ATOMS OF SPACETIME. Fourth Abdus Salaam Memorial Lecture ( ) T. Padmanabhan (IUCAA, Pune, India) Feb. 28, 2006

Transcription

1 ATOMS OF SPACETIME T. Padmanabhan (IUCAA, Pune, India) Feb. 28, 2006 Fourth Abdus Salaam Memorial Lecture ( )

2 WHAT WILL BE THE VIEW REGARDING GRAVITY AND SPACETIME IN THE YEAR 2206?

3 CLASSICAL GRAVITY = { CONDENSED MATTER PHYSICS OF SPACETIME SUBSTRUCTURE

4 CLASSICAL GRAVITY = { CONDENSED MATTER PHYSICS OF SPACETIME SUBSTRUCTURE HOW GRAVITY RESPONDS TO AND MODIFIES THE STRUCTURE OF THE VACUUM IS PROBABLY THE KEY QUESTION IN THEORETICAL PHYSICS TODAY.

5 A WORD FROM THE SPONSORS

6 A WORD FROM THE SPONSORS Of general theory of relativity, you will be convinced once you have studied it. Therefore, I am not going to defend it with a single word. A.Einstein [in a letter to A.Sommerfeld, 6 Feb 1916]

7 A WORD FROM THE SPONSORS Of general theory of relativity, you will be convinced once you have studied it. Therefore, I am not going to defend it with a single word. A.Einstein [in a letter to A.Sommerfeld, 6 Feb 1916] I do not think we have a completely satisfactory relativistic quantum mechanical theory; even one, that does not agree with nature but at least agrees with logic. Therefore, I think the renormalisation theory is simply a way to sweep the difficulties of the divergences under the rug. R.P.Feynman [1965, Nobel Prize lecture]

8 Non Relativistic Quantum Mechanics T Y Space (X or Y or Z) X In NRQM a path is [X(T ), Y (T ), Z(T )]. Paths go backward in space X, Y, Z but not in time T

9 Relativistic Quantum Mechanics s T Proper Time Time OR Space ( T or X or Y or Z) X In RQM a path is [T (s), X(s), Y (s), Z(s)] where s is the proper time. Paths go backward in space X, Y, Z and time T!

10 Particles zig zag in time! Time Space

11 Major Crisis : A particle is at 3 different places at a given time!? Particles zig zag in time! Time Space

12 Major Crisis : A particle is at 3 different places at a given time!? Particles zig zag in time! Time We need something with infinite degrees of freedom: Field = Infinite number of Harmonic Oscillators Space

13 Electrons going backwards in time Electrons going forwards in time Time Space

14 Positrons going forwards in time Electrons going forwards in time Time Space

15 Annihilation of electron positron Time Creation of electron positron Space

16 Field = infinite number of oscillators; each oscillator labeled by the momentum p of the particle with frequency ω = 2 p + m 2 Annihilation of electron positron Time Creation of electron positron Space

17 Annihilation of electron positron Time State with n( p) particles with momentum p is the state with p th oscillator in the excited state labelled by integer n. Creation of electron positron Space

18 Annihilation of electron positron Time Lowest energy ground state for the field = no particle state with n (p) = 0 Creation of electron positron Space

19 VACUUM DEPENDS ON THE SCALE OF PROBING Phonons, magnons, photons, electrons, protons, quarks... excited state of a suitably defined system of oscillators. Each can arise as an Example: Lattice vibrations when quantized will give rise to phonons. The ground state is that of zero phonons.

20 FIELD = INFINITE NUMBER OF OSCILLATORS

21 FIELD = INFINITE NUMBER OF OSCILLATORS One Oscillator: L = 1 2 q2 1 2 ω2 q 2

22 FIELD = INFINITE NUMBER OF OSCILLATORS One Oscillator: L = 1 2 q2 1 2 ω2 q 2 Many oscillators:l = k ( 1 2 q2 k ) 1 2 ω2 k q2 k with k = 1, 2,...N

23 FIELD = INFINITE NUMBER OF OSCILLATORS One Oscillator: L = 1 2 q2 1 2 ω2 q 2 Many oscillators:l = k ( 1 2 q2 k 1 2 ω2 k q2 k ) with k = 1, 2,...N Continuum infinity of oscillators: L = ( 1 d 3 k 2 q2 k 1 ) 2 ω2 k q2 k

