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BICEP2: the announcement (1-hour video)

Most of us had at least partial problems while watching the BICEP2 press conference on Monday. I urge the dear readers to find some time and watch these 60 minutes again (or for the first time):



The important event was very smoothly recorded and posted by the Harvard-Smithsonian Center for Astrophysics. In my opinion, the number of views of this video – below 1,770 at this moment – is totally inadequate for a discovery of this magnitude.




Someone introduces the speakers – including one "dispassionate external cosmologist", Marc Kamionkowski – and then the boss of BICEP John Kováč starts to talk and introduce the team. If the discovery is true, I surely believe that he is the first person who deserves the experimental (part of the) Nobel prize. If Planck manages to confirm the discovery, I would find it unthinkable for the Planck people to share the prize because they simply don't deserve it.

Note that Kováč (or Kovač) is a Slavic – well Czech (or Yugoslav) surname meaning (and playing the same role as the frequent English surname) Smith. I guess that he has some Croat, Serbian, or Slovenian roots. It is so popular name that even its version imported to Hungary – Kovács – became the most frequent surname in all of Hungary.




At any rate, Kováč shows some nice pictures from the South Pole and presents the heroic experimenters, both senior and junior ones, who have spent years with this work that seems to have ended by a happy end. Once Kováč completes his sociological and likable comments, the physicist who has surprised Andrei Linde with the great news in a touching video begins to cover "the part of the talk that has already been covered pretty well by all the rumor websites". ;-)

Incidentally, the Chinese expression for "the man who almost made Linde cry" is Chao-Lin Kuo. Apologies to him for a silly joke. :-) To apologize, let me thank Willie Soon [that's a Malaysian name at Harvard-Smithsonian] and link to this fun bio of Kuo and his family.

Rumors often surface and we get excited about them. Sometimes, the official truth turns out to be disappointing – and I would agree that it was the case of AMS and LUX (although we didn't really have positive rumors in the latter case). But the Higgs boson at CERN and now BICEP2 are examples of stories in which the rumors turned out to be accurate. That's the main reason why I don't ignore rumors in general. They just work very well way too often. We should better listen to them – and we should better be cautious while using them in certain ways, too.

You may say that the discipline inside the BICEP-KeckArray Collaboration wasn't good if it allowed the news to escape on Friday, three days before the press conference. But that would be a totally unfair appraisal. In fact, the discipline and secrecy in the experiment has been extraordinarily spectacular. Adam Mann of Wired discusses a rather spectacular story about how the signal was emerging and was kept in secret already from 2012 or so. That's quite a long time to keep your mouth shut!

Chao-Lin Kuo sketches the cosmic inflation and the existence of gravitational waves in that era of the life of the cosmos and he quickly switches to their method to see the waves. At 10:21, you may see that the symbol for the curly gravitational waves is a swastika. It may look unpopular but it is clearly the most natural symbol for that pattern, anyway, and the Nazis have stolen the symbol so they shouldn't be allowed a monopoly in reproducing it.

The vertical and horizontal parts differ by 1 part in 30 million or so only. It is a small signal but a detectable one.

Jamie Bock of Caltech speaks from 15:00 or so, focusing on the architecture of the telescope. BICEP2 is 10 times faster than BICEP1. Superconductivity helps. Clem Pryke of Minnesota shows pictures of the polarization lines in their "photograph" at 22:00 or so. Even the E-mode part of the picture would be exciting a few years ago. Now it's just background that prevents us from seeing the interesting stuff. Applause at 29:35.

Marc Kamionkowski, a top theorist and (among other things) a co-author of the important paper that divided the fluctuations to two component modes (see also Seljak-Zaldariaga who coined the E,B jargon instead of G,C), speaks afterwards. He proves he is independent from them because he doesn't have the nifty T-shirt that they only sell at the South Pole. He explains some of the detailed theory of inflation, why the scale seems to strengthen grand unification of forces etc. A fun speech. A presenter takes over at 33:00 or so and starts to take questions from the media – and then from e-mails.

