Author: Sean Carroll

Back for the third and final day of the Philosophy and Cosmology conference in honor of George Ellis’s birthday. I’ll have great memories of my time in Oxford, almost all of which was spent inside this lecture hall. See previous reports of Day One, Day Two.

It’s become clear along the way that I am not as accurate when I’m trying to represent philosophers as opposed to physicists; the vocabularies and concerns are just slightly different and less familiar to me. So take things with an appropriate grain of salt.

Tuesday morning: The Case for Multiverses

9:00: Bernard Carr, one of the original champions of the anthropic principle, has been instructed to talk on “How we know multiverses exist.” Not necessarily the title he would have chosen. Of course we don’t observe a multiverse directly; but we might observe it indirectly, or infer it theoretically. We should be careful to define “multiverse,” not to mention “exist.”

There certainly has been a change, even just since 2001, in the attitude of the community toward the multiverse. Quotes Frank Wilczek, who tells a parable about how multiverse advocates have gone from voices in the wilderness to prophets. That doesn’t mean the idea is right, of course.

Carr is less interested in insisting that the multiverse does exist, and more interested in defending the proposition that it might exist, and that taking it seriously is perfectly respectable science. Remember history: August Comte in 1859 scoffed at the idea we would ever know what stars were made of. Observational breakthroughs can be hard to predict. Rutherford: “Don’t let me hear anyone use the word `Universe’ in my department!” Cosmology wasn’t respectable. For what it’s worth, the idea that what we currently see is the whole universe has repeatedly been wrong.

So how do we know a multiverse exists? Maybe we could hop in a wormhole or something, but let’s not be so optimistic. There are reasons to think that multiverses exist: for example, if we find ourselves near some anthropic cutoff for certain parameters. More interesting, there could be semi-direct observational evidence — bubble collisions, or perhaps giant voids. Discovering extra dimensions would be good evidence for the theories on which the multiverse is often based.

The only direct observations that currently exists that might bear directly on multiverses is the prediction of giant voids and dark flows by Laura Mersini-Houghton and collaborators.

Carr believes that the indirect evidence from finely-tuned coupling constants is actually stronger. Existence of planets requires a very specific relationship between strength of gravity and electromagnetism, which happens to exist in the real world. There is a similar gravity/weak tuning needed to make supernovae and heavy elements. Admittedly, many physicists dislike the multiverse and find it just as unpalatable as God. But ultimately, multiverse ideas will become normal science by linking up with observations; we just don’t know how long it will take.

9:45: George Ellis follows Carr’s talk with what we’ve been waiting for a while — a strong skeptical take on the multiverse idea.

There are lots of types of multiverses: many-worlds, separated by space or time, or completely disjoint. Anthropic arguments are what make the idea go. The project is to make the apparently improbable become probable.

The very nature of the scientific enterprise is at stake: multiverse proponents are proposing that we weaken the idea of scientific proof. Science is about two things: testability and explanatory power. Is it worth giving up the former to achieve the latter?

The abstract notion of a multiverse doesn’t get you anything; you need a specific model, with a distribution of probabilities. (Does Harry Potter exist somewhere in your multiverse?) But if there is some process that generates universes, how do you test that process? Domains beyond our particle horizon are unobservable. How far should we expect to be able to extrapolate? Into a region which, in principle, we will never be able to observe.

In the good old days we accepted the Cosmological Principle, and assumed things continued uniformly forever beyond our observable horizon. Completely untestable, of course. If all the steps in the extrapolation are perfectly tenable, extrapolations are fine — but that’s not the case here. In particular, the physics of eternal inflation (gravity plus quantum field theory, Coleman-de Luccia tunneling) has never been tested. It’s unknown physics used to infer an unobservable realm. Inflation itself is not yet a well-defined theory, and not all versions of inflation are eternal. We haven’t even found a scalar field!

There is a claim that a multiverse is implied by the fine-tuning of the universe to allow life. At best a weak consistency test. Can never actually do statistical tests on the purported ensemble. Another claim is that the local universe, if it’s inside a bubble, should have a slight negative curvature — but that’s easily avoided by super-Hubble perturbations, so it’s not a strong prediction. We could, however, falsify eternal inflation by observing that we live in a “small” (topologically compact) universe. But if we don’t, it certainly doesn’t prove that eternal inflation is right. Finally, it’s true that we might someday see signatures of bubble collisions in the microwave background. But if we don’t, then what? Again, not a firm prediction.

Ultimately: explanation and testability are both important, but one shouldn’t overwhelm the other. “The multiverse theory can’t make any prediction because it can explain anything at all.” Beware! If we redefine science to accommodate the multiverse, all sorts of pseudo-science might sneak inside the tent.

