The Multiverse

Summary

• "The multiverse" is not one idea. It names at least five proposals with different evidence, different motivations and different consequences. Max Tegmark sorted four of them into levels in 2003, and his own summary is the point to start from: "The key question is not whether parallel universes exist (Level I is the uncontroversial cosmological concordance model), but how many levels there are."¹
• Level I — more space beyond what we can see — is close to uncontroversial. It follows from ordinary cosmology if space is infinite and roughly uniform. It does not vary the constants, so it does nothing for or against fine-tuning.
• Level II — a landscape of regions with different constants — is the only one the fine-tuning debate is about. It is the version worth arguing over, and almost every popular treatment on both sides quietly swaps one level for another.
• Level III — Everett's many-worlds reading of quantum mechanics — does not vary the constants and therefore does nothing for fine-tuning. Tegmark, who defends it, says so plainly: it "adds nothing new beyond Level I and Level II."¹ Apologists who attack many-worlds as the atheist escape from fine-tuning have hit the wrong target.
• The landscape was not bolted on to answer the design argument. Eternal inflation falls out of the same inflation models that fit the data; Bousso and Polchinski proposed a flux "discretuum" in 2000 to attack the cosmological constant problem; and the vacuum-counting programme that produced the famous 10⁵⁰⁰ was a string-theory bookkeeping exercise about predictivity.
• The 10⁵⁰⁰ figure has a specific and misreported origin. It is not in Bousso and Polchinski 2000, and it is not in Ashok and Douglas's "Counting Flux Vacua." It first appears in Michael Douglas's 2004 review, as typical parameters plugged into Ashok and Douglas's formula — and Douglas's very next sentence calls it a problem: "This is probably too large for statistical selection to work."² Ashok and Douglas's own worked example gave about 4 × 10²¹.³ A 2015 F-theory count gives 10^272,000 from a single geometry.⁴ Nobody has counted the vacua of string theory; these are estimates from formulas whose inputs are guessed.
• Anthropic selection is a real explanation and should not be waved away. If constants vary across a huge ensemble, and only a thin slice permits observers, then observers necessarily find themselves in the thin slice. Steven Weinberg used exactly this reasoning in 1987 to bound the cosmological constant before dark energy was measured, and the observed value landed inside his bound. That is the strongest card the multiverse holds and it is a real one.
• The measure problem is the hinge, and both sides concede it is unsolved. Alan Guth, David Kaiser and Yasunori Nomura: "a persuasive theory of probabilities in the multiverse has not yet been found."⁵ Without a measure, an infinite ensemble supports no probability claim at all — not the multiverse's, and not the design argument's. The same mathematics that wrecks the one wrecks the other, a point Timothy McGrew, Lydia McGrew and Eric Vestrup made against their fellow Christians in 2001.⁶
• Boltzmann brains are the sharpest internal problem. If a model predicts that most observers fluctuate out of equilibrium with false memories, then the model undercuts the evidence used to believe it. Sean Carroll's term is "cognitively unstable": such theories "cannot simultaneously be true and justifiably believed."⁷ Luke Barnes, who is a theist, thinks this "might sink the whole idea" — and says it does not falsify the multiverse.⁸
• The inverse gambler's fallacy charge is live but not decisive. Ian Hacking and Roger White argue that one improbable universe is no evidence for many, because this roll is not evidence about other rolls. Yoaav Isaacs, John Hawthorne and Jeffrey Sanford Russell mounted a systematic defence in the Philosophical Review in 2022. The dispute is unresolved and this article reports it rather than claiming it.
• One multiverse prediction has been tested and came back null. If our bubble collided with a neighbour, the scar should show in the microwave background. Stephen Feeney and colleagues searched WMAP's seven-year data and found the data "do not warrant augmenting ΛCDM with bubble collisions."⁹ That is a real test, and it failed to find anything. Most other versions predict nothing observable at all.
• An untestable model is not thereby false. It is thereby unable to earn support from evidence. This project applies that standard to young-earth cosmologies in the young-universe cosmologies article, where it does real damage to models this project would like to be true. It has to cut the same way here. The multiverse is not refuted by being hard to test; it is prevented from being confirmed.
• The theology is smaller than both sides pretend. A multiverse does not refute theism, several theists accept one, and "God could have made a multiverse" is a fair reply. It does blunt the fine-tuning argument if true. What it is not is a desperate atheist invention: Weinberg, Bousso, Polchinski, Susskind, Linde, Vilenkin, Rees and Tegmark reached it from cosmological-constant arithmetic and inflationary dynamics, and Bousso and Polchinski's 2000 paper does not mention design at all.

This is a case file under the fine-tuning article, which treats the multiverse in one section, and a companion to cosmic inflation, which treats eternal inflation as a falsifiability problem.  Both stay published in full.  This article goes into the parts they compress.

Five different things called "the multiverse"

The first job of any honest treatment is to stop using one word for five ideas.  Popular apologetics and popular science both do it.  A Christian speaker attacks "the multiverse" by attacking many-worlds quantum mechanics, which has nothing to do with fine-tuning.  A science documentary defends "the multiverse" by pointing to space beyond the horizon, which nobody disputes and which explains nothing.  Both sides then declare victory.

Max Tegmark, then at Penn, sorted the proposals into a four-level hierarchy in a 2003 chapter for a volume honouring John Wheeler.  The scheme has stuck because it is useful:  each level is a strictly larger claim than the one before, and the evidence for each is different in kind.

Tegmark's own summary of the situation is the sentence to keep:

The key question is not whether parallel universes exist (Level I is the uncontroversial cosmological concordance model), but how many levels there are.¹

Only Level II bears on fine-tuning.  That is the whole reason the taxonomy matters here.  If the constants do not vary across the ensemble, an ensemble does nothing to explain why our constants permit life — every member has the same constants and the puzzle is untouched.  Level I does not vary them.  Level III does not vary them.  Level IV varies them, but by varying everything else too, at a price almost nobody is willing to pay.

Level I: more space, and why it settles nothing

Level I is the claim that space keeps going past the edge of what we can see, filled with roughly the same stuff.  Our horizon is set by the age of the universe and the speed of light, not by any physical wall.  Nothing in the equations makes matter stop where our sight does.