What is \(r\)? It is the letter that follows \(q\). OK, it's the tensor-to-scalar ratio T/S and \(0.2\) is pretty big by the field's standards. One may see Alan Guth in the first row of the audience. Andrei Linde is on the right side. Writers from Nature, New Socialist etc. are asking. "Does the result answer what was before inflation, the multiverse etc.?" No one in our team is allowed to answer this question. :-) But Kamionkowski enjoys more freedom. The questions about the multiverse are not answered directly but the result narrows the set of allowed models so someone may figure out what it implies for the multiverse etc. An experimenter, Clem Pryke, says that "as an experimenter, he opposes theories that have no observable consequences." Laughter.

Fortunately, they have Kamionkowski over there (a very good idea to have a theorist in the panel so that the experimenters don't behave like naughty children!) who gets the last word and says that "as a theorist [another laughter], I must say that when inflation was proposed 30 years ago, it was a symbol of theoretical imagination" and some predictions could be tested, others couldn't, and the nosayers have seen their mouths shut. So... 20 years from now, people may perhaps hold another press conference in which they announce evidence for the multiverse.

Andrei Linde takes the microphone at 46:50. It wasn't clear from scratch that the inflation would bring the multiverse but in a year, it changed. The multiverse seems to be there, especially for detailed theories of inflation that seem to be favored by the data now. Alan Guth agrees – evidence for inflation pushes us to take the multiverse more seriously. (I would still like to stress that adopting the multiverse does not mean to accept the anthropic reasoning of any sort yet!)

The Boston Globe journalist asks (49:00) when they started to realize something was there, how they reacted etc. Gradual increase of confidence. The "falsifiable" experimenter Clem Pryke reveals some story and says he didn't believe the things (they would find something new) at heart. Beck adds comments. Kováč mentions the different kinds of skepticism that the data had to resist. An online question, why inflation strengthens the multiverse. Alan Guth explains that the inflaton has to have some stability for a while but it decays like the radioactive isotopes. He describes the competition between the "dying off" of the radioactive material and the exponential expansion of the surviving material.

Andrei Linde says that inflation is an exponential instability. An instability is something that can go wrong (albeit very right for us). If anything can go wrong, it will go wrong, repeatedly – like what we experienced in Russia, he says (laughter). Eternal inflation must be eternal.

A confused journalist says that "the fluctuation was 2 times as high as predicted" and asks what it means, Kováč debunks the assumption of the question. Clem Pryke suggests that the excess of \(r\) may be a statistical fluke around the South Pole, for example.

Stephen Hawking is already demanding the compensation from Neil Turok in one of these rare moments in which Hawking has apparently won a bet. Recall that he lost the $100 Higgs bet against Gordon Kane as well as the encyclopedia of basebell bet against John Preskill concerning the information loss. There's only one problem here: the Hawking-Turok bet explicitly talks about the confirmation of the B-modes by Planck, not by any experiment. So Turok may wait but he should surrender if (and as soon as) Planck confirms the BICEP's discovery. I am convinced that Turok should resign as the director of the Perimeter Institute before that. Concerning his painful calls for caution, I tell him: Tear down this wall of fog, Mr Turok.



A nine-minute tour to the BICEP2 at the South Pole (end of 2012).

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reader anna v said...

Thanks for giving the link. I am adding on the counter :).


reader a said...

What do you think about this? http://arxiv.org/abs/1403.4226


reader Umesh said...

On a related note, there seems to be some confusion regarding the status of 'the initial singularity' of the Big Bang, at least from the post at Prof. Strassler's blog. A few words from you would be much appreciated. Thank you in advance and apologies if the question is stupid.


reader Luboš Motl said...

Your paper is fascinating, A.S. I was expecting to give a clear reason why it's wrong but I don't really have any. If the numerical predictions/coincidences are true, it is really cool.

Normally I would be worried about the right behavior of black hole physics that clearly seems to have a preferred scale - the criticisms against "asymptotic safety"

http://motls.blogspot.com/2009/07/cern-weinberg-about-asymptotic-safety.html?m=1



but maybe there's a loophole out of these things. Let me think about it for a while.


reader Luboš Motl said...

Dear Umesh, after I saw your comment, I thought that Matt wrote something really wrong. But I agree with him.


Except for a terminological disagreement in the major point. I think it's right to call the initial state "singularity" because that's where the curvature invariants and temperature exceed the Planckian values, so they are "basically infinite" from the viewpoint of the classical theory (GR) that talks about the classical geometry.


For me, being so disrupted that the classical spacetime description breaks down should be *called* a singularity. So a curvature exceeding the Planck curvature at an isolated locus in the spacetime *is* a singularity.


