Higgs Non-News

Posted on October 24, 2011 by woit

The two main LHC experiments have now recorded just about 5 inverse femtobarns each of data this year (CMS here, ATLAS here). This is the last week of the proton run, so that number will be near the total available for analysis until next spring when the next proton run gets started.

For some idea of what this means for the Higgs search, see for example Tommaso Dorigo’s discussion here of last year’s ATLAS projections about this. 5 inverse femtobarns was at the high end of what was expected, and the ATLAS projection was that this would be just barely enough to expect to be able to rule out a Higgs at 95% confidence level, all the way down to the LEP limit at 114 GeV. Of course, this expectation is statistical. If the Higgs is not there, and one is lucky (downward statistical fluctuation in number of events), then one can exclude at better than 95%. If one is unlucky (upward fluctuation), or the Higgs is really there, the 95% exclusion will not be achievable.

The LHC Higgs Combination Group has now combined the ATLAS + CMS Higgs results released at the summer conferences, and plans to release this in time for the HCP 2011 conference next month. Because of the efforts of Phil Gibbs, about all that needs to be said about the LHC-HCG plot is that it looks an awful lot like his, which is available here. An SM Higgs is excluded at 95% for masses below about 480 GeV, down to a lower limit of around 135 GeV (the data is actually very flat and close to the right value to exclude the SM from 135 GeV to 145 GeV).

The huge question of course is now whether there is a Higgs with mass between 135 GeV and the LEP limit (114 GeV). The current LHC data shows no definite sign of the Higgs, but the statistics is still too low to really say anything, especially for the lower part of the region. The crucial thing to watch now is the Higgs to gamma-gamma channel, which is the only one sensitive enough to hope to rule out or see a Higgs in the 115-125 GeV region, for the current amount of data collected. I don’t know when the experiments expect to release new data in this channel, just that their goal has been to each have some sort of result in December. Perhaps they’ll release something at HCP 2011, more likely not. The only rumor I’ve heard is from someone who has seen a recent plot of the ATLAS data for this channel, and he tells me he doesn’t see any bump in this region. But work on this data is on-going, and I have no idea what CMS is seeing or not seeing (my efforts to get Tommaso Dorigo drunk in Antwerp last month didn’t yield much).

At last month’s CERN Council meeting, there was a report submitted to the Council on “The scientific significance of the possible exclusion of the SM Higgs boson in the mass range 114-600 GeV and how it should be best communicated.” The report is based on the summer 2011 data, and it emphasizes excluding the Higgs at not just 95% (2 sigma), but at 5 sigma, something that will require (if the Higgs is not there) combining the 10 inverse femtobarns of data from each of the two Tevatron experiments and a similar amount from each of the two LHC experiments, something that won’t be possible until sometime after mid 2012.

Update: One more related item. At Berkeley starting today, ATLAS is holding an Analysis Jamboree on Higgs Searches. First two days is the good stuff, open only to ATLAS members, but the last day there will be an open session with theorists allowed.

Posted in Experimental HEP News | 15 Comments

The Status of SUSY

Posted on October 22, 2011 by woit

You may have seen by now claims from various sources about evidence for SUSY coming from CMS, for instance Hints of New Physics Crop Up at LHC, A Lifeline for Supersymmetry?, and CMS sees SUSY-like trilepton excesses. This nonsense is all due to Matt Strassler, who for some reason thought it was a good idea to post a blog entry Something Curious at the Large Hadron Collider that starts off:

Finally, something at the Large Hadron Collider (LHC) that does not seem to agree that well with the predictions of the equations of the Standard Model of particle physics.

followed by various caveats, which include though the advice:

But this is clearly something to watch closely over the coming months.

As one could easily have predicted, this got picked up by the media and various blogs, mostly dropping the caveats. In a later more detailed posting, Matt carefully three times in italicized red explains that “The excess will probably disappear”. He does continue to claim that “particle physicists are paying close attention” to this statistically insignificant discrepancy between data and theory, something I suspect was true before his blog posting for an equally statistically insignificant number of particle physicists.