If space is infinite and matter is spread roughly uniformly, then any finite arrangement of particles that can occur will occur somewhere, and will occur infinitely often.  That includes arrangements identical to the room you are in.  Tegmark's estimate, stated in his abstract, is that there is "an identical copy of you about 10¹⁰²⁹ m away."¹  That figure is not a measurement.  It is a counting exercise over possible arrangements of matter, and the paper's own far more cautious version — obtained by "simply counting all possible quantum states that a Hubble volume can have that are no hotter than 10⁸ K," which Tegmark calls "an extremely conservative estimate" — puts the nearest duplicate at about 10¹⁰¹¹⁵ metres instead.¹  Two estimates whose exponents differ by a factor of 10⁸⁶ are a signal about how loose this reasoning is.  What survives the looseness is the qualitative claim:  in an infinite, roughly uniform space, every finite arrangement recurs.

Two observations make the picture reasonable rather than wild.  Measurements of the microwave background are consistent with flat, unbounded space, and searches for a finite, wrapped-around topology have found nothing.  And spatial infinity is a generic output of inflation.  Tegmark's summary:  the microwave background "allows sensitive tests of such finite models, but has so far produced no support for them — flat infinite models fit the data fine and strong limits have been placed on both spatial curvature and multiply connected topologies."¹

None of this helps the fine-tuning debate in either direction.  Every Level I region runs on the same physics with the same constants.  If gravity is too strong for stars here, it is too strong everywhere, and the extra volume buys nothing.  Level I multiplies planets, not physics.  It matters for questions about life's rarity on planets — the habitability article covers those — but not for why the constants themselves permit chemistry.

Anyone who defends "the multiverse" by describing Level I and then treats fine-tuning as answered has changed the subject.

Level II: where the varying constants come from

Level II is the version that matters.  It says that different regions of an eternally inflating spacetime settle into different vacuum states, and that the effective low-energy physics — the particle masses, the force strengths, the cosmological constant, possibly the number of large spatial dimensions — differs between them.  It has two components, and they were developed separately, by different people, for different reasons.  Neither was invented to answer the design argument.

Part one: eternal inflation supplies the mechanism

Inflation is a brief episode of accelerated expansion in the early universe, proposed by Alan Guth in 1981.  The inflation article grades the evidence for it in detail;  the short version is that it has real successes and real unsolved problems, and that the tilt of the primordial spectrum is a genuine prediction that came true.

The relevant feature here is that inflation, once started, tends not to stop everywhere.  Quantum fluctuations keep kicking the inflaton field back up its potential in some regions.  Those regions keep inflating.  Because inflating volume grows exponentially and non-inflating volume does not, the still-inflating fraction always dominates the total.  Inflation ends only in pockets — bubbles — which are then whole universes from the inside.  Guth's 2007 review states the technical position in its abstract:  "inflation is generically eternal into the future."¹⁰

How firm is that inference?  Firmer than a skeptic might guess, and softer than the confident popular treatments suggest.  Three things are true at once.

It is not an add-on.  It was discovered inside the standard models rather than imported.  Guth's own review credits it to Paul Steinhardt:  "The eternal nature of new inflation was first discovered by Steinhardt, and later that year Vilenkin showed that new inflationary models are generically eternal."¹⁰  Steinhardt is now inflation's fiercest critic, and the feature he now says makes the theory untestable is one he found.

It is generic, not universal.  "Generically eternal" is not "necessarily eternal."  Whether a given model inflates eternally depends on the shape of its potential and on the size of quantum kicks relative to classical roll.  There are non-eternal inflationary models.  They are a minority of the model space and they are not the ones that best fit the data.

And it is a statement about a spacetime nobody can observe.  The bubbles are outside each other's horizons by construction.  This is the source of everything that goes wrong later in this article.

Part two: the landscape supplies the variation

Eternal inflation on its own gives many bubbles with the same physics.  That is Level I with extra steps, and it does nothing for fine-tuning.  Level II needs a second ingredient:  a reason the low-energy constants should differ from bubble to bubble.  That reason is supposed to come from string theory.

The story starts with a problem that has nothing to do with life.  The vacuum energy predicted by quantum field theory is enormously larger than the value the universe displays.  Weinberg's own statement of the size of the mismatch, in the paper where he argues for a multiverse:  "Quantum fluctuations in known fields at well-understood energies (say, less than 100 GeV) give a value of ρ_V larger than observationally allowed by a factor 10⁵⁶."¹¹  Cancelling that requires 56 decimal places of agreement between unrelated quantities, and no symmetry principle produces it.

In April 2000 Raphael Bousso and Joseph Polchinski proposed a way out.  If several four-form gauge fluxes thread the compact extra dimensions, and each is quantised, the vacuum energy takes discrete values — but with enough independent fluxes, the discrete values are packed so densely that some fall in the observed range.  They coined a word for it.  From their abstract:

For a single flux the steps are much larger than the observational limit, but we show that with multiple fluxes the allowed values can form a sufficiently dense 'discretuum'.  Multiple fluxes generally arise in M theory compactifications on manifolds with non-trivial three-cycles.  In theories with large extra dimensions a few four-forms suffice; otherwise of order 100 are needed.¹²

Two things about this paper are worth noticing, because both are usually lost.  The number of fluxes it asks for is about 100, not 10⁵⁰⁰.  And it does not mention design, God, or the fine-tuning argument.  Its anthropic reasoning is stated in one deflationary sentence:  "In the end the observed cosmological constant is small for anthropic reasons, but in the weakest sense: we have a universe with different cosmological constants in different regions, and with galaxies only in regions of small cosmological constant."¹²

Leonard Susskind named the resulting space of vacua in 2003, in a paper whose abstract concedes exactly how speculative it is:  "In this lecture I make some educated guesses, about the landscape of string theory vacua.  Based on the recent work of a number of authors, it seems plausible that the lanscape is unimaginably large and diverse.  Whether we like it or not, this is the kind of behavior that gives credence to the Anthropic Principle."¹³  The typo is Susskind's.

Where 10⁵⁰⁰ came from — and what it actually is

The figure 10⁵⁰⁰ appears in nearly every popular account of the multiverse, usually as "string theory has 10⁵⁰⁰ solutions."  Its provenance is worth tracing, because the trail does not end where almost everyone says it does — including one Nobel laureate.

It is not in Bousso and Polchinski 2000.  A full-text search of that paper finds no 10⁵⁰⁰.  Their working figure is about 100 fluxes;  the number of vacua they need to solve the cosmological constant problem is about 10¹²⁰, matching the size of the mismatch they are trying to cancel.

