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

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. So volumes like ours, we're (arbitrarily) 1 and the nearest copy is 2. It is distinguished by being nearest. Of course the copy of me over there considers his volume to be 1 and ours (of which he is unaware) to be 3 because there happens to be another one closer to him. We're both unaware of the actual locations of those copies, so identical state is maintained. It is an objective ordering. Anyway, they're identical in state, but still objectively distinguishable and thus objectively countable.
I think it is a mistake to say this then:

There are a countable infinity of INDISTINGUISHABLE Hubble Volumes, which diverge. — 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.

Heck, with that definition, maybe every Hubble Volume is identical state, and yes, that would mean uncountable.
Sorry for this post. Just thinking out loud.

They’re both metaphysical issues which physicalists are trying to solve by infinite ad hoc additions to physical theory. — Wayfarer

Funny, I see them as subtractions.

The short version: the ‘many worlds theory’ is based on avoiding the philosophically unsavoury implications of the observer problem.

The multiverse - ditto for the unsavoury implications of the fine-tuning problem.

I find them elegant solutions. The unsavory feeling you get seems to be a challenge to a religious view of what you are. Yes, I would find that unsavory, and cause for further investigation, not a terminus because it threatens my biases.

Not going to happen.
— noAxioms

You are passing up a valuable learning opportunity! Go on, give it a try! — tom

I mean the 1m3 expanding to infinity is not going to happen. OK, I worded it ambiguously, and you took it to mean that I'm not going to attempt the math.

I cannot think of anyone who has put forth a scientific hypothesis that mermaids don't exist. You have a link to such a proposal?

In practice, we don't need to worry about a time zero for either a spatially finite or a spatially infinite universe, because the General Theory of Relativity, which is used to do the backwards projection, loses validity as the scale becomes very small, and we have no theory to replace it. We can't use quantum mechanics because it ignores gravitational effects and in a very dense universe those cannot be ignored. — andrewk

I don't know my cosmology enough to describe the actual workings of our big bang. Inflation theory says there was different physics for a short time, low temperature, and perhaps the usual notions of 'density' wouldn't apply. The mass of the universe, if existing in some sort of finite volume, would form a black hole and never get off the ground.

Suffice it to say that for the purposes of this thread, the declaration that space is infinite implies it was always infinite ever since it was space. The material/energy probably never fully interacted. There is stuff that never was part of our causal history, even going all the way back. No reason to worry about it anyway since the Earth contains finite state and thus has no need of that history to be identical to another Earth.
We do have history though. If an exact duplicate Boltzmann Earth suddenly popped into existence in orbit around a plausible star, I would be on it and that 'me' would notice damn fast that it wasn't the native Earth.

I haven't gone through this idea carefully, but I'm moderately confident there is no 'reasonable' mathematical model in which a spatially infinite universe contains a time zero. If that's correct then there is no question of whether the universe was infinite or a single point at that time, since there is no such time. — andrewk

If the model has a event 0, there is no space to have a size. That's what makes it a singularity.

Maybe you should show your working? — tom

I did. I took the question for sarcasm and responded in kind when you persisted.

Given an initial 1m3 of space-time, what expansion rate is required to turn it into literally infinite volume in any finite time?

Not going to happen. Universe was never 1m3 it seems.

So, what rate of expansion do you think might be required to turn a subatomic spec into a literally infinite universe in 13.8 billion years? Have you done the calculation? — tom

You persist with this. Is it a serious question? 6 days, after which enough expansion took place to qualify as infinite. On the 7th day, the expansion rested. I really don't know how else to answer that.

The rate of expansion may be static, increasing, or decreasing. As long as there is a +ve Hubble constant, there will be Hubble Volumes.

A Hubble volume is not a type-1 universe. It is just the volume containing the matter whose distance from us is growing at sub-lightspeed. The Type-1 universe is bounded by the event horizon, beyond which things cannot ever have a causal effect here. It is something like 16BLY in radius at this time (comoving coordinates again).
About the Hubble constant, it is not a constant since the expansion rate is increasing. The constant is just what the value is now, and thus can only be measured to so much precision.
I looked at its description on space.com and found text more worthy of the New York Post:

As of March 2013, NASA estimates the rate of expansion is about 70.4 kilometers per second per megaparsec. A megaparsec is a million parsecs, or about 3.3 million light-years, so this is almost unimaginably fast. — space.com

km/sec per megaparsec is not a velocity, so not sure how this could be unimaginably fast. 70km/sec is not much more than the orbital speed of Mercury, and I think I can manage the imagination of it. Sorry. I was hoping for better from a site like that.

