# A Question about space and the multiverse

My question is about space and the multiverse. I was reading work by Max Tegmark and he sees the multiverse as Level 1-4. A Level 1 multiverse seems like it's self evident and I was wondering about the evidence against it. It's simple:

Space expands faster than we can observe it so we exist in a pocket or bubble universe that's simply a sphere determined by the speed of light in every direction. So our observable universe is just limited by how far we can see in any direction.

If you go to a galaxy a billion light years away, couldn't you say it's observable universe is a sphere that's determined by the speed of light in every direction from that point and will include space outside of our observable universe.

Wouldn't there be an infinity of the sphere's or pockets as space expands? Does space end because we can't observe it?

Just curious.

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phinds
Gold Member
My question is about space and the multiverse. I was reading work by Max Tegmark and he sees the multiverse as Level 1-4. A Level 1 multiverse seems like it's self evident and I was wondering about the evidence against it. It's simple:

Space expands faster than we can observe it so we exist in a pocket or bubble universe that's simply a sphere determined by the speed of light in every direction. So our observable universe is just limited by how far we can see in any direction.

If you go to a galaxy a billion light years away, couldn't you say it's observable universe is a sphere that's determined by the speed of light in every direction from that point and will include space outside of our observable universe.

Wouldn't there be an infinity of the sphere's or pockets as space expands? Does space end because we can't observe it?

Just curious.
Yes, that's the definition of Observable Universe, BUT ... you are mistaken if you think that they are in any way disconnected from each other. Every single point in the universe has its own OU, but so what? That is not a multiverse in the normal sense of that term. [When you get far enough away you ARE causally disconnected, yes, but that's still not what's normally meant by a multiverse] Because every point has its own OU, they are a continuum.

Yes, that's the definition of Observable Universe, BUT ... you are mistaken if you think that they are in any way disconnected from each other. Every single point in the universe has its own OU, but so what? That is not a multiverse in the normal sense of that term. [When you get far enough away you ARE causally disconnected, yes, but that's still not what's normally meant by a multiverse] Because every point has its own OU, they are a continuum.
This is my point. I said I'm talking about Tegmark's level 1 multiverse not the Parallel universes of QM and Schrodinger's Cat or Inflation.

So, yes, they would be connected. All of these observable universes would share the same physics and the same space. The only thing that would determine these observable universes is the speed of light. So a planet in the Andromeda Galaxy has a different observable universe than earth. So this planets observable universe would consist of space that's not in earth's observable universe and vice versa.

Unless space vanishes because we can't observe it. What's the flaw in this line of thinking?

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phinds
Gold Member
What's the flaw in this line of thinking?
There is none. I am not familiar w/ the various forms of "multiverse" and have never considered what you are talking about to be one. If someone wants to define it that way, well OK.

Bandersnatch
Space expands faster than we can observe it so we exist in a pocket or bubble universe that's simply a sphere determined by the speed of light in every direction. So our observable universe is just limited by how far we can see in any direction.
Just a note here: The first sentence here is not entirely correct - we can see farther than where the recession velocities reach the speed of light. I've noticed Tegmark makes confusing statements in his classification - e.g. here: https://arxiv.org/pdf/0905.1283.pdf he calls what is the particle horizon (how far we can see, i.e. our observable universe; ~46 billion light-years) the Hubble volume (##c/H##; i.e. where expansion reaches the speed of light; ~14.4 billion light years). It's clear that he means the former, since he includes the size. Whereas if somebody then checks the term on the Wikipedia or in a cosmology textbook (e.g. B.Ryden, Introduction to Cosmology) they'll find the latter.
Also, he uses cosmic horizon synonymously with observable universe, which can lead to confusion with cosmic event horizon - which is the maximum possible extent of the observable universe.
Treat every mention of Hubble volume (or cosmic horizon) as the size of the observable universe, and you should be fine.

If you go to a galaxy a billion light years away, couldn't you say it's observable universe is a sphere that's determined by the speed of light in every direction from that point and will include space outside of our observable universe.

Wouldn't there be an infinity of the sphere's or pockets as space expands? Does space end because we can't observe it?
As far as I understand, Tegmark's level 1 calls for observable universes that are entirely non-overlapping. I.e. you need to go to a galaxy 2*the radius of the OU away to momentarily be in another lvl 1 universe. The point being that we are currently completely causally disconnected from any event happening in our next-door neighbour, so in this sense the universes are separate.
However, since the classification is arbitrary, we could very well adopt an overlapping scheme for our own classification (maybe call it level 0 multiverse). Then every one of the infinite number of observers would have their own, at least slightly non-overlapping, lvl 0 universe.
I don't understand why you think this constitutes evidence against Tegmark's lvl 1 multiverse, though.

Just a note here: The first sentence here is not entirely correct - we can see farther than where the recession velocities reach the speed of light. I've noticed Tegmark makes confusing statements in his classification - e.g. here: https://arxiv.org/pdf/0905.1283.pdf he calls what is the particle horizon (how far we can see, i.e. our observable universe; ~46 billion light-years) the Hubble volume (##c/H##; i.e. where expansion reaches the speed of light; ~14.4 billion light years). It's clear that he means the former, since he includes the size. Whereas if somebody then checks the term on the Wikipedia or in a cosmology textbook (e.g. B.Ryden, Introduction to Cosmology) they'll find the latter.
Also, he uses cosmic horizon synonymously with observable universe, which can lead to confusion with cosmic event horizon - which is the maximum possible extent of the observable universe.
Treat every mention of Hubble volume (or cosmic horizon) as the size of the observable universe, and you should be fine.

