Yongpyung 2012, Greenpia Condo, Feb. 21st 2012
GENERALIZING ENTROPIC FORCE FORMALISM
Jin-Ho Cho (Hanyang University)
w/ Hosin Gong, Hyosung Kim (POSTECH) Motivation (for the entropic force) Quantum Gravity
.....not successful so far
the role of gravity in AdS/CFT tree level supergravity (closed string) / quantum SYM (open string)
Fundamental or Emergent? Entropic Force
rubber band tends to increase the entropy
S : larger
S : smaller
[Halliday et al., Fundamentals of Physics] Verlinde’s Idea [Erik Verlinde, 1001.0785] entropic force : F x = T S 4 4
3 holographic principle : Ac /G~ = N
E = NkBT/2
T = ~a/2 kBc entropy change : S =2 kB( x mc/~) 4 4 (for a screen shift x ) 4 Newtonian Physics
Newton’s law : (a planar screen) T = ~a/2 ckB S =2 kB( x mc/~) 4 4 F x = T S 4 4 ~a 2 kBmc x = 4 2 k c ✓ B ◆✓ ~ ◆ = ma x 4
3 Gravitational force : (a spherical screen) N = Ac /G~ 2 Mc = E = NkBT/2 1 Ac3 ~a r2c2 = = a 2 G 2 c ✓ ~ ◆✓ ◆ G Q1: Cosmological Constant ?
g R ab R + ⇤g =8⇡GT ab 2 ab ab
3 Ac /G~ = N F x = T S S =2 kB( x mc/~) 4 4 E = NkBT/2 4 4
T = ~a/2 kBc ‘Volume Energy’
NkBT E = Mc2 +↵V = 2
N~ a ~a = T = 4⇡c 2⇡ckB 2 Ac a 3 = N = Ac /G~ 4⇡G 4⇡GM 4⇡G↵V a = + A Ac2 Determination of ↵ spherically symmetric case
GM 4⇡G↵r a = + = r2 3c2 r GM c2⇤r = Newtonian limit of Einstein eq. r2 3
c4 ↵ = ⇤ 4⇡G Einstein equation
4 c NkBT E = Mc2 ⇤V = 4⇡G 2 c4 k c3 Mc2 ⇤ dV = B TdN = adA 4⇡G 2 4⇡G Z Z Z
1 a b 1 a b 2 T Tg n ⇠ dV ⇤gabn ⇠ dV ab 2 ab 4⇡G Z⌃ ✓ ◆ Z⌃ 1 = R na⇠b dV 4⇡G ab Z⌃ Q2: Entropic Coulomb Force ? [JHC & Hyosung Kim, 2012 J. Phys.: Conf. Ser. 343 012024 (talk in QTS7)] Erik Verlinde’s new idea : .....gravity as an entropic force [Erik Verlinde, 1001.0785] .....more specifically as an adiabatic reaction force [Erik Verlinde, STRING 2011 talk] Q : what about the Coulomb force?
Some earlier attempts : [Tower Wang, Phys.Rev.D81:104045,2010]
[Peter Freund, arXiv:1008.4147]
Kaluza-Klein addon Moving Sources a cylinder along Kaluza-Klein direction
M0 ⇥0 = 0 2 L0 2 E0 =(⇥0 2 L0) c
1 = 1 (v/c)2 q M0 2 ⇤ = = ⇤0 2⇥L0/ 2 E =(⇤ 2⇥L0/ ) c = E0 Some Kinematics (I) from M 0 -rest frame to m 0 -rest frame : 2
A(5)c3 A(4)2 Lc3 A(4)c3 N 0 = = = = N G(5)~ G(4)2 L~ G(4)~
(4) 3 2 1 1 A c ~a0 2M0c = E0 = N 0kBT 0= 2 2 G(4) 2 c ✓ ~ ◆✓ ◆ r2c2 = a0 G(4) Some Kinematics (II) from m 0 -rest frame to observer-rest frame : 1
M = 1 2M0
m = 1m0