is
called Causal Structure
Wormhole Physics
Quantum Wormhole Physics
Summary
Wormholes as Time Machines
• Let’s have a traversable wormhole with two mouths , A and
B. If B is accelerated with respect to A, or put near an
enormous gravity. The latter will be in different ”time” than
the first. Hence, A and B are not only spatially separated, but
also temporally.
Wormhole Physics
Quantum Wormhole Physics
Summary
Wormholes as Time Machines
• Let’s have a traversable wormhole with two mouths , A and
B. If B is accelerated with respect to A, or put near an
enormous gravity. The latter will be in different ”time” than
the first. Hence, A and B are not only spatially separated, but
also temporally.
Wormhole Physics
Quantum Wormhole Physics
Wormholes as Time Machines
• If an observer jumps in A and comes out in B. They will be
travelling back in time. This might not affect causality if A
and B are speacelike separated such as no immediate causal
connection between them is possible.
Summary
Wormhole Physics
Quantum Wormhole Physics
Wormholes as Time Machines
• If an observer jumps in A and comes out in B. They will be
travelling back in time. This might not affect causality if A
and B are speacelike separated such as no immediate causal
connection between them is possible.
• One might ask however about the mass/energy and charge
conservation in the universe at each ”time”. A traveller
through such wormhole might seem to violate those
conservation laws. Nevertheless, calculation [17][5] suggests
that the wormhole pays for the energy/charge/ angular
momentum of the traveller. This known from the no-hair
theorem .
Summary
Wormhole Physics
Quantum Wormhole Physics
Outline
Wormhole Physics
Introduction
What are Wormholes?
Can Einstein Rosen Bridges Allow Spacetime Travel ?
Traversable wormholes
Wormhole and Time Travel
Quantum Wormhole Physics
Preliminaries
Mathematical and Physical Results
Summary
Wormhole Physics
Quantum Wormhole Physics
Summary
Preliminaries: Quantum Entanglment
Pure states
A quantum particle is described by a state ray, or a ket |ψi . If one
has more than one particle. Their overall state is described by a
tensor ( direct) product. |ψi ⊗ |φi. Measurement of one particle
does not affect or give information about the other. This
configuration for states is knows as pure states.
Wormhole Physics
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Summary
Preliminaries: Quantum Entanglment
Entangeled states
However, there is another extreme configuration for quantum
states description of two particle system. Which is Bell Pair , the
two particles are described by one quantum state:
1
|Ψi = √ (|A, 1i|B, 0i + |A.0i|B, 1i)
2
(2)
Where A and B are the particles that take either state |0i or |1i. (
they are abstract information states/ bits).
Wormhole Physics
Quantum Wormhole Physics
Summary
Preliminaries: Quantum Entanglment
Theorem (Monogamy of Entanglement)
Let A be entangled to B, A ∼ B . This relation implies that if
B ∼ C ⇒ A = C . A particle cannot be maximally entangled with
more than one independent system.
This is an important result that we will be needing in the next
discussion. It shall unfold a deep connection between quantum
mechanics and wormholes.
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Summary
Preliminaries: Quantum vacuum
• The vacuum in quantum field theory is nothing but empty ! It
is composed of never-resting particles that pop-out from
nothing and disappear in short time. These particles are called
virtual particles or quantum fluctuations
Wormhole Physics
Quantum Wormhole Physics
Summary
Preliminaries: Quantum vacuum
• The vacuum in quantum field theory is nothing but empty ! It
is composed of never-resting particles that pop-out from
nothing and disappear in short time. These particles are called
virtual particles or quantum fluctuations
• One cannot detect those particles directly, unless a specific
experiment is conducted to affect or modify the vacuum so
that these particle effects appear e.g. Casimir effect.
Wormhole Physics
Quantum Wormhole Physics
Summary
Preliminaries: Quantum vacuum
• The vacuum in quantum field theory is nothing but empty ! It
is composed of never-resting particles that pop-out from
nothing and disappear in short time. These particles are called
virtual particles or quantum fluctuations
• One cannot detect those particles directly, unless a specific
experiment is conducted to affect or modify the vacuum so
that these particle effects appear e.g. Casimir effect.
