Thursday, March 27, 2014

The Universe really began with the Big Bang singularity

Matt Strassler wrote two recent blog posts that attempt to denounce a singularity at the beginning of the expansion of our Universe and to question the Big Bang itself.

While I agree with most of the detailed technical claims he is making (e.g. with the constantly repeated notion that the closer to the Big Bang we dive, the more uncertain our knowledge about the phenomena becomes etc.), the truth value and purpose of the main propositions that Matt wants to defend remain mysterious to me. (See also my conversation with Umesh.)

Our whole universe was in a hot dense state,
Then nearly fourteen billion years ago expansion started. Wait...
The Earth began to cool,
The autotrophs began to drool,
Neanderthals developed tools,
We built a wall (we built the pyramids),
Math, science, history, unraveling the mysteries,
That all started with the big bang!

"Since the dawn of man" is really not that long,
As every galaxy was formed in less time than it takes to sing this song.
A fraction of a second and the elements were made.
The bipeds stood up straight,
The dinosaurs all met their fate,
They tried to leap but they were late
And they all died (they froze their asses off)
The oceans and Pangea
See ya wouldn't wanna be ya
Set in motion by the same big bang!

It all started with the big BANG!

Tens of millions of viewers are being assured about these insights every week and Matt hasn't complained yet. The song is totally accurate so far. It only starts to be wrong when they sing
It's expanding ever outward but one day
It will pause and start to go the other way,
Collapsing ever inward, we won't be here, it won't be heard
Our best and brightest figure that it'll make an even bigger bang!
(these extended verses haven't made it to TV, however) because our Universe actually has a positive cosmological constant, so the expansion will never stop. It will keep on continuing – in fact, accelerating – converging ever closer to the empty de Sitter space which is why there will never be any Big Crunch although this conclusion was unknown as recently as 20 years ago. If the dressed male musicians spent less time pretending that they are Barenaked Ladies and more time with studying the cosmological discoveries since the late 1990s, they would know it as well. ;-)

But the main point is that the Big Bang theory is correct and among other things, it implies that the conditions had to be basically infinitely extreme at the beginning.

When Matt suggests that there was no singularity and that the Big Bang could have been non-existent, his claims are not quite sharply defined. Whether you consider them true or false, defensible or indefensible, depends on the definition of the "Big Bang", the definition of the "singularity", the degree of certainty and the kinds of confirmations (empirical, direct, indirect) that you require to say that you "know something", and on the choice of the mathematical formalism that is connected with the notoriously vague words used in the human language.

Because I think that Matt's claims are either downright false or at least "morally untrue", I want to spend some time with a discussion of these issues. First, let us ask:

Is it realistically conceivable that the Big Bang will be proven wrong sometime in the future?

I don't think so but in order to add some details, we should agree what we mean by the phrase "the Big Bang". By the Big Bang, we mean either
  1. the observed current outward motion of galaxies from each other, or
  2. the same outward motion of the galaxies or matter in some distant past, or
  3. the even more prehistorical "cause" of all this expansion.
Now, the relevance of the term "the Big Bang" slightly depends on which of the three definitions above we prefer. These three processes are of course related, however. Also, they overlap and they (especially (2), of course) could be divided to "subitems" that depend on various eras. The first one (1) is the most indisputable one: we are observing the red shift of distant galaxies (that obeys Hubble's law) and this red shift may be interpreted as the Doppler red shift proving some kind of an "outward velocity". An "outward velocity" that is apparently proportional to the distance (Hubble's law) already looks like an explosion of a sort, and it's enough to justify the word "bang". At the most general level, the "bang" isn't supposed to mean anything more specific than that.

It was "big" because the whole Universe and its stars' kinetic energy was involved.

There's very strong evidence that the laws governing the expansion were "pretty much the same" billions of years ago, too. So the more extreme process identified as (2) has almost certainly taken place, too. The cosmic microwave background and the right composition of the isotopes from nucleogenesis ("first three minutes": yes, the Universe needed the same time to cook the light elements as you need to cook an instant soup) helps. We seem to have the right theory describing the evolution of the Universe from the first minutes to the present. And that's what we call "the Big Bang theory".

