A lot of confusion seems to arise about what an observer-moment is. I would like to propose the following distinction between a physical observer-moment and a psychological observer moment, along the same lines that I discussed under the thread copying.
A physical observer moment is defined by an observer physical quantum state accompanied by the set of all consistent histories justifying this state. It requires and includes a causal light cone to be drawn from that point extending toward the past (and expending toward the future). Hence a given physical OM includes several pasts and multiple futures. Because of the QM Non-cloning theorem two identical physical OMs cannot be copied. In addition because two identical OMs must comprise identical causal cones they must be one and the same in the same visible universe. Of course copies may exist beyond the causal cone or in other universes.
Since a physical OM cannot be copied, the measure of a physical OM cannot be increased within the causal cone.
A psychological observer moment is defined by a set of observer states which cannot be distinguished from each other by a subjective test performed by the observer. This definition is significantly looser than the one for physical observer-moment. Thus a single psychological observer moment can encompass a large number of physical observer moments. Note that according to this definition the set of observer states may also encompass states with inconsistent histories as long as they are indistinguishable. (I am not sure if I should enforce "consistent histories" on psychological OMs by replacing "observer states" by "physical observer moments")
The consideration of what is the measure of a psychological observer moment forces us to differentiate between physical first person and psychological first person.
>From a physical first person point of view, a psychological OM can include multiple physical OMs and therefore can have a high or low measure. However, from a psychological first person point of view, since all the physical OMs are indistinguishable, the measure cannot be increased by increasing the number of physical OMs.
An interesting thought is that a psychological first person can surf simultaneously through a large number of physical OMs.