Please explain it to me. If there are no measure zero events, then NO distribution of states to universes is possible. Just like if you flip infinitely many coins. Whatever result comes up, that was a measure zero event. — fishfry
An ergodic random field whose harmonic oscillator coefficients span {1,2,3,4,5,6} with a Gaussian distribution centred on 3.5. The field is in a state of superposition and decoheres for infinite time. What is the probability that the decoherence branch with initial condition "4" will be encountered in the multiverse?
I think maybe you should either accept the physics or try to understand it. — tom
I have not noticed such an explanation. But it's a long thread and I haven't read it all. Can you please point to one such explanation? — andrewk
After finite time there are a countably infinite number of indistinguishable Hubble Volumes — tom
Yes. If you're going to say a result is established in physics, and is obvious. It should come with either a reference to either the paper or popular science article that establishes it, or a description of the text which suggests it.* — fdrake
I don't understand how you can say this, yet claim you don't understand the idea of countably many coin flips. They're the same mathematical idea. — fishfry
You have countably many regions, or universes, or coin flips. Each region or universe or flip is assigned one out of finitely many possible states. One out of a zillion in the case of physics, or one out of 2 in the case of coin flips, but the math is exactly the same either way. — fishfry
You can't mock the idea of coin flips and then come back with the exact same idea in the guise of countably many universes. There's no mathematical difference between a 2-sided coin or a gazillion-sided coin. If the number of states is finite, then probability theory applies. In the large, it is "almost certain" that all states recur infinitely many times, but it is not absolutely certain. The case of coins or universes are exactly the same. It only depends on there being countably many coins or universes or regions, each taking up one out of at most finitely many states. — fishfry
After finite time there are a countably infinite number of indistinguishable Hubble Volumes, which, as time progresses, may diverge. — tom
[My bolding in both quotes]Umm, no. There are uncountably many Hubble Volumes instantiating countably many initial states — tom
In one post you said there are countably many Hubble volumes, and in another post you said there were uncountably many. Can you clarify this? — fishfry
My understanding of your argument is that at the moment of the creation of the multiverse every possible state gets instantiated.
As I understand it, the argument for that conclusion is probabilistic. — fishfry
Hi Sophisticat. I skimmed that article you linked and was interested to note that Vilenkin makes statements like:For those interested, the argument that, as a generic consequence of inflationary cosmology, there almost certainly exist exact duplicates of Earth (among other interesting things) is given here: Many worlds in one, J. Garriga, A. Vilenkin, Phys.Rev. D64 (2001). (This is still within the parameters of "level-I multiverse.") — SophistiCat
where I think what he means is "there is almost surely an infinite number of .....". That is, I think he over-simplified his statement, presumably because he wanted to make it more accessible to the non-physicist reader, since it is a non-technical article. — andrewk
You're being illusive. Wayfarer has a point, and you know the next question.You might explain for us hoi polloi how indistinguishable things can be counted, because we would have thought that distinguishing something is a prerequisite for counting it.
— Wayfarer
I didn't say you could count them. You can't count them. — tom
They must be distinguishable but have at least identical state. If identical state, how can they diverge? You must consider the full set of worlds as the one state, else there is no 'current state' with which another volume can be identical. To do so presumes a QM interpretation like Copenhagen with real chance and action at a distance and a bunch of baggage that muddies the statement that the two volumes are actually identical.There are a countable infinity of INDISTINGUISHABLE Hubble Volumes, which diverge. — tom
You're being illusive. Wayfarer has a point, and you know the next question.
Countable means you can assign a number to any of these volumes, and to do that they must be distinguished. If they can't be, they're not countable. — noAxioms
If identical state, how can they diverge? You must consider the full set of worlds as the one state, else there is no 'current state' with which another volume can be identical. — noAxioms
The distinction is that the Volumes have the same history, not necessarily the same future. — tom
That's why I brought up QM interpretations.If they have the same history, and if determinism is the case, then wouldn't they also have the same future? — Michael
I did in the post to which you replied. Perhaps you think that countable means you can know how many there are, but then the integers are not countable, so you're working from a different rule book.No it doesn't. You can't count your clones. Physics tells us that the cardinality of your clones is Aleph_0.
If you think it is possible to count your clones, I urge you to try. — tom
I think you need to expand on what you mean by these terms since we seem to be talking past each other.I said the Hubble Volumes are INDISTINGUISHABLE not identical.
If they have the same history, and if determinism is the case, then wouldn't they also have the same future? — Michael
I thought you pushed the view that you're married to both of them, a deterministic view.If you perform a quantum measurement - e.g. a measurement of z-spin of a particle prepared in x-spin-up configuration, and choose your spouse based on the result, in half your futures you are married to Mary, in the other half it's Jane. Same past different futures.
Determinism is dead. Long live Unitarity! — tom
I thought you pushed the view that you're married to both of them, a deterministic view.
I just now see Michael's edit where he notes the same view shift. — noAxioms
I skimmed that article you linked and was interested to note that Vilenkin makes statements like:
"there are an infinite number of O-regions with identical histories up to the present"
where I think what he means is "there is almost surely an infinite number of .....". That is, I think he over-simplified his statement, presumably because he wanted to make it more accessible to the non-physicist reader, since it is a non-technical article.
I note that in your post you included the crucial qualifier "almost certainly", although it does not occur in the paper. Interestingly, Tegmark also omits the qualifier (bottom of first column on page 4 of this article you linked) but, like Vilenkin, gives no explanation for the omission, and his article is also more pop science than academic.
Do you have a view on why they omitted the 'almost certain' qualifier from their articles? — andrewk
There is still a possible/impossible distinction though. But is there, really? If "an event A is impossible" means for you that you should live your life as though A will never happen, then events with an extremely low probability are as good as impossible. You live your life assuming that the air will not suddenly evacuate the room through the window, leaving you choking on the floor, even though science says that such an event is possible (and even has a well-defined, finite probability!) — SophistiCat
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