The words "the Big Bang theory" could make you think that it is a theory explaining why the "bang" was there at the beginning but it's not really the case. The theory really assumes that there was an outward "impulse" at the beginning and it deduces the observable consequences of this assumption (using Einstein's equations of general relativity and some other general laws of physics).

A more advanced theory, especially the inflationary cosmology which seems to be the winner now, actually explains "why" there was the initial outward impulse, why there was the bang. Using Alan Guth's words, inflation gives the "bang" to the "Big Bang" (and yes, every time I write the "Big Bang", I am deciding once again whether I want to capitalize it or not; sorry for all the apparent inconsistencies).

The inflationary cosmology is work in progress. Excitingly enough, the observation of the primordial gravitational waves directs the research of cosmic inflation in a certain direction. In a few years, we are likely to know more than we know today. And sometime in the future, physicists may consider even more advanced theories that go "beyond" the cosmic inflation, theories that even describe what was happening before the inflation, and perhaps those theories will be connected with some observations, too.

But what I would like to stress is that these future advances will not disprove the key assertions about the Big Bang because by the Big Bang, we simply do not mean some extremely esoteric processes before the cosmic inflation. We mean the more "mundane" processes whose right effective theory has already been sufficiently validated.

When we say that the Big Bang theory is true, we don't mean that some naive classical equations of general relativity are exactly true all the way back to the Planck time (if not beyond). What we mean by the proposition is something more modest: the explosion-like outward motion of the galaxies affects the whole observable Universe and may be extrapolated into the distant past when the expansion had to be produced by some "really strong forces". These insights won't really change in the same sense as the claim that "we know that there is a Higgs boson in Nature" or "the Earth is round" or "different species have evolved from the same ancestors".

Science indicates that these statements are almost certainly correct. This correctness does not mean that we have a complete theory and the full understanding of everything in Nature. When we say that the Higgs boson exists, we don't say that the Standard Model with the Higgs boson is the exact theory at all distance and energy scales; it almost certainly isn't. But whatever the more accurate theory is (or will be), it will contain something that looks like the Higgs boson, swims like the Higgs boson, and quacks like the Higgs boson. So we should better call it the Higgs boson. Even supersymmetric or grand unified theories contain something that may be called the Higgs boson. Theories may get more sophisticated, convoluted, advanced, and accurate, but something deserving the name "Higgs boson" in these theories just won't go away (although the concept may become and probably will become less fundamental than it is today; its epistemic status will keep on changing).

Similarly, when we say that the "Earth is not flat", we don't mean that we have understood the exact theory describing everything that governs the Earth. For example, you could say that the people who said that the Earth was not flat were ignorant about quantum mechanics. Quantum mechanics described everything including the Earth by a linear Hilbert space and linear vector spaces, you know, are flat. But the statement that the "Earth is not flat" isn't supposed to exclude the possibility of a more accurate theory where something that is completely flat describes everything in Nature. We are saying that the Earth is spherical and that's a different statement, one whose meaning may be operationally defined by some very particular observations. And it's been established.

When we say that "different species have evolved from common ancestors", we don't say that we have understood all the details about the origin of life, including the production of the first RNA or DNA molecules or proteins and the location and conditions where the production took place. But this isn't supposed to be a part of the proposition that "species have common ancestors". The proposition clearly says something nontrivial about some recent enough events that are "sufficiently close" to the well-known processes of the reproduction of humans that we know from the everyday life (or at least every-nine-months life). So a completely new "protein folding theory at cosmic dust" theory of the life's true beginnings won't really debunk the claim that "species have common ancestors".

Now, the status of the claim that "there was the Big Bang" is completely analogous. Like other claims in science, this sentence doesn't include the bold and unrealistic proposition that we have understood everything (or the claim that everything in Nature looks and has always looked like the Big Bang). Instead, the words in this sentence (especially the "big bang") are supposed to describe some objects or events that exist within some incomplete, effective theories that are only meant to approximately describe a limited class of observations and phenomena. And the validity of such insights may be scientifically established independently of the fact that more esoteric processes will be observed and theories that can deal with these more esoteric processes will keep on evolving.