Sure, your Hubble volume and my Hubble volume might be slightly different in 14 billion years. In the mean time, there are an infinite number of Hubble volumes that were never in causal contact with ours. — tom

The example was about the nearby overlapping ones, not the countless more distant ones.

Why do you think Hubble Volumes were ever in contact or overlap? — tom

Another note: Level 3 universes overlap as well. There is amazing symmetry between the level 1 and level 3 concepts.
Level 1 is just Schrodinger's box implemented with distance instead of technology.

How much expansion is required to produce a literally infinite universe from a point in a mere 13.8 billion years? — tom

The comment here only makes sense if interpreted as sarcasm. It implies that there might have been finite hubble volumes, and after enough time, that goes to infinite. The greater the expansion, the less time it takes to do this. No, not my view.
The way I see it: If the geometry is such that the universe wraps (like the sphere of the balloon analogy), then there are finite Hubble-volumes. Assuming not, then if the expansion rate is increasing, there are infinite such volumes. If the rate is not increasing, light will eventually get from anywhere to anywhere else, and the universe is a single Hubble volume. At no point does "13.8 billions years" play into that.

Why do you think Hubble Volumes were ever in contact or overlap?

Why do you think they don't? We are at the exact center of our Hubble volume. Isn't that amazing? From the perspective of a planet 10 BLY away to the left (all this is in comoving coordinates BTW), they are centered on a different volume that encompasses us way to the right. Their volume ends further to the right of us, but not a whole lot further. Some distant galaxy to our right can be seen from here but can never ever be seen by them. It is outside their Hubble Volume. Our volumes overlap else we couldn't see each other.
To say they're all nonoverlapping implies there are discreet chunks of disjoint space with one preferred point in each of them which is their center. My model doesn't look like that.

There are also Level 2 multiverse earths.

I would think so, yes. Level 4 as well.

Thanks guys. Didn't think it would work. A few holes to point out, but in the end, the state of Earth does not require all the universe to have been this and thus.

Now, an atom has a finite number of configurations, or states that it can possibly be in (10 for hydrogen, I think). — SophistiCat

One atom has no position, velocity, or other relations. But a group does, and each atom has innumerable additional states that make up its relationships with the others. Really innumerable??? Maybe not.

Our visible universe may well have been the size of a point at the Big-Bang, but the entire Level 1 Multiverse was not. — tom

Maybe my model is incorrect, but this seems wrong. Since the level-1 spheres overlap, they're all points in the beginning, and all the same point at that, else they'd not overlap. I don't totally grasp eternal inflation theory, where perhaps the inflation stuff rips away as normal space forms in the bubble, but that is not a description of a point except the point where the bubble first began, not necessarily being the point that represents our hubble sphere.

As I've mentioned several times, the Bekenstein bound severely limits the number of states available to any volume of space. — tom

Limits it given finite energy. If the initial infinite universe was actually a point, there is infinite energy/information there. But this actually kills my idea. Earth is a limited space with limited energy. The bound applies. Earth cannot be in a unique state that requires the history of the entire set of material that was once in its causal past. Tegmark was working on a bound such as this, and then just computed how much space was required to make it likely that a good majority of those (valid) states were realized.

Information must be preserved, but like other conserved things, it need not all be conserved here. Most of that information is shipped off elsewhere.

The number line has to be both continuous yet discrete at the same time. — apokrisis

I just picked this out. Agree with your post. My history-of-everything assumes no discreetness at all. Any tiny difference way below Planck constant would still yield a measurable difference after chaos gets to do its thing. Sort of invalidates the Planck concepts.
I hate discreet anything. How slow can something go? If it moves one Planck length each hour, what does it do while it waits for the next one? A discreet universe would exhibit jaggies. Ewww....

The set of possible outcomes from an infinite sequence of coin tosses is uncountable. — andrewk

Right. Can count only the finite ones (trivially at that). The coin model works, and thus 1 followed by all zeros is possible. Shot down again.