It is not in Ashok and Douglas, "Counting Flux Vacua."  That is the paper that did the mathematics.  Sujay Ashok and Michael Douglas, at Rutgers, derived an asymptotic formula for the number of supersymmetric flux vacua of type IIb string theory on a Calabi-Yau, and then worked one concrete example.  Their number for it is:

∼ 4 · 10²¹ for L = 32.³

Four sextillion, not 10⁵⁰⁰.  Their own description of Bousso and Polchinski, at the top of the paper, gives 10¹²⁰:  Bousso and Polchinski "suggested that a large number of flux vacua, say N_vac ∼ 10¹²⁰, might provide a solution of the cosmological constant problem."³  And their motivation is explicitly about predictivity, not about life:  "it is very important to bound the number of string vacua which resemble the Standard Model and our universe, because if this number is infinite, it is likely that string/M theory will have little or no predictive power."³

The 10⁵⁰⁰ first appears in Michael Douglas's 2004 review, "Basic Results in Vacuum Statistics," in Comptes Rendus Physique.  He takes the Ashok-Douglas formula, plugs in ranges for its two inputs, and reports the result — with a verdict attached in the very next sentence:

Typical K ∼ 100 − 400 and L ∼ 500 − 5000, leading to N_vac ∼ 10⁵⁰⁰.  This is probably too large for statistical selection to work.²

That is where the famous number comes from:  a guessed range for two parameters, substituted into an asymptotic formula, in a review article whose author immediately calls the answer a problem.  Douglas's concern is that if there are that many vacua, string theory cannot be used to predict anything, because some vacuum will match any observation.  The number was published as a worry, not as a triumph.

The mis-citation is worth documenting because of who committed it.  In "Living in the Multiverse," Steven Weinberg writes:  "Ashok and Douglas estimated the number of these vacua to be of order 10¹⁰⁰ to 10⁵⁰⁰," and footnotes it to the Counting Flux Vacua paper.¹¹  Neither number is in that paper.  The 10¹⁰⁰ is in Douglas's separate 2003 survey;¹⁴ the 10⁵⁰⁰ is in the Comptes Rendus review, which Weinberg cites elsewhere in the same lecture for a different point.¹¹  Nothing important turns on it, and Weinberg's argument survives the correction untouched.  But a reader who wants to check "10⁵⁰⁰" against a source will not find it where the trail says it is.

Later counts are much bigger and no better grounded.  In 2015 Washington Taylor and Yi-Nan Wang at MIT applied the same estimation method to F-theory and found that one particular elliptic Calabi-Yau fourfold dominates everything:

Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold M_max gives rise to O(10^272,000) F-theory flux vacua, and that the sum total of the numbers of flux vacua from all other F-theory geometries is suppressed by a relative factor of O(10⁻³⁰⁰⁰).⁴

They also record the honest status of the type IIB figure everyone quotes:  "For type IIB string theory, the number of flux compactifications on certain geometries is famously estimated at ∼ O(10⁵⁰⁰)."⁴  Famously estimated.  Not counted.

What all of this means for the argument.  Nobody has enumerated the vacua of string theory.  Nobody has constructed even one fully explicit, fully stabilised vacuum matching the observed Standard Model.  What exists is a family of counting formulas whose inputs are geometric parameters chosen for plausibility, applied to a theory that has not been experimentally confirmed at all.  The landscape may be right.  But "string theory predicts 10⁵⁰⁰ universes" is not a measurement, and anyone who quotes the number as though it were should be asked which paper it is in.  For most of the last twenty years, the answer given has been the wrong one.

Level III: many-worlds, and why it is the wrong target

Hugh Everett III's 1957 Princeton dissertation proposed that the wavefunction never collapses.  Every term in a superposition persists;  the observer becomes correlated with each outcome;  what looks like collapse is decoherence separating the branches so they cannot interfere.  On this reading a quantum measurement does not select one result.  All results happen, each on its own branch.

Whether Everett's reading is correct is a live question in the foundations of physics, and this article takes no side on it.  What matters here is narrower and it is not disputed even by the interpretation's defenders:  many-worlds does not vary the constants of nature, and therefore contributes nothing to the fine-tuning debate.

Tegmark defends Level III and says so himself:

If physical constants, spacetime dimensionality etc. can vary as in Level II, then they too will vary between parallel quantum branches at Level III. … In short, the Level III multiverse, if it exists, adds nothing new beyond Level I and Level II — just more indistinguishable copies of the same universes, the same old storylines playing out again and again in other quantum branches.¹

Read the conditional in the first sentence carefully.  Level III branches carry different constants only if Level II already supplies varying constants.  On its own, with the laws and constants fixed, Everett's picture gives you every outcome of every quantum event running the same physics.  Every branch has the same fine structure constant.  If that value forbids chemistry, it forbids chemistry on all of them.

Tegmark notes the irony that this is the level people fight about:  "It is ironic and perhaps due to historic coincidence that Level III is the one that has drawn the most fire in the past decades, since it is the only one that adds no qualitatively new types of universes."¹

The practical upshot for apologists is unwelcome and worth stating plainly.  A large amount of popular Christian writing attacks "the multiverse" by attacking many-worlds — the branching, the copies of you, the strangeness of it.  That criticism, whatever its merits in quantum foundations, does not touch the multiverse that the fine-tuning argument has to answer.  Attacking Level III and declaring the fine-tuning argument safe is arguing against the wrong proposal.  The same error runs the other way:  a documentary that explains many-worlds and then says the constants no longer need explaining has made a mistake Tegmark's own paper corrects.

Level IV, and the ensembles outside the ladder

Level IV is Tegmark's own proposal:  every mathematical structure that exists as a mathematical structure exists physically, and the physical world is one of them.  It is an attempt to answer why these equations rather than others by removing the "rather than."  Almost nobody else holds it.  It is worth knowing that it exists, mostly so that a reader can recognise when a popular account has slid into it.  Nothing in this article depends on it.

Outside the ladder sit ensembles that are not inflationary at all.

Cyclic and bouncing cosmologies generate a sequence of universes in time rather than a set of bubbles in space.  Whether the constants reset at each bounce depends on the model.  Steinhardt, who rejects the inflationary multiverse, works on cyclic models, which is one reason this is a distinct family and not a variant of Level II.

Cosmological natural selection, proposed by Lee Smolin in 1992, is the most interesting of them, because it is the only landscape-style proposal that has ever made a risky prediction.  Smolin's idea:  black holes give birth to new universes with slightly altered constants;  universes that make many black holes therefore have many descendants;  after many generations the population is dominated by parameter values that maximise black hole production.  No anthropic reasoning is used.  Smolin's own claim for it is explicitly methodological — that his conditions show "it is possible to continue to do physics on a landscape without invoking the anthropic principle."¹⁵

Its first prediction, and what happened to it, are covered under testability below.

