Mountains on the Moon: The Multiverse and the Limits of Physics by Richard Easther

Interstellar travel is trivially accomplished with a wholly unremarkable engine. One need merely go backward in time as one goes forward in space. One can then go anywhere essentially instantaneously even at a trivially slow local speed. This requires nothing more remarkable than any engineering or theoretical scheme heretofore proposed.

Dear Richard,

Congratulations on a very well argued and enjoyable essay. Some time ago, my first inclination is to dismiss the whole multiverse idea as too crazy because it is at odds with the apparent uniformity and uniqueness of the laws of nature of the observable universe which we may even have a decent chance of proving mathematically. But a simple question by Guth changed my perception when he asked: "why is our universe happening only once?" because this is at odds with a Copernican principle point of view. I have a (real wild) speculation about how to answer this question properly, and if inflation and landscape are real, then we would have in fact a multiverse of multiverses (I can elaborate on this if you are interested). What I would like to ask you is how would you answer Guth's question in the inflation scenario?

Regards,

Florin

Greetings Richard,

I enjoyed reading your essay. I am not a tremendous fan of the multiverse proposition, but I attempt to entertain the possibility in a fairly vigorous way. As luck would have it; I mention one multiverse in my contest essay The Possibility for Answers from Physics, but I also spoke about the inflationary multiverse concept last month, in a talk on Fractals in the Cosmos.

The paper I cite in my essay, by Laura Mersini-Houghton, might be of interest to you. She has a unique approach to the String Theory landscape problem, which involves entanglement between the 'branches' of the multiverse, and a process of 'natural selection' based on non-local connections via decoherence theory. Birth of the Universe from the Multiverse arXiv: 0809.3623

In my comments about Oldershaw's essay, I remarked that it seems as though there is some verbal sleight of hand here, in that some people would rather refer to a 'multiverse' than to state that the universe is fractal at the ultra-large scale. If we say that the term universe or cosmos means all there is, then the idea of a multiverse is absurd as it implies something beyond everything or all. If by universe one means that part which is or might be observable, then one does not need to get into regions where the Physics is different to leave the universe, but it is still part of our singular cosmos - just too far to see.

I do get that adjacent bubbles, in the inflationary and other multiverse scenarios you are discussing, are inherently too far apart to communicate and moving further apart always. Still; I wonder if maybe we should reserve the term multiverse for something more like the Everettian concept of 'multiple universes' or 'parallel universes' which contain the diversity of different outcomes in a branching scenario.

What are your thoughts on these questions?

All the Best,

Jonathan J. Dickau

Richard

It is often unclear what people mean scientifically by a multiverse. Can you give me your / the definition.

For comparison my definition of a Universe is "A label for EVERYthing taken together and regarded as an inseparable whole, such that every thing is directly or indirectly connected to every other thing; i.e. there are no holes in it or things separated from it." This does not preclude limitations on current measurability due to observable limitations arising from finite e-m speed etc. For me there is / can only be one universe, and although any one observer can only observe part of it what she can observe is influenced by (Boundary conditions) the unobservable portion.

Checking back,

I echo Terry's sentiment, and look forward to seeing how you deal with Florin's question and my comments, as well.

Jonathan

Uncle Al,

I enjoy your joking.

Eckard

Dear Dr. Easther,

I enjoyed your article. I do have a few questions. It is my understanding the inflaton field is similar, though not identical, to the Higgs field. A lot of work these days focuses on the slow rolling of the field, which then enters into an mφ^2/2 phase. So the inflaton field is most likely not perfectly quadratic in the φ field, though it might be argued that near the minimum it is approximately so.

I have some problems with aspects of the multiverse idea, or in particular the pocket universe idea. The argument for this is of course that distant regions of the universe are inflating away so rapidly that communication with them is not possible. Yet I can't help but think we might be able to peer beyond the opaque boundary of the CMB. If we get very good at neutrino astronomy or in detecting gravitational radiation from the earliest moments of the universe we could in principle observe the universe up to the inflationary period. If this is possible it would then make sense to me that these very early, and now horrendously distant, regions of the universe operate on the same vacuum we observe locally.

