Download - Emergent Gravity - Thermodynamic perspective
Emergent Gravity - Thermodynamic perspective
Emergent Gravity - Thermodynamicperspective
Pranjal Dhole
Institute of Theoretical PhysicsUniversity of Cologne
April 19, 2015
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 1 / 14
Emergent Gravity - Thermodynamic perspective
Why emergent gravity?
Classical gravity has same conceptual status aselasticity/hydrodynamics.
Descriptions are given in terms of some effectivedynamical variables, e.g. density, viscosity, etc.Emergence → Change of dynamical variables in thedescription
One can obtain wide class of gravitational theoriesfrom thermodynamic extremum principle.Horizon Thermodynamics ←→ Gravity
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 2 / 14
Emergent Gravity - Thermodynamic perspective
Why emergent gravity?
Classical gravity has same conceptual status aselasticity/hydrodynamics.
Descriptions are given in terms of some effectivedynamical variables, e.g. density, viscosity, etc.Emergence → Change of dynamical variables in thedescription
One can obtain wide class of gravitational theoriesfrom thermodynamic extremum principle.Horizon Thermodynamics ←→ Gravity
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 2 / 14
Emergent Gravity - Thermodynamic perspective
Why emergent gravity?
Classical gravity has same conceptual status aselasticity/hydrodynamics.
Descriptions are given in terms of some effectivedynamical variables, e.g. density, viscosity, etc.Emergence → Change of dynamical variables in thedescription
One can obtain wide class of gravitational theoriesfrom thermodynamic extremum principle.Horizon Thermodynamics ←→ Gravity
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 2 / 14
Emergent Gravity - Thermodynamic perspective
Why emergent gravity?
Classical gravity has same conceptual status aselasticity/hydrodynamics.
Descriptions are given in terms of some effectivedynamical variables, e.g. density, viscosity, etc.Emergence → Change of dynamical variables in thedescription
One can obtain wide class of gravitational theoriesfrom thermodynamic extremum principle.Horizon Thermodynamics ←→ Gravity
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 2 / 14
Emergent Gravity - Thermodynamic perspective
Before Boltzmann
Why does a gas exhibit thermal phenomena, storeand exchange energy?⇒ Boltzmann’s explanation : Atomic structure ofmatter. Equipartition of energy connectsthermodynamics to microscopic d.o.f.
E =12NkBT
Temperature of matter told you that it has atomicstructure
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 3 / 14
Emergent Gravity - Thermodynamic perspective
Before Boltzmann
Why does a gas exhibit thermal phenomena, storeand exchange energy?
⇒ Boltzmann’s explanation : Atomic structure ofmatter. Equipartition of energy connectsthermodynamics to microscopic d.o.f.
E =12NkBT
Temperature of matter told you that it has atomicstructure
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 3 / 14
Emergent Gravity - Thermodynamic perspective
Before Boltzmann
Why does a gas exhibit thermal phenomena, storeand exchange energy?⇒ Boltzmann’s explanation : Atomic structure ofmatter. Equipartition of energy connectsthermodynamics to microscopic d.o.f.
E =12NkBT
Temperature of matter told you that it has atomicstructure
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 3 / 14
Emergent Gravity - Thermodynamic perspective
Before Boltzmann
Why does a gas exhibit thermal phenomena, storeand exchange energy?⇒ Boltzmann’s explanation : Atomic structure ofmatter. Equipartition of energy connectsthermodynamics to microscopic d.o.f.
E =12NkBT
Temperature of matter told you that it has atomicstructure
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 3 / 14
Emergent Gravity - Thermodynamic perspective
You can heat up matter
The density of degrees of freedom needed to storeenergy ∆E at temperature T is given by
∆n =∆E
12kBT
Equipartition Law:
E =12nkBT →
∫dV
dndV
12kBT =
12kB
∫dnT
demands granularity with finite n; degrees of freedomscales as volume.
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 4 / 14
Emergent Gravity - Thermodynamic perspective
You can heat up matter
The density of degrees of freedom needed to storeenergy ∆E at temperature T is given by
∆n =∆E
12kBT
Equipartition Law:
E =12nkBT →
∫dV
dndV
12kBT =
12kB
∫dnT
demands granularity with finite n; degrees of freedomscales as volume.
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 4 / 14
Emergent Gravity - Thermodynamic perspective
Spacetimes can be hot!!
