Regarding the many worlds theory of quantum mechanics.
In essence the many world theory states that every time there is the probability of two (or more) events happening the universe splits i.e. both events occur but in separate universes.
If two universes by different paths achieved quantum states that are identical in every respect (including all quantum states of particles) would two identical (at that one moment in time ) universes exist or is there some kind of Pauli exclusion principle in the many worlds theorem that would force the probability paths to converge to one universe?
Well, number one the Pauli Principle only applies to fermions whose spatial separation is such that their wavefunctions overlap and for two totally separate universes it wouldn’t come into play.
Secondly, quantum mechanics is inherently statistical in nature and any concept of two identical ensembles is meaningless.
Hmm. I don’t know that I’d agree, Ring. In principle, Fermi statistics apply to well-separated fermions, yes? Consider, for example, the EPR paradox.
That said, I don’t see why the many worlds approach would require each world to be different, or even how; I do agree with Ring in that two entirely separate universes, Fermi statistics oughtn’t matter.
The fermions just have to be part of the same quantum system and identical.
Many Worlds theory doesn’t obviously deal with identical universes as such things unless proved otherwise would be against the thinking of Occam’s razor (something that many accuse the many worlds theory itself of being).
I believe Feynman’s theory of light is that each photon leaving point A can take ANY path to point B. Including the one around Jupiter, to the North Star, and so forth. I think there’s some experimental evidence to back up his theory. The thing is (of course) that it is just incredibly unlikely for a photon to take a path much different than the one you’d expect, i.e. the one you’d draw in a simple ray-diagram. So wouldn’t that mean the many worlds theory would say that there are an infinite number of universes for EACH photon? Or take a photon or electron in a double-slit experiment. They have a finite probability of being anywhere on the screen (excpet, in the model, at a dark minimum).
That said, and unless the many world theory does not apply to such things, I think it a bogus theory. Our universe is RUN by probabilities. You don’t walk through trees or see faces in interference patterns because it’s incredibly unlikely. Heck, entropy increases only because it’s more probable (am I right?). To suppose there is a universe for every event, and of course these universes are undetectable, seems to me to be a crazy thought experiment to sooth the minds of someone who doesn’t like that our world is merely probabilistic.
The Pauli Principle is a specific case of the more general phenomenon of Exchange Forces (which really aren’t forces at all). If you calculate the expectation value of the spatial separation of two quantum particles you get a result for bosons that includes the term
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And for fermions
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So fermions tend to be found further apart then bosons when their wavefunctions overlap. But the above term vanishes if there is no overlap. (I think this is covered inGriffiths)
From Quantum Physics of Atoms, Molecules,…… By Eisberg and Resnick pg 316
“Many Worlds” is a mathematically correct alternative to the Copenhagen interpretation of the collapse of the wavefunction. It has nothing to do Feynman’s Sum Over Histories.
It is true that we don’t need to worry about exchange interactions at large enough distances because they fall off fairly rapidly. But the minute I consider two hydrogen atoms at some large but finite separation, the wavefunction for the entire system still has to be antisymmetric. This may have (and in fact does have) a negligible effect on pretty much anything one might care to measure, but the convenience of Fermi statistics being unimportant is no reason to pretend that Fermi statistics aren’t satisfied.
As I read it, what Eisberg and Resnick are saying is that Fermi statistics are unimportant (true), so for practical purposes, you can ignore them (true), but not necessarily that they stop being obeyed (which wouldn’t be true).