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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

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

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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)

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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)

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Thermodynamics V in out

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

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

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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 )

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Evidence for bulk-boundary correspondence V1V1 OV1OV2OV1OV2 S(B(V 1 ) B(V 2 )) OV1OV2OV1OV2 V2V2 OV1OV2OV1OV2 V1 V2 V1 V2 O V 1 O V 2 - O V 1 O V 2 Pos. of V 2

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A working example Large N limit

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Summary V Area scaling of Fluctuations due to entanglement Unruh radiation and Area dependent thermodynamics VV 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*.

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

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

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AdS observer V VV V AdS ? CFT ?

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

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Entanglement of a single string l ( M) 2 ln( l )

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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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