The anthropic argument, stated at its strongest

Before the objections, the argument deserves its best form, because it is a good argument and dismissing it is a mistake.

Start with what nobody disputes.  An observation-selection effect is real and unremarkable.  If a survey only questions people who own telephones, its results are about telephone owners.  If a fossil record only preserves hard parts, the record is about hard parts.  Nobody calls this a fallacy;  it is a correction that competent researchers apply routinely.

Now apply it to physics.  Suppose the constants take different values in different regions of a very large ensemble.  Only a thin slice of parameter space permits atoms, stars and chemistry.  Observers can only arise in that slice.  Therefore every observer, without exception, finds their local constants inside the life-permitting slice, no matter how thin it is and no matter how the values were distributed.  The observation "our constants permit life" is then guaranteed, not lucky, and needs no further explanation.

The structure is exactly the structure of the telephone survey.  What it needs, and what makes it a substantive claim in physics rather than a triviality, is the ensemble.  Without varying constants there is no selection to perform.

And it has one genuine success on the board.  This is the part that critics of the multiverse tend to skip, and it should not be skipped.

In 1987 Weinberg published an anthropic bound on the cosmological constant in Physical Review Letters.¹⁶  His reasoning: if the vacuum energy were much larger than the matter density at the epoch when galaxies condense, expansion would outrun gravity and galaxies would never form.  So any observer must find a vacuum energy below that bound.  His 1989 review in Reviews of Modern Physics states the number:  the anthropic requirement is a vacuum energy density "no larger than, say 100ρ_M," with the more careful bracketed form giving 410ρ_M.¹⁷  At the time, the prevailing expectation was that the cosmological constant was exactly zero, cancelled by some symmetry nobody had found.

In 1998 Hugo Martel, Paul Shapiro and Weinberg pushed further and computed the distribution of vacuum energies that observers throughout such a multiverse would see.  Weinberg's account of what they concluded, and of the fight to publish it:

In this way we concluded that if Ω_Λ turned out to be much less than 0.6, anthropic reasoning could not explain why it was so small.  The editor of the Astrophysical Journal objected to publishing papers about anthropic calculations, and we had to sell our article by pointing out that we had provided a strong argument for abandoning an anthropic explanation of a small value of ρ_V, if it turned out to be too small.¹¹

That is a stated falsification condition, published in 1998, in a peer-reviewed journal, before the answer was known.  Then supernova cosmology measured Ω_Λ ≈ 0.7.  Weinberg's next sentence:  "Of course, it turned out that ρ_V is not too small."¹¹

Two things are true about this and both should be said.

It is a real success and it is the only one of its kind.  A hypothesis said in advance what would refute it, the test was run, and it was not refuted.  Anybody arguing that the multiverse has never made a prediction has to deal with this case.

And the prediction was loose.  The observed vacuum energy is about 2.2 times the present matter density.  Weinberg's 1987 upper bound was about a hundred times higher, and the "principle of mediocrity" expectation that ρ_V "should be not very different from the mean of the values suitable for life"¹¹ points to a value well above what we observe.  Getting an answer inside a bound two orders of magnitude wide is a pass, not a bullseye.  It should be reported as a pass.

What goes wrong: the measure problem

This is the deepest problem and it is not a debating point.  Both sides state it in the same words.

An eternally inflating spacetime contains infinitely many bubbles.  Every outcome that has any chance of happening happens, infinitely often.  Guth, in a section headed "Difficulties in Calculating Probabilities":

In an eternally inflating universe, anything that can happen will happen; in fact, it will happen an infinite number of times.  Thus, the question of what is possible becomes trivial—anything is possible, unless it violates some absolute conservation law.  To extract predictions from the theory, we must therefore learn to distinguish the probable from the improbable.¹⁰

To say a theory predicts something is to say that something is likely given the theory.  In an infinite ensemble where every outcome occurs infinitely often, "likely" needs a rule for comparing infinite sets — a way of saying that this infinite class of bubbles is bigger than that one.  Such a rule is called a measure.  Choosing one requires a cutoff:  count bubbles up to some time, or in some volume, or by some other scheme, then take a limit.

Different cutoffs give different answers, and nobody has found a principled reason to prefer one.  Guth, Kaiser and Nomura, defending inflation against its critics, concede the point in their concluding section:  "although significant progress has been made in recent years, a persuasive theory of probabilities in the multiverse has not yet been found."⁵  Earlier in the same paper:  "To us, the measure problem is simply an important problem that remains to be solved."⁵

Some measures produce results that are obviously wrong.  Bousso and Freivogel showed in 2006 that the natural "global" way of counting observers in a multiverse gives a self-contradictory answer:

We use an argument by Page to exhibit a paradox in the global description of the multiverse: the overwhelming majority of observers arise from quantum fluctuations and not by conventional evolution.  Unless we are extremely atypical, this contradicts observation.¹⁸

That is not a fringe objection.  Bousso is one of the two authors of the paper that started the landscape programme, and he is reporting that the obvious way of doing the arithmetic breaks.

Luke Barnes, writing as a Bayesian and a theist, gives the cleanest statement of what the problem actually is.  It is not that infinity is spooky.  It is that probability theory has a known rule for handling infinite sets and the multiverse breaks it:

Jaynes (2003, p. 486-7) warns that "attempts to apply the rules of probability theory directly and indiscriminately on infinite sets" leads to paradoxes, and that the only cure for this disease is that "an infinite set should be thought of only as the limit of a specific (i.e. unambiguously specified) sequence of finite sets."…  The problem for an infinite multiverse is that there is no such limit — the infinity in question is "completed", an actually infinite set of universes and observers.¹⁹

Why this matters more than it first appears.  Every quantitative claim made for the multiverse runs through the measure.  "Most observers see a small cosmological constant."  "Typical bubbles have three large dimensions."  "It is unsurprising that we find ourselves here."  Each of these is a probability statement about an infinite ensemble, and none of them has a defined value until the measure is fixed.  The multiverse's explanatory power is entirely a promissory note against a calculation nobody can currently do.

And the same mathematics cuts the other way.  This is the part a Christian reader should sit with rather than skip.

In 2001 Timothy McGrew, Lydia McGrew and Eric Vestrup — all three Christians, and the last a measure theorist who wrote a textbook for Wiley — published "Probabilities and the Fine-Tuning Argument: A Sceptical View" in Mind.⁶  Their objection is that "the life-permitting range is a tiny fraction of the possible range" has no defined value when the possible range is unbounded.  Under countable additivity no uniform distribution over an infinite range exists.  Under finite additivity one exists and assigns probability exactly zero to every finite window, including windows a billion orders of magnitude wide.  The fine-tuning article works this through in detail, along with the replies from Robin Collins, Jeffrey Koperski and Luke Barnes.