Am still enjoying the concept. Perhaps a proof that no copy is possible then? The distant Earth might be outside our causal cone now, but it wasn't always. All matter (or whatever it was back then) was at the big bang and is part of the causal history of this planet. Since information is preserved, a perfect copy has it all. Thin ice there. Maybe the info was shipped out of reach, even if preserved.
Anyway, if that works, Earth (or just an apple say), contains the history of its entire causal cone in the past and cannot be recreated without that entire past, which is infinite stuff.
Tegmark assumes Earth can be represented with finite state, and computes the distance needed to get the probability of a repro up to about 1. If if the state is no finite number, then no copy.

In an infinite sample space, Probability zero is not the same as Impossible. The term 'almost surely' was invented to cover exactly this case. It is applied to an event that is in the sample space (ie 'possible') but has zero probability. — andrewk

I realized that I had made an error and backed off my 'certainly' claim pending a redo. In the end, I decided that no-Earth was not in sample-space. It's not the same as stabbing at an infinite list of impossible to hit things, inevitably hitting one of them.
That math might not be right either (I didn't show it), but it seems to hold the probability of hitting a specific countable number in random sample of the uncountable reals.
I am basing a lot of my claims on another thread debating why 0.999... is 1, not just infinitesimally close to it. It was explained by someone who knows their stuff far better than I.

With the usual binomial model of fair coin tossing, the event of an infinite sequence of heads is one that 'almost surely' will not occur, which is not the same as saying it cannot occur. — andrewk

Not sure if a model of fair coin tossing applies. In an uncountable sample space, the one you actually hit cannot be represented by any number of coin tosses.

Does anyone here disagree that speed is a measurement defined as velocity = distance/time? — AngleWyrm

Speed is distance/time. Velocity is a vector, so it has a directional component. One can accelerate (also a vector quantity) and change velocity without changing speed.
Speed and velocity are not absolute properties of objects. They are relations between things.

If distance loses it's meaning of 1 lightyear = 1 lightyear then I suggest that isn't science it's some sort of perspective modification that is creating meaninglessness.

It is still distance, but Meta's post above is correct. Distance is a local measurement that begins to alter meaning for significantly separated things.

Had a hard time picking out a consistent point being made in that long post, so I picked this little bit out.

It's difficult to believe that such beings would observe events on our planet without instituting the policing that would protect us from eachother. ...as in Clarke's Childhood's End. — Michael Ossipoff

This sort of makes the assumption that we're worth saving. How can a species that has the collective maturity of an ebola outbreak be the thing they want to save? If there's a test, we certainly have yet to pass it.

Does the red-shift seen in the color of light from distant stars represent the distance between us and that star, as in has distance been tightly correlated to that effect through another reliable measure of distance?

Because there's other interpretations, such as a doppler frequency shift due to velocity between us, which looks a bit odd in the face of light-speed is always the same in every frame of reference. — AngleWyrm

Doppler shift, yes. Light is the same speed in any frame. It is not the same frequency or wavelength. Those are frame dependent measurements.
A photon has no objective wavelength or frequency, but a full spectrum beam of light bears the fingerprint of the frame of the source of the light. Hence the speed of some distant star can be assessed by the measurable shift of the light frequency.

I'm not sure about this. I wonder if the principle behind the Boltzmann brain hypothesis can also apply here. It is more likely that an Earth-like planet spontaneously forms than for a Hubble volume to grow and develop as ours is believed to have done. — Michael

Interesting. Perhaps we could define a duplicate as not just a state, but one that persists for a second or so as a natural duplicate should. A Boltzmann Earth duplicate ceases to be a duplicate immediately just like the brain ceases to be a brain in a moment

Does it means that absolute time is some dimension not known or measured by us on this planet?? — vesko

Absolute time is fiction. I can't prove there are no invisible pink unicorns, but I can't detect them either.
To say there is no absolute time is to say there is no detectable actual time of the universe. It is meaningless to say exactly when some supernova occurred in Andromeda galaxy for instance. An arbitrary frame of reference must be presumed to do that. Pretty much any statement without a specified reference frame presumes absolute time and/or space. Absolute time would imply that all events anywhere are objectively ordered and that there is a correct frame, but again, no way to determine that frame if light speed is the same in all frames.
Light speed being the same in all frames is the only empirical evidence that led to relativity. Myttenar's picture of things (somebody is wrong) can be falsified by lightspeed measurements.

