Quantum gravity and aspects of relativity · B. Crash course in Canonical Quantum Gravity-you can...
Transcript of Quantum gravity and aspects of relativity · B. Crash course in Canonical Quantum Gravity-you can...
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Quantum gravityand
aspects of relativity
Branislav Nikolic
Institute for Theoretical Physics,University of Cologne
Bonn-Cologne Graduate School inPhysics and Astronomy
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Gravitation and Relativity research groupProf. Dr. Claus Kiefer, Prof. Dr. Friedrich Hehl
who are we???
- have a look at the webpage of our group!
www.thp.uni-koeln.de/gravitation/
- Institute of Theoretical Physics, Cologne
- have a look at the webpage of our group!
www.thp.uni-koeln.de/gravitation/
- email us if you have any questions, don’t be afraid!
- join us at our seminars: Tuesdays 12h, Seminar Room 215
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what are we going to do today?
- tell you about what kind of interesting things we are doing in our group
- hang out with you during the coffee breaks and lunch
This talk:
A. Crash course in General Relativity
B. Crash course in Canonical Quantum Gravity
C. Overview of today’s talks
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A. Crash course in General Relativity
- Einstein, ~1916
geometry of non-empty (non-vacuum) 4D spacetime is not flat, but curved!
Minkowski metric general metric(encodes gravitational field)
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A. Crash course in General Relativity
- Einstein, ~1916
geometry of non-empty (non-vacuum) 4D spacetime is not flat, but curved!
Minkowski metric general metric(encodes gravitational field)
geometry of 4D spacetime <~> matter- Einstein’s Equations:
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A. Crash course in General Relativity
- Einstein, ~1916
geometry of non-empty (non-vacuum) 4D spacetime is not flat, but curved!
Minkowski metric general metric(encodes gravitational field)
geometry of 4D spacetime <~> matter- Einstein’s Equations:
curvature ( )
cosmological constant
energy-momentum tensor
given matter distribution/symmetry
find the metric
to solve EE means:
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A. Crash course in General Relativity
- for example:
- Friedman-Lemaitre-Robertson-Walker metric (models a homogeneous andisotropic universe)
scale factor Friedmann equations:
(rate of universe’s expansion interms of what’s inside it)
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A. Crash course in General Relativity
- for example:
- Friedman-Lemaitre-Robertson-Walker metric (models a homogeneous andisotropic universe)
scale factor Friedmann equations:
- Schwarzschild solution (non-rotating Black Hole!)
(rate of universe’s expansion interms of what’s inside it)
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A. Crash course in General Relativity
- for example:
- Friedman-Lemaitre-Robertson-Walker metric (models a homogeneous andisotropic universe)
scale factor Friedmann equations:
3. Black Holes and Naked Singularities (Alessandro)
2. Singularities in Generalized Chaplygin Gas model(Arezu)
- Schwarzschild solution (non-rotating Black Hole!)
(rate of universe’s expansion interms of what’s inside it)
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B. Crash course in Canonical Quantum Gravity
- unavoidable singularities in GR is a motivation to change something:
1 – quantize the theory and see if we can avoid singularities
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B. Crash course in Canonical Quantum Gravity
- unavoidable singularities in GR is a motivation to change something:
1 – quantize the theory and see if we can avoid singularities
2 – make a different theory of gravity
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B. Crash course in Canonical Quantum Gravity
- unavoidable singularities in GR is a motivation to change something:
1 – quantize the theory and see if we can avoid singularities
2 – make a different theory of gravity3 – both
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B. Crash course in Canonical Quantum Gravity
- unavoidable singularities in GR is a motivation to change something:
1 – quantize the theory and see if we can avoid singularities
2 – make a different theory of gravity3 – both
- other things make us think towards quantizing gravity:
- three interactions of Nature can be unified in a common framework;include gravity (“theory of everything”) ? gravitational field must also bequantized!
- three interactions of Nature can be unified in a common framework;include gravity (“theory of everything”) ? gravitational field must also bequantized!
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B. Crash course in Canonical Quantum Gravity
- unavoidable singularities in GR is a motivation to change something:
1 – quantize the theory and see if we can avoid singularities
2 – make a different theory of gravity3 – both
- other things make us think towards quantizing gravity:
- three interactions of Nature can be unified in a common framework;include gravity (“theory of everything”) ? gravitational field must also bequantized!
- three interactions of Nature can be unified in a common framework;include gravity (“theory of everything”) ? gravitational field must also bequantized!
- the problem of time:4D spacetime (described by metric tensor) is fixed in QFT
VSin GR, spacetime is dynamical
so how do you describe a quantum field propagating on a cruved background?