This is perhaps just a terminological difference from Matt. I agree with him that the classical theory that produces really infinite results is a wrong description, so in this naive sense, the singularity probably isn't there. But I have also often emphasized that quantum gravity actually often preserves many singularities. For example, the orbifold singularity is exact according to perturbative string theory. One may use the orbifold background spacetime with the exactly special point as well as a smooth spacetime.


reader Umesh said...

Hmm...I see..yes, I remember reading with great interest your comments earlier about what the nature of singularities are and how a theory of quantum gravity (string theory) deals with them, what're the (possibly) correct physical questions to ask, etc. Thanks again for your reply.


reader Luboš Motl said...

Just an exchange over there:

Lubos Motl | March 21, 2014 at 11:29 AM | Reply

Dear Matt, I think that I agree with you about all the “true physics” you have stated here. The classical GR breaks down over there etc. But you may be using a slightly different terminology than others when you feel dissatisfied about the claim that the “universe started with a singularity”.

For me, and probably some professional physicists at many places, the point when the temperature or curvature invariants are so high – Planckian values etc. – that the classical theory surely breaks down may be *called* a singularity. One doesn’t need a strictly infinite value for that. With this modified or “regulated” definition, it is totally OK to say that it started with a singularity. The definition is OK because a singularity is a classical notion so it should only be applied with the classical accuracy, and if the curvature radius becomes smaller than the Planck length, it is “zero” within the error margin, so within the error margin that is inevitable for the vocabulary we are using (“singularity” belongs to some classical language), the beginning slice really *is* a singularity.

I think it’s also important to stress that quantum gravity doesn’t have to “smoothen” all singularities in a classical sense, to turn the singular shapes into smooth but still classical shapes. Sometimes, it preserves the shape but regulates just the physics on the background. Sometimes it invalidates the classical geometric description entirely. For an example of the first case, perturbative string theory on orbifolds contains the exact orbifold singularity to all orders (similarly for conifold points in the spacetime as well as the moduli space etc.), and this point – while singular from the viewpoint of classical geometry – leads to perfectly well-defined, finite predictions of probabilities in the (quantum) string theory because whatever could look like a source of inconsistency in a classical theory is canceled by new contributions. For an example of the other case, AdS/CFT has the CFT description that doesn’t directly contain metric degrees of freedom from the bulk (it seems) and they may only be reconstructed within some limited accuracy, too.

Matt Strassler | March 21, 2014 at 11:42 AM | Reply

Hi Lubos — all of what you say is true. But I would argue that the very fact that it takes two paragraphs of jargon to elucidate is exactly the reason why we should not be telling the public that the universe started with a singularity.

For one thing, we don’t know it’s true even with your definition of singularity… and I think you agreed with me on that point.

For another, if we don’t mean that there’s actually infinite density and infinite heat — i.e., if we don’t mean that *physical observables* show infinities — then we should use another term in addressing the public.

I think we should not blithely say that “the universe started with a singularity” without being much more clear about what we don’t know, and also about the fact that the statement comes with a dozen caveats about what “singularity” means when you go beyond Einstein’s equations.


reader Umesh said...

Cool, the point regarding the orbifolds is very well put in my opinion.


reader Luboš Motl said...

Thanks. I've added some more arguments over there, won't repost everything here. For example, I linked to Seiberg who talks about the Big Bang singularity as a part of physics

http://arxiv.org/abs/hep-th/0201039



Sociologically, Matt is almost certainly in a minority of true experts who have a trouble with the term "Big Bang singularity" as a part of physics.


reader Umesh said...

My thoughts too! I don't think it's such a sin to use the word 'singularity'; more so if one understands the qualifiers and fine print.


reader Luboš Motl said...

Dear Umesh, very well.

It may be surprising but I feel that Matt shares the misconception with some of the people around loop quantum gravity who are obsessed with the totally incorrect belief that the main hard problem of "quantum gravity" is that there are objects that look like singularities, and they must be replaced by something that doesn't look like singularity.

But this is not true. Quantum gravity is able to make the final product consistent even if the background looks like - and, in some cases, literally is - a singular classical geometry (not a smooth manifold).

