This week’s hype comes to us from Discover Magazine, which has Is Our Universe One of Many? Here’s How We Can Find Out. Needless to say, the author doesn’t actually tell us how we can find out, just repeats the usual “maybe we’ll see bubble collisions” argument often discussed here. We’re also told that

It is important to keep in mind that the multiverse view is not actually a theory, it is rather a consequence of our current understanding of theoretical physics.

It seems that our “current understanding of theoretical physics” is the string theory landscape. If you ask what the evidence is for string theory, you’ll be given the usual circular reasoning that we don’t have evidence because of the multiverse.

For next week’s hype, there will be a promotional public talk in Paris next Tuesday entitled String Theory: results, challenges and magic. Presumably this will be much the same as the speaker’s String theory: results, magic and doubts from two years ago. The argument for string theory seems to be that it is “magic”, and somehow in the past two years the “doubts” have turned into “challenges”. The abstract describes string theory poetically as having

soured and captured the imagination of a generation of high energy physicists.

which I would say is a deep truth, if probably not one the speaker intended.

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The word “soured” is rather hard to emend. I incline toward “spurred” rather than “soared”, but neither is really satisfactory.

Perhaps from “faire tourner” which can mean rotate, revolve, churn or sour.

Soured…how very odd…soared, perhaps, with a split clause.

The author of the Discover Magazine piece (Crux blog post) also flirts yet again with conflating the multiverse with the Many Worlds interpretation of quantum mechanics, although he seems to back away from that in the last section (“Testing the Theory”).

Carlo Rovelli posted recently a refreshing essay which demolishes most of ‘our mathematical universe’ and its incarnation in the multiverse.

“…science can be said to be nothing else than the denotation of a subset of David Lewis’s possible worlds: those respecting certain laws we have found. But Lewis’s totality of all possible world is not science, because the value of science is in the restriction, not in the totality.”

Rovelli C., Michelangelo’s Stone: arXiv:1508.00001 [math.HO]

My layman’s understanding of the concept of multiverse as “… a consequence of our current understanding of theoretical physics,” is that it would be a consequence of inflation, not string theory (and that one does not depend upon the other.) Wrong?

perhaps (in a French-speaking context referring to imagination)

‘soured’ = ‘piqued’ ?

Patrick Dennis,

The “inflation implies multiverse” claim is a common one, and I’ve often written about the problems with it. This particular author though is not talking about inflation, but writes

“Instead the idea that the universe is perhaps one of infinitely many is derived from current theories like quantum mechanics and string theory.”

putting string theory and QM on a par.

Thanks, “a l”, for the link to Carlo Rovelli’s Michelangelo’s Stone: an Argument against Platonism in Mathematics. It’s an interesting read (and I will read it again), but it’s not very convincingly written.

Not a believer in hard-core Platonism myself. I like to consider Mathematical Structures as computers (syntactic machines) with no limits imposed by computational complexity, whose actual (entirely imagined) behaviour one wants to unravel. Very much linked to the real world.

However, Carlo Rovelli’s examples seem rather ill-chosen and trying too hard. In particular, they are free of constraints that the real world would impose. Alien intelligences that don’t develop counting? Nice for Asimov’s Magazine of Science Fiction but I can only say good look in the real-world predation game with THAT. Marvin Minsky handled this rather better in 1985 in Communication with Alien Intelligence. Develop Riemannian geometry before Euclidean one? Possible, but general ideas (highly compressed and with book-length contextual baggage) do not spring fully-formed out of someone’s real-world brain machinery, it’s a building-up process from simple ideas. Always. Linear algebra not so universal? I really don’t think so, and the fact that it was formulated rather recently is not an argument against its universality. We don’t program a computer to slowly unravel the platonic world’s theorems because we want to find the interesting ones only? Of course not! It’s because no-one is mad enough to use computers on problems clearly far, far, far outside of the polynomial complexity problem set (itself a platonic concept, actually), Gödel’s completeness theorems notwithstanding. I suspect Carlo Rovelli might profit from a course in the Theory of Computation.

It made me think of Hilary Putnam’s, The Logic of Quantum Mechanics (Originally, “Is Logic Empirical”, Boston Studies in the Philosophy of Science Vol. V, 1969), wherein the (entirely unsurprising) claim is made that classical logic is actually not universal and that this can be illustrated by the necessity of having other logics to describe QM for example (no mention is made of Linear Logic for this, still in the future). It’s like “Dude! No need to crash in. That door was open. Take a seat, I’ll buy you a drink.”

But this is getting rather off-topic.

a1/Yatima,

“But this is getting rather off-topic.”

Yes, I left the link to Rovelli because people might be interested, but it has little to do with the topic of the posting, and this is not a great place to discuss it.

Reading Rovelli’s piece might give you a somewhat different perspective on the multiverse topic. Otherwise it’s once again “not testable, blah blah”. If our knowledge of mathematics is contingent, it looks less convincing that something is real just because there is a theory for it.