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B. Crash course in Canonical Quantum Gravity
semiclassical Einstein equations:
classical metric(classical geometry)
quantum matter
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B. Crash course in Canonical Quantum Gravity
semiclassical Einstein equations:
quantum matterclassical metric(classical geometry)
but Psi depends on the metric, which we cannot find without solving EE!?!very, very, very non-linear problem!
but Psi depends on the metric, which we cannot find without solving EE!?!very, very, very non-linear problem!
approximation to a more fundamental theory, which includesquantized metric, too
a quantum theory of gravity
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B. Crash course in Canonical Quantum Gravity
…but how…?!
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B. Crash course in Canonical Quantum Gravity
Many approaches to Quantum Gravity
Covariant(Path Integrals, RG, perturbations…) Canonical
String Theory
…
…but how…?!
Gravity fromthermodynamic
perspective
…
Loop quantum gravity
Quantum Geometrodynamics…
… of GR or…?
…
Gauge Theory
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B. Crash course in Canonical Quantum Gravity
Many approaches to Quantum Gravity
Canonical
…this is how we try…
Gravity fromthermodynamic
perspective
Quantum Geometrodynamics…
… of GR or…?
Gauge TheoryLoop quantum gravity
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B. Crash course in Canonical Quantum Gravity
-you can write down the Hamiltonian for a particle in a potential(using Hamiltonian formulation) - write
H = H (gen. coord., conj. mom.)
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B. Crash course in Canonical Quantum Gravity
-you can write down the Hamiltonian for a particle in a potential(Hamiltonian formulation) - write
H = H ( gen. coord., conj. mom.)
- you can even write down the Hamiltonian of General Relativity! …how?
- separate spacetime into 3D space + time, and look at geometry of 3D space only(write, hypersurfaces)
3-metric“coordinate”
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B. Crash course in Canonical Quantum Gravity
-you can write down the Hamiltonian for a particle in a potential(Hamiltonian formulation) - write
H = H ( gen. coord., conj. mom.)
- separate spacetime into 3D space + time, and look at geometry of 3D space only(write, hypersurfaces)
- you can even write down the Hamiltonian of General Relativity! …how?
3-metric“coordinate”
conjugate momentum
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B. Crash course in Canonical Quantum Gravity
-you can write down the Hamiltonian for a particle in a potential(Hamiltonian formulation) - write
H = H ( gen. coord., conj. mom.)
- separate spacetime into 3D space + time, and look at geometry of 3D space only(write, hypersurfaces)
- you can even write down the Hamiltonian of General Relativity! …how?
- Hamiltonian of GR (ADM formalism):
3-metric“coordinate”
conjugate momentum
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B. Crash course in Canonical Quantum Gravity
- as in ordinary quantum mechanics, Dirac quantization procedure:
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B. Crash course in Canonical Quantum Gravity
Wheeler-DeWitt equation
- as in ordinary quantum mechanics, Dirac quantization procedure:
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B. Crash course in Canonical Quantum Gravity
Wheeler-DeWitt equation
- as in ordinary quantum mechanics, Dirac quantization procedure:
…with which you can do almost no physics…
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B. Crash course in Canonical Quantum Gravity
Wheeler-DeWitt equation
- as in ordinary quantum mechanics, Dirac quantization procedure:
wave functional, lives in Superspace
no space, no time
…with which you can do almost no physics…
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B. Crash course in Canonical Quantum Gravity
Wheeler-DeWitt equation
- as in ordinary quantum mechanics, Dirac quantization procedure:
- what is Psi and defined on what kind of space?
- Hilbert space and unitarity?!
wave functional, lives in Superspace
no space, no time
…with which you can do almost no physics…
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B. Crash course in Canonical Quantum Gravity
…that is why you have to pick a model… (minisuperspace model)
- gravity + scalar field wave function of the Universe:
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B. Crash course in Canonical Quantum Gravity
…that is why you have to pick a model… (minisuperspace model)
- gravity + scalar field wave function of the Universe:
- semiclassical approximation: expansion in terms of Planck mass:- semiclassical approximation: expansion in terms of Planck mass:
- let’s see what happens order by order…
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B. Crash course in Canonical Quantum Gravity
…that is why you have to pick a model… (minisuperspace model)
zeroth order:
1st order: Schroedinger equation
2nd order:
quantum gravitational corrections toSchroedinger equation
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B. Crash course in Canonical Quantum Gravity
…that is why you have to pick a model… (minisuperspace model)
-- apply to the Cosmic Microwave Background power spectrum:
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C. Overview of today’s talks
Canonical
Quantum Geometrodynamics…
… of GR …of ConformalGravity
Gravity fromthermodynamic
perspective
Gauge TheoryLoop quantum gravity
6. Pranjal
… of GR …of ConformalGravity
2. Arezu3. Alessandro
7. Branislav
5. Patrick 4. Jens