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.