Rabinovici is not the first to invoke magic. Did not Witten himself suggest that the M in M-theory could stand for “magic”?

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What struck me (a mathematician with very limited knowledge of physics) in the Discover article is the claim that ‘The universes predicted by string theory and inflation live in the same physical space (unlike the many universes of quantum mechanics which live in a mathematical space), meaning they can overlap or collide.’

This seems a huge improvement over multiverses where the universes are truly disjoint and cannot be detected from within one another. But it also left me with a very basic question: what is the definition of a universe? This ‘same physical space’ sounds pretty much like what I would naively call the universe. What do I miss?

Vincent,

The cosmological multiverse and the QM many-worlds multiverse are two completely different things. In both cases the “universes” are part of a larger structure. In the many-worlds case there is one overall state space, with different subsectors that “decohere”, so can effectively be treated as independent. In the cosmological case, there is one space-time manifold, with different “bubble universes” which are causally independent. The “bubble collision” business is about the possibility in some multiverse models of a violation of causal independence, an interaction of the bubbles. However there is no evidence this is happening in our “bubble”, and no reason at all to expect it to.

BBC’s popular science documentary series “Horizon” aired an episode about the multiverse last week – featuring Max Tegmark, Seth Lloyd …..

Available to watch here (I think only in UK)

http://www.bbc.co.uk/programmes/b0695t56

Ronan,

Here in the US we got to enjoy that last fall:

http://www.math.columbia.edu/~woit/wordpress/?p=7352

I was thinking that Hebrew would be a better angle to approach this one from than French, but that wasn’t particularly promising, either, without acrobatics (m.m.

Sauerstoff).I’m inclined toward a typo in an odd construction using “sourced”; it doesn’t quite seem to be at the mystery level of “homologous recombinaltion

tiniker.”I vote for roused. Somehow the r and s got exchanged.

“Soared” would be consistent with Discovery writing style, so I suspect a typo, maybe Freudian. I have to say, though, that despite the occasional exaggerations, Discovery magazine has become better that Scientific Amercian, in my opinion, but maybe only because SciAm has become so awful.

If it is a typo, “sourced” seems more likely to me..

I would guess ‘soured’ should be ‘stirred’ as in the collocation ‘stirred the imagination’. So the phrase would be ‘stirred and captured the imagination of a generation of high energy physicists.’

“The universes predicted by string theory and inflation..can overlap or collide. Indeed, they INEVITABLY MUST COLLIDE…” (caps mine)

Oh really? Am I wrong, or is there no consensus on this, even among Lanscapers and Eternal Inflators?

Peter or anyone, I have a quick question which hopefully isn’t off-topic here… In eternal inflation, SM, Landscape or otherwise, bubble universes will nucleate amidst larger inflating regions and reheat in the usual manner. Presumably this means that each nucleating bubble “neighborhood” is surrounded by isotropic inflating regions out of which other bubble universes are nucleating. So… how can bubble universe collisions occur between bubbles that are all inflating away from each other in full afterburner? Am I missing something…?

Scott,

I don’t know your background so I’ll give some detail. You’re getting somewhat more than you asked for!

To do its job, inflation must smooth out and/or dilute preexisting inhomogeneities of the pre-cosmological space by rapidly expanding the space, and then it must stop. General relativity offers a way: a space that contains a constant, positive energy density will expand exponentially as

exp(Ht)in all directions. The energy density determines the rateH(“Hubble parameter”);tis the time.In the simplest models, the vacuum is presumed to be filled with a

scalar fieldwhose associated potential energy curve has special characteristics; more complicated models may employ more than one field. The curve generally has a (nearly) flat part or/and a metastable “bowl,” both at a high energy where inflation does most of its job; this is followed by a steep drop to a stable (or at least metastable) minimum where reheating and subsequent cosmological evolution occur. The scalar field and its potential energy curve exist to cause inflation: they are imposed byfiat, not by anything in the Standard Model. Beyond general characteristics, the particular assumed shape of the potential depends on the model. Since there is noa priorichoice that is dictated by a fundamental theory there is substantial freedom to choose the potential to give you what you want in terms of consistency with observational evidence.The scalar field must somehow get into the state of high energy density for inflation to begin; an actual inflation

theorywould explain this, ideally. Once it starts, inflation will continue as long as the scalar field state remains there, e.g. while the “inflaton” “rolls” down the gently sloping part of the potential (the Hubble parameter decreases slowly as the inflaton rolls down). It ends when the inflaton rolls down the steeply falling region and reaches the stable/metastable lower energy state.(You can think of inflaton motion at some point “x” in the space as the time-dependent change of energy density of the scalar field at x. Note that we’re talking about energy

density— the energy density can have different values at different points, and different values correspond to different places on the potential energy curve.)In some models the potential curve has a metastable high energy “bowl” where the inflaton remains trapped for a time. Since the energy density remains stuck there with a constant value, the Hubble parameter