Indeed, if such a separation of the "effective theories" from the "exact final truth" couldn't be made, science would be impossible! Matt's musings about the invalidity of the Big Bang singularity and the possible future falsification of the Big Bang itself seem to directly contradict this "independent existence of effective theories", something I consider a cornerstone of the scientific reasoning, and I am really surprised that no one else than Matt Strassler is displaying this kind of a misunderstanding because he's been working with effective theories at the top global level for decades.

Later, I will also mention a few related words about the meaning of the "existence of singularities". But before I do so, I want to address a relatively independent question:

Is it OK to say that the Big Bang was an explosion?

Yes and No. Some people take the analogy (or identity) of the Big Bang with an explosion too literally and derive many incorrect conclusions out of it. Their excessively explosion-like way visualization of the Big Bang leads them to some wrong ideas.

On the other hand, I think that many people – perhaps including Matt Strassler – seem to fail to realize that for most purposes, the Big Bang really is an explosion and the main local observational consequences of the Big Bang really coincide with the predictions of an explosion.

OK, so in what sense the Big Bang wasn't an explosion? Last week, I got many questions during a popular talk and one of them was effectively about the center of the Big Bang explosion or the direction from which the cosmic microwave background radiation should be coming, and so on. You get the point.

So I had to explain what everyone would have to explain. The CMB is coming from all directions because the Universe is and always has been uniform and isotropic at these longest scales. That also means that the Universe didn't have a center. An explosion may have a center, a preferred "galaxy" from which everyone else is receding, but the Big Bang doesn't imply such preferred places. Galaxies are like the coins attached to the surface of a balloon. When we inflate the balloon, the sizes of the coins remain constant while the distances between the coins increase. But the balloon is de facto spherical so no coin on the surface is "more central" than others.

Similarly, when CMB was created, the whole Universe looked like the surface of a balloon. The whole Universe was filled with something like a "star" and we still live inside this "star". Like in an oven, the radiation inside this "star" is coming from all the directions, and that's why we see the CMB in all directions, too. I have also explained how "far from us" the CMB photons were when they were created. All of them had the same distance from the Earth and all of them had the right directions so that they could end in the terrestrial telescopes. The "current" (at the cosmological time i.e. proper time from the Big Bang \(t=13.8\) billion years at any place in 3D) distance of the places from which the photons were emitted is something like 46 billion light years because most of the naive "14 billion light years" (especially those on the "young Universe, ancient" parts of the CMB photon's world line) continued to expand up to the present. I think that those explanations have clarified lots of things.

But there is also a sense in which the picture of the Big Bang as an explosion is pretty much perfect. When you take scissors and cut a region of the spacetime that covers 1,000 nearby galaxies (very small distance, relatively to the radius of the Universe) in the recent 5 billion years, you will get a piece of the four-dimensional Minkowski-signature "paper" that may be completely flattened because it's so thin in the spatial directions. In this "strip of 4D paper", the galaxies will follow some trajectories, and those trajectories will be exactly like the trajectories of galaxies that result from an ordinary explosion that may have a preferred center.

In other words, you may always locally use some special relativistic description of the physics. And in this local special relativistic description, the outward motion of the galaxies is exactly the same as it would be in a flat special relativistic Minkowskian spacetime where an ordinary TNT-like explosion with a preferred center took place! In particular, all the red shifts may be perfectly interpreted as the ordinary Doppler red shifts. Even special relativity allows us to say that no galaxy – and no inertial reference frame – is better than others, so even within the special relativistic description, we may sort of defend the "non-existence of the preferred center".

If we want to arrange the locations of all events across the whole observable Universe during the last 13.8 billion years, we do need a curved spacetime simply because ours is curved. In the curved spacetime, we may use slightly different mathematical equations and decide that the red shift was "cosmological" and not just "Doppler" red shift. But these are just modifications of our language that the curvature-based general relativity imposes upon us. If we're satisfied with a local description of the "thin strip of the 4D paper", special relativity is enough and the outward motion is described as an ordinary explosion, including all of its details, and we should be aware of this isomorphism.

As you can see, I do believe that the fight against "the Big Bang as an explosion" is being overfought. Up to a certain "threshold" in the space of questions, it's just OK – not just for the laymen, but for the professionals – to imagine that the Big Bang expansion is an example of an explosion.

Was there a Big Bang singularity?