During this past week or so, there has been a lot of various news about SUSY at the LHC, all of it bad. For some background, one should look at Mike Peskin’s write-up of his summary talk at LP2011, which he posted last week to the arXiv. See pages 37-41 for his discussion of the state of SUSY. He explains why one would expect that all SUSY mass terms are of the order of a few hundred GeV, with the Tevatron bounds on gluino and squark masses (around 300 GeV) already making one suspicious. Similar LHC bounds are already around 1000 GeV, getting close to the limit (around 1200 GeV) of what can be produced at current beam energy. When the LHC comes back on-line with higher beam energy in 2014, these bounds should then go up to 2000 GeV or more. Much has been and is being made of the fact that one can find SUSY models that evade these bounds, with LHC results then giving lower limits in the range 500 GeV and above.

Peskin writes:

As the LHC experiments become sensitive to hypothetical new particles with TeV masses, we are reminded of the phrase from the Latin Requiem Mass:

Confutatis maledictis, flammis acribus addictis, voca me cum benedictus.

A loose translation is: Thousands of theory papers are being tossed into the furnace. Please, Lord, not mine!

…

Before the startup of the LHC, I expected early discovery of events with the jets + missing transverse energy siignature of supersymetry. It did not happen. A particularly striking comparison is shown in Fig. 33. On the left I show the expectation given in 2008 by De Roeck, Ellis, and their collaborators for the preferred region of the parameter space of the constrained Minimal Supersymmetric Standard Model (the cMSSM, also know as MSUGRA). The red region is the 95% confidence expectation. On the right, I show the 95% confidence excluded region from one of the many supersymmetry search analyses presented by CMS at LP11. No reasonable person could view these figures together without concluding that we need to change our perspective.

Peskin goes on to argue though that the thing to do is not to abandon SUSY since it hasn’t shown up where it was supposed to, but to “acknowledge that, to test SUSY, we must search over the full parameter space of the the model”. The obvious problem with this is that the “full parameter space of the model” is huge, containing all sorts of corners that will never be accessible to the LHC, or that can be made arbitrarily difficult to rule out, requiring intensive effort from LHC experimenters for decades to come.

For details on what has been going on, various recent sources to consult include Anyes Taffard’s FNAL talk on ATLAS SUSY searches (“SUSY was NOT ‘just around the corner’ … must be hiding well … Or may be … need to go back to the drawing board”) and the many talks at the Berkeley Workshop on Searches for Supersymmetry at the LHC which included a huge array of negative SUSY results, including the one that for some reason got Matt so excited. Besides the kinds of models that Peskin expected to see at the LHC, lots of other more obscure ones are being ruled out by new LHC analyses. These include some that had gotten a lot of popular attention, such as split supersymmetry and F-theory models. These predicted things like long-lived gluinos or staus, which have now been searched for and ruled out in regions where they were supposed to show up. For example see here for more about F-theory and the stable staus, which CMS now says are not there where they were supposed to be (below 300 GeV).

For some other recent news, see the talks at the BNL conference running the past couple days, A First Glimpse of the Tera Scale.

Finally, for the best in recent HEP news, see this from Warren Siegel.

Posted in Experimental HEP News, This Week's Hype | 45 Comments

Solvay Centenary

Posted on October 19, 2011 by woit

The first Solvay conference was in 1911 (at the Hotel Metropole in Brussels, where I stayed one night of my recent trip to Belgium, without knowing the history), attended by the great men of the early days of quantum theory, and one woman (Marie Curie). For more about the 1911 conference, see this recent paper by Norbert Straumann. Today the 25th Solvay conference got underway in Brussels City Hall, celebrating the 100th anniversary of the first conference.

Like the first one, this conference is by invitation only, and it upholds a policy of confidentiality that goes back to 1911, with not even a schedule or list of attendees for the scientific session publicly available that I can see (just the statement that they are “most of the prominent physicists working on the subject). We do however have Lisa Randall reporting on Twitter about the proceedings. Evidently she’s the only woman there [note added: wrong interpretation, Eva Silverstein is also there, but the number of participants has doubled since 1911]:

Seems ratio of x to y chromosomes hasn’t changed in 100 years since first Solvay conference in 1911…

The only other source of info on the internet seems to be this Cal Tech news item, which lists the Solvay chair as David Gross and rapporteurs as:
John Preskill (Quantum Computation)
Anthony Leggett (Quantum Foundations)
Ignacio Cirac and Steven Girvin (Control of Quantum Systems)
Frank Wilczek (Particles and Fields)
Edward Witten (String Theory)
Alan Guth (Cosmology)

The gender distribution may have stayed the same, but it looks like the age distribution is somehat different. Today the average age of the chair and Rapporteurs is about 61, back then it was about 46.

