Many Worlds And Schrodingers Cat Are 100% infinite dimensional and should be noted that Here it says The systems of This multiverse requires a span of infinite dimensions according to Schrodingers analysis on Quantum Mechanics
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Level III multiverses are those of Schrodingers Cat And Multiverse Theory.
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Level III: A kind of space different from the space-time of our universe exists (called "Hilbert space," which is infinite-dimensional and abstract), where the laws of quantum mechanics generate multiple universes via innumerable branchings. (This is based on taking seriously the quantum wave function, which is a probability amplitude of the quantum state of the system.) The universe branches into different whole-world realities with every tick of time, whether at every Planck time, which is 10^-43 seconds (the time it takes a photon, traveling at the speed of light, to travel one Planck length, 10^-35 m), or at every instant of time when an observation is made. These other whole worlds would not be far away in terms of our kind of space — so in a sense they are right here — but branched out immensely into this different kind of (Hilbert) space. (This is the "many-worlds" interpretation of quantum mechanics, devised by the then relatively unknown physicist Hugh Everett in 1957 and now enjoying new respectability.)
Hilbert Spaces and Such used in Quantum Mechanics are Infinite Dimensional
And https://en.m.wikipedia.org/wiki/Dimension#Vector_spaces
It should also be noted that Wave Functions, something used in Many Worlds and Schrodingers Cat uses Hilbert Spaces as A Tool for Quantum Theory (also known as Many Worlds and Schrodingers Cat):
