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.

So yes, I backtracked. — noAxioms

Appreciate that. Just trying to carve out some clarity in a fuzzy discussion.

An infinite sequence is not 'some number' — noAxioms

Is 1/3 = .3333.... = 3/10 + 3/100 + 3/1000 + ... some number?

There's no difference in principle between decimal and binary notation. And binary notation is just a sequence of H/T choices. A real number between 0 and 1 is an infinite sequence of head/tail choices. If you are picking them randomly then the chance of any particular one is zero. But they all exist. That's the point. In infinite probability spaces, probability zero events may occur.

.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.

You're entirely correct about that, but now you are understanding and agreeing with my point. If you throw a dart at the real line, you'll hit a noncomputable number -- a number whose binary or decimal expansion is random -- with probability 1. And you'll hit some computable number with probability zero. But there are plenty of computable numbers.

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'.

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? — noAxioms

That's exactly right. The set of computable numbers is said to have "measure zero." https://en.wikipedia.org/wiki/Null_set

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'. — noAxioms

It's not impossible. The computable numbers exist. You might hit one. There are infinitely many of them, after all. In infinite probability spaces, probability zero events may occur; and probability 1 events are not absolutely certain.

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 have a twin, but probably not you or me.

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.

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

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. — noAxioms

By typical you mean random, or noncomputable. Alan Turing described computable numbers as numbers whose decimal (or binary, same concept) expression can be generated by a program. So numbers like 1/3 are computable. Pi is computable since there are many closed-form expressions that could be programmed into a computer.

The noncomputable, or random reals are the ones whose decimal digits can't be expressed or computed by any program. If you throw a dart at the real number line, the chance that you hit a noncomputable number is 1, and the chance that you hit a computable number is 0. But all the speciic numbers we use in math or science are computable.

I do agree with you that if there are infinitely many universes and only finitely many possible state of matter, it would be very unlikely for only one state to occur infinitely many times. But then again, perhaps there are laws of nature that make some configurations of matter more likely than others, so we don't actually know the true probabilities.

ps -- There's another wrinkle to this. If someone believes that the universe is a computation -- this is the "computable universe hypothesis" -- then the noncomputable numbers don't even exist. Only computable numbers exist. I have a hard time with that because then the real line would be full of holes. But some speculative thinkers believe it.

Multiverse theory, string theory, speculative theories that have zero experimental basis and that can't be experimentally verified even in theory. — fishfry

The quantum multiverse has been known about since 1950s. Schrödinger mentioned it in lectures, several other physicists discovered it independently, most famously Everett in his PhD thesis. The video shows that Hawking accepts it, Feynman discovered it independently, and that Penrose admits it is an inescapable consequence of quantum mechanics.

Many Worlds is at least 60 years old, and has not only passed every test, but has led to the discovery of decoherence and the quantum computer. Every quantum interference experiment is a test of Many Worlds, as are interaction free measurements and many other technological examples.

Many Worlds is at least 60 years old, and has not only passed every test, but has led to the discovery of decoherence and the quantum computer. Every quantum interference experiment is a test of Many Worlds, as are interaction free measurements and many other technological examples. — tom

Perhaps I stand corrected. Are we talking about interpretations of QM? Or actually proven multiverses? My understanding is that Many Worlds is an interpretation, not an experimentally verified fact. But if Feynman and Penrose say so, well ok. I don't know.

Perhaps I stand corrected. Are we talking about interpretations of QM? Or actually proven multiverses? — fishfry

Many Worlds is the only known interpretation of quantum mechanics.

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

Copenhagen is the tricky one, that has caused all the confusion. It suffers from a variety of problems, such as the measurement problem, and led many famous physicists to believe consciousness is responsible for wavefunction collapse. It is largely responsible for Deepak Chopra. It is a different theory from MW because it claims reality does not exist (MW claims it does) and it has the Born Rule as an axiom (MW does not).

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

I can only go by the Wiki article. https://en.wikipedia.org/wiki/Many-worlds_interpretation

They say it's an interpretation. You say it's a done deal. I'm not convinced. Where are all these universes supposed to live? But really that's not the point. The point is that Wiki says MW is an intepretation and you say it's the only known interpretation. I"m in no position to evaluate your claim versus Wiki's except that in this case I tend to believe Wiki.

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.

