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Dragonfall
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If we accept the many-worlds interpretation, how many parallel worlds are there? Finite? Countable? Uncountable? Even bigger? Do we need to bring the continuum hypothesis into it?
Dmitry67 said:different branches which don't interact.
MathematicalPhysicist said:Unaccountable.
2^null_aleph
The explanation is rather simple, if every bit of infomartion is decoded to 0 or 1 (nay or yay) then the number of world is the number of sequences of 0 and 1, which we know from set theory what it is.
Max Tegmark said:The answer is that there are only a finite number of possible states that a Hubble volume can have, according to quantum theory
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Although classical physics allows an infinite number of possible states that a Hubble volume can be in, it's a profound and important fact that quantum physics allows only a finite number.
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Let's first ignore the important complication of past history and ask how many physically distinct states N there are in a volume V. In classical physics, N is infinite (indeed uncountably infinite) as you say, since even specifying the position of a single particle requires infinitely many decimals. In quantum mechanics, however, N is finite: if the temperature never exceeds T, we of course have N < ln S, where S is the entropy of the thermal state with temperature T (I'm taking Bolzmann's constant k=1). Interestingly, the number of states appears to be finite even when taking general relativity into account, which is closely related to the holographic principle: the entropy is maximized if all the matter in V is in a single black hole, in which case, as you know, the Bekenstein-Hawking formula says that N is of order the surface area measured in Planck units. So yes, I see your reasoning, and find it quite striking that quantum mechanics, uncertainty principle and all, contrary to what one might expect, gives fewer states than classical physics. In the limit V->oo, quantum mechanics therefore gives a countable rather than uncountable infinity of states
Quantum physics tells you that before experimenting you have a probability for certain outcomes.Dragonfall said:I don't see how this is related to quantum physics, or the many-worlds interpretation.
yossell said:I didn't understand your reply. How are these strings of 0s and 1s being generated? Why does every outcome correspond to an infinite string of 0 and 1, and why does every infinite string of 0 and 1 correspond to an outcome? You need a 1-1 correspondence between the two to get the result.
Scientists define parallel worlds as separate universes that exist alongside our own, with their own distinct physical laws and characteristics.
There is currently no scientific consensus on the exact number of parallel worlds. Some theories suggest that there may be an infinite number, while others propose a finite but extremely large number.
At this time, there is no definitive proof of the existence of parallel worlds. The concept remains a topic of theoretical discussion and speculation among scientists.
Scientists study parallel worlds through various theoretical frameworks, such as string theory and quantum mechanics. They also use mathematical models and simulations to explore the potential existence and properties of parallel worlds.
While the concept of parallel worlds has often been explored in science fiction, it is also a topic of serious scientific inquiry. Many respected physicists and researchers have proposed theories and conducted studies on the possibility of parallel worlds.