# On the role of gravity in Holography Current work: A Minkowski observer restricted to part of space will observe: Radiation. Area scaling of thermodynamic.

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On the role of gravity in Holography Current work: A Minkowski observer restricted to part of space will observe: Radiation. Area scaling of thermodynamic quantities Bulk boundary correspondence*. Future directions: Kruskal observer AdS observer Entanglement of a single string Experimental verification

A Minkowski observer in part of Minkowski space. V in out V in out = No access Restricted measurements

Radiation  (x,0)=  (x) x t  ’(x)  ’’(x) Tr out  (  ’  ’’   in (  ’ in,  ’’ in ) =  in  ’ in  ’’ in    Exp[-S E ] D   (x,0 + ) =  ’ in (x)  (x,0 - ) =  ’’ in (x)  (x,0 + ) =  ’ in (x)  out (x)  (x,0 - ) =  ’’ in (x)  out (x)   Exp[-S E ] Df  D  out  ’’ in( x)  ’ in( x)  (x,0 + )=  ’(x)  (x,0 - )=  ’’(x)  (x,0 + )=  ’(x)  (x,0 - )=  ’’(x)

Explicit example x t  ’ in (x)  ’’ in (x)  in  ’ in  ’’ in    Exp[-S E ] D   (x,0 + ) =  ’ in (x)  (x,0 - ) =  ’’ in (x)  ’| e -  H R |  ’’  Kabbat & Strassler (1994)

Thermodynamics V in out

Entropy: S in =Tr(  in ln  in ) S in =S out Srednicki (1993)

Other quantities Heat capacity: Generally, we consider: R. Brustein and A.Y. (2003)

Area scaling of fluctuations  (O V ) 2  =  V  V  O (x) O (y)  d d x d d y =  V  V F(|x-y|) d d x d d y =  D(  ) F(  ) d  Since F(  ) =  e iq  cos  F (q) d d q and F (q) ~ q  F(x)=  2 f(x)  (O V ) 2  = -  ∂  (D(  )/  d-1 )  d-1 ∂  f(  ) d  Introduce U.V. cutoff short  ~ 1/  distances  ∂  (D(  )/  d-1 )    S  D(  )=  V  V  (  x  y  ) d d x d d y = G V V  d-1 – G S S(V)  d +O(  d+1 )

Evidence for bulk-boundary correspondence V1V1 OV1OV2OV1OV2 S(B(V 1 )  B(V 2 )) OV1OV2OV1OV2 V2V2 OV1OV2OV1OV2  V1 V2 V1 V2  O V 1 O V 2  -  O V 1  O V 2  Pos. of V 2

A working example Large N limit

Summary V Area scaling of Fluctuations due to entanglement Unruh radiation and Area dependent thermodynamics VV Boundary theory for fluctuations Statistical ensemble due to restriction of d.o.f V A Minkowski observer restricted to part of space will observe: Radiation. Area scaling of thermodynamic quantities. Bulk boundary correspondence*.

Future directions Kruskal observer AdS observer Entanglement of a single string Experimental verification

V VV V Kruskal observer Kruskal Observer Restricted observer Schwarschield observer Israel (1976)General relation Non unitary evolution of  in

Experimental verification Prepare a pure quantum state. Make repetitive measurements. Measure part of the system.

Entanglement of a single string l  (  M) 2  ln( l )

Summary Radiation, area scaling laws and a bulk- boundary correspondence may be attributed to entanglement. It is unclear whether gravity alone is responsible for area dependent quantities or if it is supplemented by quantum entanglement.

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