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. — noAxioms

Non-locality doesn't necessarily have to violate causality. From what I've read, FTL effects can be accepted without retrocausation provided one give up the principle of relativity and adopt a preferred frame of reference. It can be a price to pay in it's own right for some, since it sort of takes the relativity out of relativity theory but if it takes away the problem of killing your own grandfather then it all comes down to what one thinks is preferable. As someone once said, “Relativity, causality, and FTL: pick any two”.

I sort of wonder whether this is the reason why the Bohmian interpretation is said to require a preferred frame of reference. In a sense, it does seem like a very 19th century theory. Non-locality was never a problem until Einstein showed up (Newtonian gravity I think was non-local), and a deterministic, realistic, and non-relativistic theory sounds like something that would be popular then (though maybe not today).

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. — noAxioms

Interference experiments are a test of Many Worlds. Interaction free measurements test Many Worlds, as does the quantum computer.

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. — noAxioms

Bohmian mechanics is Many Worlds in a state of chronic denial. A valiant attempt at realism, but by making ad-hoc modifications to a theory, it goes against the scientific method. Non-relativistic QM is not the last word, it's just a handy regime in which to discuss ideas. Bohmian mechanics has not successfully been made relativistic. And let's not forget that both local and non-local hidden variables are ruled out experimentally. Still, there may be loopholes, so the task of looking for them continues.

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. — noAxioms

With MW you get a standard scientific theory. It explains what is happening in terms of elements of reality that are real and interact locally. There is no measurement problem, and no spooky action at a distance. What is weirder, a reality that consists of many parallel worlds that we can detect by their interactions, and cooperate with in our technologies, or a reality that is not really there and that we are not allowed to question?

I

Non-locality doesn't necessarily have to violate causality. — Mr Bee

Unitary Quantum Mechanics is a local theory. It is only when you ad-hoc modify it or burden it with metaphysical baggage like collapse, hidden variables, and unreality that are you forced to appeal to acausal interactions from beyond spacetime.

Copenhagen preserves locality by giving acausal spooky actions at a distance a different name. It calls them "correlations", as if that changes anything.

Unitary Quantum Mechanics is a local theory. It is only when you ad-hoc modify it or burden it with metaphysical baggage like collapse, hidden variables, and unreality that are you forced to appeal to acausal interactions from beyond spacetime. — tom

What are "acausal interactions from beyond spacetime" supposed to mean?

What are "acausal interactions from beyond spacetime" supposed to mean? — Mr Bee

That would be non-locality a.k.a. spooky action at a distance.

How does the second sentence follow from the first? Do the [level-I multiverse] universes share the same history? Why should they do that? — fishfry

Some of them do.

...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.

Tegmark gives a rough estimate of how far away the nearest one is likely to be, and of course it's a very great distance.

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.

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

Though the matter isn't established, there seems to be agreement among various qualified sources, that the evidence is piling-up in favor of this universe being infinite.

Michael Ossipoff

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. 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.

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.

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

Note that fishfry's source for this claim is, apparently, the bizarre little argument that follows it, and not what scientists actually write, which would be something like the following from a NASA site:

We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe. — NASA

Actually, when they say that the near-flatness of the universe "suggests that the Universe is infinite in extent" - that's an oversimplification. 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.

Be that as it may, you would be hard-pressed to find many cosmologists who dismiss the possibility of an infinite universe on such preposterous a priori grounds.

you would be hard-pressed to find many cosmologists who dismiss the possibility of an infinite universe — SophistiCat

I never dismissed the possibility. I pointed out -- correctly -- that current theory says that the universe is finite. Your own examples support this.

I can see now that an infinitely large number of planets is not needed for the argument, so thanks for correcting me on that.

I remained unconvinced, though, that an infinite number (can there be more than one?) could be specified; because it would seem that any specifiable number must be finite. This is not to deny that an unspecifiable number might be useful for mathematical operations. In any case I see no reason to believe there are infinitely many planets; but admittedly I am no expert on cosmology. — Janus

I have alluded to some more exotic mathematics in which an infinite number can actually be specified (and yes, more than one) - that goes all the way to Cantor. But that's really beside the point. All these fanciful cosmologies that are bandied around here are backed by nothing more exotic than standard calculus. And while calculus used be called "infinitesimal calculus," it has long since eschewed any explicit references to the infinitely small or the infinitely large. When we say things like "an infinite number," that's just a shorthand that, in a more rigorous formulation, unpacks into the kind of weaselly formulation that I gave you above, where I offer you to play a game: give me any number and I can give you an even bigger (but still finite) number. It turns out that that's all we need to get going.