As far as I understand, Tegmark's level 1 calls for observable universes that are entirely non-overlapping. I.e. you need to go to a galaxy 2*the radius of the OU away to momentarily be in another lvl 1 universe. The point being that we are currently completely causally disconnected from any event happening in our next-door neighbour, so in this sense the universes are separate.
However, since the classification is arbitrary, we could very well adopt an overlapping scheme for our own classification (maybe call it level 0 multiverse). Then every one of the infinite number of observers would have their own, at least slightly non-overlapping, lvl 0 universe.
I don't understand why you think this constitutes evidence against Tegmark's lvl 1 multiverse, though.
I accept Tegmark's Universes accept for the non overlapping part and when he says these universes can have different initial conditions therefore different laws of physics. I think that's in the realm of speculation. That goes to things like string theory and 10^500 false vacua.

I'm talking about overlapping observable universes based on current understanding of the universe. So if you have the infinite expansion of space then their will be multiple observable universes that overlap unless earth is the center of the universe and everything vanishes because we can't observe it.

So our observable universe is determined by the speed of light in every direction. If you stand on a planet a billion light years from earth, then the observable universe would be determined by the speed of light in every direction.

So the observable universe from that point in space would include space that isn't apart of our observable universe and vice versa. All of these observable universes would share the same initial conditions and the same laws of physics.

So if the configuration of matter is finite as some Scientist say, then in an infinitely expanding space our universe will occur again and again with different versions of you in some of them. Hawking talked about reducing all of these universes with different initial conditions in his final paper.

A smooth exit from eternal inflation?

The usual theory of inflation breaks down in eternal inflation. We derive a dual description of eternal inflation in terms of a deformed Euclidean CFT located at the threshold of eternal inflation. The partition function gives the amplitude of different geometries of the threshold surface in the no-boundary state. Its local and global behavior in dual toy models shows that the amplitude is low for surfaces which are not nearly conformal to the round three-sphere and essentially zero for surfaces with negative curvature. Based on this we conjecture that the exit from eternal inflation does not produce an infinite fractal-like multiverse, but is finite and reasonably smooth.
Hawking

Say you have a galaxy 11 billion light years away. This just means it took light from that galaxy 11 billion years to reach us. We're seeing it as it was 11 billion years ago. We can never see it in it's current state unless we find a new way to observe objects. So presently, this galaxy has to exist in space outside of our observable universe. If it doesn't where is it?

phinds
Gold Member
I'm talking about overlapping observable universes based on current understanding of the universe. So if you have the infinite expansion of space then their will be multiple observable universes that overlap unless earth is the center of the universe and everything vanishes because we can't observe it.
Yes, that's just a description of our universe. That is not a multiverse, really. There are not "multiple" observable universes, there are an infinite number of them. Every possible 4D space-time location has an observable universe.

EDIT: Ha. I see I already said all of that in post #2

phinds
Gold Member
Say you have a galaxy 11 billion light years away. This just means it took light from that galaxy 11 billion years to reach us. We're seeing it as it was 11 billion years ago. We can never see it in it's current state unless we find a new way to observe objects. So presently, this galaxy has to exist in space outside of our observable universe. If it doesn't where is it?
This is not correct. The object is still inside our observable universe. Today we see it as it was 11 billion years ago. Tomorrow we'll see it as it was 11 billion years and 1 day ago.

I'm talking about overlapping observable universes based on current understanding of the universe
We need to consider first that Multiverse are somewhere between the lines of conjecture and hypothesis. Second. We need to established some literature of what he meant by Level 1.

"...Observationally, the lower bound has grown dramatically with no indication of an upper bound. We all accept the existence of things that we cannot see but could see if we moved or waited, like ships beyond the horizon. Objects beyond cosmic horizon have similar status, since the observable universe grows by a light-year every year as light from further away has time to reach us4 . If anything, the Level I multiverse sounds trivially obvious. How could space not be infinite? Is there a sign somewhere saying ”Space Ends Here–Mind the Gap”? If so, what lies beyond it? In fact, Einstein’s theory of gravity calls this intuition into question. Space could be finite if it has a convex curvature or an unusual topology (that is, interconnectedness). A spherical, doughnut-shaped or pretzel-shaped universe would have a limited volume and no edges. The cosmic microwave background radiation allows sensitive tests of such scenarios."

The argument is based on our observable universe having a finite, nonzero probability since there is only a finite number of distinguishable configurations within a finite radius (as given by the Bekenstein bound). This is your epsilon. So the measure of our local universe configuration is non-zero, and hence in a sufficiently large and randomly initialized universe (whether spatially infinite or an eternal inflation structure) there will be an infinite number of instances.

He argued that initial conditions (the densities and motions of different types of matter early on) were created by quantum fluctuations during the inflation epoch. This quantum mechanism generates initial conditions that are for all practical purposes random, producing density fluctuations described by what mathematicians call an ergodic random field.

https://arxiv.org/pdf/0905.1283.pdf

PeterDonis
Mentor
2020 Award
Say you have a galaxy 11 billion light years away. This just means it took light from that galaxy 11 billion years to reach us.
Not quite, because the universe expanded while the light was traveling. If the galaxy is 11 billion light-years away "now" (i.e., that's the spatial distance in a spacelike surface of constant FRW coordinate time ##t = t_{\text{now}}##), then the light we see from that galaxy now was emitted less than 11 billion years ago (about half of that, if I'm estimating correctly).