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
In[]:=
MultiwaySystem[{"A""AA"},"AA",4,"StatesGraph"]
Out[]=
In[]:=
MultiwaySystem[{"A""AA"},"AA",4,"AllStatesListUnmerged"]
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