I'm just watching a program called "The Universe - Parallell Universes". They keep insisting that every possibility is realized in some universe. For example, there would be universes where George W. Bush never became president. However, it seems to me that that assumes that the number of possible universes has the same (or lower) cardinality, in the sense of Gödel, as the number of parallel universes. That's not obvious to me. Are there any publications that discuss this ?
It's all speculative and there is ZERO hard evidence for alternate universes. Some physicists DO insist that it's the only reasonable interpretation of quantum mechanics, but it is STILL just speculation with no evidence. EDIT: and by the way, as you will find in numerous threads on this forum, you should NEVER believe that anything you see on TV shows is serious physics. Some of it is but much of it is not and they make NO distinction between the two and often make outrageously stupid and/or untrue statements and if you don't know which is which they will just confuse you.
It seems to me that talk of other universes is inherently not science. What makes a statement scientific is that it can be empirically tested. There is no way to observe other universes, so therefore claims about them can never be empirically tested. I know that serious physicists talk about multiple universes, but it sounds to me like quasi-religious nonsense. I'm not an expert, but I am pretty confident that no truly scientific theory could actually require multiple universes. /end rant
Since the thread question says 'could', then yes... nothing disproves the possible existence of every universe existing. It 'could' be the case. But looking at the question more closely... if another universe exists of which there is no theoretical let alone practical way to communicate with it in any way, then is there really any difference between it existing and not existing?
Contrary to popular belief, it's sometimes possible to prove the negative. Some things are logical impossibilities and we therefore know that they can't exist. For example, there are no round squares. My question is if it might be a mathematical impossibility that all possible universes exist. Even if one believes that there is an infinite number of parallel universes that doesn't prove that all possible universes exist. This is so, because Gödel showed that infinite numbers can be assigned a cardinality and, in simple terms, some infinities are larger than others. What I'm really looking for are published papers that discuss Gödel's theorem in this contect. I'm as sceptical of parallel universes as anybody. The idea that all possible events and histories are realized in some universe strikes me as particularly absurd. I'm wondering if there is yet another theoretical argument against that idea, which isn't frequently discussed.
I don't have a source to cite for you, but I am sure if you someone else must. Yes you're correct - if there were an infinitely large universe or infinite any universes, it doesn't mean that everything that can possibly happen must happen.
Cardinality is a property of infinite sets. For example, the infinite set of integers have a lower cardinality than the infinite set of real numbers. This is easy to understand, because there is a real number for every integer, but there is also an infinite set of real numbers between every integer. Hence, there is no '1 to 1' mapping between real numbers and integers. In other words, there are more real numbers than integers. The cardinality of the set of parallel would be determined by how it's generated. Obviously, that depends on what theory is considered, but I would think that a detailed theory would allow the cardinality to be determined. The cardinality of all possible universes, likewise depends on what is meant by that. If one simply means all possible values of the fundamental constants of physics, there is probably no problem. However, if one assumes that every observation, i.e. reduction of wave functions to specific states, 'forks off' a parallel universe, then it seems to me that the cardinality of such a set got to be pretty high. However, I'm not a matematician, only a humble theoretical physicist, so I would like to read some peer reviewed papers on this.
I know. My question was if there is a limit to cardinality. Can you have an infinite set of infinite cardinality?
Caution is warranted when arbitrarily 'ruling out impossible outcomes' : Niels Bohr commenting on Pauli's lecture on a Pauli- Heisenberg unified field theory: [From one of the m ost eminent physiscts of a bygone era] What 'hard evidence' shows there are no parallel universes?
I don't know, that's a mathematics question. My guess is that cardinalities are countably infinite. Given a set of a certain cardinality, it seems plausible that a set with higher cardinality can be constructed.
How do you conclude that ? The infinite set of of universes would have a certain cardinality determined by it's nature. This cardinality may, or may not, be high enough to accomodate all possilble universes. The nature of the set of parallel universes is presumably determined by physical principles. It would be exceedingly poor science to invent some multiverse just for the purpose of accomodate the idea that all possible universes exist, which is an absurd idea to begin with.
There is one interpretation of quantum mechanics called the many worlds interpretation in which any time a quantum process occurs, a new universe splits off. There would could be a universe in which a uranium atom decays at a slightly different time, causing a chain reactions in which Bush never became President. Also, not *every* possibility is realized. You still have conservation laws (mass, energy, etc.) Mathematical rules. And the laws of physics are still the same in all universes. Start with the "interpretations of quantum mechanics" page.
Seems to me like a combination of sensationalistic journalism for the purpose of boosting ratings combined with bad mathematics. A lot of that going around these days.