# Observer Theory

Observer Theory

#### Is there a factored version of critical pair convergence?

Is there a factored version of critical pair convergence?

The statement of critical pair convergence is a lemma about equivalence of 2 hypergraphs

These lemma define equivalences between hypergraphs (that generalize the pure isomorphism equivalence).

Static vs. dynamic equivalence

Static vs. dynamic equivalence

“Measurement” is the “conceptual replacement” of a whole equivalence class with its canonical member

#### Unmerged multiway system

Unmerged multiway system

Tree of possible states

Classical probability: observer just picks a branch

Multithreaded observer: observer notices equivalences of branches

#### Consider two subsystems....

Consider two subsystems....

In the separate branches case, each subsystem makes its own branches

"A""AA"

With initial condition AA, we will get two binary trees, if we don’t merge

MultiwaySystem[{"A""AA"},"AA",4,"StatesGraph"]

In[]:=

Out[]=

MultiwaySystem[{"A""AA"},"AA",4,"AllStatesListUnmerged"]

In[]:=

Out[]=

In the unmerged case, we just get multiple trees, and we can compute probabilities by just enumerating branches...

To get the same probabilities in the merged case, branches will have to be weighted.....

(In order to keep track of things, do you need more than a scalar)

(In order to keep track of things, do you need more than a scalar)

How do you combine merged graphs?

#### The fact that the observer is in the same universe defines what they will consider to be dynamically equivalent

The fact that the observer is in the same universe defines what they will consider to be dynamically equivalent

### Many worlds theory

Many worlds theory

https://plato.stanford.edu/entries/qm-manyworlds/