Read a good tutorial on relativity, especially some of the initial thought experiments that led to the SR parts, and not just the articles that teach the conclusions. The thinking behind it helps so much, and helps one to drop the ingrained presumption of absolute time.

With the twins, the travelling twin's time is dilated in the Earth frame, but in the space ship frames, it is the Earth twin whose time is dilated and exhibits less duration.

A man can be wrong without creating a paradox. — Myttenar

Who is wrong? The guy who labelled as a paradox the twin-experiment? It is indeed not a paradox. But you're also labelling it a perceptual problem, so again, who's perceptual problem?

↪vesko this is not a paradox but a simple error of judgment on behalf of the twin who perceives the ships' clock to be ticking slower. — Myttenar

OK, you think one of the twins has a perceptual problem. Not so. He sees his clock ticking at normal pace, and he's right. If you assert that he is wrong about this, then please don't explain this stuff to vesko.

can you explain to me what is perceptual problem,if possible with examples. Thanks. — vesko

There isn't one. Everybody is correct about their ages and the durations of their experience. The only problem is the presumption of absolute time, which is something no instrument can measure, and hence has no evidence of existence.

As for A and B series being the same, yes, but both work for a place, even one that moves around. For any place (say where this ping-pong ball is), events are ordered the same way for both series. There is no difference. For two locations (say here and planet Zog), events are ambiguously ordered, both in A and B series. Either way, there is no difference between the series. Neither is an assertion of a metaphysical stance and hence neither is right or wrong. It's just two different ways of referencing the same things.

Who would benefit from hiring a philosopher? The whole point seems to be thinking of things with no practical application. If there is something practical about it, it isn't philosophy, it becomes science. Those guys tend to be ignored as well if they're not talking about immediate benefits.
So what specific contribution do you think a philosopher has to offer?

I agree they are not other universes. — apokrisis

The type-3 ones are also not other universes, for more or less the same reasons.

So spatial infinity would seem to guarantee that there should be an infinity of Earths where you and me are having this exact discussion - plus every other even faintly similar or utterly different interactions. We could be discussing hair-do's, speaking in Korean, typing random sequences. And the fact any of those might be the case would mean that all those varieties of cloned Earths would have to be infinite in number themselves. There would be an infinite number of replica planets with us speaking Korean, etc.

You mean there is a pile of near-replicas to go with each actual replica. Yes. Those aren't so far away, depending on how loose you allow your definition of 'near replica' to be.

There just is no end to the madness once you let actual infinity run riot in your ontology.

You seem to be apeirophobic *. I followed the argument until it was suddenly labelled madness.
* The word seems to mean more fear of eternity, not infinities of the non-temporal sort. So fear of realities that involve infinities. Could find no better word for that.

Anyway, even in a spatially infinite universe, we would presume that it all expands and cools in the same way. And cooling steadily - or in fact, exponentially - removes material possibilities. If every portion of the universe is losing energy density at a shared rate, that means there is only a tiny time window for replica earths to actually form.

Of course. Any replica of Earth would be the exact same age. A replica cannot begin to form by chance for example, centuries from now on the other side of our galaxy.

Even in Euclidean space, as soon as you introduce something to break the symmetry, you already have some kind of "preference." For example, in a universe that is a flat space with one black hole there is an obvious "center." — SophistiCat

That one makes a bit of a hash of the Copernican principle at least. Ossipoff's initial post on the prior page was such a violation, but there is no such principle in the view he was supporting there.

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

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.

If there is an exact copy of Earth way out there, then there is an exact copy of me on it. Is that guy me? There are arguments to both sides of that question, so "depends" is all that can be said for now.

Oh I see your point. Yes, the torus is orientable. — fishfry

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.

A curved spherical space is not orientable. You'd see a copy of Earth in all directions, or at least you would if light speed was infinite or Earth was polite enough to hold still. With a flat 3-torrid manifold, the nearest Earths in the sky would be in 6 directions, hence the orientation suggestion.

I tried it with a 3-klein bottle and saw my backside reflection. Weird. And yes, no suggested way to look to do that. It is beyond my imagination to see the distorted picture of diverging ray tracing in such a space.

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

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.

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

I should have quoted more.
I meant to ask if there was no grid in the sky if the space was torrid manifold. I then gave the example of the asteroids game which is played on such a manifold, 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.

