Yongpyung 2012, Greenpia Condo, Feb. 21st 2012

GENERALIZING FORMALISM

Jin-Ho Cho (Hanyang University)

w/ Hosin Gong, Hyosung Kim (POSTECH) Motivation (for the entropic force) Quantum

.....not successful so far

the role of gravity in AdS/CFT tree level (closed ) / 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 : Ac /G~ = N

E = NkBT/2

T = ~a/2kBc entropy change : S =2kB( x mc/~) 4 4 (for a screen shift x ) 4 Newtonian Physics

Newton’s law : (a planar screen) T = ~a/2ckB S =2kB( x mc/~) 4 4 F x = T S 4 4 ~a 2kBmc x = 4 2k 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 2c ✓ ~ ◆✓ ◆ G Q1: Cosmological Constant ?

g R ab R + ⇤g =8⇡GT ab 2 ab ab

3 Ac /G~ = N F x = T S S =2kB( x mc/~) 4 4 E = NkBT/2 4 4

T = ~a/2kBc ‘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 2L0 2 E0 =(⇥0 2L0) 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)2Lc3 A(4)c3 N 0 = = = = N G(5)~ G(4)2L~ G(4)~

(4) 3 2 1 1 A c ~a0 2M0c = E0 = N 0kBT 0= 2 2 G(4) 2c ✓ ~ ◆✓ ◆ r2c2 = a0 G(4) Some Kinematics (II) from m 0 -rest frame to observer-rest frame : 1

M = 12M0

m = 1m0

= 12

2 in terms of 1 and :

1 2 2 = = 1 1 2 1 1 1 qp1 p = 1 p m0c M0c Coulomb Force

entropic force exerted on m 0 :

GM0 p1 p GM0m0 F = m a0 = m = 0 0 2 r2 1 m c M c r2 ✓ 0 0 ◆ GmM Gp1p GmM ke e = = 1 r2 c2r2 r2 r2 charge as the KK momentum :

n ~ G pn G en = lpqp = kn = Rs c r k c r k Conclusions ✴ The cosmological constant is nothing but the coefficient of the ‘volume energy’ contained in the holographic surface. ✴ If gravity is not fundamental but emergent, Coulomb force can be emergent too !! ✴ For the equal sign of charges, the entropic Coulomb force acts in the opposite direction to that of the gravitational force. ✴ Entropic force idea cannot single out the gravitational force from others, but might be a new paradigm applying for all forces.