24 FIELD = INFINITE NUMBER OF OSCILLATORS One Oscillator: L = 1 2 q2 1 2 ω2 q 2 Many oscillators:l = k ( 1 2 q2 k 1 2 ω2 k q2 k ) with k = 1, 2,...N Continuum infinity of oscillators: L = ( 1 d 3 k 2 q2 k 1 ) 2 ω2 k q2 k... is the same as a field φ(t, x) = d 3 k q k (t) exp ik.x

25 FIELD = INFINITE NUMBER OF OSCILLATORS One Oscillator: L = 1 2 q2 1 2 ω2 q 2 Many oscillators:l = k ( 1 2 q2 k 1 2 ω2 k q2 k ) with k = 1, 2,...N Continuum infinity of oscillators: L = ( 1 d 3 k 2 q2 k 1 ) 2 ω2 k q2 k... is the same as a field φ(t, x) = d 3 k q k (t) exp ik.x Ground state has quantum fluctuations in q, p: ψ(q) = N exp( q2 2 2 ); 2 =< q 2 >= 2mω

26 FIELD = INFINITE NUMBER OF OSCILLATORS One Oscillator: L = 1 2 q2 1 2 ω2 q 2 Many oscillators:l = k ( 1 2 q2 k 1 2 ω2 k q2 k ) with k = 1, 2,...N Continuum infinity of oscillators: L = ( 1 d 3 k 2 q2 k 1 ) 2 ω2 k q2 k... is the same as a field φ(t, x) = d 3 k q k (t) exp ik.x Ground state has quantum fluctuations in q, p: Ground state of electromagnetic field: [ P exp 1 16π 3 c ψ(q) = N exp( q2 2 2 ); 2 =< q 2 >= 2mω ] E(x) E(y) d 3 xd 3 y x y 2 Key Point: You can never make the fluctuations go away.

27 CASIMIR EFFECT: YOU CAN T IGNORE NOTHING!

28 CASIMIR EFFECT: YOU CAN T IGNORE NOTHING! A beautiful example of power of vacuum. Not fully understood yet in spite of hundreds of papers!

29 CASIMIR EFFECT: YOU CAN T IGNORE NOTHING! A beautiful example of power of vacuum. Not fully understood yet in spite of hundreds of papers! Two conducting plates, kept in vacuum separated by a attracts each other with a force F A = π2 c 240a. 4 The energy of the configuration is E A = π2 c 720a ; 3 F = de da

30 VACUUM STATE HAS RANDOM FIELD MODES

31 SOME OF THESE MODES VIOLATE BOUNDARY CONDITIONS AT PLATES

32 NEW VACUUM STATE IS DIFFERENT FROM THE ORIGINAL ONE!

33 CASIMIR EFFECT: YOU CAN T IGNORE NOTHING! A beautiful example of power of vacuum. Not fully understood yet in spite of hundreds of papers! Two conducting plates, kept in vacuum separated by a attracts each other with a force F A = π2 c 240a. 4 E A = π2 c 720a 3 ; One dimensional scalar field example: F = de da With plates : k = (2π/a)n, n = 0, 1, 2,... Without plates : k = (2π/a)n, 0 < n <

34 CASIMIR EFFECT: YOU CAN T IGNORE NOTHING! A beautiful example of power of vacuum. Not fully understood yet in spite of hundreds of papers! Two conducting plates, kept in vacuum separated by a attracts each other with a force F A = π2 c 240a. 4 E A = π2 c 720a 3 ; One dimensional scalar field example: F = de da With plates : k = (2π/a)n, n = 0, 1, 2,... Without plates : k = (2π/a)n, 0 < n < Difference in energy: E = 1 2 2πc a [ n n 0 ] ndn = π c 24a

35 CASIMIR EFFECT: YOU CAN T IGNORE NOTHING! A beautiful example of power of vacuum. Not fully understood yet in spite of hundreds of papers! Two conducting plates, kept in vacuum separated by a attracts each other with a force F A = π2 c 240a. 4 E A = π2 c 720a 3 ; One dimensional scalar field example: F = de da With plates : k = (2π/a)n, n = 0, 1, 2,... Without plates : k = (2π/a)n, 0 < n < Difference in energy: E = 1 2 2πc a [ n n 0 ] ndn = π c 24a Pattern of vacuum fluctuations change when external conditions change.

