On a Developing Entanglement Based on Which-Way Information: The Significance of One-to One Correspondence and Its Loss

A developing entanglement involving two entities can be based on which way information supplied by one of the entities. This developing entanglement can be lost because of the loss of the 1 to 1 correspondence between events involving the entities (e.g., an atom and a photon that the atom emits in one of two micromaser cavities) when a measurement is made (e.g., this atom passing through a two slit arrangement after exiting the cavity system). The significance of this 1 to 1 correspondence (e.g., between photon in upper cavity and atom through upper slit or between photon in lower cavity and atom through lower slit) to the developing entanglement based on which-way information is noted, and the consequence of the loss of this correspondence (e.g., through opening the shutter separating the cavities as the atom leaves the cavity system) is discussed. A developing entanglement of two entities based on which way information can be represented by: $\psi $ = 1/$\surd $2 [(A{\_}u)$\vert $P{\_}u$>$ + (A{\_}l)$\vert $P{\_}l$>$] where $\vert $P{\_}u$>$ and $\vert $P{\_}l$>$ are orthogonal. With the loss of 1 to 1 correspondence between (A{\_}u) and $\vert $P{\_}u$>$ and between (A{\_}l) and $\vert $P{\_}l$>$, which way information and the developing entanglement dependent on this information are lost. The wave function is then $\psi $ = [1/$\surd $2 [(A{\_}u) + (A{\_}l)]] [1/$\surd $2 [$\vert $P{\_}u$>+\vert $P{\_}l$>$]] or $\psi $ = (A{\_}s)$\vert $P{\_}s$>$ where (A{\_}s) and $\vert $P{\_}s$>$ are symmetric wave functions. This change in $\psi $ is haunted quantum entanglement.