There are also political/sociological issues. Orthodoxy is based on the beliefs held by elites. Consider the story of Peter Coles, who tried to claim back in the 1990’s that the matter density was only 30% of the critical density. He was threatened by a cosmological bigwig, who told him he’d be regarded as a crank if he kept it up. On a related note, we have to admit that even scientists base beliefs on philosophical agendas and rationalize after the fact. That’s often what’s going on when scientists invoke “beauty” as a criterion.

Multiverse theories invoke “a profligate excess of existential multiplicity” in order to explain a small number of features of the universe we actually see. It’s a possible explanation of fine tuning, but is not uniquely defined, is not scientifically testable, and in the end “simply postpones the ultimate metaphysical question.” Nevertheless — if we accumulated enough consistency tests, he’d be happy to eventually become convinced.

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The previous post on the Philosophy and Cosmology conference in Oxford was growing to unseemly length, so I’ll give each of the three days its separate post.

Monday morning: The Case for Multiverses

9:00: We start today as we ended yesterday: with a talk by Martin Rees, who has done quite a bit to popularize the idea of a multiverse. He wants to argue that thinking about the multiverse doesn’t represent any sort of departure from the usual way we do science.

The Big Bang model, from 1 second to today, is as uncontroversial as anything a geologist does. Easily falsifiable, but it passes all tests. How far does the domain of physical cosmology extend? We only see the universe out to the microwave background, but nothing happens out there — it seems pretty uniform, suggesting that conditions inside extend pretty far outside. Could be very far, but hard to say for sure.

Some people want to talk only about the observable universe. Those folks need aversion therapy. After all, whether a particular distant galaxy eventually becomes observable depends on details of cosmic history. There’s no sharp epistemological distinction between the observable and unobservable parts of the universe. We need to ask whether quantities characterizing our observable part of the universe are truly universal, or merely local.

So: what values of these parameters are consistent with some kind of complexity? (No need to explicitly invoke the “A-word.”) Need gravity, and the weaker the better. Need at least one very large number; in our universe it’s the ratio of gravity to electromagnetic forces between elementary particles. Also need departure from thermodynamic equilibrium. Also: matter/antimatter symmetry, and some kind of non-trivial chemistry. (Tuning between electromagnetic and nuclear forces?) At least one star, arguably a second-generation star so that we have heavy elements. We also need a tuned cosmic expansion rate, to let the universe last long enough without being completely emptied out, and some non-zero fluctuations in density from place to place.

If the amplitude of density perturbations were much smaller, the universe would be anemic: you would have fewer first-generation stars, and perhaps no second-generation stars. If the amplitude were much larger, we would form huge black holes very early, and again we might not get stars. But ten times the observed amplitude would actually be kind of interesting. Given an amplitude of density perturbations, there’s an upper limit on the cosmological constant, so that structure can form. Again, larger perturbations would allow for a significantly larger cosmological constant — why don’t we live in such a universe? Similar arguments can be made about the ratio of dark matter to ordinary matter.

Having said all that, we need a fundamental theory to get anywhere. It should either determine all constants of nature uniquely, in which case anthropic reasoning has no role, or it allows ranges of parameters within the physical universe, in which case anthropics are unavoidable.

10:00: Next up, Philip Candelas to talk about probabilities in the landscape. The title he actually puts on the screen is: “Calabi-Yau Manifolds with Small Hodge Numbers, or A Des Res in the Landscape.”

A Calabi-Yau is the kind of manifold you need in string theory to compactly ten dimensions down to four, picked out among all possible manifolds by the requirement that we preserve supersymmetry. There are many examples, and you can characterize them by topological invariants as well as by continuous parameters. But there is a special corner in the space of Calabi-Yau’s where certain topological invariants (Hodge numbers) are relatively small; these seem like promising places to think about phenomenology — e.g. there are three generations of elementary particles.

Different embeddings lead to different gauge groups in four dimensions: E₆, SO(10), or SU(5). Various models with three generations can be found. Putting flux on the Calabi-Yau can break the gauge group down to the Standard Model, sometimes with additional U(1)’s.

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Greetings from Oxford, a charming little town across the Atlantic with its very own university. It’s in the United Kingdom, a small island nation recognized for its steak and kidney pie and other contributions to world cuisine. What you may not know is that the UK has also produced quite a few influential philosophers and cosmologists, making it an ideal venue for a small conference that aims to bring these two groups together.