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

Not always there. No new thing at all, so nothing to always have been there.
Schrodinger's cat is the best example. The cat is both dead and alive, without the creation of a new cat, one of which doesn't survive. Still one cat in superposition. They've done this with a macroscopic object now. They have a box that holds something that can be seen without aid, and put that thing in superposition, not create a second thing, both of which are in the box.

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

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.
This seems to counter what you're saying. There can be a continuous finite 2-space that does not exhibit this property? I can't think of how that would work.

This all has relevance to MWI multiverse hype. The big problem - if you believe in the reality of principles like the conservation of energy, or causal closure, at all - is that MWI violates energy conservation in the most fundamental fashion. That is at the guts of an instinctive objection.

Now if you are not used to taking the materiality of the Universe seriously, then perhaps it is easy just to imagine the free creation of endless worlds, or endless world branches. — apokrisis

MWI is not an ontological stance. No creation of new universes or new material ('somewhere' as fishfry puts it) occurs, and energy conservation laws are safe.
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.

A locally flat(tish) universe is compatible with some finite topologies, such as a 3-torus. These guys did some serious number-crunching with WMAP data and came to the conclusion that out of several likely topologies that they considered, a certain compact (finite) topology provided a better fit than the infinite flat topology. — SophistiCat

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 and I just had a lengthy conversation disproving this very point. — fishfry

Unconvinced we disproved it. I left convinced that a random stab will hit a zero-probability 'typical number' which are uncountably infinite. There are also infinite specific numbers, and they are countable. An exact copy of Earth is a specific number. The odds of it being never copied in infinite space is thus zero, with certainty. Of course it was also posted that contemporary physics puts a finite size on the universe, which dispells the whole infinite data-set thingy. Still level 1 places, but not necessary a copy of us.

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 means there will never be enough time. It requires the expansion to be accelerating since steady expansion still allows light to travel from anywhere to anywhere else eventually.

By the way, I'd expect that if an infinite universe means that there are other civilizations in the universe, then the nearest one is so far away that, for all practical purposes, including communication or transportation, it's the same, for us, as if it weren't there. — Michael Ossipoff

How do you get this? It seems, especially in the context of this thread, to follow from an assumption that other civilizations must be essentially identical to us to be, well, civilizations.

Could there not be any other civilizations in this universe, if the universe is infinite?

You just got finished saying there is an exact copy of us out there, given infinite space.

Maybe, if, as a form of high-tech quarantine, our belligerent and aggressive species, along with its planet, has been re-located into a universe that was specifically designed, by an advanced technology, to not have any life other than us.

This statement is quite a break from the usual stance I've seen from you. You gone all ID on us? Tegmark for instance described a universe not in need of creation, not designed, nor one where we are special.

We need a thread on the Fermi paradox. Much more relevant to this sort of discussion.

Many Worlds is the only known interpretation of quantum mechanics. — tom

Well, you list others, so there are other known interpretations. Support of MWI is growing among physicists, but it has yet to reach a majority. For the record, my opinion rests with the MWI guys, but without a falsification test, it remains an interpretation, not a theory.

Bohmian mechanics - adds hidden variables to QM, thus a different theory. Doesn't work.

Why are hidden variables disallowed? I think you're right actually in that it was proved somewhere that there can be no hidden variables, but its supporters obviously don't think the proof carries weight.

GRW - ads stochastic collapse to QM, thus a different theory. Doesn't work.
Transactional - I really don't care.

These are new ones to me, but again, why does this addition disqualify them?
Copenhagen is not mentioned, and it carries a lot of voting support still.

My personal aversion to most of the other interpretation is non-locality. Bohmian doesn't necessarily have it, but the others do. The ability to alter the past seems a nastier pill to swallow than the (mostly religious) implications of what MWI does to one's biased ideas of personal identity.

It's not impossible. The computable numbers exist. You might hit one. — fishfry

Well, I hit a different one that cannot be hit, so I'm on thin ice to counter this. But having hit this computable number, I must in addition throw infinite coins and come up heads on them all, or else I just got close to it. I don't need to do that with the 'typical number'. Is there a term for that? I made that up.

Getting back to our original point, this is why even if there are infinitely many universes, SOME state must recur infinitely many times, but not necessarily any particular one. SOME person might exist infinitely many times, but probably not you or me. — fishfry

I would suggest 'possibly not'. If someone has infinite copies, I probably do as well. But I must back off the 'definitely' stance.