Posted in Uncategorized | 37 Comments

This Week’s Hype

Posted on October 19, 2011 by woit

A couple people have written to tell me about the new BBC Faster Than the Speed of Light? documentary on superluminal neutrinos which evidently featured trademark hype from string theorist Mike Duff about how string theory could explain this. For better or worse, I don’t think I have access to the show from the US, although I’m sure that sooner or later it will arrive on our shores.

Update: Philip Gibbs has more here.

Update: The BBC program is now on Youtube, see here.

Posted in This Week's Hype | 13 Comments

String Theory Finds a Bench Mate

Posted on October 19, 2011 by woit

There’s a nice article this week in Nature about AdS/CMT, entitled String Theory Finds a Bench Mate. According to the article, the whole thing is (partly) my fault:

But in 2006, string theory took a public battering in two popular books: Not Even Wrong by Peter Woit, a mathematician at Columbia, and The Trouble With Physics by Lee Smolin, a physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada. Both books excoriated the theory’s isolation from experiment.

“It’s hard to say whether the interest in condensed-matter applications is a direct response to those books because that’s really a psychological question,” says Joseph Polchinski, a string theorist at the Kavli Institute for Theoretical Physics in Santa Barbara. “But certainly string theorists started to long for some connection to reality.”

The main point of the story is to tell about what is probably the hottest topic in hep-th these days, attempts to use AdS/CFT to say something about some models in condensed matter physics. For some idea of what this is all about, see the review article What can gauge-gravity duality teach us about condensed matter physics? by Subir Sachdev, and take a look at the online talks from the KITP workshop Holographic Duality and Condensed Matter Physics.

The article does go into the history of this in some detail, including its roots in efforts to use AdS/CFT to say something about heavy-ion physics phenomena observed at RHIC (for the string theory promotional campaign surrounding this, see e.g. here). I had expected to see a lot about this topic when higher energy results from heavy-ion collisions at the LHC were released earlier this year, but it seems to have gone quiet, perhaps because of the kind of comparison of data with AdS/CFT predictions that Sabine Hossenfelder points out here:

As the saying goes, a picture speaks a thousand words, but since links and image sources have a tendency to deteriorate over time, let me spell it out for you: The AdS/CFT scaling does not agree with the data at all.

My knowledge of condensed matter theory is minimal, and the hype level surrounding string theory makes it hard to know whether to take at face value many of the claims being made. On general principles, this looks a bit more promising than the heavy-ion case, since there are many different kinds of systems one might look at, and the connections are more to QFT than to string theory. Experts quoted in the Nature article give opinions ranging from:

Polchinski admits that the condensed-matter sceptics have a point. “I don’t think that string theorists have yet come up with anything that condensed-matter theorists don’t already know,” he says. The quantitative results tend to be re-derivations of answers that condensed-matter theorists had already calculated using more mundane methods.

to condensed matter theorist Andrew Green’s:

“Maybe string theory is not a unique theory of reality, but something deeper — a set of mathematical principles that can be used to relate all physical theories,” says Green. “Maybe string theory is the new calculus.”

Time will tell whether this suffers the same fate as in the case of heavy ions.

Posted in Uncategorized | 9 Comments

Welcome to the Multiverse

Posted on October 19, 2011 by woit

The October issue of Discover magazine has a new feature, a column by Sean Carroll, whose inaugural effort is now on-line as Welcome to the Multiverse. Sean makes the argument that opposition to multiverse mania is due to people having too naive an idea about what science is. They don’t realize that testing those parts of a theory you can directly observe allows you to draw conclusions about those parts you can’t directly observe:

A lot of people, both inside and outside the scientific community, are viscerally opposed to the idea of other universes, for the simple reason that we can’t observe them—at least as far as we know. It’s possible that another universe bumped into ours early on and left a detectable signature in the cosmic background radiation; cosmologists are actively looking. But the multiverse might be impossible to test directly. Even if such a theory were true, the worry goes, how would we ever know? Is it scientific to even talk about it?