The structural point for this article is simple.  The multiverse's measure problem and the design argument's normalizability problem are the same problem.  Both are attempts to extract a probability from an unbounded space with no natural measure on it.  An apologist who says "the multiverse can't compute probabilities, so it explains nothing" has to accept that "the constants are improbable on chance" is under the same disability.  Ellis, who is a critic of the multiverse, makes exactly this observation about the anthropic prediction of the dark energy density:  "we cannot apply a probability argument if there is no multiverse to apply the concept of probability to.  This argument thus assumes the desired outcome before it starts."²⁰  The knife has two edges.

What goes wrong: Boltzmann brains

Here is the second internal problem, and it is the one physicists take most seriously.

In a universe that lasts forever in a state of near-thermal equilibrium — which is what a de Sitter space with a positive cosmological constant looks like in the far future — random fluctuations will occasionally assemble ordered structures out of the noise.  Given infinite time, they will assemble anything, including a brain, complete with a set of memories that were never lived.  These are Boltzmann brains, named after Ludwig Boltzmann, whose 1890s discussion of fluctuation cosmology introduced the idea.

The problem is arithmetic.  Ordinary observers arise once per galaxy-forming epoch in each bubble.  Fluctuation observers arise forever, at a fantastically low rate, in an infinite volume of empty space.  Multiply a tiny rate by an infinite duration and the fluctuation observers can win — in many measures, by an enormous margin.

If most observers are Boltzmann brains, then the theory says you are probably one.  A Boltzmann brain's memories are noise.  So the theory tells you that your memory of reading the evidence for the theory is probably fabricated.  Sean Carroll's abstract states the consequence exactly:

The issue is not that the existence of such observers is ruled out by data, but that the theories that predict them are cognitively unstable: they cannot simultaneously be true and justifiably believed.⁷

And in the body:

The randomly-fluctuating universe scenario is therefore self-undermining, or as Albert has characterized similar situations in statistical mechanics, cognitively unstable.  If you reason yourself into believing that you live in such a universe, you have to conclude that you have no justification for accepting your own reasoning.  You cannot simultaneously conclude that you live in a randomly-fluctuating universe and believe that you have good reason for concluding that.⁷

Carroll's conclusion is that cognitive instability is grounds for rejecting a cosmological model, not merely for finding it awkward:

We therefore conclude that the right strategy is to reject cosmological models that would be dominated by Boltzmann Brains (or at least Boltzmann Observers among those who have data just like ours), not because we have empirical evidence against them, but because they are cognitively unstable and therefore self-undermining and unworthy of serious consideration.⁷

He is careful about what this does not establish:  "We can't say for sure that it is not true – it's possible that we do live in a fluctuation away from equilibrium, perhaps with completely false memories of the past."⁷

How bad is this for the multiverse?  Honestly reported, it is serious and not fatal.  Whether a given multiverse model is Boltzmann-brain-dominated depends on the measure — which is unsolved — and on the lifetime of metastable vacua, which is unknown.  Several proposed measures avoid the problem.  None of them is independently motivated.

Luke Barnes, who argues for theism, gives the fair verdict, and it cuts both ways:

But those Boltzmann Brains are a worry.  A multiverse that avoids them must favour biological life forms — like us — over isolated, freak observers.  This might sink the whole idea.⁸

"Might sink the whole idea" is a strong statement from a friendly witness.  It is also not "has sunk."  Anyone quoting Barnes on Boltzmann brains should quote the whole sentence.

What goes wrong: the inverse gambler's fallacy

This is the philosophers' objection, and it is the one that has produced the largest literature.

Ian Hacking raised it in 1987 against John Wheeler's oscillating-universe model.  His illustration, as quoted by his critics:

The kibitzer asks, 'Is this the first roll of the dice, do you think, or have we made many a one earlier tonight?'  The gambler … says, 'Can I wait until I see how this roll comes out, before I lay my bet with you on the number of past plays made tonight?'  The kibitzer, no fool, agrees, although charging a slight fee for allowing this extra "information."  The roll is double-six.  The gambler foolishly says, 'Ha, that makes a difference—I think there have been quite a few rolls.'²¹

The gambler is wrong.  Dice have no memory.  The chance of double-six on this roll is 1/36 no matter how many rolls preceded it.  Learning the outcome of one roll tells you nothing about how many rolls there were.

Roger White developed the argument against multiverse cosmology in Noûs in 2000.  His formal point separates two propositions that look alike and behave differently:  E, "our universe is life-permitting," and E′, "some universe is life-permitting."  A multiverse raises the probability of E′.  It leaves the probability of E untouched, because our universe's constants were fixed by whatever process fixed them, independent of how many other universes exist.  White's summary:

Given M, it is likely that some universe instantiates T₁, and it is true that a instantiates some T_i, but it is highly improbable that the T_i instantiated by a is T₁, regardless of the truth of M.²²

And the diagnosis:

The mistake is in supposing that the existence of many other universes makes it more likely that this one—the only one that we have observed—will be life-permitting.²²

The observation-selection reply, and White's answer to it

The obvious reply is that this is not like dice, because there is a selection effect:  we could not have found ourselves in a lifeless universe.  White anticipates it and answers with a pair of cases.

In his Case B, Jane sleeps while dice are rolled and is woken as soon as any double-six comes up.  On waking she may reasonably infer many rolls, because the converse holds — if any double six is rolled, she is woken.  Her waking is connected to the whole series.  In his Case B, each sleeper has one dedicated roller and is woken only if her own* partner rolls double six.  Now her waking tells her nothing about how many other sleepers there are.

White's claim is that our situation is Case B*, not Case B:

It is certainly not sufficient for us to exist in some universe b, that b is fine-tuned, or even that b is qualitatively exactly as a actually is.  After all, if we postulate enough universes, the chances are that there exist several life-permitting universes, perhaps even universes with precisely the same initial conditions and fundamental constants as our universe, and containing human beings indistinguishable from us.  But we do not inhabit these universes, other folks do.²²

This is the "this universe versus a universe" distinction, and it is the real heart of the objection.  A multiverse explains why some universe is life-permitting.  What needs explaining, White says, is why this one is.