At the risk of theory mongering, let me propose a toy model here to make a point about the multiverse. The universe may well have emerged from some sort of quantum fluctuation. An easy model for this is a virtual wormhole. The wormhole consists of two black hole-like bodies, but just above or on the horizon there is a Lanscoz junction which forces mass-energy approaching one horizon to appear outside the horizon of the other opening. Inside this region there exists a three-ball of space, and the junction results in a topological suturing of these two 3-balls into a three sphere. Now assume that inflation takes place by puncturing a hole in the three ball. This point or the boundary is removed "to infinity" from the perspective of the antipodal point and the space is converted to R^3 plus pt. If we consider the "reciprocal" of this space with r - -> 1/r the point that is removed is a singularity or in complex variables (complexified coordinates) a pole. An integration around this point of field propagators might then result in a branch point which connects this R^3 to another R^3. For various reasons I find this to be a more aesthetic picture of what might be called the multiverse.

I will have to read your paper arXiv:0805.2154[astro-ph] to understand more completely your argument leading to figure 1. I will say that based on your paper it does appear that you have clearly argued for the quadratic inflaton potential.

Cheers LC

In response to Lawrence,

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It is my understanding the inflaton field is similar, though not identical, to the Higgs field. A lot of work these days focuses on the slow rolling of the field, which then enters into an m phi^2/2 phase. So the inflaton field is most likely not perfectly quadratic in the phi field, though it might be argued that near the minimum it is approximately so.

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The inflaton is likely a scalar degree of freedom (like the Higgs) but it is very different from the Higgs, in that it must couple weakly to all other kinds of matter in order to preserve the flatness of the potential (which will otherwise be corrected by loop terms).

The m^2 phi^2/2 is a toy model, and it is not clear how good it is -- you are right that any minimum will look quadratic, but in models which try to work out the inflaton potential "honestly" this quadratic region is often fairly small -- but the basic dynamics is still representative, making it good enough for my purposes.

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I will have to read your arXiv:0805.2154[astro-ph] to understand more completely your argument leading to figure 1. I will say that based on your paper it does appear that you have clearly argued for the quadratic inflaton potential.

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We are not arguing FOR the quadratic potential, but were really exploring how the potential can be constrained with data for general inflationary models. We plotted the predictions of a couple of well known models primarily as a service for the reader, not because we think any of them have been "proven" (although it is well know that the quartic model is not a good fit).

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Yet I can't help but think we might be able to peer beyond the opaque boundary of the CMB. If we get very good at neutrino astronomy or in detecting gravitational radiation from the earliest moments of the universe we could in principle observe the universe up to the inflationary period.

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There are several things going on here. The CMB decouples from the rest of the universe relatively late, when compared to neutrinos (which do not interact with the rest of the universe from a minute or so after the big bang) and gravitational waves (which can be sourced at any time, but do not interact significantly when the density is significantly below the Planck scale). However, the initial conditions for the CMB (in particular the amplitude and scale dependence of the primordial fluctuations) are set during inflation, maybe 10-30 seconds after the big bang (if you just naively extrapolate back in time). The "peaks" in the CMB power spectrum arise much later, but it is relatively straightforward to back those out and recover the primordial spectrum. So in that sense, the CMB is directly sensitive to inflationary physics, despite the late decoupling time relative to neutrinos or gravitons.

However, if you consider a moment during inflation at which the universe will grow (say) 100100 times large larger before inflation came to an end, a graviton which existed then with a wavelength larger than the Planck length would now have a wavelength far larger than the visible universe (thanks to the redshift factor) - and the total inflationary growth can be far larger than 100100. So even if the graviton is "there" in some sense, it is not possible to detect it. We ARE sensitive to very long wavelength gravitational waves (ie modes whose wavelength is roughly the same as the current size of the visible universe), since these directly source the polarization of the CMB, and this signal is being actively searched for. But significantly beyond that limit, it does not seem reasonable to think of a detection.

Hope this helps,

Richard

Florin,

In response to "then we would have in fact a multiverse of multiverses" -- I think I see what you mean, and by assuming complicated potentials with many minima, you can certainly imagine this happening. (Although whether you would CALL it a multiverse of multiverses would be up to you.

For instance Bousso and his collaborators refer to "terminal vacua", meaning low-lying minima of a complicated potential -- and once you arrive in one of these you cannot climb out. (All the vacua of m^2 phi^2 and lambda phi^4 are terminal vacua, so I did not need to make this distinction)

Conversely, one can imagine a potential with any number of different, meta-stable minima. A pocket which found itself "settled" in one of these could then generate new "sub-pockets" -- and you could potentially think of each of these pockets as a self-contained multiverse, but it would also be embedded in some larger structure.