36 DOES VACUUM GRAVITATE?

37 DOES VACUUM GRAVITATE? M M

38 DOES VACUUM GRAVITATE? M M G ab = κ T ab

39 DOES VACUUM GRAVITATE? M M G ab = κ T ab T ab = T ab (M)

40 DOES VACUUM GRAVITATE? M M G ab = κ T ab T ab = T ab (M) + T ab (vacuum)

41 IS VACUUM DOMINATING OUR UNIVERSE? Our Universe has a totally preposterous composition which no cosmologist wanted! Ω total 1 Ω radiation Ω neutrinos Ω baryons 0.04 Ω wimp 0.31 Ω darkenergy 0.65 What is this Dark Energy?

42 Spacetime and causal structure T X A

43 Spacetime and causal structure T C B X A Newtonian physics: A can communicate with B and C.

44 Spacetime and causal structure T C HORIZON B X A Special Relativity introduces a causal horizon; A cannot communicate with B.

45 Spacetime and causal structure T HORIZON X O 1 O 2 O 3 A family of observers (O 1, O 2, O 3,...) have a causal horizon

46 Example 1: Schwarzschild spacetime T HORIZON r = const > 2 M S X r = 2 M S ds 2 = (1 2MrS ) dt 2S + ( 1 2M r S ) 1 dr 2 S = Q 2 S (T, X)( dt 2 + dx 2 )

47 Example 2: De Sitter spacetime T HORIZON r ds = const < H 1 X 1 r = H ds ds 2 = ( 1 H 2 r 2 ds = Q 2 ds (T, X)( dt 2 + dx 2 ) ) dt 2 ds + ( ) 1 Hr 2 1 ds dr 2 ds

48 Example 3: Rindler (flat!) spacetime T HORIZON x = const > 0 R X x = 0 R ds 2 = 2κx R dt 2 + (2κx R ) 1 dx 2 R = dt 2 + dx 2

49 KEY NEW FEATURE IN COMBINING GRAVITY AND QUANTUM THEORY VACUUM STATE IS OBSERVER DEPENDENT!

50 Plane wave viewed by different observers Warm-up: Inertial Observer T T = X = τ (1 v 2 ) 1/2 vτ (1 v 2 ) 1/2 X TRAJECTORY OF INERTIAL OBSERVER

51 Plane wave viewed by different observers Warm-up: Inertial Observer T T = X = τ (1 v 2 ) 1/2 vτ (1 v 2 ) 1/2 X TRAJECTORY OF INERTIAL OBSERVER φ(t, X) = exp[ iω(t X)]

52 Plane wave viewed by different observers Warm-up: Inertial Observer T T = X = τ (1 v 2 ) 1/2 vτ (1 v 2 ) 1/2 X TRAJECTORY OF INERTIAL OBSERVER ( ) 1 v 1/2 φ(t, X) φ (T (τ), X(τ)) = exp iω τ 1 + v ( ) Doppler effect: Ω = Ω 1 v 1/2 1 + v

53 Plane wave viewed by different observers Observers with a causal horizon T T = x sinh(κτ) X = x cosh(κτ) x = X 2 T 2 = constant X UNIFORMLY ACCELERATED OBSERVER HORIZON φ(t, X) = exp[ iω(t X)]

54 Plane wave viewed by different observers Observers with a causal horizon T T = x sinh(κτ) X = x cosh(κτ) x = X 2 T 2 = constant X UNIFORMLY ACCELERATED OBSERVER HORIZON exponential redshift! {[ }} ]{ Ω φ(τ) = φ(t (τ), X(τ)) = exp i κ e κτ

55 RUNNING THROUGH THE VACUUM CAN HEAT YOU UP!

56 RUNNING THROUGH THE VACUUM CAN HEAT YOU UP! A mode φ(t, x) = exp[ iω(t x)] frequency Ω will lead to φ(τ) = exp[iωa 1 exp( aτ)] = 0 dν[a(ν)e iνt + B(ν)e iνt ]