Now, let me return to the vocabulary of effective theories. In his first anti-Big-Bang posts, Matt would claim that it's wrong for the journalists and others to claim that the Universe began with the Big Bang singularity. Haven't they noticed that this opinion has been invalidated?

Well, they haven't, and neither have I. I haven't because it's untrue. As long as we use the kind of an "operational language" rooted in operational definitions and linked to concepts in effective theories, we know that there had to be a singularity. We don't mean that the singularity has experienced "exactly infinite" temperatures and curvatures and we surely don't mean that such a singularity had to imply that the laws of physics are internally inconsistent. But there simply is something that is described as a singularity by classical general relativity – it looks, swims, and quacks like a singularity – and the existence of this something within the appropriate approximation is actually guaranteed if Einstein's equations are valid within the same approximation.

This much can be proven by solving Einstein's equations. Similarly, singularity theorems due to Penrose and Hawking (and their followers) guarantee that within the approximations of classical general relativity, a singularity will arise during the gravitational collapse of a heavy enough generic star. You can't avoid it. There is an object that is insanely dense and hot and extreme and that we call the singularity because it looks downright singular according to classical general relativity.

But by endorsing the idea that the Big Bang singularity exists, we don't claim that the classical general relativity is exactly accurate and all of its conclusions about quantities' being infinite at the singularity are strictly right. We never mean such things. When we talk about the Higgs boson, we don't claim that the Standard Model with its simplest Higgs boson is the exact theory of Nature. When we talk about the round Earth, we don't claim the exact knowledge of all geological (and surely not quantum) processes. When we talk about the common ancestors of observed species, we don't claim that we know the final exact theory about the origin of life. But these concepts are meant to be relevant for an approximate, effective description of some phenomena and statements about them are meant to be operationally verified using procedures that are relevant for these approximate, effective theories, too.

Just like the claims "there has to be a Higgs field", "the Earth is round", and "species have common ancestors", science has equally well established that "the life of the Universe began with something that a classical theory has to call a sigularity". A more complete theory of quantum gravity allows us to study processes around this object or locus called the "singularity" in some detail. It allows us (or would allow us or will allow us, if you wish) to define new relevant quantities that are finite and whose fate is predictable by these more complete laws of physics. But they still describe an object that looks, swims, and quacks like the singularity to the "imperfect eyes" of the classical field theory (and classical general relativity).

So something that has similar enough properties to the classical GR's "singularity" will continue to exist and any more refined theory of physics will be obliged to be compatible with its existence – and will be expected to tell us a more accurate and detailed story about the fate of the singularity and the processes that are happening over there. If the singularity were supposed to be eliminated from the vocabulary of physics altogether, much like wrong theories such as the phlogiston or the luminiferous aether, people would really have to prove that the classical general relativity is completely wrong, even in the modest enough conditions where it is believed to be valid. And that probably won't happen.

If the classical GR coupled to matter is an accurate enough description for curvatures and densities up to 0.001 times the Planck scale, or something like that, well, we can use its equations and prove that the conditions at the beginning of the life of the Universe had to be really extreme. If these conditions are written down parameterically and we send \(\hbar\to 0\), as we do in the classical limit, we will just get infinite values. So the densities and temperatures and curvatures could have been "just" Planckian but the Planckian values are huge and within the "limited eyesight" of the classical approximation, they are infinite.

One may speculate that some new phenomena change the fate of the Universe near the extreme, e.g. Planckian, conditions. There are different levels of such theories and they are convincing or plausible or implausible to different degrees: eternal inflation in the multiverse, Veneziano's pre-Big-Bang cosmology, big bounces, cyclic models (now in real trouble), or things like loop quantum cosmology, to cover the straight pseudoscience as well. But all these theories require us to include some "competing forces" that may change the sign of the cosmic expansion even when it's very fast. And these forces are "infinitely strong" according to the "classical eyesight", too. Some pre-history may exist but there will always be a locus in the spacetime of the visible Universe that deserves to be called the "singularity" because it's the locus whose existence we have known about from classical GR and whose knowledge will only evolve "gradually". The singularity will never go completely away.