The 2022 reply

In 2022 Yoaav Isaacs, John Hawthorne and Jeffrey Sanford Russell published a systematic answer in the Philosophical Review.  Their opening move is a complaint about the state of the debate that both sides should recognise:  "as this flurry of conflicting analogies shows, we don't yet have a sufficient understanding of this issue to see which analogies are apt and which are not.  More systematic theorizing is needed."²³

Rather than offer another dice story, they build a formal framework for self-locating evidence — evidence about where you are, not just about what exists — apply the three leading rules for updating on it, and show all three agree that our universe's containing fine-tuned life confirms a multiverse.  They then prove two theorems.  The gist of the second:  "given the other assumptions, the only way that a large multiverse can fail to be confirmed in the presence of fine-tuning is if our posteriors are 'extraordinary,' which is to say (roughly) that in the absence of fine-tuning a multiverse is disconfirmed."²³

Their own summary of what they have and have not done is worth quoting because it is unusually modest:

If being in a universe with fine-tuned life is not evidence for the existence of a multiverse, then some principle in the multiverse confirmation theorems must fail: in the case of "small" multiverses, this means that priors are not separable, evidence is not local, or posteriors are not evidential.  This is not to end the debate, but it provides a framework in which to continue it.²³

Verdict on this dispute:  unresolved, and this article does not claim it.  What can be said is that the fallacy charge is not the knockdown it is often presented as in apologetics, that its defenders now have to engage formal self-locating epistemology rather than trade analogies, and that the "this universe versus a universe" distinction remains the sharpest form of it.  It is also worth noting who is on which side.  Klaas Landsman endorses the fallacy charge against the multiverse and argues that the design inference fails for related reasons.  He is hostile to both.

Is it testable?

The honest answer has three parts:  a few versions make real predictions and some of those have been tested;  most versions predict nothing observable;  and the standard we apply to that fact has to be the same one we apply to our own models.

Tests that have been run

Bubble collisions.  This is the best of them, and it is a genuine test of eternal inflation.  If our bubble nucleated inside an inflating background alongside others, some neighbours should have run into ours.  A collision leaves a circular scar — a disc-shaped temperature modulation — on the microwave sky.  The signature is specific enough to search for.

Stephen Feeney, Matthew Johnson, Daniel Mortlock and Hiranya Peiris ran the search on WMAP's seven-year data and reported the result in Physical Review Letters in 2011:

We present the first observational tests of eternal inflation, performing a search for cosmological signatures of collisions with other bubble universes in cosmic microwave background data from the WMAP satellite.  We conclude that the WMAP 7-year data do not warrant augmenting ΛCDM with bubble collisions, constraining the average number of detectable bubble collisions on the full sky N̄_s < 1.6 at 68% CL.⁹

A follow-up with a better pipeline, published in Physical Review D in 2013, tightened the bound and added cosmic textures to the search:  "We conclude that the WMAP 7-year data do not favor the addition of either cosmic textures or bubble collisions to ΛCDM…  The expected numbers of bubble collisions and cosmic textures on the CMB sky within our detection thresholds are constrained to be fewer than 4.0 and 5.2 at 95% confidence, respectively."²⁴

Nothing was found.  That should be said plainly, and it should also be said plainly that a null result here does not refute the multiverse — the expected number of visible collisions depends on the bubble nucleation rate, which is unknown and may be tiny.  What the search does establish is that the picture is not wholly beyond the reach of data, which cuts against the strongest form of the untestability charge.

Cosmic topology.  If space wrapped around on itself at a scale smaller than our horizon, it would be finite, and most inflationary multiverse pictures would be dead.  The signature is matched circles of identical temperature pattern in opposite parts of the sky.  Planck searched and found nothing:  "These searches yield no detection of a compact topology at a scale below the diameter of the last scattering surface."²⁵  Ellis, who is a critic, states the right conclusion about it:  "Observers have looked for and failed to find any such patterns.  But this null result cannot be taken as a point in favor of the multiverse."²⁰

Varying constants.  If the constants are environmental rather than fixed by law, one might hope to catch them varying across our own sky or over cosmic time.  John Webb and collaborators have reported a spatial dipole in the fine structure constant from quasar absorption spectra.  The result is disputed and most astronomers do not regard it as established.  Ellis's summary is the fair one:  "Some astronomers claim to have found such variations.  Most, though, consider the evidence dubious."²⁰

Cosmological natural selection — the test that came back negative.  Smolin's model predicts that neutron stars are kaon-condensate stars with an upper mass limit near 1.6 solar masses, because the strange quark mass can be tuned to move that limit without disturbing supernova physics.  Writing in 2006 he reported the prediction holding:  "So far all the well measured neutron stars have masses between 1.3 and 1.45 solar masses."¹⁵

Four years later that stopped being true.  Paul Demorest and colleagues measured the millisecond pulsar PSR J1614−2230 by its Shapiro delay and published in Nature:

The implied pulsar mass of 1.97 +/− 0.04 M_sun is by far the highest yet measured with such certainty, and effectively rules out the presence of hyperons, bosons, or free quarks at densities comparable to the nuclear saturation density.²⁶

A kaon condensate is a boson condensate.  1.97 ± 0.04 is roughly nine standard deviations above 1.6.  Smolin's prediction was risky, it was published in advance, and the measurement went against it.  That is what a falsifiable multiverse proposal looks like, and it is worth recording that the only landscape theory to have stuck its neck out is the one whose neck was cut.  Smolin has defended the model since;  the prediction as stated in 2006 did not survive.

A note on "typicality," the tool usually used for these tests.  The standard way of claiming a multiverse prediction is to say that our observed value of some constant sits near the peak of the distribution the theory predicts — that we are typical.  Barnes shows the move is weaker than it looks:  "typicality is neither a necessary nor a sufficient condition for a multiverse theory to be a good theory.  The problem with typicality is that it compares values of the likelihood at different values of α, when we should be comparing different theories by evaluating their likelihoods at the observed value of α."¹⁹  He is not dismissing it — under stated conditions it is a useful rule of thumb — but a "prediction" defended by typicality alone is doing less work than its advocates claim.

Weinberg's cosmological constant bound — described above — is the one case on the other side of the ledger.  A stated falsification condition, published before the measurement, that the measurement did not violate.

What most versions predict

Nothing.  This has to be said without softening.