57 RUNNING THROUGH THE VACUUM CAN HEAT YOU UP! A mode φ(t, x) = exp[ iω(t x)] frequency Ω will lead to φ(τ) = exp[iωa 1 exp( aτ)] = 0 dν[a(ν)e iνt + B(ν)e iνt ] with A 2 1 e βν 1 ; B 2 eβν e βν 1 ; β = 2πc a

58 RUNNING THROUGH THE VACUUM CAN HEAT YOU UP! A mode φ(t, x) = exp[ iω(t x)] frequency Ω will lead to φ(τ) = exp[iωa 1 exp( aτ)] = 0 dν[a(ν)e iνt + B(ν)e iνt ] with A 2 1 e βν 1 ; B 2 eβν e βν 1 ; β = 2πc a Exponential redshift occurs near any horizon with a determined by surface gravity at the horizon.

59 RUNNING THROUGH THE VACUUM CAN HEAT YOU UP! A mode φ(t, x) = exp[ iω(t x)] frequency Ω will lead to φ(τ) = exp[iωa 1 exp( aτ)] = 0 dν[a(ν)e iνt + B(ν)e iνt ] with A 2 1 e βν 1 ; B 2 eβν e βν 1 ; β = 2πc a Exponential redshift occurs near any horizon with a determined by surface gravity at the horizon. For a black hole, a = GM/R 2 at R = 2GM/c 2. This gives k B T = c 3 /8πGM, the Hawking temperature.

60 AN INTERPRETATION OF EINSTEIN S EQUATIONS

61 AN INTERPRETATION OF EINSTEIN S EQUATIONS Metric: ds 2 = f(r)dt 2 f(r) 1 dr 2 r 2 (dθ 2 + sin 2 θdφ 2 ) f(r)dt 2 f(r) 1 dr 2 dl 2

62 AN INTERPRETATION OF EINSTEIN S EQUATIONS Metric: ds 2 = f(r)dt 2 f(r) 1 dr 2 r 2 (dθ 2 + sin 2 θdφ 2 ) f(r)dt 2 f(r) 1 dr 2 dl 2 Consider the case with horizon at r = a; that is, f = 0 at r = a with f (a) = B > 0. Temperature of horizon: k B T = cb/4π.

63 AN INTERPRETATION OF EINSTEIN S EQUATIONS Metric: ds 2 = f(r)dt 2 f(r) 1 dr 2 r 2 (dθ 2 + sin 2 θdφ 2 ) f(r)dt 2 f(r) 1 dr 2 dl 2 Consider the case with horizon at r = a; that is, f = 0 at r = a with f (a) = B > 0. Temperature of horizon: k B T = cb/4π. At r = a. Einstein s equation gives: [ c 4 1 G 2 Ba 1 ] 2 = 4πT t t a 2 = 4πT r r a 2

64 AN INTERPRETATION OF EINSTEIN S EQUATIONS Metric: ds 2 = f(r)dt 2 f(r) 1 dr 2 r 2 (dθ 2 + sin 2 θdφ 2 ) f(r)dt 2 f(r) 1 dr 2 dl 2 Consider the case with horizon at r = a; that is, f = 0 at r = a with f (a) = B > 0. Temperature of horizon: k B T = cb/4π. At r = a. Einstein s equation gives: [ c 4 1 G 2 Ba 1 ] 2 = 4πT t t a 2 = 4πT r r a 2 Multiply da to write: cb 4π c 3 ( ) 1 G d 4 4πa2 1 2 c 4 da G = T r r d ( ) 4π 3 a3

65 AN INTERPRETATION OF EINSTEIN S EQUATIONS Metric: ds 2 = f(r)dt 2 f(r) 1 dr 2 r 2 (dθ 2 + sin 2 θdφ 2 ) f(r)dt 2 f(r) 1 dr 2 dl 2 Consider the case with horizon at r = a; that is, f = 0 at r = a with f (a) = B > 0. Temperature of horizon: k B T = cb/4π. At r = a. Einstein s equation gives: [ c 4 1 G 2 Ba 1 ] 2 = 4πT t t a 2 = 4πT r r a 2 Multiply da to write: cb 4π c 3 ( ) 1 G d 4 4πa2 1 2 c 4 da G ( ) 4π = T r r d 3 a3 }{{} P dv