In the paragraphs above, the "singularity" was supposed to be defined in a sufficiently tolerant way – as the locus or the object that looks, swims, and quacks like the singularity in the approximation of classical GR. I admitted that nothing has to be strictly infinite or unsmooth about the singularity according to the complete laws. But even if you defined the singularity as something where the smooth-manifold description of the physics has to break down and whose curvature invariants actually are strictly infinite, it is totally plausible that even the singularity defined in this strong way will be defended by the future research in physics.

It is in no way guaranteed that the complete consistent quantum theory of gravity has to make "everything" look and be smooth and finite. The only actual condition is that it deals with some observables that may be linked to doable experiments and these observables – the final results of the theoretical calculations (or, on the other side, values that are measured by actual apparatuses) – have to be finite. But all the intermediate and auxiliary quantities used by the theory are completely allowed to be infinite, unsmooth, discontinuous, and divergent! In particular, string theory is allowing us to calculate – completely well-defined, finite – cross sections and similar things for strings, branes, and other objects that are moving on the background that is exactly singular according to the definitions of classical GR!

In particular, we may study string theory on singular orbifolds or conifolds, and so on. The precise geometry of this spacetime background is singular, in the sense of classical geometry. Physics of classical GR on this background would be problematic or ill-defined or unpredictive. It could lead to indeterminate forms like \(\infty-\infty\). But string theory is actually totally well-defined on these backgrounds. String theory (and/or, more generally, a consistent theory of quantum gravity) may swallow backgrounds that look singular. It may still use these singular backgrounds as the starting point to describe the physical phenomena in a completely well-defined way.

So the attempts to make "all intermediate constructs and quantities" smooth and regular is really fundamentally misguided and the history of physics is already full of examples showing how much misguided this approach is. People like the "physicists" doing loop quantum gravity and similar things are scared of the infinities we may get in loop diagrams etc. They think that they're problems themselves. But they are not automatic proofs of any problems. The infinities may get subtracted, and in renormalizable field theories, they indeed get nicely subtracted, before we reach the final predictions for the cross sections and other truly observable quantities. The intermediate results may require quantities that are infinite when we "take the epsilons to the limit" dictated by the physical constraints. The geometry on which the physics is defined may be singular but the resulting theory may still be complete and totally healthy and consistent.

Moreover, Maldacena's and Susskind's ER-EPR correspondence (along with some older realizations) seems to suggest that you may choose more or less any background you want – at least a background with a bridge between two black holes or without it – and physics will still allow you to describe all the states (of the two black holes, in this case) in the Hilbert space in some way. By generalizing this observation just a little bit, it seems very likely that the right laws of quantum gravity are actually guaranteed to allow us to describe the processes in the early Cosmos exactly as some phenomena that are occurring on a spacetime background that includes the initial spacelike Big Bang singularity.

Matt Strassler sometimes suggests that he is a fan of the consensus science and says that it's important to say what the "research community" collectively thinks about various questions. Well, I largely disagree with that (because the scientific method isn't based on the assumption that a majority in any ensemble is right; it is based on the evidence) but if we decide that it's important for everyone to be told about the "collective awareness" of the researchers (e.g. because they are more well-informed than others), one should actually walk the walk and not just talk the talk. I am convinced that Matt's views on the Big Bang singularity are idiosyncratic, he is in a minority, and he has failed to convey this sociological point. If you look at the literature, you will find out that pretty much none of the well-known, achieved researchers shares the psychological problem with the "existence of the Big Bang singularity" with Matt.

I chose this paper by Seiberg to be a highly representative one. Even though it talks about possible "big bounces", it takes the Big Bang singularity as a fact and Section 2 of the paper is actually reviewing the argument why the Big Bang singularity is unavoidable (the huge force reversing a contraction to an expansion would violate some of the [positive] energy conditions). I am totally convinced that if you made a poll among physicists who are at least remotely comparable to Seiberg and if you asked them whether the Universe began with the Big Bang singularity, without giving them some additional "disclaimers" or "explanations", a majority would say that the Universe did begin with a singularity. They would probably understand the question just like I do, as a potential assault against the Big Bang theory. And indeed, such an assault is indefensible.

One may define the singularity (or decide to predefine the singularity, whenever a new theory is found – because we obviously can't write down an exact, theory-based definition of a concept within a theory if we don't know what the theory is!) so that Matt's claim that "there has been no Big Bang singularity" becomes formally true. But I just don't understand why one would be stretching the language in this way; according to strict definitions, Matt's claims may be right or wrong but they are quite certainly "morally wrong".

