- #1

nomadreid

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(A) If I understand correctly (no guarantee to that), in an Everett-type Many-Worlds-Theory of Quantum Mechanics, every probability amplitude is associated with a world. This would mean, for a single particle, that there would be as many worlds ("be" in the sense of a model similar to a Kripke Frame, without taking a stand on any other type of existence) as the continuum. In fact, not only for a particle, but for a point (or quantum grain) in spacetime. Given that the largest proposed cardinality for the number of points or grains seems to also be that of the continuum, the product still ends up giving the number of worlds as the continuum. Is this a valid conclusion?

(B) However, (and here is where things get really shaky), given 2 particles, then are there also various possible relations between the two particles in the different worlds (e.g., different strengths of gravity,etc.), or are these considered to be the same (that is, if two particles are the same in two different worlds, can one assume that the interactions between them are also the same?). In the former case, then given c (continuum) particles (or grains, or points), the number of relations would be 2

^{c}, thus giving 2

^{c}number of worlds, whereas in the latter case, the number of worlds would remain at c. Which one, or neither, is applicable?

(I am not sure whether physicists care about cardinality, but a mathematician definitely would.)