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
Well, I cannot answer for Vilenkin or Tegmark, but I think they were speaking informally. — SophistiCat
How we interpret these results depends on how we think about probability. If we interpret probability as a quantitative measure of credence, or degree of belief, then there isn't really a difference between "almost surely" and "surely": in either case, the credence is exactly zero. This failure to make a distinction between possibility and impossibility may be a deficiency of the epistemic interpretation of probability (not to mention the problems of formal probabilistic modeling that have been raised here). — SophistiCat
But if we further think about our concepts of probability and possibility, this might be argued to be a distinction without a difference. We can hardly tell the difference in credence between an event that has a probability of 10-10 in a single trial and one with a probability 10-100. We stop making a difference long before "almost surely". — SophistiCat
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
The general point that I wanted to make is that if there are separate systems with a finite number of possible states between them, then for them to be found in the same state at some moment, they do not have to have identical histories up to that moment — SophistiCat
Not sure which post brings on this reply. I brought up an insanely complex quantum equation in my prior post, but never suggested it was in need of being expressed or solved.The case of a simple bound system, such as a hydrogen atom, is easier to analyze than a more general case: we can actually solve the quantum equations and enumerate every possible state. — SophistiCat
We're talking a hubble-volume in this case, which has a finite but large degree of freedom. My wave function was based on that. Interestingly, I think it was a mistake to specify an inertial frame in my description. The full wave function of the one event is enough. If another event somewhere has the same wave function, it defines a clone Hubble sphere to ours.There is, however, a theorem for the general case in quantum mechanics, which puts a limit on the number of possible states, or degrees of freedom, given a volume and energy density within that volume.
Agree with this. Yes, I think I alluded to the opposite at first, but you're right. This was pointed out to me in a prior post.The general point that I wanted to make is that if there are separate systems with a finite number of possible states between them, then for them to be found in the same state at some moment, they do not have to have identical histories up to that moment. Even in a purely deterministic universe, as these systems transition from one state to another, they may end up in the same state at some point simply by chance. What that chance is - high, low, "almost surely" - will depend on a more detailed analysis.
They do not say that they are speaking precisely and formally in their books. It is only you that says that. The evidence points to the opposite being the case. The absence of equations is a big clue.I've quoted from Vilenkin's book. Nerither he not Tegmark were speaking informally. — tom
No it doesn't. You can't count your clones. Physics tells us that the cardinality of your clones is Aleph_0. — tom
I think the cosmological principle allows such exceptions, but just says that the probability of us being that exception is sufficiently infinitesimal to preclude explanations that require us to be that exception.We need another assumption. the cosmological principle, which says in effect that there are no measure zero misbehaviors! — fishfry
I think the cosmological principle allows such exceptions, but just says that the probability of us being that exception is sufficiently infinitesimal to preclude explanations that require us to be that exception. — noAxioms
Well actually the author has misused the cosmological principle, which implies nothing of the sort. The cosmological principle states that each constant-time hypersurface of the universe ('this spacetime') is homogeneous and isotropic at the large scale. When formalised (which is quite tricky to do - see this discussion), this is a statement about observed average quantities as the size of the hypersurface subsets we average over approaches infinity.We need another assumption. the cosmological principle, which says in effect that there are no measure zero misbehaviors! — fishfry
So the cosmological principle says absolutely nothing about microphenomena such as whether a particular teensy-weensy arrangement of molecules like the Earth recurs. — andrewk
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