The bubbles of an eternally inflating spacetime are outside each other's horizons by construction.  Ellis puts the difficulty in one sentence:  "All the parallel universes lie outside our horizon and remain beyond our capacity to see, now or ever, no matter how technology evolves.  In fact, they are too far away to have had any influence on our universe whatsoever."²⁰

And the link between eternal inflation and varying constants — the link Level II depends on — is not itself established.  Ellis again, and this is the most precise criticism in his article:

The basic mechanism for eternal inflation does not itself cause physics to be different in each domain in a multiverse; for that, it needs to be coupled to another speculative theory.  Although they can be fitted together, there is nothing inevitable about it.²⁰

He is right, and it is the thing most popular accounts obscure.  Eternal inflation gives you many bubbles.  String theory is what is supposed to make them different.  String theory has no experimental confirmation.  Two unconfirmed theories bolted together do not add up to one confirmed one.  Ellis's version:  "But string theory is not a tried-and-tested theory; it is not even a complete theory.  If we had proof that string theory is correct, its theoretical predictions could be a legitimate, experimentally based argument for a multiverse.  We do not have such proof."²⁰

Ellis's own position deserves stating because it is more careful than either camp's caricature.  He accepts Level I:  "Nearly all cosmologists today (including me) accept this type of multiverse, which Max Tegmark calls 'level 1.'"²⁰  He accepts that Level II would explain the dark energy density if it were true, calling it "arguably… the only scientifically based option we have right now," and adds in the same breath, "But we have no hope of testing it observationally."²⁰  His conclusion is about naming things accurately:  "Nothing is wrong with scientifically based philosophical speculation, which is what multiverse proposals are.  But we should name it for what it is."²⁰

In December 2014 Ellis and Joe Silk pressed the same case in Nature under the title "Scientific method: Defend the integrity of physics," arguing that exempting speculative cosmology from experimental test damages science as a whole.²⁷

The standard, applied evenly

Here is where this article has to do something uncomfortable.

An unfalsifiable model is not thereby false.  It is thereby unable to earn support from evidence.  Those are different claims and conflating them is the standard move in bad apologetics and bad popular science alike.  If a proposal makes no observable difference, no observation can count against it — and no observation can count for it either.  It does not become wrong.  It becomes evidentially inert.

This project already applies that standard where it hurts.  The young-universe cosmologies article grades the eight published creationist answers to the distant-starlight problem and finds that most of them make no distinguishing prediction.  Jason Lisle says so of his own anisotropic synchrony convention:  it "is not a scientific model;  it does not make testable predictions.  It is a convention of measurement and cannot be falsified any more than the metric system can be falsified."²⁸  Danny Faulkner says of his own miracle proposal:  "Since my modest proposal appeals to a miracle, there may be no physical predictions and hence nothing that we can test."²⁹  That article's verdict, in its own words:

An unfalsifiable model is not thereby false;  it is thereby unable to earn support from evidence.  The article's claim is narrow:  none of these models can be confirmed by observation either, so nobody should present them as scientific results.  The same standard applied to the multiverse cuts the same way, and this project applies it there too.³⁰

So here it is applied.  The Level II multiverse is not refuted by being hard to test.  It is prevented from being confirmed.  It remains a possible description of reality.  What it cannot presently be is a result.  Anyone who presents it as established science is overclaiming in exactly the way a creationist overclaims when presenting an untestable starlight model as a solution.

The symmetry is not a debating trick.  It is the same rule, and a rule that only ever runs in one direction is not a rule.

The theology, kept small

Three claims, and no more than three.

A multiverse does not refute theism.  Nothing in the idea of many universes entails that none of them was made.  If God created, God could have created an ensemble as easily as a single instance;  the question of why there is a multiverse rather than nothing is the same question one level up.  Ellis, who is a critic of the multiverse, states this cleanly:

All the same issues that arise in relation to the universe arise again in relation to the multiverse.  If the multiverse exists, did it come into existence through necessity, chance or purpose?  That is a metaphysical question that no physical theory can answer for either the universe or the multiverse.²⁰

Several theists accept a multiverse, and one of them is worth naming.  Don Page is a theoretical physicist at Alberta, Kip Thorne's student, and for years Stephen Hawking's collaborator — the Hawking-Page phase transition and the Page curve carry his name.  He is a Christian, and he argues for the multiverse.  He wrote a paper about it in 2008 whose stated purpose was:

One primary purpose is to persuade my fellow Christians that multiverse ideas are not necessarily opposed to theism and to Christianity.  A secondary purpose, and one of the main reasons for posting it on the physics eprint archives, is to show other scientists that not all Christians are opposed to multiverse ideas, just as not all Christians are opposed to evolutionary ideas, even though some Christians have opposed both.³¹

He goes further than most apologists will find comfortable.  He grants the fine-tuning fully — "in our part of the universe, the constants of physics do in fact seem to be fine tuned for our kind of life"³¹ — and then declines to use it:  "I personally think it might be a theological mistake to look for fine tuning as a sign of the existence of God."³¹  His reason is scriptural, from Matthew 12:38-41:  "I regard the death and resurrection of Jesus as the sign given to us that He is indeed the Son of God and Savior He claimed to be, rather than needing signs from fine tuning."³¹

He also states the honest cost of the multiverse for the design argument, without flinching in either direction:

For example, a theist might feel that a multiverse theory would undercut the fine-tuning argument for the existence of God.  I shall not deny that it would undercut the argument at the level of the constants of physics… However, the loss of one argument does not mean that its conclusion is necessarily false.³¹

That is the right accounting.  If a Level II multiverse is real, the fine-tuning argument from the constants loses most of its force.  Saying otherwise is wishful.  Losing an argument for a conclusion is not losing the conclusion.

"The multiverse was invented to avoid design" is false, and this article will not print it.  Page wrote his paper partly to answer a Catholic cardinal who had said exactly that.  Page's words:

Here I wish to go on record as a Christian who respectfully differs from Cardinal Schönborn's opinion that the multiverse idea was "invented to avoid the overwhelming evidence for purpose and design found in modern science" and that it is "an abdication of human intelligence."³¹

The historical record supports Page.  Everett proposed his interpretation in 1957 to remove an ugly discontinuity from quantum mechanics.  Bousso and Polchinski proposed the discretuum in 2000 to attack a 56-order-of-magnitude discrepancy in vacuum energy, in a paper that never mentions design.  Steinhardt and Vilenkin found eternal inflation while working out what inflation implies.  Ashok and Douglas counted flux vacua because they were worried that string theory might not predict anything.  These are the actual origins, and none of them is an escape from God.

What is fair to say is that some proponents do deploy it against design, and say so.  Weinberg's Trinity College lecture is titled "Living in the Multiverse" and its whole argument is that anthropic reasoning has become respectable in physics.  Susskind's 2005 popular book on the landscape is subtitled String Theory and the Illusion of Intelligent Design.³²  The idea's origins are one thing and its uses are another, and confusing them — in either direction — produces bad history.