And Matt is apparently doing these things all the time. He wants to question any statement about the established science even though it is very clear in most cases that he doesn't have any important point. The existence of the Big Bang – and the Big Bang singularity – is an extraordinarily important conclusion of the research in a discipline of science (general relativity and cosmology). It is about as important as the common ancestors of the species in biology or the existence of the Higgs boson or the roundness of the Earth. Why does Matt – and why would someone else – write blog posts with largely correct technical claims whose ultimate goal seems to be spread doubts about if not indifference towards these important scientific insights?

Matt is writing lots of correct and insightful things in his texts but when it comes to the general tone and message of his pieces, he is doing a disservice to science and the laymen's understanding of science by these constant "doubts about all important insights that are not covered by any appropriately strong points or evidence". I think that such knee-jerk 50-50-like attitudes to every question are both disrespectful to the great scientists who have found some important answers about the Universe (such as the existence of the Big Bang or the common ancestors of species) as well as the current and future researchers (whose important insights probably will not be reflected in the way how Matt talks about the scientific knowledge, either: grey mush before, grey mush afterwards); and they may ultimately allow us to say that Matt is writing the same grey mush about every Yes/No question in the world which means that his answers to actual questions may be classified as noise.


  1. Hey ho, I heard that the Big Bang was more like a phase transition, just like ice freezes instantly when you take it out of the fridge and shake it a bit.

  2. Great post, another "bocatto di cardinale" at the Reference Frame. Congrats! I loved specifically the use of Higgs Boson (and Standard Model), the "round Earth", and the evolutionary biology, for explaining what a theory is... or better, what a theory is not. +100.

  3. Not sure about those drooling autotrophs - seems more like a heterotrophic trait to me...

  4. I think Matt Strassler tries way to hard to write politically correct texts about physics, which makes him drop tons of fog bombs that are very confusing instead of helpful. The second article (about different the uncertainty of different eras of the evolution of the universe) I have not jet fully read, but his commemts about the big bang possibly getting replaced by some misterious, magic, etc are highly confusing to say the least for example. He surely knows about effective theories as described in this TRF article ...

    I really wished he would convert the effort he puts into trying to be politically correct, avoid "confusing" / "misleading" (what is misleading about discussing physics using the correct terms and language?) any layman, etc into LaTex, that would highly improve the readability of his posts at least for me ...

    Matt Strassler's putting political correctnes from a layman point of view (!) over correctness and clarity of definitions and concepts as applied by physicists is very tiresome up confusing or even annoying ... :-/

  5. Thanks Lubos.....I appreciate another point of view.

  6. Nice article. One totally irrelevant question: In light of the very likely success of inflation, doesn't the 'balloon analogy' need to be retired now? Can we now say that the flatness problem has been solved and the universe is almost flat and unbounded since mod(K)<<1 ? Instead can't we use the 'infinite-stretchy-(mildly deformed)flat-sheet' analogy?

  7. LOL, if you use a narrow definition of drooling, then Yes. But the very production of organic stuff out of CO2 in autotrophs may be called drooling, too.

    For example,

    Dunaliella salina is a green micro-algae and a chemoautotroph that gets all its organic stuff from CO2 and produces high concentrations of glycerol to resist the osmotic pressure. Some companies were actually planning to produce glycerol using this organism which is possible but not too profitable. At any rate, glycerol has a similar physical behavior like saliva, so this micro-algae is arguably "drooling".

  8. See, you can do baby talk as well as Strassler :). You may think it trivial, but your inside a "star" paragraph made clear many things. Equally the CMB explanation.

  9. oops...meant to edit out that last sentence...

  10. Strassler lacks a sense of wonder in a wonderful universe. History says consensus is never correct. Clever folks were historically killed. Now, don't fund them. Regression toward the mean is now a stampede. The mean escapes by getting meaner.

    Do opposite shoe vacuum free fall identically? Nobody knows, and therein awaits the wonder of it all. 6.68×10^22 pairs of opposite shoes sum to eight small marbles, about 5 grams each, plus a vertical torsion balance. Look.