66 AN INTERPRETATION OF EINSTEIN S EQUATIONS Metric: ds 2 = f(r)dt 2 f(r) 1 dr 2 r 2 (dθ 2 + sin 2 θdφ 2 ) f(r)dt 2 f(r) 1 dr 2 dl 2 Consider the case with horizon at r = a; that is, f = 0 at r = a with f (a) = B > 0. Temperature of horizon: k B T = cb/4π. At r = a. Einstein s equation gives: [ c 4 1 G 2 Ba 1 ] 2 = 4πT t t a 2 = 4πT r r a 2 Multiply da to write: cb 4π }{{} k B T c 3 ( ) 1 G d 4 4πa2 1 2 c 4 da G ( ) 4π = T r r d 3 a3 }{{} P dv

67 AN INTERPRETATION OF EINSTEIN S EQUATIONS Metric: ds 2 = f(r)dt 2 f(r) 1 dr 2 r 2 (dθ 2 + sin 2 θdφ 2 ) f(r)dt 2 f(r) 1 dr 2 dl 2 Consider the case with horizon at r = a; that is, f = 0 at r = a with f (a) = B > 0. Temperature of horizon: k B T = cb/4π. At r = a. Einstein s equation gives: [ c 4 1 G 2 Ba 1 ] 2 = 4πT t t a 2 = 4πT r r a 2 Multiply da to write: cb 4π }{{} k B T c 3 ( ) 1 G d 4 4πa2 }{{} ds 1 c 4 da } 2{{ G } de ( ) 4π = Tr r d 3 a3 }{{} P dv

68 AN INTERPRETATION OF EINSTEIN S EQUATIONS Metric: ds 2 = f(r)dt 2 f(r) 1 dr 2 r 2 (dθ 2 + sin 2 θdφ 2 ) f(r)dt 2 f(r) 1 dr 2 dl 2 Consider the case with horizon at r = a; that is, f = 0 at r = a with f (a) = B > 0. Temperature of horizon: k B T = cb/4π. At r = a. Einstein s equation gives: [ c 4 1 G 2 Ba 1 ] 2 = 4πT t t a2 = 4πT r r a2 Multiply da to write: cb 4π }{{} k B T Read off (L 2 P G /c3 ): c 3 ( ) 1 G d 4 4πa2 }{{} ds 1 c 4 da } 2{{ G } de ( ) 4π = Tr r d 3 a3 }{{} P dv S = 1 (4πa 2 ) = 1 A H ; E = c4 4L 2 P 4 L 2 P 2G a = c4 G ( ) 1/2 AH 16π

69 AN INTERPRETATION OF EINSTEIN S EQUATIONS Metric: ds 2 = f(r)dt 2 f(r) 1 dr 2 r 2 (dθ 2 + sin 2 θdφ 2 ) f(r)dt 2 f(r) 1 dr 2 dl 2 Consider the case with horizon at r = a; that is, f = 0 at r = a with f (a) = B > 0. Temperature of horizon: k B T = cb/4π. At r = a. Einstein s equation gives: [ c 4 1 G 2 Ba 1 ] 2 = 4πT t t a2 = 4πT r r a2 Multiply da to write: cb 4π }{{} k B T Read off (L 2 P G /c3 ): c 3 ( ) 1 G d 4 4πa2 }{{} ds 1 c 4 da } 2{{ G } de ( ) 4π = Tr r d 3 a3 }{{} P dv S = 1 (4πa 2 ) = 1 A H ; E = c4 4L 2 P 4 L 2 P 2G a = c4 G In normal units, there is still no in T ds! ( AH 16π ) 1/2

70 HOLOGRAPHIC DUALITY OF EINSTEIN GRAVITY T.P.,gr-qc/ ; gr-qc/

71 HOLOGRAPHIC DUALITY OF EINSTEIN GRAVITY T.P.,gr-qc/ ; gr-qc/ Einstein-Hilbert Lagrangian: L EH R ( g) g = L bulk + L sur.

72 HOLOGRAPHIC DUALITY OF EINSTEIN GRAVITY T.P.,gr-qc/ ; gr-qc/ Einstein-Hilbert Lagrangian: L EH R ( g) g = L bulk + L sur. There is remarkable relation between L bulk and L sur : glsur = a (g ) gl bulk ij ( a g ij ) allowing a dual description of gravity using either L bulk or L sur!

