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