Moreover, the appearance of singularities in the classical approximation may be *demonstrated*. As long as the approximation (classical GR equations) holds, well, we may use it, and if we use it, we may deduce the singularity theorems for the black hole singularities (they exist under generic initial conditions!) or the Big Bang singularity (it's how it had to start). Only dramatic "counter forces" which are "infinite" from the viewpoint of the classical approximation - which uses SI-like units in which "hbar=0" almost - can change the behavior, but the counteraction in such dramatic conditions won't change the fact that the region *looks* and *quacks* like a singularity, so it should better be called a singularity.

Matt wants to use a classical-physics-independent or observation-independent meaning of the word "singularity" but that's only possible if he has a full theoretical framework that allows such a thing and defines a singularity. He doesn't have one and even if he had one, the singularity could still be singular according to all linguistically sensitive definitions, and it could be singular even according his artificially picked definition.

Of course, if one means "an inconsistency of the exact laws of physics" by a singularity, it's never there. But a thing that "never exists" is meaningless and shouldn't have the monopoly for such an important word. A singularity means a very specific feature of a geometry and we should never redefine it to something that is completely unrelated to its original meaning.


reader Umesh said...

Amen! Perfectly so.


reader Dilaton said...

Note that my upvote holds only for Lumo's part of the comment ... ;-)

I always disagreed with Matt Strassler using (or even inventing !) strange baby language to "not confuse the public" by all means, instead of using clear terms as defined and used by physicists working in the field.

I am not sure if the baby language really helps the targetted audience Matt Strassler has in mind, and in my opinion for people who already have some knowledge (who know how to properly use the correct terms) it is confusing and has the potential to unjustifiedly make them think that what they have learned and understood is wrong, the physicists who use the correct terms in their work are wrong, etc ...

In summary, Matt Strasslers use of baby language and refusal of applying the correct terms and notions can be highly confusing up to misleading, which is not helpful at all ... :-/

So Lumo, you should really not use such scary terms that make all kids hide under the bed and cry ;-P. And anybody up to learning physics at a more or slightly technical level should consider this when coming to Matt Strassler's site:

http://www.istopfor.com/content/products/large/0501%20BABY%20ZONE.jpg

Of course many articles over there do contain very interesting information, but the at times exagerted and superficial avoiding of any terms considered "too technical" does not make the posts better understandable, on the contrary ... :-/


reader Luboš Motl said...

LOL, exactly, Dilaton. Matt wants to create some parallel baby language for science that isn't quite the same as the real science for adult physicists but that is nevertheless designed to convey "the exactly right message" so that the laymen are not confused. In all cases, what is right or wrong is only decided arbitrarily by Matt himself.

I don't believe that this gap between the physicists and laymen should be artificially grown and nurtured in this way and I don't think that a misleading (baby) language may be justified as the most appropriate one.

In this particular case, I have no clue what he wants to achieve. The classical GR implies that the Big Bang had to start with a singularity - only superextreme (quantum gravity) forces unknown from the normal GR may modify the behavior - so it is right and important to say that the life of this Universe began with a singularity when the conditions were infinitely extreme. It - the Big Bang Theory - is one of the most important insights in science and it is true from the layman's viewpoint as well as the expert's viewpoint. It makes no sense whatsoever to invent bizarre ideologies and baby languages whose only purpose is to emit lots of fog on this elementary point that the distances between two galaxies have been as small as you can get, that the Universe was once compressed so that in any ordinary sense of scale, it is really an infinite compression.


reader lukelea said...

Dear Lubos, you write: "(I would still like to stress that adopting the multiverse does not mean to accept the anthropic reasoning of any sort yet!)"

My question: Is it conceivable that all these universes have the same constants of nature, particles, etc.? In which case the depressing scenario of the heat death of the universe is not quite so depressing. There are plenty of other universes just like ours in which life and intelligence are thriving.

Of course such "emotional arguments" have nothing to do with scientific truth. Still, human beings by their nature seek comfort and consolation where they can find it. Who knows, that might be a law of nature too! :)


reader Luboš Motl said...

Dear Luke, in some primitive models, all the Universes may have the same low-energy properties (particle spectrum, parameters). In a realistic theory - and in string theory in particular - the multiverse surely contains a huge diversity of distinct vacua with different particle spectra.