So at best, the "in an infinite universe there must be two earths" is false in an absolute sense, and is at best a probabilistic argument. Which I think we already agreed on.

Yes

Trying to discredit my own statements.
You take a stab at a number line with a pointer and you will hit a 'typical number' as I call it. That number cannot be expressed with any amount of digits. It has zero probability of being hit, and yet it was hit.
Is that more what you're after?

Edit: I wrote that before reading your last post. Creepy...
No, I would say it is impossible to hit a computable (or expressible) number, except to say 'this one'.

.3333... is not a sequence of random digits with equal probability. It is in fact the decimal notation for 1/3, something that can be expressed in a few characters. A typical real number is inexpressible because it actually is a sequence of random digits, be they base 2, 10, or 37.
If you can express it in finite language, it is not a typical number, it is a special one.

Well yeah, that's my point. You claimed there's a dup earth, I asked you to support your claim, and you have apparently backtracked. Yes? — fishfry

I am told that contemporary models are not of infinite comoving space. Not being an expert, I have no ground to assert otherwise. So yes, I backtracked.

I pointed out that ANY specific infinite sequence has probability zero. Are you unclear on this point? — fishfry

Clear, and it makes no sense. Any infinite sequence cannot be a specific one. That seems to be the point on which we differ. An infinite sequence is not 'some number' any more than its length is.

Which is good, because contemporary physics holds that the universe is finite. — fishfry

If so, the dup-Earth bit kinda falls apart, eh?

In infinite probability spaces, probability zero events may still happen. Suppose you flip infinitely many coins and they come up in any sequence whatsoever: hthhthththththhthttthhthththt... say. A completely random sequence. What's the probability? Well, the prob that flip 1 is h is 1/2. The prob that flip 2 is t is 1/2. Etc. The prob of the first n flips being exactly what they are is 1/2^n, and that goes to zero as n goes to infinity. Every particular sequence has probability zero. Do you follow that point? — fishfry

No, disagree with this. A finite sequence has a nonzero probability. An infinite one is not a specific one, and has probability zero and does not happen.
Every particular sequence has half the probability of the flip sequence of one-less flip. That is not zero. Some probability-zero sequence is not a particular sequence and thus does not in fact occur.

A 3-manifold, e.g. a 3-sphere, is finite with no edge. — tom

Good point.

It is psychologically interesting that people generally accept the existence of the Type 1 multiverse, when there is absolutely no evidence for it. I'm not sure if evidence for it is even possible? — tom

Isn't just a curvature measurement enough? If flat enough, there are places sufficiently separated to never interact. Yes, expansion is required for that, but not infinite space.

First, why is the space infinite? Your premise is that the universe is finite but sufficiently large that there are regions inaccessible to each other due to light not having had enough time to get from one place to the other. That doesn't require an infinite universe. — fishfry

Indeed, it doesn't require infinite space. It (a type 1 world, not a duplicate) does at least require an expanding universe, else eventually light would have time to cross the distance. The dup-Earth requires space big enough to form duplicates of something, which could in theory be close enough to be visible from here once light had time to make the trip. That is more probable than what you show below where it by chance just never happens.

Secondly, even if the universe is finite AND the possible states in a given region of space are finite, you STILL are not guaranteed a duplicate earth. Say there are two states, and infinitely many universes:

0, 1, 1, 1, 1, 1, 1, ...

Not guaranteed, no. A coin may flip tails forever. It's just a probability after enough distance.

Edit: I think that mathematically, a coin cannot come up tails forever. There cannot not be a dup Earth given infinite space. The probability of of that is 0.000... which is zero.

Again thought, you're betraying your original premise. You started with TWO regions of the universe that are causally and informationally isolated from one another. That's two, not infinitely many.

Not sure I follow this. If there is a duplicate, there would seem to be an infinite number of them. There is simply a probability as to how far away (measured in non-linear units) the nearest one is. There are infinite type-1 worlds given infinite universe size. In fact, each point in space is centered on such a world, so you are in a different one than I am. Light can in theory reach (immortal) you from your slightly-left-shifted world but never reach me in mine. That means that by the time the light gets to you, the expansion of the universe separates us so far that we're forever isolated from each other.