But if the universe is a 3-torus, all three axes have a preferred orientation, — noAxioms
You seem to have a very biased picture of what MWI is. All it states is that any closed system evolves according to Schrodinger's equation. — noAxioms
MWI is not an ontological stance. No creation of new universes ('somewhere' as fishfry puts it) occurs — noAxioms
A bit off topic, but I've always noted that the orientation of the three spatial axes (X, Y, and Z) is arbitrary. If there is an actual x axis, which way is it? But if the universe is a 3-torus, all three axes have a preferred orientation, and this defines a preferred frame as well, even if not an inertial one. If the spatial axes are fixed, the temporal one, orthogonal to the others, is fixed as well.
This is only a minor violation of the principle of relativity, but it galls me enough to discount the significant probability of such a finite topology. — noAxioms
Is this true? I play asteroids in a flat 2-torus space, not on the surface of a donut embedded in three-space. If I fly along either axis, I return to my starting point, but if I angle it a little, I don't. The two axes are obvious even if I'm presented only with a circular screen displaying the local area.In math, the idea of a manifold is more abstract than that. When we imaging the 2-torus, like a big donut in space, we imagine the donut embedded in Euclidean three-space. We can use the equations of the ambient space to describe and manipulate points on the torus. — fishfry
Not always there. No new thing at all, so nothing to always have been there.That's pretty mysterious to me. Do you mean that the new universes don't come into existence? Are you saying that they're always there? — fishfry
Is this true? — noAxioms
I play asteroids in a flat 2-torus space, not on the surface of a donut embedded in three-space. — noAxioms
I should have quoted more.Is this true?
— noAxioms
That a manifold is a locally Euclidean object that exists on its own and does not live in an ambient Euclidean space? Most definitely. — fishfry
Well, only if the space was smaller than the hubble-sphere (which it very much is in asteroids). You could see the repetitive things line up in certain directions. With larger space, that can't be done. The grid is objectively there but the event horizon is too far away to detect the grid.Apologies. I thought your mention of a torus was a typo. Didn't realise it had been introduced into the thread. If we lived in a 3-torus, we would be able to detect that global alignment as you say. — apokrisis
I should have quoted more.
I meant to ask if there was no grid in the sky if the space was torrid manifold. — noAxioms
I then gave the example of the asteroids game which is played on such a manifold, — noAxioms
and there is very much a noticeable grid to it, despite the lack of lines painted through the space or the fact that the screen happens to line up with it. — noAxioms
Well, only if the space was smaller than the hubble-sphere — noAxioms
OK, My terminology is wrong. Orientable, yes. There is no obvious origin, hence no actual grid. It is the orienting that suggests a preferred reference frame.Oh I see your point. Yes, the torus is orientable. — fishfry
I comment on something like this earlier. Such a space is not flat, so it would need to be big enough to account for whatever measure of flatness they've made so far. It's enough that there are places that cannot be reached by light from here, ever. So steering things back on topic, that means it has never been a really alien concept that there are undetectable portions of our universe. Are those places other universes? Not like they're discreet with boundaries where one stops and the next starts.The simplest compact space that would make the point about the Universe being "finitely infinite" would be a sphere.
The story would then not change no matter how big your hubble factor. Or at least not until all that escaping light came back at you from the opposite direction. :) — apokrisis
"because the level-1 multiverse notion assumes that this universe is infinite. In an infinite amount of space, with an infinite number of solar-systems and planets, there inevitably, somewhere, will be an identical copy of Earth, with, of course, a copy of you. ...an infinite number of exact Earth copies, in fact". — Michael Ossipoff
NoAxioms and I just had a lengthy conversation disproving this very point. — fishfry
Could you please review those posts?
What you say is simply not true. At best you have a probabilistic argument that falls short of certainty.
Secondly, the level-1 multiverse only requires a finite universe sufficiently large that light hasn't had time to get from one point to some other point in the age of the universe.
it has never been a really alien concept that there are undetectable portions of our universe. — noAxioms
Are those places other universes? Not like they're discreet with boundaries where one stops and the next starts. — noAxioms
So spatial infinity would seem to guarantee that there should be an infinity of Earths — apokrisis
If there are two states and infinitely many universes they could be 0, 1, 1, 1, 1, 1, ... — fishfry
If 0 is the "earth" state, there is no other earth. 1 is maybe Mars. So Mars exists infinitely many times but not earth. — fishfry
Maybe there's only one earth even though there are infinitely many copies of Mars. It's perfectly possible. — fishfry
Yeah. But you get to pick these infinite sequences out of an infinite hat. So you would pick that exact sequence an infinite number of times. — apokrisis
Your maths doesn't give that result as I've argued. You are trying to hardwire in the restriction that Earth or Mars is the binary choice that reality is having to toss a coin on. But this is about a coin with an infinity of faces - one for every possible state of the world. — apokrisis
But now you are changing the rules of your own game. Instead of Earth = 0, not-Earth = 1, you are saying reality only has the two options of Earth or Mars. And for some reason, nothing else will get pulled out of the hat. — apokrisis
A bit off topic, but I've always noted that the orientation of the three spatial axes (X, Y, and Z) is arbitrary. If there is an actual x axis, which way is it? But if the universe is a 3-torus, all three axes have a preferred orientation, and this defines a preferred frame as well, even if not an inertial one. If the spatial axes are fixed, the temporal one, orthogonal to the others, is fixed as well.
This is only a minor violation of the principle of relativity, but it galls me enough to discount the significant probability of such a finite topology. — noAxioms
I refer you to NoAxoms' argument. Read it carefully this time. — Michael Ossipoff
NoAxioms and I just had a lengthy conversation disproving this very point. Could you please review those posts? What you say is simply not true. At best you have a probabilistic argument that falls short of certainty. — fishfry
Secondly, the level-1 multiverse only requires a finite universe sufficiently large that light hasn't had time to get from one point to some other point in the age of the universe. — fishfry
Now in the more realistic case there are zillions of possible state. Still finite, but very large. But then it's still the case that R1 might be in state 0, and every other region is in some other state. It's still the case that it is possible that some state never repeats. — fishfry
You obviously can't fit in an infinite number of copies of each, which is what you need for a multiverse. — tom
I'm not the one claiming the universe is infinite. I'm simply pointing out that in an infinite collection of regions, with each region taking on one of a finite number of possible states, there's no reason that any particular state must be necessarily be shared by two regions. — fishfry
It's called ergodicity. I have mentioned that ergodicity is a requirement for Type 1 multiverse several times. — tom
So you are requiring the assumption that you are then claiming is true? Well by that logic you're certainly right. If you pre-load your desired conclusion into an assumption, your conclusion falls out at the end. — fishfry
But this is about a coin with an infinity of faces - one for every possible state of the world. And it gets toss an infinity of times, so lands on every one of those faces an infinite number of times. — apokrisis
It might not. It might land on one face an infinite number of times. It might have been Mars all the way down. — Michael
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