To reconcile the eternal inflation with the naive picture of the infinite future empty de Sitter space is a bit subtle. But you must have seen the Penrose diagrams for eternal inflation

http://quantumfrontiers.files.wordpress.com/2014/02/multiverse.jpeg



I don't find much satisfaction in the idea that there are many other universes we will never see. I am totally emotionally neutral about such things, I really am ;-), but even if a physicist had emotions, he shouldn't allow these emotions to overshadow her rational evaluation of the evidence.


reader kashyap vasavada said...

Hi Lubos: Now it seems that concept of inflaton field is
getting a strong support. Just as a speculation (!) is it possible that after the inflation is over, the inflaton field becomes a CC for most of the history of our universe? Or is this
completely absurd? If that is true it would be economical since both contribute to expansion, in one case very rapid and in the other case lot slower.


reader Rick said...

When was the connection between gravitaitional radiation and CMB tensor modes first appreciated theporetically?


reader H said...

I would not have been able to stop the deletion countdown, as for some reason I was 'suspended', without warning.


reader lukelea said...

Thanks. You are always so kind to me! Are there similarities between the eternal inflation idea and the old steady state cosmology? In the latter, as I recall, particles pop out of thin "air" as space expands, in the former whole universes.


reader Art said...

Thx for the link! At the very end, Dr. Kuo makes a comment about increased tension (with Planck, I suppose) if future data puts r near 0.3. Isn't he the project manager for the follow-on to BICEP2? Is he tipping his hand?


reader Bohuš said...

Miloš,
the surname "Kováč" indeed translates as "Smith" in English.
"Kováč" is spelled that way only in Slovak. In Czech that name is spelled as "Kovář". Bosnian and Croatian version is "Kovač", and Hungarians have "Kovácz".
Bulgarians and Serbians write it as "Kовач", which is azbuka-version of the same name.
Bohuš


reader Dilaton said...

Can you give a link to your account? What pretext do they mention (to cool down or whatever)?

Suspending somebody who wants to get his accounts deleted is the most nonsensical ridiculous and craziest thing I ever heard about ...

This makes absolutely no sense. Seems having too much power has not only corrupted some moderators, but it obviously has completely eaten their brain away ...


reader H said...

My account is deleted - the time ran out while the 'suspension' (for so called rule violations) was in effect.


reader Luboš Motl said...

Hi Bohuš, I am Luboš, not Miloš LOL. Kováč is less frequent than Kovář but there are still 3170 Kováč's in Czechia

http://www.kdejsme.cz/prijmeni/Kov%C3%A1%C4%8D/hustota/

against 7019 Kovářes

http://www.kdejsme.cz/prijmeni/Kov%C3%A1%C5%99/hustota/



so it's just by a factor of two less frequent.


reader CentralCharge15 said...

What? The pre-text is "for rule violations"? That's the most meaningless, vague pretext I have heard! Not that the usual ones are specific of course.


reader H said...

Irony is that it could have been a 'bug'... but Iam not so sure... but no matter, on to bigger and better things.


reader Morbert said...

Hi Lubos,

Is there any tension between the eternal inflation Linde alludes to at the end of this video, and the paper by Borde Guth and Vilenkin where they argue that inflationary models must be geodescially incomplete in null and past timelike directions.


reader Luboš Motl said...

Dear Morbert, good question. There's no direct contradition. By "eternal" inflation, we may eternal in the future only.


reader W.A. Zajc said...

Dear Luke: I don’t think there is much similarity between eternal inflation and steady state cosmology (I’m sure Lubos will correct me if I’m wrong). Proponents of steady state cosmology were trying to reconcile the idea of a serene static universe that had always been there and always would be with the observed expansion; the steady-state hypothesis was their next best thing to a static universe. In eternal inflation, each of those lower vertices in the Penrose diagram is a Big Bang for some particular universe, and the diamonds are those universes that end in a big crunch. So I suppose one could argue that to an external (hypothetical) meta-being capable of observing all of these various universes wink in and out of existence, the eternal nature of these processes in some meta-time is a “steady-state”, but to any observer in one of those universes the situation is anything but that of steady-state.

Think of a pot of boiling water. If it’s a big enough pot that you don’t have to worry about boil-off, and the heat source is constant, you could argue that it is sort of in a steady state, just as the meta-being would conclude for the eternally inflating multiverse. But to a bacterium riding an expanding bubble as it rises to the surface, it’s living in a strongly time-dependent “universe”. (I hesitate to call this an analogy, because it’s so easy to break, so consider it an extended metaphor.) But since we’re closer to bacteria than meta-beings in this picture, we’re pretty far removed from being able to declare eternal inflation as a 21st century version of steady-state cosmology.


reader H said...