These concerns stem from an overly simple demarcation between science and nonscience. Science depends on being able to observe something, but not necessarily everything, predicted by a theory. It’s a mistake to think of the multiverse as a theory, invented by desperate physicists at the end of their imaginative ropes. The multiverse is a prediction of certain theories­—most notably, of inflation plus string theory. The question is not whether we will ever be able to see other universes; it’s whether we will ever be able to test the theories that predict they exist.

Sean makes quite clear that multiverse mania is driven by string theory. Inflation is part of the story, but it’s not a fundamental theory by itself. All it can tell you is that your fundamental theory should have an inflaton field of some kind, with a potential satisfying certain properties. The big idea that justifies the multiverse is that:

In short, string theory predicts that the laws of physics can take on an enormous variety of forms, and inflation can create an infinite number of pocket universes. So the different laws of physics predicted by string theory might not be just hypothetical. They might really be out there somewhere among the countless parts of the multiverse. This is not a situation that cosmologists dreamed up in a flight of fancy; it is something we were led to by trying to solve problems right here in the universe we observe.

The problem that Sean doesn’t mention is one of circularity. Since you can’t observe anything about it directly, the multiverse must be justified in terms of another theory that can be tested and this is string theory. But if you talk to string theorists these days about how they’re going to test the unified theory that string theory is supposed to provide, their answer is that, alas, there is no way to do this, because of the multiverse. You see, the multiverse implies that all the things you would think that string theory might be able to predict turn out to be unpredictable local environmental accidents.

So, the multiverse can’t be tested, but we should believe in it since it’s an implication of string theory, but string theory can’t be tested because of the multiverse.

Until recently, string theorists would sometimes hold out hope that the LHC would see low-energy strings, extra dimensions, or supersymmetry, and that these discoveries would somehow pick out a predictive version of string theory from the landscape of the multiverse. This year’s data from the LHC has pretty much destroyed such hopes.

Sean ends with the inspirational admonition:

The proper scientific approach is to take every reasonable possibility seriously, no matter how heretical it may seem, and to work as hard as we can to match our theoretical speculations to the cold data of our experiments.

What’s going on in this story though is not a concerted effort to match theoretical speculation to experimental data, but something very different, a concerted effort to build a theoretical framework perfectly insulated from testability, and sell it to the rest of the physics community and the public, hoping no one notices the circularity.

Update: Besides the usual spam, this topic seems to attract mostly empty comments supposedly agreeing with me, and comment moderation is unusually annoying. I think I’ll turn off comments on this posting, and encourage people who want to discuss the topic to do so over at Cosmic Variance, where Sean has a posting devoted to this.

Posted in Multiverse Mania | 2 Comments

Weinberg on Symmetry

Posted on October 10, 2011 by woit

The latest New York Review of Books has an article by Steven Weinberg entitled Symmetry: A ‘Key to Nature’s Secrets’. It’s a bit unusual for the NYRB, since it is both scientifically more technical than usual for them (coming from a write-up of Weinberg’s talk at this conference), and doesn’t review any books. The printed version tells readers to go to the web version for footnotes, but some of these just note that things are being over-simplified. One of the footnotes is worse than useless: the editors have replaced x^3=x as an example of an equation with solutions that break a symmetry (x goes to -x) by “x 3 equals x”, an equation with the same symmetry but only a symmetric solution (x=0). The idea seems to have been to remove or replace any symbols in the equation that might upset people.

Weinberg tells the conventional story of how the Standard Model emerged during the 60s and early 70s out of the realization that non-abelian gauge symmetries were important and an understanding of what happens when symmetries are spontaneously broken. He tries to do some much more ambitious things, explaining the idea of “accidental symmetries” that are due to the limited number of possible renormalizable terms you can build out of a specified list of fields, but I’m not sure the typical reader of the NYRB is going to get much out of this.

The question of how to explain the notion of “symmetry” is an interesting one, and I thought a lot about it when writing Not Even Wrong, the book. To my mind, most such explanations mix up two conceptually distinct things: the group of symmetries (a group), and the action of the group on some other mathematical object (the representation: mathematically a homomorphism from the group to the group of automorphisms of something). It’s both the group and the representation that are important in the use of symmetries in physics, although often what is important is the trivial representation. From a mathematician’s point of view, the simplest representations to look at are unitary representations on a complex vector space, so the mathematical structure of quantum mechanics is very natural. To each symmetry generator you get a conserved quantity, and it appears in quantum mechanics as the thing you exponentiate (a self-adjoint operator) to get a unitary representation. In Weinberg’s piece, which aims at sophisticated issues in particle theory, the question of the basic relation of symmetries and conservation laws is relegated to a footnote which says only “For reasons that are difficult to explain without mathematics…”.