The proximate reason for this particular conference is George Ellis’s 70th birthday party. Ellis is of course a well-known general relativist, cosmologist, and author. Although the idea of a birthday conference for respected scientists is quite an established one, Ellis had the idea of a focused and interdisciplinary meeting that might actually be useful, rather than just bringing together all of his friends and collaborators for a big party. It’s to his credit that they invited as many multiverse-boosters as multiverse-skeptics. (I would go for the party, myself.)

George is currently very interested and concerned by the popularity of the multiverse idea in modern cosmology. He’s worried, as many others are (not me, especially), that the idea of a multiverse is intrinsically untestable, and represents a break with the standard idea of what constitutes “science.” So he and the organizing committee have asked a collection of scientists and philosophers with very different perspectives on the idea to come together and hash things out.

It appears as if there is working wireless here in the conference room, so I’ll make some attempt to blog very briefly about what the different speakers are saying. If all goes well, I’ll be updating this post over the next three days. I won’t always agree with everyone, of course, but I’ll try to fairly represent what they are saying.

Saturday night:

Like any good British undertaking, we begin in the pub. I introduce some of the philosophers to Andrei Linde, who entertains us by giving an argument for solipsism based on the Wheeler-deWitt equation. The man can command a room, that’s all I’m saying.

(If you must know the argument: the ordinary Schrodinger equation tells us that the rate of change of the wave function is given by the energy. But for a closed universe in general relativity, the energy is exactly zero — so there is no time evolution, nothing happens. But you can divide the universe into “you” and “the rest.” Your own energy is not zero, so the energy of the rest of the universe is not zero, and therefore it obeys the standard Schrodinger equation with ordinary time evolution. So the only way to make the universe real is to consider yourself separate from it.)

Sunday morning: Cosmology

9:00: Ellis gives the opening remarks. Cosmology is in a fantastic data-rich era, but it is also coming up against the limits of measurement. In the quest for ever deeper explanation, increasingly speculative proposals are being made, which are sometimes untestable even in principle. The multiverse is the most obvious example.

Question: are these proposals science? Or do they attempt to change the definition of what “science” is? Does the search for explanatory power trump testability?

The questions aren’t only relevant to the multiverse. We need to understand the dividing line between science and non-science to properly classify standard cosmology, inflation, natural selection, Intelligent Design, astrology, parapsychology. Which are science?

9:30: Joe Silk gives an introduction to the state of cosmology today. Just to remind us of where we really are, he concentrates on the data-driven parts of the field: dark matter, primordial nucleosynthesis, background radiation, large-scale structure, dark energy, etc.

Silk’s expertise is in galaxy formation, so he naturally spends a good amount of time on that. Theory and numerical simulations are gradually making progress on this tough problem. One outstanding puzzle: why are spiral galaxies so thin? Probably improved simulations will crack this before too long.

10:30: Andrei Linde talks about inflation and the multiverse. The story is laden with irony: inflation was invented to help explain why the universe looks uniform, but taking it seriously leads you to eternal inflation, in which space on extremely large (unobservable) scales is highly non-uniform — the multiverse. The mechanism underlying eternal inflation is just the same quantum fluctuations that give rise to the density fluctuations observed in large-scale structure and the microwave background. The fluctuations we see are small, but at earlier times (and therefore on larger scales) they could easily have been very large — large enough to give rise to different “pocket universes” with different local laws of physics.

Linde represents the strong pro-multiverse view: “An enormously large number of possible types of compactification which exist e.g. in the theory of superstrings should be considered a virtue.” He said that in 1986, and continues to believe it. String theorists were only forced to take all these compactifications seriously by the intervention of a surprising experimental result: the acceleration of the universe, which implied that there was no magic formula that set the vacuum energy exactly to zero. Combining the string theory landscape with eternal inflation gives life to the multiverse, which among other things offers an anthropic solution to the cosmological constant problem.

Still, there are issues, especially the measure problem: how do you compare different quantities when they’re all infinitely big? (E.g. number of different kinds of observers in the multiverse.) Linde doesn’t think any of the currently proposed measures are completely satisfactory, including the ones he’s invented. A big problem with Boltzmann brains.

Another problem is what we mean by “us,” when we’re trying to predict “what observers like us are likely to see.” Are we talking about carbon-based life, or information-processing computers? Help, philosophers!

Linde thinks that the multiverse shows tendencies, although not cut-or-dried predictions. It prefers a cosmological constant to quintessence, and increases the probability that axions rather than WIMPs are the dark matter. Findings to the contrary would be blows to the multiverse idea. Most strongly, without extreme fine-tuning, the multiverse would not be able to simultaneously explain large tensor modes in the CMB and low-energy supersymmetry.

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