Good points, upvoted. But in fairness, I think the ink blot analogy is a decent one.
Imagine you asked the question about the ink blot to a philosopher in ancient Greece, how might he answer? He might say there is no definite number. Or he might say there must be some underlying reality, even though he doesn’t know for sure what it is; and the best guess says it’s based on atoms; so he might reply that he doesn’t know the answer, but hopefully it might be possible in principle to calculate it if you could count atoms.
I think that’s about where we are regarding the Born probabilities and number or measure of different worlds in MWI right now.
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.
Good points, upvoted. But in fairness, I think the ink blot analogy is a decent one.
Imagine you asked the question about the ink blot to a philosopher in ancient Greece, how might he answer? He might say there is no definite number. Or he might say there must be some underlying reality, even though he doesn’t know for sure what it is; and the best guess says it’s based on atoms; so he might reply that he doesn’t know the answer, but hopefully it might be possible in principle to calculate it if you could count atoms.
I think that’s about where we are regarding the Born probabilities and number or measure of different worlds in MWI right now.
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)wherekis your strictness of what counts as a world,ris how many decoherence events happen per time, andtis time. I chose a base of 2 because all decoherence complexes can be approximately reduced to single splits.rcan be adjusted if some other base is more natural.