Editing Many-worlds interpretation (section)

=== Relative state ===
Everett's original work introduced the concept of a ''relative state''. Two (or more) subsystems, after a general interaction, become ''correlated'', or as is now said, [[quantum entanglement|entangled]]. Everett noted that such entangled systems can be expressed as the sum of products of states, where the two or more subsystems are each in a state relative to each other. After a measurement or observation one of the pair (or triple, etc.) is the measured, object or observed system, and one other member is the measuring apparatus (which may include an observer) having recorded the state of the measured system. Each product of subsystem states in the overall superposition evolves over time independently of other products. Once the subsystems interact, their states have become correlated or entangled and can no longer be considered independent. In Everett's terminology, each subsystem state was now ''correlated'' with its ''relative state'', since each subsystem must now be considered relative to the other subsystems with which it has interacted.

In the example of [[Schrödinger's cat]], after the box is opened, the entangled system is the cat, the poison vial and the observer. ''One'' relative triple of states would be the alive cat, the unbroken vial and the observer seeing an alive cat. ''Another'' relative triple of states would be the dead cat, the broken vial and the observer seeing a dead cat.

In the example of a measurement of a continuous variable (e.g., position ''q'') the object-observer system decomposes into a continuum of pairs of relative states: the object system's relative state becomes a [[Dirac delta function]] each centered on a particular value of ''q'' and the corresponding observer relative state representing an observer having recorded the value of ''q''.<ref name="everett56"/>{{rp|57–64}} The states of the pairs of relative states are, post measurement, ''correlated'' with each other.

In Everett's scheme, there is no collapse; instead, the [[Schrödinger equation]], or its [[quantum field theory]], relativistic analog, holds all the time, everywhere. An observation or measurement is modeled by applying the wave equation to the entire system, comprising the object being observed ''and'' the observer. One consequence is that every observation causes the combined observer–object's wavefunction to change into a quantum superposition of two or more non-interacting branches.

Thus the process of measurement or observation, or any correlation-inducing interaction, splits the system into sets of relative states, where each set of relative states, forming a branch of the universal wave function, is consistent within itself, and all future measurements (including by multiple observers) will confirm this consistency.