Observers who perceive a null surfaceas horizon attribute a temperature to it
kBT =~c
( g2π
)[Davis-Unruh temperature]
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 5 / 14
Emergent Gravity - Thermodynamic perspective
Free-fall observer
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 6 / 14
Emergent Gravity - Thermodynamic perspective
Local Rindler observer
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 7 / 14
Emergent Gravity - Thermodynamic perspective
Equivalence Principle
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 8 / 14
Emergent Gravity - Thermodynamic perspective
Gravitational field equations asthermodynamic identity
Static, spherically symmetric spacetime with horizon
ds2 = −f (r)c2dt2 + f −1(r)dr 2 + r 2dΩ22
Location of horizon is at r = a, f (a) = 0
Temperature of horizon: kBT =~cf ′(a)
4π
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 9 / 14
Emergent Gravity - Thermodynamic perspective
Gravitational field equations asthermodynamic identity
Static, spherically symmetric spacetime with horizon
ds2 = −f (r)c2dt2 + f −1(r)dr 2 + r 2dΩ22
Location of horizon is at r = a, f (a) = 0
Temperature of horizon: kBT =~cf ′(a)
4π
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 9 / 14
Emergent Gravity - Thermodynamic perspective
Gravitational field equations asthermodynamic identity
Einstein equation evaluated at horizon r = a:
c4
G
[12f ′(a)a− 1
2
]= 4πPa2
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 10 / 14
Emergent Gravity - Thermodynamic perspective
Gravitational field equations asthermodynamic identity
Horizons at a and a + da:
~cf ′(a)
4π︸ ︷︷ ︸kBT
c3
G~d(144πa2
)︸ ︷︷ ︸
dS
− 12c4daG︸ ︷︷ ︸
dE
= Pd(4π3a3)
︸ ︷︷ ︸PdV
S =1
4L2P
(4πa2) =14AH
L2P
E =c4
G
(AH
16π
) 12
L2P = G~
c3
Field equations become of the form TdS = dE + PdV
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 11 / 14
Emergent Gravity - Thermodynamic perspective
Implications of the Paradigm
To explain essential role of quantum mechanics inexplaining gravity.
If we fail:
(a) The world is fundamentally quantum mechanicaleven on macroscopic scales.
(b) Quantum mechanics is also emergent from somedeeper structure, representation of a stochastic processor as a form of organizational rule as statisticalmechanics.
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 12 / 14
Emergent Gravity - Thermodynamic perspective
Implications of the Paradigm
To explain essential role of quantum mechanics inexplaining gravity.
If we fail:
(a) The world is fundamentally quantum mechanicaleven on macroscopic scales.
(b) Quantum mechanics is also emergent from somedeeper structure, representation of a stochastic processor as a form of organizational rule as statisticalmechanics.
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 12 / 14
Emergent Gravity - Thermodynamic perspective
Implications of the Paradigm
To explain essential role of quantum mechanics inexplaining gravity.
If we fail:
(a) The world is fundamentally quantum mechanicaleven on macroscopic scales.
(b) Quantum mechanics is also emergent from somedeeper structure, representation of a stochastic processor as a form of organizational rule as statisticalmechanics.
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 12 / 14
Emergent Gravity - Thermodynamic perspective
Implications of the Paradigm
To explain essential role of quantum mechanics inexplaining gravity.
If we fail:
(a) The world is fundamentally quantum mechanicaleven on macroscopic scales.
(b) Quantum mechanics is also emergent from somedeeper structure, representation of a stochastic processor as a form of organizational rule as statisticalmechanics.
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 12 / 14
Emergent Gravity - Thermodynamic perspective
Implications of the Paradigm
To explain essential role of quantum mechanics inexplaining gravity.
If we fail:
(a) The world is fundamentally quantum mechanicaleven on macroscopic scales.
(b) Quantum mechanics is also emergent from somedeeper structure, representation of a stochastic processor as a form of organizational rule as statisticalmechanics.
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 12 / 14
Emergent Gravity - Thermodynamic perspective
Challenges
What new physics can be learnt from this?
Matter sector is put in by hand. If spacetime isemergent then matter d.o.f. must also be emergent.Do this properly!
Falsifiable predictions to rule out the paradigm?
A new level of observer dependence inthermodynamic variables, vacuum fluctuations vs.thermal fluctuations. Broader implications?
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 13 / 14
Emergent Gravity - Thermodynamic perspective
Challenges
What new physics can be learnt from this?
Matter sector is put in by hand. If spacetime isemergent then matter d.o.f. must also be emergent.Do this properly!
Falsifiable predictions to rule out the paradigm?
A new level of observer dependence inthermodynamic variables, vacuum fluctuations vs.thermal fluctuations. Broader implications?
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 13 / 14
Emergent Gravity - Thermodynamic perspective
Challenges
What new physics can be learnt from this?
Matter sector is put in by hand. If spacetime isemergent then matter d.o.f. must also be emergent.Do this properly!
Falsifiable predictions to rule out the paradigm?
A new level of observer dependence inthermodynamic variables, vacuum fluctuations vs.thermal fluctuations. Broader implications?
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 13 / 14
Emergent Gravity - Thermodynamic perspective
Challenges
What new physics can be learnt from this?
Matter sector is put in by hand. If spacetime isemergent then matter d.o.f. must also be emergent.Do this properly!
Falsifiable predictions to rule out the paradigm?
A new level of observer dependence inthermodynamic variables, vacuum fluctuations vs.thermal fluctuations. Broader implications?
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 13 / 14
Emergent Gravity - Thermodynamic perspective
Thank you!
Literature
T. Padmanabhan, ‘Thermodynamical Aspects ofGravity : New insights’, [arXiv:gr-qc 0911.5004]
T. Padmanabhan, ‘Gravitation - Foundation andFrontiers’, Cambridge University Press, 2010
T. Padmanabhan, ‘Gravity as an emergentphenomenon: A conceptual description’ [ arXiv:gr-qc0706.1654]
Pranjal Dhole (Institute of Theoretical Physics University of Cologne)Emergent gravity April 19, 2015 14 / 14