• The quantum vacuum satisfies a special symmetry , called
conformal symmetry, one of the results of this symmetry that
each ”patch” of the vacuum is entangled with an opposite one
to it. When a boundary surface is taken into consideration.
Wormhole Physics
Quantum Wormhole Physics
Figure: A schematic showing a result of conformal symmetry of the
quantum vacuum. Every ”imaginary”patch is entangled with the one
opposite to it of the same size. Such that measurement for virtual
particle in one implies knowledge of the other.
Summary
Wormhole Physics
Quantum Wormhole Physics
Outline
Wormhole Physics
Introduction
What are Wormholes?
Can Einstein Rosen Bridges Allow Spacetime Travel ?
Traversable wormholes
Wormhole and Time Travel
Quantum Wormhole Physics
Preliminaries
Mathematical and Physical Results
Summary
Wormhole Physics
Quantum Wormhole Physics
Chronology Protection Conjecture
• Time-machine solutions and others (like Gödel solution to
EFE’s or Tippler’s Cylinder) seems to violate the causal
structure, but not the principles of relativity.
Summary
Wormhole Physics
Quantum Wormhole Physics
Summary
Chronology Protection Conjecture
• Time-machine solutions and others (like Gödel solution to
EFE’s or Tippler’s Cylinder) seems to violate the causal
structure, but not the principles of relativity.
• The causal structure is not rigorously proven, and seems to be
threatened by the above solutions
Wormhole Physics
Quantum Wormhole Physics
Summary
Chronology Protection Conjecture
• Time-machine solutions and others (like Gödel solution to
EFE’s or Tippler’s Cylinder) seems to violate the causal
structure, but not the principles of relativity.
• The causal structure is not rigorously proven, and seems to be
threatened by the above solutions
• Thus, S. Hawking had proposed a conjecture to save
chronology of the universe by the quantum effects that are
ignored in classical GR.[9]
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Quantum Wormhole Physics
Summary
When quantum correction to GR are taken into an account, closed
timelike cures will not be stable. As quantum field vacuum
fluctuations will be amplified and blow up to infinity [19] .
Nevertheless, some semi-classical calculations had shown that
some CTC’s do not do that [11]. It remains for a complete theory
of quantum gravity to solve this puzzle. ( String theory for
example seems to support chronology protection [2].)
Figure: A famous painting by Salvador dali La persistencia de la memoria.
Often linked to the arrow of time and our modern view of it
Wormhole Physics
Quantum Wormhole Physics
Summary
The figure below shows blue shift of normal modes fluctuations by
Minser spacetime that contains a CTC. This illustrates the
quantum effects contribution to chronology protection.
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Summary
Quantum Entanglment and Wormholes ER= EPR
• Quantum entanglement is not only for microsystems. One can
create macrosystems entangled by constructing them out of
entangled microsystems [16]
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Summary
Quantum Entanglment and Wormholes ER= EPR
• Quantum entanglement is not only for microsystems. One can
create macrosystems entangled by constructing them out of
entangled microsystems [16]
• It was shown that Blackholes decay via Hawking-Unruh
radiation. And that radiation is Entangled with the blackhole
matter [8]
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Quantum Wormhole Physics
Summary
Quantum Entanglment and Wormholes ER= EPR
• Quantum entanglement is not only for microsystems. One can
create macrosystems entangled by constructing them out of
entangled microsystems [16]
• It was shown that Blackholes decay via Hawking-Unruh
radiation. And that radiation is Entangled with the blackhole
matter [8]
• Hence, if we created two blackholes out of a collapsing
entangled matter. The blackholes will seem to violate one of
the well-tested principles Unitarity, General Covariance or
Quantum Field theory.
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Summary
Quantum Entanglment and Wormholes ER= EPR
To see this, recall that at the boundary of the blackhole - the event
horizon- the vacuum is assumed to behave well, and satisfy the
conformal symmetry discussed earlier. Therefore, and since the two
blackholes are entangled ( or similarly for hawking radiation) this
will go against the monogamy of entanglement.
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Summary
Quantum Entanglment and Wormholes ER= EPR
The previous paradox is knows as the Firewall Paradox or the
AMPS-from the paper authors’ names: Ahmed Almheiri, Donald
Marolf, Joseph Polchinski, and James Sully- paradox . It is a
serious threat to quantum feild theory and/or general relativity. [1].