... I offer you to play a game: give me any number and I can give you an even bigger (but still finite) number. It turns out that that's all we need to get going. — SophistiCat

False.

Consider the Peano axioms. Given a number n, there's a greater number called the successor of n.

That gives us a sequence 0, 1, 2, 3, ...

However, that is NOT ENOUGH to get calculus off the ground. To do that, you need a completed set of numbers {0, 1, 2, 3, ...} which is given by the axiom of infinity.

In other words Peano + Infinity = Calculus.

Without the axiom of infinity, each number has a successor but there is no set of all the numbers; no infinite set; and no calculus.

To say this another way: ZFC is stronger than Peano. Important to keep this in mind when slinging around ideas like infinite numbers of planets.

Without the axiom of infinity, each number has a successor but there is no set of all the numbers; no infinite set; and no calculus — fishfry

Sure, you are right. Though "the axiom of infinity" is just a name for an axiom that posits the existence of a set with certain properties. But those properties do not include being "infinite" in some basic sense. But thanks for the qualification.

This does not change what I was saying though: like it or not, most of modern physics does use calculus. You can claim that most of modern physics is misguided (for what that would be worth), but you cannot deny the facts.

I never dismissed the possibility. I pointed out -- correctly -- that current theory says that the universe is finite. Your own examples support this. — fishfry

I take back the bit about not denying facts! And this is why I don't usually engage this person.

This does not change what I was saying though: like it or not, most of modern physics does use calculus. — SophistiCat

Stating the totally obvious.

You can claim that most of modern physics is misguided — SophistiCat

I have never said any such thing.

And this is why I don't usually engage this person. — SophistiCat

If only.

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

The contemporary view would seem to be more subtle than simply that the Comos is "finitely infinite" like the surface of a sphere.

The spacetime sphere is also a material thing. It both expands and cools in reciprocal measure. So in some sense, the surface is thinning as fast as it is growing. The maths has to represent that fact. And so the area of the sphere is now measured entropically in terms of an event horizon with some ultimate number of bits.

Making it really tricky, to actually arrive at some future finite Heat Death or entropy limit requires the further thing of a cosmological constant or dark energy. The geometry of spacetime can't be either perfectly flat and infinite, nor finite by being a closed hypersphere, but must in fact be made finite by being faintly hyperbolic and open in its curvature.

So contemporary physics knows from observation - unless dark energy can be explained away as observational artefact - that the finitude is looking secondary to an infinitude. Something is faintly accelerating the Universe so that it is generally flexed hyperbolically - it bends away from flat infinity in the other direction. And that is what is actually necessary to fix a future date on when the material contents of an expanding/cooling surface will come to a halt at a fixed temperature.

So finitude is the long-term fate. But for reasons still left open until we can account for the "force" creating the faintly open hyperbolic curvature.

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.

But contemporary physics is pretty concerned with an entropic view of reality. Even quantum theory has been "fixed" by welding on statistical mechanics to give us the new and improved decoherence formalism.

The irony is that MWIers latched onto that to peddle their "free lunch" multiverse. But fads come and go. Decoherence is a way to put a thermally coherent limit on a spacetime volume. It brings in the conserving machinery of event horizons.

MWIers still use sleight of tongue to claim infinite branching within the one collective "space". The cost of producing an unlimited number of observers with an unlimited number of points of view is not yet counted by even the expanded quantum formalism, so they can take refuge in that fact.

The maths still only puts numbers on the observables. There is no conservation rule limiting the multiplicity of individual observer. I can be split across as many alternative worlds as you think might be required at "no cost". And so a certain brand of metaphysical nonsense can be promoted as "quantum mechanics with nothing added".

Anyway, the general point is that we do tend to produce simple mathematical frameworks that are open, unbounded and therefore point towards infinity. Then physics comes along and starts to discover the constraints that in fact bound reality and give if some concrete, rather classical-looking, finitude.

The tension between the maths and the physics boils down to issue of how to handle materiality now. Maths is traditionally a view that is spatial. It simplifies by getting rid of time and change and energy within its conceptual metaphysics. But now time and change and energy need to be re-introduced to the mathematical modelling at a fundamental sort of level. They have to indeed emerge from mathematical considerations, not just get tacked on.

Hence string theory, loop quantum gravity, thermal time, anti-de sitter spaces, decoherent QM, holography and other important research projects in contemporary physics.

Multiverse speculation is just the modern equivalent of time travel or "consciousness" based interpretations of QM. A populist sideshow. Metaphysics-lite for the entertainment of the masses.

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.

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.