Objections and responses

"The multiverse is unfalsifiable, so it isn't science."  Half right, and the half that is wrong matters.  Falsifiability attaches to specific models, not to a family of ideas.  Some multiverse models made real predictions:  eternal inflation predicted bubble-collision scars, and they were searched for;  Smolin's cosmological natural selection predicted a neutron-star mass ceiling, and it was measured and broken;  Weinberg's anthropic bound on the cosmological constant was stated with a falsification condition before the measurement.  Most versions predict nothing observable, and that is a serious defect.  But the correct statement of the defect is that those versions cannot be confirmed, not that they are false.  Anyone who runs this objection has to accept it running the other way against untestable creationist cosmologies.

"There is no evidence for even one other universe."  True, and it should be conceded without hedging.  Nobody has observed a second universe and nobody has observed a constant taking a different value.  What exists is indirect motivation:  eternal inflation falls out of inflation models that do fit data, and the landscape is a possible answer to a real and unsolved problem about vacuum energy.  Physics does accept indirect evidence — nobody has isolated a free quark either.  But the disanalogy is decisive:  confined quarks have measurable consequences inside our horizon, and other bubbles, by construction, do not.

"You are postulating infinitely many unobservable universes to explain one.  Ockham's razor cuts it away."  Ellis presses this:  "we are supposing the existence of a huge number—perhaps even an infinity—of unobservable entities to explain just one existing universe.  It hardly fits 14th-century English philosopher William of Ockham's stricture that 'entities must not be multiplied beyond necessity.'"²⁰  The standard reply is that the razor counts kinds of thing, not copies:  a single simple law that generates endless universes may be simpler than a stipulation that fixes twenty-six constants by hand.  That reply has force.  What weakens it here is that the Level II package is not one simple law.  It is eternal inflation, plus a string landscape, plus a measure — three unconfirmed components that have to be bolted together, which is Ellis's actual complaint.

"A universe-generating mechanism would itself have to be fine-tuned."  This is right and it is the strongest reply available to the design side.  Inflation is not a free lunch:  it needs a potential of the right shape, a field with the right couplings, and initial conditions in the right region.  Barnes states the general point sharply:  "Inflation thus represents a very special case.  Waiting inside the life-permitting range (L) is another physical parameter (p)…  There can be no inflation-like dynamical solution to these fine-tuning problems because dynamical processes are blind to the requirements of intelligent life."³³  The multiverse does not remove tuning;  it relocates it into the generator.  Two honest qualifications.  Relocating a problem can still be progress if the new tuning is milder or better motivated, and a multiverse advocate will say it is.  And nobody has quantified the tuning of the generator, so this reply is a real objection rather than a calculation.

"Many-worlds is well-supported physics, so we get the multiverse for free."  No.  Everett's many-worlds does not vary the constants.  Every branch runs the same physics.  Tegmark, who defends it, says it "adds nothing new beyond Level I and Level II."¹  Whatever one concludes about quantum foundations, it does not settle anything about fine-tuning.

"If we live in a multiverse, everything happens somewhere, so nothing can be explained."  Overstated as usually put, but there is a real problem underneath it, and it is the measure problem.  It is not that explanation becomes impossible;  it is that probability statements about the ensemble have no defined value until someone finds the right way to count.  Guth, Kaiser and Nomura:  "a persuasive theory of probabilities in the multiverse has not yet been found."⁵  The sharpest form of the worry is Boltzmann brains, which threaten not explanation in general but the reliability of the reasoning used to reach the theory.

"The multiverse is a faith position, just like belief in God."  There is something to this and something wrong with it.  What is right:  neither can be checked directly, both are held partly for reasons of coherence and elegance, and both let their holders account for the data.  What is wrong:  the multiverse is tied to physical theories with independent track records, and it has generated at least three testable predictions, one of which failed.  Faith positions do not usually get falsified by pulsar timing.  A fair statement is that the Level II multiverse is currently underdetermined by evidence, which is a weaker and more accurate charge than "faith."

"Fine-tuning is evidence for the multiverse, so the multiverse is confirmed."  Contested.  Isaacs, Hawthorne and Russell argue for it with two theorems;  Hacking, White and Landsman argue against it;  the debate turns on how to update on self-locating evidence, and there is no settled theory of that.  This article does not claim the point in either direction.

"Since nobody can decide, the right answer is 'we don't know.'"  That is a real position and it has serious holders.  Klaas Landsman rejects both;  Smolin builds a landscape theory precisely to avoid anthropic reasoning;  Steinhardt rejects the inflationary multiverse without proposing a designer.  Landsman's abstract states the double rejection:  "we conclude that cosmic fine-tuning supports neither Design nor a Multiverse, since both of these fail at an explanatory level as well as in a more quantitative context of Bayesian confirmation theory."³⁴  A reader who ends up there is not being unreasonable.  What the position costs is any explanation at all of a pattern its holders concede is real.

"String theory predicts 10⁵⁰⁰ universes."  It does not predict them;  it has been estimated to permit that many vacua, by formulas whose inputs are chosen for plausibility.  The number first appears in Douglas's 2004 review, attached to the judgement "This is probably too large for statistical selection to work,"² and a later count using the same method gives 10^272,000 from one geometry.⁴  Quote the number if it is useful, but quote what it is:  an estimate from an unconfirmed theory, published as a worry about predictivity.

What would change the verdict

Four things, in rough order of how likely they are.

A confirmed detection of a bubble collision signature.  This is the only near-term route to direct evidence.  The searches so far are null but not exhaustive, and better polarisation data narrows the parameter space.  A confirmed circular scar with the right profile would be as close to seeing another universe as physics is ever likely to get.

Experimental confirmation of string theory.  Not the landscape specifically — the framework.  If string theory acquired an independent empirical footing, its vacuum-counting results would inherit that footing, and Level II would go from speculation to inference.  Ellis says the same:  "If we had proof that string theory is correct, its theoretical predictions could be a legitimate, experimentally based argument for a multiverse."²⁰

A solution to the measure problem.  If someone derives a measure from first principles rather than choosing one, the multiverse becomes able to make quantitative predictions and to be checked against them.  This is the hinge.  Everything quantitative waits on it.

A demonstration that eternal inflation does not follow.  If the inflationary models that survive the data turn out not to be eternal, or if inflation is replaced by a bouncing model, the main mechanism for Level II disappears.  Steinhardt is working on precisely this, which is why his position — anti-inflation, anti-multiverse, pro-cyclic — is coherent rather than merely contrarian.

None of these is close.  Until one of them lands, the correct description of the Level II multiverse is what Ellis called it:  scientifically based philosophical speculation, which should be named for what it is.

Sources