# A Question about the Multiverse

Another question from St. Paul, the reader from New Zealand:

I hope that you are well and that you are having fun with your work. I see that you posted our email exchange on your blog, it was a great answer and much appreciated.

I actually have another question I would like to ask, (although I realise that you may well be planning on writing about it already) but as always I completely understand if you don't have the time!

I've been reading about the recent detection of gravitational waves and how they confirm the theory of inflation. What I have found interesting is that there have been quite a few articles reporting that most models of inflation imply the existence of a multiverse, with quotes from Alan Guth, etc. I realise that the term "multiverse" can be used for several quite different situations, but they seem to be referring to one with variation of the laws of physics, meaning the anthropic principle can be invoked.

I was wondering what you make of this new discovery and what your take on the idea of the multiverse is? I have always felt that the fine-tuning argument was a helpful pointer to God, so I am curious about the implications of confirming inflation (although the existence of multiple universes certainly doesn't rule Him out).

Paul

A quick explanation concerning "fine-tuning" and the "multiverse".   Fine-tuning refers to the observation that the fundamental constants of Nature seem to take special values which appear to be necessary to the existence of life.   The fine-tuning argument is a theistic argument which claims that this is good evidence for the existence of God.

One common atheistic retort is to say that maybe there are lots and lots of universes—with different laws of physics in each universe—and that any observers would therefore have to live in the universes which permit life.  This idea is a called the multiverse.

This may sound like crazy science fiction thinking, but I actually think it is the most plausible naturalistic response, given what we now know about physics.  Although there is no really good reason to believe in the multiverse, it seems much more plausible then any of the attempts to construct physical mechanisms to account for this fine-tuning.

However, it is not really clear to me that the multiverse is the sort of thing that ought to count as an explanation for fine-tuning.  In some moods it seems to me like cheating.  Science normally works by postulating theories to fit the observed data, not by postulating (new and unobservable) data to make the theories we have seem less weird.

In fact, there are in fact some serious controversies as to how to properly do Bayesian reasoning in the context of a multiverse.  Pretty much all viewpoints lead to some horrendous paradoxes.  Since the proper way to do probabilistic reasoning in this context is unclear, it is also unclear to what extent the multiverse would be an explanation for fine-tuning.  But this is a complicated question I don't have time to go into right now.

Instead, Paul asks the different question of to what extent the multiverse is supported by real, actual Science.  In particular, the very recent results from last March about inflation.  For those of you who have been living under a rock, there was a recently announced experimental result in cosmology.  The BICEP2 experiment claims to have seen the gravitational waves resulting from inflation, a very early period in our universe's history where the size of the universe expanded at an extremely quick, exponential pace.

[Update: the BICEP2 results have since been discredited.]

I wrote to Paul roughly as follows:

Most models of inflation predict "eternal inflation", meaning not that there wasn't a beginning, but that in some regions of the universe, inflation continues forever towards the future.

In order to have a multiverse of the sort that might be conceivably relevant to fine-tuning, you need to meet two criteria: (a) a mechanism for producing gazillions of different universes (at least $10^{150}$ without supersymmetry, or $10^{60}$ with supersymmetry), and (b) in these different universes, there are an equally large number of different effective parameters describing the low energy physics in each of the universes.

Eternal inflation is conducive to (a) insofar as it would result in widely separated regions which can never causally communicate with each other even at the speed of light.  But it does not by itself do anything to meet condition (b).  The best argument for (b) is probably string theory, which seems to have gazillions of different types of metastable vacua, but there is currently no successful experimental predictions for string theory.  (String theory does seem to imply the existence of gravity, but that's more of a retrodiction, and isn't unique to string theory...)

I am a postdoctoral researcher studying quantum gravity and black hole thermodynamics at the Institute for Advanced Study in Princeton. Before that, I read Great Books at St. John's College (Santa Fe), got my physics Ph.D. from U Maryland, and did my first postdoc at UC Santa Barbara.
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### 7 Responses to A Question about the Multiverse

1. Nick H says:

Is there any sense in which the multiverse could be considered a timeless, infinite entity that would eliminate the need for God as a beginning to the universe?

2. Aron Wall says:

The "multiverse" is just a bunch of evolving universes, so it's not timeless. If by a multiverse one effectively means one big universe with a lot of regions, then most of the same arguments that I discussed in the series "Did the Universe Begin" would also apply to a multiverse.

3. Scott Church says:

Aron, I've got a quick question as well. It seems to me that as you said, within the context of the standard model eternal inflation by itself does nothing to give us child universes with wildly different laws of physics. For any given bubble universe appearing from some excited inflaton potential state I don't see how reheating alone could lead to any differences in how underlying symmetries (like say, the Higgs mechanism, or electroweak symmetry) actually break leading to differing parameters. It seems to me that from the standpoint of fine tuning, the multiverse idea requires the string vacua of M-theory to have any teeth. To my understanding those vacua are defined by the underlying $10^{500}$ calabi yau manifold configurations possible within the framework.

If so, are these vacua actually metastable in the sense that any of the possible topologies could, for lack of better terms, "freeze out" of an underlying 11-dimensional "foam" as the larger universe cools, or do they merely reflect a lack of knowledge of the underlying one that constrains string states? Cosmologists these days talk about eternal inflation and a multiverse with gazillions of different sets of physical laws as though they're synonymous. But it seems to me that this is only possible if M-theory is true specifically in the former sense.