His constant so that the exponential expansionexp(Ht)produces a de Sitter (hyperbolic) space. This is probably the kind of scenario you are referring to. Being a quantum mechanical entity, the inflaton can probabilistically tunnel through the “bowl wall” onto a gently sloping/ steeply sloping/ stable minimum region of the assumed potential, depending on the model. Spatially, in the bubble universe scenario the tunneling event corresponds to formation of a spherical region of finite radius; this region has the energy density given by the tunneled-to part of the potential curve, and subsequent evolution inside continues from there down the curve to the minimum energy.In this scenario, the newly formed spherical region has a lower energy density than the ambient de Sitter vacuum (maybe even zero), and thus a domain wall forms to separate the “inside” region from the ambient vacuum. This is the bubble wall, initially stationary with respect to the bubble center. Being of lower energy than the ambient vacuum, the wall continually “eats” energy of the surrounding high-energy vacuum and thereby adds to its kinetic energy, causing the wall to rapidly accelerate outward into the de Sitter space. If the tunneled-to region of the assumed potential is gently sloping, the bubble interior will meanwhile undergo a secondary but less rapid inflationary period until it drops into the stable “true vacuum” state.

Of course, the de Sitter vacuum outside the bubble continues its exponential expansion all the while: the de Sitter space expands faster than the space inside the bubble, so compared to the exponentially increasing volume of a “box” that contains the bubble, the exponentially increasing bubble volume occupies a rapidly decreasing fraction of the (expanding) box volume over time. Inflation is eternal in this scenario (as in nearly all inflation models) because, even though inflation will eventually end “almost surely” at every point in the de Sitter space via tunneling, the expansion of space occurs faster than tunneling can stop that expansion.

(Some people get confused by exponential expansion, since it implies that an object far enough away will be moving away faster than the speed of light. The bubble wall speed increases exponentially from the center, but “speed of light” in an expanding space is only meaningful if measured locally: at any given moment the wall speed is with respect to a

fixedpoint infinitesimally distant from the wall at that moment, whereas the wall can move faster than the speed of light relative to a point afinitedistance from the wall.)Having a quantum mechanical origin, bubble nucleation is a probabilistic event. Nucleation events are independent, so two bubbles will sometimes form nearby. Both bubbles expand and their walls accelerate toward each other. Now to answer your specific question (finally!): If two bubbles form

sufficiently closely, the acceleration of their respective walls toward each other can “outrun” the accelerated expansion of the ambient de Sitter vacuum between them, and they will collide.This is all hypothetical of course… In principle, the aftermath of a bubble collision could be detected today if it had occurred under very optimistic/ideal (and probably very unlikely) conditions. Such an event would presumably have a marked effect on the energy density in the collision region which would ultimately manifest as a strong, circularly symmetric inhomogeneity of the cosmic microwave background. But no such inhomogeneity has convincingly shown up, yet at least. Importantly, only collisions that occurred very soon after nucleation would cover a significantly large region of the sky to be observable; later collisions, if their effect could reach us at all, would subtend too small an angle to be statistically discernible.

Sorry Scott (and Peter!) for such a long comment!

As a side comment to my previous one, the kind of eternal inflation that arises from single field inflation models should lead to all bubbles having essentially the same particle content and laws of physics. A scalar field has no obvious properties that should affect what kinds of particles appear during the reheating phase that immediately follows the inflationary phase, nor do they indicate why fundamental constants should be bubble-dependent (to me, anyway). That seems to make the kind of multiverse indicated by most inflation models less than WOW!-worthy, but that’s just my opinion…

Marty,

I think the question that always comes up is whether inflation implies endless new bubble universes, which must “inevitably” collide. Some experts seem to say no (e.g. Katie Freese), Lim and others say yes, although often in the context of popular articles like this one that are chock-full of other misinformation, so hard to take seriously. I’m not expert enough on the details of all inflationary models to judge who is right here, and, honestly, there seem to be much better ways to spend ones time than trying to sort this one out. If anyone knows of a reliable source with a definitive answer, please do tell.

Marty,

That was magnificent. Thank you.

Marty, sorry for the delayed response… I just got back from a week in Alaska and am finally settled in again. Thanks so much for your thoughtful and informative response! I do have a physics background (MS level) and was aware of much of that already. But the key piece I was missing–which you so graciously provided–was that domain walls will acquire kinetic energy from their immediate inflating deSitter neighborhoods at a rate that can allow bubbles that are suitably near each other to grow faster than the underlying inflation can separate them, thus leading to collisions. Now it makes sense.

Of course, as Peter points out this still leaves us not only with the question of whether there is evidence of such collisions occurring (the answer to date being a resounding No), but also whether they’re inevitable within the extant chaotic inflationary framework, with or without M-theory. The question is important, I think, if for no other reason because should it turn out that such collisions

areinevitable within those frameworks, the fact that they aren’t observed raises some serious issues with chaotic inflation. I too would be interested in finding reliable sources with a definitive answer.Best.