the ink blot analogy is not quite so good for counting worlds because it implies more ambiguity than there is.
In reality the most ambiguous amplitude-blot is the inside of a quantum computer. The difference between considering that as all one world or many not-quite-decohered worlds is at most a constant factor on the exponentially growing total number. Most different worlds are very much distinct. The amplitude blots are quite small (atom scale) and infinite-dimensional configuration space is huge. All it takes is one photon to have gone a different way and the blobs are lightyears apart.
Assuming all branches are intact and active (as implied by conservation of amplitude), the number of worlds is approximately k*2^(r*t) where k is your strictness of what counts as a world, r is how many decoherence events happen per time, and t is time. I chose a base of 2 because all decoherence complexes can be approximately reduced to single splits.r can be adjusted if some other base is more natural.
the ink blot analogy is not quite so good for counting worlds because it implies more ambiguity than there is.
In reality the most ambiguous amplitude-blot is the inside of a quantum computer. The difference between considering that as all one world or many not-quite-decohered worlds is at most a constant factor on the exponentially growing total number. Most different worlds are very much distinct. The amplitude blots are quite small (atom scale) and infinite-dimensional configuration space is huge. All it takes is one photon to have gone a different way and the blobs are lightyears apart.
Assuming all branches are intact and active (as implied by conservation of amplitude), the number of worlds is approximately
k*2^(r*t)
wherek
is your strictness of what counts as a world,r
is how many decoherence events happen per time, andt
is time. I chose a base of 2 because all decoherence complexes can be approximately reduced to single splits.r
can be adjusted if some other base is more natural.