Weinberg ends with a landscape sort of picture, involving symmetries emerging only when a specific ground state emerges out of an initial chaotic inflation state. Philosophically this is a popular view of the future of the subject these days, but one that has so far led nowhere, and one that I think even in principle can never lead anywhere. Much more interesting would be to try and draw lessons from what has worked well in the past: exactly the gauge symmetries and spontaneous symmetry breaking phenomena that led to the standard model. We may very well soon find out there is no Higgs particle, turning this whole subject into a wide-open one. Future progress may come from exactly the same place as in the past: new ideas about how to exploit the mathematical structures inherent in quantum mechanical symmetries.

Update: The missing exponentiation in the on-line footnote has been fixed.

Posted in Uncategorized | 22 Comments

News From Europe

Posted on October 7, 2011 by woit

A few items with a European flavor:

  • The news from Dublin is that Witten will be in town soon to give the Hamilton Lecture, with the Irish Times reporting that

    Witten’s Hamilton Lecture will abandon string theory, however, in favour of knots, with a talk entitled: The Quantum Theory of Knots.

    He may be there the previous day, when they hold the annual Hamilton Walk, commemorating Hamilton’s discovery of quaternions and inscription of the quaternion relations on a bridge.

    In other mathematical physics coverage by the Irish Times, one of their columnists describes the interaction of the Irish revolutionary leader de Valera with Schrodinger and Dirac, speculating (humorously) that the three of them might have come up with an Irish “unified field theory.”

  • From a meeting today in Madrid, here’s an overview of theoretical particle physics in Spain. There’s the same pattern reported as has been going on in the US for a while: “moving from more formal and mathematical developments to phenomenology and also astroparticle/cosmology”, as well as trying to get theorists more involved in LHC physics. Another similar pattern to the US, the threat of “decreasing funding support for basic science in difficult economic times.”
  • The question of what future facilities for particle physics should be is not just a European one, but I fear that in practice a higher energy machine is not likely to be built anywhere except at CERN. This week at CERN there was an ICFA Seminar on Future Perspectives in HEP, which gives a good overview of the state of the field and prospects for the future. The question of what to build next to get information at the energy frontier is very unsettled, pretty much completely up in the air waiting to find out if there’s a Higgs particle or not. The SUSY and extra dimensional models used as partial selling points for the LHC are dying and won’t be convincing arguments for what the next generation should do.
    • Posted in Experimental HEP News, Uncategorized | 22 Comments

    What’s That at the Top of This Page?

    Posted on October 5, 2011 by woit

    The graphic chosen years ago as the header for this blog is an event display from the UA1 detector in 1982, of historical importance since it was the first event found with a W candidate. To be honest, the reason it’s there is that I was looking for something quick to use at the interactions.org Imagebank, figuring these were graphics I could steal without getting sued. What I ended up with is a cropped, lower-resolution version of the much better image available here.

    Even stripped of identifying info, UA1 experimentalist Jim Rohlf of course recognized it, and recently wrote me to tell me some more about it. He also tells me that he will soon be blogging at Quantum Diaries, and I look forward to seeing that. So, here’s the story behind that image:

    The collision is Run 2958, Event 1279 and was the very first W candidate that was found. It was recorded in the Fall of 1982 with UA1. As a newly minted junior faculty member and CERN scientific associate, I was resident at CERN and the first round of the W event selection and analysis was completed during the CERN holiday shutdown. On 23 January 1983 we submitted the W discovery paper for publication (Phys. Lett. 122 B, 103 (1983)). The details of the events were given in this paper. Within a few days, I got a letter from Lev Okun who had become a good friend of mine due to his frequent visits to CERN and his great interest in the working details of our experiment. In this letter which was several pages long he referred to this event as a “monster” because it decayed in the “wrong direction” and asked if we could have made a measurement error. Then the obvious hit me instantly- nobody had thought of this before- we don’t measure the longitudinal momentum of the neutrino due to the singularity in the direction of beam pipe but we can solve it to a quadratic ambiguity knowing the W mass. Furthermore, I saw that the kinematics of a 80 GeV object being produced with a relatively low cm energy of 540 GeV gave a remarkable result: often one of the 2 solutions was kinematically forbidden and when it wasn’t, the two solutions were often close together. Therefore, we could solve for the longitudinal momentum of the neutrino and be able to transform to the rest frame of the W. Since the W was polarized because it was produced in proton-antiproton collisions, we could measure the angle of the decay wrt the spin direction. Very simple idea, but be the first to do it and it becomes interesting and fun. I immediately wrote this up as a UA1 internal note in which I acknowledged the contribution of Okun. This technique subsequently became a standard at the Tevatron and now at the LHC.
    In the following months, we collected more data and the next international conference to come along was at Fermilab and I was told by Rubbia to give the talk which was published (J. Rohlf, “Physics at the Proton-Antiproton Collider,” Proceedings of the 12th International Conference on High Energy Accelerators, Fermilab, 619 (1983). I reported the first measurement direct observation of parity violation in (real) W decay and measurement of the spin. I attach a slide from a talk I gave at Fermilab 20 years later in 2003 where I pulled up some of my 1983 slides. (Notice I fit the W mass to 2% and got the right answer.) You can see the “monster” event in the bin at cos(theta) =-1. This W decayed in the wrong direction. We went on to collect about 300 W events in UA1. We never saw another one go in the wrong direction. We also could not find anything wrong with that original event 1279. So you see the event was “not even wrong”.

    Update: A copy of the talk slide that Jim Rohlf refers to is here.

    Update: Jim Rohlf’s blog at Quantum Diaries is now up here. His first blog entry is great, it’s about, independent of the Higgs issue, the fundamental problem the LHC hopes to investigate: what is causing electroweak symmetry breaking? He emphasizes that one way to study this is to try and see the self-interactions of Ws and Zs, which become strong at the TeV scale.

    Posted in Uncategorized | 14 Comments

    P-adic Numbers and Cosmology

    Posted on October 4, 2011 by woit

    The next math department colloquium at Stanford will feature Lenny Susskind lecturing on p-adic numbers and cosmology, here’s the abstract:

    The biggest conceptual problem of cosmology is called the measure problem. It has to do with the assignment of probabilities in an exponentially inflating universe, which falls apart into separate causally-disconnected regions. Neither I nor my friends had ever intended to learn about p-adic numbers until we realized how similar such a universe is to an endlessly growing tree-graph. The result has been some new insights from p-adic number theory into the measure problem and other puzzles of eternal inflation. Within the constraints of a one-hour lecture, I will explain as much of this as I can.

    I’ve no idea what this is about, but I’m guessing that Susskind is somehow drawing inspiration from two facts:

  • p-adic integers can be represented using a “tree” diagram vaguely remniscent of the logo for the Stanford theoretical physics group on their web-site.
  • The p-adic integers, unlike the usual integers, are compact, so you can put a finite measure on them.

    • It’s hard to believe that any of the special features of these mathematical structures will make the problems of eternal inflation go away, but who knows…

    Coincidentally, I’ve spent a lot of time recently learning about the p-adics, with a very different motivation. The way these things come up in mathematics is that you can think of number theory as being about a space, the space of prime numbers. The p-adics appear naturally when you decide to ask what happens locally near one point (i.e. at one prime). P-adic integers correspond to power series expansions, p-adic numbers to Laurent series. Various people have thought about analogies between conformal field theories on a Riemann surface, where one also wants to focus on what happens at a point and use representation theory methods, and the Langlands program which does something similar in number theory. This is part of the geometric Langlands story, and has roots in a remarkable paper of Witten’s from 1988 entitled Quantum field theory, Grassmannians, and algebraic curves.

    As I’ve mentioned before, this semester here at Columbia we have Harvard’s Dick Gross as Eilenberg lecturer, and he’s giving a wonderful series of lectures starting with local Langlands. I’m hoping at some point to put together what I’ve been learning about this and possible connections to QFT in some readable form, but at the moment things are still too speculative and hazy. In any case, no sign that these ideas are going to solve the problems of cosmology…

    Update: The Susskind et al. paper on this topic is now out at the arXiv. A p-adic model is studied, but no reason is given to believe that it has anything to do with eternal inflation and cosmology.

    Posted in Multiverse Mania | 18 Comments