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Summary
Quantum Entanglment and Wormholes ER= EPR
One of the most elegant and rather captivating solutions to the
AMPS paradox is suggested by Prof L. Susskind. This solution is
given a short name ER= EPR [13].
In his paper, Susskind shows that and Einstein-Rosen Bridge is
formed between two entangled blackholes. This resolves the
paradox by assuming the points A and C shown previously to be
one point . He even go further to generalise this result and give a
geometric meaning to entanglement as Plank-scale ER bridges
between particles.
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Summary
Summary
• The general theory of relativity had changed how we view
space and time Perhaps, wormholes could allow interstellar or
even intergalactic travel one day! .
• Paradoxes push theoretical physics forward, it makes scientists
think and discover solution that advances our understanding
of nature. Such as the chronology protection or ER=EPR.
• Outlook
• We need a complete theory of quantum gravity to be able to
fully understand spacetime.
• Plank-sized wormholes could be what makes up the spacetime
at the micro-scale and hold it together. In our current work,
we are trying to study the implications of this conjecture such
as Bekenstein-Hawking entropy counting assuming
multiply-connected spacetime.
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Quantum Wormhole Physics
Thank You !
Summary
Appendix
Ahmed Almheiri, Donald Marolf, Joseph Polchinski, and James
Sully.
Black holes: complementarity or firewalls?
Journal of High Energy Physics, 2013(2):1–20, 2013.
Marco M Caldarelli, Dietmar Klemm, and Pedro J Silva.
Chronology protection in anti-de sitter.
Classical and Quantum Gravity, 22(17):3461, 2005.
Albert Einstein.
Die grundlage der allgemeinen relativitätstheorie.
Annalen der Physik, 354(7):769–822, 1916.
Albert Einstein and Nathan Rosen.
The particle problem in the general theory of relativity.
Physical Review, 48(1):73, 1935.
Allen Everett and Thomas Roman.
Appendix
Time travel and warp drives: a scientific guide to shortcuts
through time and space.
University of Chicago Press, 2012.
Robert W Fuller and John A Wheeler.
Causality and multiply connected space-time.
Physical Review, 128(2):919, 1962.
Elias Gravanis and Steven Willison.
mass without mass from thin shells in gauss-bonnet gravity.
Physical Review D, 75(8):084025, 2007.
Stephen Hawking, Juan Maldacena, and Andrew Strominger.
Desitter entropy, quantum entanglement and ads/cft.
Journal of High Energy Physics, 2001(05):001, 2001.
Stephen W Hawking.
Chronology protection conjecture.
Physical Review D, 46(2):603, 1992.
Appendix
Michael Kramer.
Tests of general relativity.
In 25TH TEXAS SYMPOSIUM ON RELATIVISTIC
ASTROPHYSICS (TEXAS 2010), volume 1381, pages 84–97.
AIP Publishing, 2011.
Li-Xin Li.
Must time machines be unstable against vacuum fluctuations?
Classical and Quantum Gravity, 13(9):2563, 1996.
David Lovelock.
The einstein tensor and its generalizations.
Journal of Mathematical Physics, 12(3):498–501, 1971.
Juan Maldacena and Leonard Susskind.
Cool horizons for entangled black holes.
Fortschritte der Physik, 61(9):781–811, 2013.
Michael S Morris, Kip S Thorne, and Ulvi Yurtsever.
Appendix
Wormholes, time machines, and the weak energy condition.
Physical Review Letters, 61(13):1446, 1988.
Nikodem J Poplawski.
Cosmology with torsion: An alternative to cosmic inflation.
Physics Letters B, 694(3):181–185, 2010.
Nicolò Spagnolo, Chiara Vitelli, Fabio Sciarrino, and Francesco
De Martini.
Entanglement criteria for microscopic-macroscopic systems.
Physical Review A, 82(5):052101, 2010.
Leonard Susskind.
Wormholes and time travel? not likely.
arXiv preprint gr-qc/0503097, 2005.
Matt Visser.
Traversable wormholes: Some simple examples.
Physical Review D, 39(10):3182, 1989.
Appendix
Matt Visser.
The quantum physics of chronology protection.
The future of theoretical physics and cosmology: celebrating
Stephen Hawkings 60th birthday, pages 161–175, 2003.