73 HOLOGRAPHIC DUALITY OF EINSTEIN GRAVITY T.P.,gr-qc/ ; gr-qc/ Einstein-Hilbert Lagrangian: L EH R ( g) g = L bulk + L sur. There is remarkable relation between L bulk and L sur : glsur = a (g ) gl bulk ij ( a g ij ) allowing a dual description of gravity using either L bulk or L sur! We can obtain dynamics of gravity using only the surface term of the Hilbert action.

74 GRAVITY: THE DUAL DESCRIPTION T.P.,gr-qc/ ; gr-qc/

75 GRAVITY: THE DUAL DESCRIPTION T.P.,gr-qc/ ; gr-qc/ Einstein s equations arise from the demand that A tot = A sur + A matter should be invariant under virtual displacements of the horizon normal to itself.

76 GRAVITY: THE DUAL DESCRIPTION T.P.,gr-qc/ ; gr-qc/ Einstein s equations arise from the demand that A tot = A sur + A matter should be invariant under virtual displacements of the horizon normal to itself. Action is the free energy of spacetime solid ; gravitational degrees of freedom in the bulk is dual to that in the surface.

77 GRAVITY: THE DUAL DESCRIPTION T.P.,gr-qc/ ; gr-qc/ Einstein s equations arise from the demand that A tot = A sur + A matter should be invariant under virtual displacements of the horizon normal to itself. Action is the free energy of spacetime solid ; gravitational degrees of freedom in the bulk is dual to that in the surface. Einstein s equations as a thermodynamic identity: T ds pdv de = 0

78 GRAVITY: THE DUAL DESCRIPTION T.P.,gr-qc/ ; gr-qc/ Einstein s equations arise from the demand that A tot = A sur + A matter should be invariant under virtual displacements of the horizon normal to itself. Action is the free energy of spacetime solid ; gravitational degrees of freedom in the bulk is dual to that in the surface. Einstein s equations as a thermodynamic identity: T ds pdv de = 0 temperature and entropy from variation of A sur

79 GRAVITY: THE DUAL DESCRIPTION T.P.,gr-qc/ ; gr-qc/ Einstein s equations arise from the demand that A tot = A sur + A matter should be invariant under virtual displacements of the horizon normal to itself. Action is the free energy of spacetime solid ; gravitational degrees of freedom in the bulk is dual to that in the surface. Einstein s equations as a thermodynamic identity: T ds pdv de = 0 temperature and entropy from variation of A sur work in virtual horizon displacement

80 GRAVITY: THE DUAL DESCRIPTION T.P.,gr-qc/ ; gr-qc/ Einstein s equations arise from the demand that A tot = A sur + A matter should be invariant under virtual displacements of the horizon normal to itself. Action is the free energy of spacetime solid ; gravitational degrees of freedom in the bulk is dual to that in the surface. Einstein s equations as a thermodynamic identity: T ds pdv de = 0 temperature and entropy from variation of A sur work in virtual horizon displacement change in the energy; from A matter

81 SAKHAROV PARADIGM Gravity as an Emergent Phenomenon

82 SAKHAROV PARADIGM Gravity as an Emergent Phenomenon SOLIDS SPACETIME Mechanics; Elasticity (ρ, v...) Einstein s Theory (g ab...) Statistical Mechanics of atoms/molecules Statistical mechanics of atoms of spacetime

83 SAKHAROV PARADIGM Gravity as an Emergent Phenomenon SOLIDS SPACETIME Mechanics; Elasticity (ρ, v...) Einstein s Theory (g ab...) Thermodynamics of solids Statistical Mechanics of atoms/molecules Statistical mechanics of atoms of spacetime

84 SAKHAROV PARADIGM Gravity as an Emergent Phenomenon SOLIDS SPACETIME Mechanics; Elasticity (ρ, v...) Einstein s Theory (g ab...) Thermodynamics of solids Statistical Mechanics of atoms/molecules Thermodynamics of spacetime Statistical mechanics of atoms of spacetime

85 KEY NEW RESULT: AREA QUANTISATION In semi-classical limit, demanding exp ia sur = exp 2πin leads to area quantization: Area = (8πL 2 P )n

86 VACUUM FLUCTUATIONS AND ρvac

87 VACUUM FLUCTUATIONS AND ρ vac The structure of the vacuum must change due to its own gravitational force. Can this reduce ρ V to acceptable values?