Now, that I am out of SE, I have started at ResearchGate - a far better place for scientists! True science and networking is encouraged there.


reader CentralCharge15 said...

Danu on PSE has requested a tag for QFT on curved spacetime.

http://meta.physics.stackexchange.com/questions/5648/a-tag-for-qft-in-curved-spacetime

David Zaslavaskly tells him to do something foolish like mix the "curvature" and qft tags. What the crap.


reader Dilaton said...

Yes I was the first to downvote his completely useless answer ;-)

This pointless suggestion leaves the impression that he opposes the creation of any new advanced topics tags useful for technical questions whereas stupid tags such as food, airplain, etc created by askers of popular basic questions are tolerated.

But we all, apart from Joshphysics, know that popular basic non-technical questions is what every googling dimwit can understand and appreciate and it is therefore this kind of content SE supports in the long run. And for this, neither experts and serious students nor advanced technical tags are needed ...

David Z just perfectly represents this attitude and SE point of view ...


reader CentralCharge15 said...

WOW, there are still some people who have not at all been exposed to meta... David H seems like a sensible person, he wouldn't go the evil side if exposed to meta I think.


reader CentralCharge15 said...

And now his bad answer is steadily gaining upvotes, too!


reader H said...

that is a mighty fine astronomy question, Dilaton!


reader Dilaton said...

Ha ha thanks :-)

At present, I am dumping all my cosmology questions, related to primoridial gravity waves for example, there (and on Quora) ... ;-P


reader Dilaton said...

CentralCharge15


Have you seen how this anti string theory zealot is now really throwing close votes on very high-level technical string theory questions

http://physics.stackexchange.com/review/close/38109


I would bet quite a large amount of money that the second trolling closevoter is, as always, Brandon Enright...


These two APODs should really be banned, at least from the review queues if not from the site as a whole, as they effectively do nothing else there apart from highly enhoy playing out their power to attack high-level/theoretical/technical questions...


And not even Qmechanic steps up to take it out of the close queue, he does absolutely nothing to defend theoretical physics ...



On PhysicsOverflow we will not tolerate such things :-(0) ...


reader Dilaton said...

Now PhysicsOverflow is live :-) !

http://www.physicsoverflow.org/


reader John McVirgo said...

Congratulations!


You and Dimension10 must be very proud, and amazed, at what you've achieved over the past few months.


reader Rehbock said...

Very nice.


reader Luboš Motl said...

Congratulations, Dilaton, it's really impressive!


reader CentralCharge15 said...

@John McVirgo



Please don't forget to mention polarkernel (our system developer)!


reader CentralCharge15 said...

Thanks a lot, Lubos, for actually setting up this thread here in the first place!

By the way, do you have any comments make about the Reviews section (summary) which is yet to come?



It will probably come by late August (and when it does, Physics Overflow will graduate (no pun intended regarding graduate-level and graduation)!) but Ron (whose idea the reviews section is) is optimistic that it can be done in one or two months...


reader CentralCharge15 said...

Here's the welcome post I think that new public beta users should read.


reader CentralCharge15 said...

I suddenly get an error when accessing PO. Does anyone else reproduce this?


reader Dilaton said...

I have written a blog post ...


reader John McVirgo said...

It looks great so far, but bear in mind that the Theoretical Physics site ended up with around 0.7 questions/day 199 visits/day just before the plug was pulled:

http://area51.stackexchange.com/proposals/23848/theoretical-physics

Getting the new site to run at those sort of figures is perhaps the next milestone, while maintaining graduate/research level standards.


reader Dilaton said...

Thanks John,


yes I know ...


But one of the many advantages of living outside the SE network (of course the software is less polished and we can not yet offer all the convenient features SE has) is that PhysicsOverflow does not have to fullfill any externally prescribed hard activity criteria. Nobody will pull the plug against the will of the community ... ;-)

If the hosting provider has too many technical glitches, such as the current database server issue, the site can with more or less effort be migrated.


Cheers


reader Dilaton said...

Dear Lumo,

do you have an answer to this ;-) ?

http://www.physicsoverflow.org///13605/quantization-of-cosmic-strings