As to Guth's question, I can see no reason to expect that there is only 'one' multiverse (and thus one universe). The full spacetime of most multiverse models is connected, in that one can draw a path between any two point (even if almost all of these paths cannot be physically traversed). However, there does not seem to be any theoretical reason as to why there would not be other volumes of spacetime which "exist" but cannot be reached from ours by any path, so in that sense I would say that our universe "happens" more than once. Nothing I have said in my essay bears directly on this, but again I was trying to avoid this sort of top down approach and instead focus on what we can learn from measurements we know we can actually perform.

Richard

The CMB is thought to be sensitive to inflation and early gravitons in the structure of the CMB. Gravitons which decoupled from the inflationary gemish are stretched out into classical gravitational waves which result in anisotropies observed in the CMB, which may appear more explicitly as B-modes. We will have to wait for the Planck spacecraft to complete it survey to determine if these ideas bear fruit. Directly detecting this radiation is likely not possible. Depending on the number of e-folds this gravitational radiation is likely stretched out too far for direct LIGO detection. Yet I can't help but think that if this is directly coupled to radiation we observe today that this suggests a common vacuum structure.

This is a part of why I ponder whether the universe involves Riemann-like sheets connected by a branch cut (if we complexify variables) on a "reciprocal R^3 sheet." If we detect anisotropies in the CMB and other details which connect to inflationary physics I would think we are detecting physical effects connected to a common vacuum. You argue in your paper that we can make judgments about the structure of the inflaton potential, so we are using some astronomical "mirror: to see the mountain on the dark side of the moon, so to speak. In general though, I have questions about theories of other universes as a method for understanding our universe, particularly when those other universes are not observable.

Cheers LC

Hello Again,

I see my earlier comments and questions remain unanswered. So I ask again professor Easther. Have you checked out the "Universe from Multiverse" paper I mentioned, and if so do you think it's relevant? And second; would you be so kind as to give a more precise definition of when it's proper to use the term Multiverse.

As I stated above; it seems there is some ambiguity, or a disagreement about precisely when to use that term. For me, it is more natural to picture a fractal branching pattern hanging in spacetime, and to view that as a single cosmos, unless the various branches consist of alternate possibilities which might inhabit the same location in space and time.

Do the multiverse candidates you are writing about satisfy this criterion? Is it automatic that the Physics in different bubbles has different fundamental relations, or that they represent alternate possibilities playing out on the same stage? Or do you see things as playing out as a multiverse which stretches mainly into adjacent patches of space (different stages or arenas)?

The favor of a reply is requested.

All the Best,

Jonathan J. Dickau

Jonathan

By multiverse I am referring to the collection of physically distinct pockets of spacetime (i.e. a "universe") where the energy density is substantially below the threshold at which the motion of the scalar field is dominated by it stochastic (or quantum evolution). These pockets are topologically disconnected, in the sense that any path which connects "low density" regions in different pockets necessarily traverses a "high density" region between the pockets.

In comoving coordinates (ie coordinates that do not "expand" with the growth of the universe, the structure of the multiverse is fractal in the sense that it has structure over a huge range of physical scales (although you need to be very careful about you precise choice of coordinates when making these statements -- this goes back at least as far as the work of Linde and collaborators in the mid 90s), and would look something like a "Sierpinski Gasket" but in the simple models I considered, there is no nesting or branching.

What you choose call a multiverse is entirely up to you, of course, but debates over the appropriateness of definitions usually do not tell us much about physics, so I tend to avoid them. (My usage of the term is conventional among people who work in this field).

As a matter of practice, for the models I considered, within a single pocket the perturbations inside two well-separated subvolumes (ie those that are separated by a distance many times larger than the radius of the visible universe) are effectively uncorrelated, just as they would be if they were in separate pockets. On the other hand, in scenarios where the "particle physics" differs between pockets, any observers in the same pocket would agree about (say) the mass of the electron, no matter how far apart they were.

Richard

Hello again,

Thanks for the detailed answer, Richard. That satisfies my need for specificity, for now. It's agreed one could get into 'terminology wars' that result in no greater understanding of the Physics involved. On the other hand, I can find plenty of examples where two different sciences (or related branches of Math and/or Engineering) have used the same concept in similar ways, but can't come to an agreement because they have defined the same term differently - which makes things confusing.

So your reply helps to cut through or reduce some of the confusion.

All the Best,

Jonathan

I might then take it that pocket universes are topologically disconnected then have quantum fields which have S-matrix domains of causality which are not connected to each other.

Cheers LC