88 VACUUM FLUCTUATIONS AND ρ vac The structure of the vacuum must change due to its own gravitational force. Can this reduce ρ V to acceptable values? Given L P and L H we have ρ UV = c/l 4 P and ρ IR = c/l 4 H.

89 VACUUM FLUCTUATIONS AND ρ vac The structure of the vacuum must change due to its own gravitational force. Can this reduce ρ V to acceptable values? Given L P and L H we have ρ UV = c/l 4 P and ρ IR = c/l 4 H. The observed value of dark energy density is: ρ DE ρ UV ρ IR c L 2 P L2 H c2 H 2 G

90 VACUUM FLUCTUATIONS AND ρ vac The structure of the vacuum must change due to its own gravitational force. Can this reduce ρ V to acceptable values? Given L P and L H we have ρ UV = c/l 4 P and ρ IR = c/l 4 H. The observed value of dark energy density is: ρ DE ρ UV ρ IR c L 2 P L2 H c2 H 2 G The hierarchy: ρ vac = c L 4 P + c L 4 P ( LP L H ) 2 + c L 4 P ( LP L H ) 4 +

91 VACUUM FLUCTUATIONS AND ρ vac The structure of the vacuum must change due to its own gravitational force. Can this reduce ρ V to acceptable values? Given L P and L H we have ρ UV = c/l 4 P and ρ IR = c/l 4 H. The observed value of dark energy density is: ρ DE ρ UV ρ IR c L 2 P L2 H c2 H 2 G The hierarchy: ρ vac = c L 4 P + c L 4 P ( LP L H ) 2 + c L 4 P ( LP L H ) 4 + vacuum renormalisation makes this zero (?)

92 VACUUM FLUCTUATIONS AND ρ vac The structure of the vacuum must change due to its own gravitational force. Can this reduce ρ V to acceptable values? Given L P and L H we have ρ UV = c/l 4 P and ρ IR = c/l 4 H. The observed value of dark energy density is: ρ DE ρ UV ρ IR c L 2 P L2 H c2 H 2 G The hierarchy: ρ vac = c L 4 P + c L 4 P ( LP L H ) 2 + c L 4 P ( LP L H ) 4 + vacuum renormalisation makes this zero (?) observed value; can come from fluctuations

93 VACUUM FLUCTUATIONS AND ρ vac The structure of the vacuum must change due to its own gravitational force. Can this reduce ρ V to acceptable values? Given L P and L H we have ρ UV = c/l 4 P and ρ IR = c/l 4 H. The observed value of dark energy density is: ρ DE ρ UV ρ IR c L 2 P L2 H c2 H 2 G The hierarchy: ρ vac = c L 4 P + c L 4 P ( LP L H ) 2 + c L 4 P ( LP L H ) 4 + vacuum renormalisation makes this zero (?) observed value; can come from fluctuations thermal energy density of de Sitter ρ rad T 4 GH

94 CONCLUSIONS

95 CONCLUSIONS The conventional approach: g ab and its dynamics is the key.

96 CONCLUSIONS The conventional approach: g ab and its dynamics is the key. No deep principle to fix the dynamics of spacetime.

97 CONCLUSIONS The conventional approach: g ab and its dynamics is the key. No deep principle to fix the dynamics of spacetime. Hilbert action has peculiar features for which there is no explanation

98 CONCLUSIONS The conventional approach: g ab and its dynamics is the key. No deep principle to fix the dynamics of spacetime. Hilbert action has peculiar features for which there is no explanation Thermal properties of horizon is an optional extra.

99 CONCLUSIONS The conventional approach: g ab and its dynamics is the key. No deep principle to fix the dynamics of spacetime. Hilbert action has peculiar features for which there is no explanation Thermal properties of horizon is an optional extra. The alternative perspective: Gravity is an emergent, long wavelength, phenomenon. Observer dependent horizon thermodynamics is central.

100 CONCLUSIONS The conventional approach: g ab and its dynamics is the key. No deep principle to fix the dynamics of spacetime. Hilbert action has peculiar features for which there is no explanation Thermal properties of horizon is an optional extra. The alternative perspective: Gravity is an emergent, long wavelength, phenomenon. Observer dependent horizon thermodynamics is central. Every light cone is a horizon for some family of observers.