Am I missing anything?

4. Scott Church says:

Hmmm... I thought I did the LaTex per your instructions and copied out of Notepad, but it didn't seem to render right. Could it be an ascii/unicode thing? Guess I'm still getting used to this. :-)

[Fixed. The problem was somehow you used ∧ rather than the standard ASCII carat ^ ---AW]

5. Aron Wall says:

Scott,
That's right, the Standard Model by itself does not allow child universes with "different laws of physics", so to speak. It has got only one vacuum state. In order to get enough vacua to potentially explain fine-tuning, you need a significantly more complicated theory. For example, string theory (I'm not sure I know of any other plausible examples, but that may just be due to our lack of knowledge about quantum gravity.)

I'm not an expert on string theory model building, but I gather that the $10^{500}$ number doesn't come from the number of Calabi-Yau manifolds alone. (Calabi-Yau manifolds are the ways of compactifying 6 dimensions of the 10 dimensional string theory, in a way which preserves supersymmetry.) While no one knows exactly how many Calabi-Yau's there are (it might even be infinite), currently there are only about 30,000 known-to-be-distinct choices. To get a number like $10^{500}$, you need to include "flux compactifications" in which various higher dimensional versions of electromagnetism have different amounts of electric flux wrapped around various cycles. I think you also need to include various types of higher dimensional membranes to build realistic models. To break supersymmetry you need to include "antibranes" which have the opposite electric charge from the other branes; it is controversial which of these models are unstable, but at least some of them are probably okay (assuming string theory is true to begin with). This is the KKLT scenario.

A metastable state is one which lasts for a while and then eventually decays (as opposed to an unstable state, which decays right away, or a stable state which lasts forever in the absence of an external force). Normally in QM, one expects that there will always be a tiny probability to decay into a lower energy state, unless the state has the lowest possible energy given its conserved quantities. If there are an enormous number of possible vacua, one expects that most of them will be metastable, that is there will be a small probability to decay. (If our own vacuum is metastable, the halflife must be at least billions of years, or one would expect it to have already decayed to something else.)

I think you are using the term "metastable" in a confusing way in your question. Normally when people talk about a vacuum being metastable, they are referring to the probability of decay FROM the vacuum, whereas you seem to be interested in the probability of decay TO our vacuum state. Let me rephrase your question as "What is the probability that a vacuum like ours would form from some particular simple initial 11 dimensional spacetime foam state, by some reasonable spacetime history?" (supposing the universe began in such a state). I don't think anybody knows how to calculate the answers to questions like this...

On the other hand, I think most string theorists generally expect (it isn't proven, but it's plausible, see this paper for an argument) that any inflating vacuum will have some nonzero probability to decay to any other particular inflating vacuum state. If so, and if eternal inflation occurs, then with probability 1 there will exist a bubble of any particular kind we like SOMEWHERE in the multiverse. To what extent this counts as a prediction / explanation of what we see is a very deep and difficult philosophical question.

6. Scott Church says:

Aron, thanks! As usual, this is just what I needed. And yes, you formulated my question better than I did. What I had in mind was decay TO one or more vacuum states during post-inflation reheating, and whether that would result in child universes with physics just like ours or different physics. It always seemed to me that given eternal inflation, string/M-theory is required to make the latter possible. And thanks for clarifying the nature of those vacua as well. I was under the mistaken impression that within the formalism, Calabi-Yau manifold topology alone determined the landscape. I've been meaning to read the original KKLT paper but haven't got around to it yet. I'll read the other one you linked as well.

Speaking of string/M-theory, I just finished Peter Woit's book Not Even Wrong and thoroughly enjoyed it. I've been dropping in at his blog too (when I'm not here :-) ). He gets a lot of traffic from string theorists and some of them are seriously pissed at him for his stance on M-theory and the multiverse. He gets regular visits from some heavyweights too... Lee Smolin drops in from time to time, and so does Susskind. Spending time there really gives one a feel for the controversy surrounding all this... at times it sounds almost like a religious war. To me that's revealing, if for no other reason because it provides an antidote to all the big-name folks that treats M-theory and the multiverse like they're self-evidently a done deal. In the wake of the Carroll-Craig debate, I'm beginning to see why Carroll gets so testy when folks bring up the subject of falsifiability.

And you confirmed my LaTex Fail theory as well. I usually write my posts in Notepad and copy/paste them. For development-related reasons I have my Notepad configured for Unicode rather than ASCII, and I've been wondering if that wasn't my problem. Sounds like it was.

Blessings!

7. Aron Wall says:

Scott,
You're welcome.

BTW, I think the standard eternal inflationary multiverse picture is that there are different possible vacua during inflation, with some probabilities to tunnel between them, but that once you start exiting inflation (i.e. during reheating) it is already pretty much determined which kind of universe you will end up in... so "reheating" isn't the relevant time period for universe selection. (Here I'm assuming that inflation ends by some field slowly rolling down its potential, and not by suddenly tunneling into a noninflationary state. This "slow roll" assumption is needed to get cosmologies that look like ours.)

Only part of the inflationary potential is eternally inflating (and there are some models of inflation that are not eternal).