#### Alladi Ramakrishnan Hall

#### Causality and Entanglement in Quantum Field Theory

#### A. P. Balachandran

##### Syracuse University

*Some years ago, Rafael Sorkin argued that standard quantum measurement *

theory and relativistic causality are not compatible because of the existence of

entangled quantum states . He showed this by devising experiments using entangled

states which transmit information to spacelike distances. This talk elaborates on this

result in the framework of Algebraic Quantum Field Theory ( AQFT). The observables in

AQFT are localised in finite spacetime regions O and form von Neumann algebras A

(O) . There are no normal states, that is, density matrices, in A(O).

If A(O)’ is the causal complement of A(O ) ( i.e. consisting of elements commuting

with those of A(O) ) , then the algebra generated by A(O) and A(O)’ does have density

matrices. But they are

all

entangled across A (O) and A(O)’ and cause causality

problems.

Such entanglement can be avoided by thickening O to a region containing O

and assuming the ’ split property’ which the talk explains.Then unentangled density

matrices do exist.

Projection operators of local observables, while commuting for space like

separations, are not orthogonal. Experiments in O involve these projectors. But they do

not seem to give causality problems.

Done