101 CONCLUSIONS The conventional approach: g ab and its dynamics is the key. No deep principle to fix the dynamics of spacetime. Hilbert action has peculiar features for which there is no explanation Thermal properties of horizon is an optional extra. The alternative perspective: Gravity is an emergent, long wavelength, phenomenon. Observer dependent horizon thermodynamics is central. Every light cone is a horizon for some family of observers. Physics beyond horizon is encoded in a surface term which is the entropy.

102 CONCLUSIONS The conventional approach: g ab and its dynamics is the key. No deep principle to fix the dynamics of spacetime. Hilbert action has peculiar features for which there is no explanation Thermal properties of horizon is an optional extra. The alternative perspective: Gravity is an emergent, long wavelength, phenomenon. Observer dependent horizon thermodynamics is central. Every light cone is a horizon for some family of observers. Physics beyond horizon is encoded in a surface term which is the entropy. Virtual displacements of the horizon leads to T ds = de + pdv which is the same as Einstein s equations.

103 CONCLUSIONS The conventional approach: g ab and its dynamics is the key. No deep principle to fix the dynamics of spacetime. Hilbert action has peculiar features for which there is no explanation Thermal properties of horizon is an optional extra. The alternative perspective: Gravity is an emergent, long wavelength, phenomenon. Observer dependent horizon thermodynamics is central. Every light cone is a horizon for some family of observers. Physics beyond horizon is encoded in a surface term which is the entropy. Virtual displacements of the horizon leads to T ds = de + pdv which is the same as Einstein s equations. Locally inertial observers Kinematics of spacetime; Locally accelerated observers Dynamics of spacetime;

104 CONCLUSIONS The conventional approach: g ab and its dynamics is the key. No deep principle to fix the dynamics of spacetime. Hilbert action has peculiar features for which there is no explanation Thermal properties of horizon is an optional extra. The alternative perspective: Gravity is an emergent, long wavelength, phenomenon. Observer dependent horizon thermodynamics is central. Every light cone is a horizon for some family of observers. Physics beyond horizon is encoded in a surface term which is the entropy. Virtual displacements of the horizon leads to T ds = de + pdv which is the same as Einstein s equations. Locally inertial observers Kinematics of spacetime; Locally accelerated observers Dynamics of spacetime; Dual description to the conventional one; the full Hilbert action becomes the free energy of spacetime.

105 CONCLUSIONS The conventional approach: g ab and its dynamics is the key. No deep principle to fix the dynamics of spacetime. Hilbert action has peculiar features for which there is no explanation Thermal properties of horizon is an optional extra. The alternative perspective: Gravity is an emergent, long wavelength, phenomenon. Observer dependent horizon thermodynamics is central. Every light cone is a horizon for some family of observers. Physics beyond horizon is encoded in a surface term which is the entropy. Virtual displacements of the horizon leads to T ds = de + pdv which is the same as Einstein s equations. Locally inertial observers Kinematics of spacetime; Locally accelerated observers Dynamics of spacetime; Dual description to the conventional one; the full Hilbert action becomes the free energy of spacetime. Obvious implications for quantum gravity.

106 REFERENCES T. Padmanabhan, The Holography of gravity encoded in a relation between Entropy, Horizon Area and the Action for gravity, Gen.Rel.Grav., (2002) [gr-qc/ ] [Second Prize essay; Gravity Research Foundation Essay Contest, 2002] T. Padmanabhan, Classical and Quantum Thermodynamics of horizons in spherically symmetric spacetimes, Class.Quan.Grav. 19, 5387 (2002). [gr-qc/ ] T. Padmanabhan, Why gravity has no choice: Bulk spacetime dynamics is dictated by information entanglement across horizons, Gen.Rel.Grav., 35, (2003) [Fifth Prize essay; Gravity Research Foundation Essay Contest, 2003] T. Padmanabhan, Gravity and the Thermodynamics of Horizons, Phys. Reports, 406, 49 (2005) [gr-qc/ ] T. Padmanabhan, Holographic Gravity and the Surface term in the Einstein-Hilbert Action, Plenary talk at DICE-2004, Brazilian Jour.Phys. (Special Issue) 35, 362 (2005) [gr-qc/ ]