  11. Yes, the Big Bang was "like" a phase transition. Well, I would say that several known phase transitions and probably several yet unknown phase transitions have taken place since the Big Bang.

    Quite generally, as the temperature is cooling down, more symmetry was being broken. The normal materials give us a simple example: the gases and plasmas have the perfect symmetry between all atoms that move chaotically. In liquids, they're in contact, so the neighbors become qualitatively "closer" than distant molecules. In solids, like crystals, the full rotational symmetry of the gas/liquid is reduced to the rotational symmetry by 90 degrees, or other elements of the crystallographic group.

    These were the real "high school" phase transitions that were taking place. But there were others. The Higgs mechanism - by which the Higgs field gave masses to other particles - is a form of phase transition that occurred even earlier, at much higher temperatures than the boiling point. A symmetry was broken to a smaller one, much like when the water freezes to ice. And there were probably more exotic freezing points (perhaps stringy ones) before that, too.

  12. Thanks for your kind words, Eclectikus.

  13. By its straight honesty and level of generality, "Clever folks were historically killed" sounds like some good black humor. Maybe there were eras when it wasn't that bad, and perhaps even the opposite bias has existed at some points.

  14. Dear DOC, what do you mean by MOD? Except that the Universe is really really big after inflation - but we have known this fact even before we learned about inflation - I think that the balloon is just fine even as an explanation of inflation. After all, inflation is what we do with the balloons, and it's no coincidence that the name was chosen in this way. It's an exponentially inflating balloon.

    If you mean that the Universe is spatially flat, we don't know whether it holds exactly, but we didn't know it before inflation, either. Well, some people claim that they have already made the choice and that the tunneling in the multiverse implies that k is negative (hyperboloid-like infinite), But the balloon analogy is supposed to be used for any choice of K. Of course, the real-life balloon also has K=+1, and is spatially compact, but one is not supposed to use this property of the balloon as a dogma for the Universe. At the same moment, it may still be true that this compactness holds for the Universe, too.

  15. Could we postulate, that the Big bang was the splitting and evaporation of the big cunch black hole into what I call a black hole splitting fractal inflation creating the Lyman Alpha tree structure?

  16. Dear Dilaton, I also believe that he knows all the concepts of effective field theories well or extremely well. But maybe he is ignorant about some important facts from general relativity when he writes about this hypothetical mud possibly replacing the Big Bang. The future theory may become more abstract, using completely new concepts and laws, but when its conclusions are translated to the present language, it will still be true that there is a violent, effectively infinite explosion at the beginning.

    Just look at page 2, section 2, "Singularity in our past", in this paper by Seiberg

    One would effectively need superluminal and/or negative energy densities to avoid the singularity in the past, and those have very good reasons to be absent forever. A singularity may look like a sick thing, a regression, but it's surely the case that general relativity - a more accurate description of spacetime and gravity than what Newton was using - actually does imply that these "sick" things exist and have to exist even though we didn't know about them before.

    In this sense, Matt is really dreaming about some "counter revolution" in physics, much like the people who want to believe that the quantum revolution will be undone in the future and we will return to an "objective" (=classical) description of physics. Well, we won't. That was an approximate theory that has worked for a while but it's been falsified and superseded. It can't be unfalsified. In the same way, the existence of the Big Bang singularity - even if one views it with negative emotion - is an irreversible insight because the "singularity-free" evolution of the Universe has really been falsified (here, I include the Planckian extreme conditions among "singularities").

  17. I meant absolute value of K. I understand your reasoning, so I guess we can stick with the balloon analogy. So you're saying that the universe, may appear like a sheet, but for all we know could actually a deformed sphere(compact)?

    Is there anyway experimentally to determine once and for all (in our lifetimes) whether on not this compactness holds? I thought that we could sent a signal and see how long it take to receive it back (assuming that a co-moving satellite sent it), but it seems that even for K=+1 the signal would never reach us. What other ways can we employ, if any? You also said that from the multiverse and tunnelling we can say that the universe is hyperbolic, does it give any experimental means to determine this?

  18. The absolute value of K is either zero or one. Maybe you mean something else than K.

    Yes, all the empirical evidence we have allows a spherical Universe as long as the current radius of the sphere is greater than something like 500 billion light years or what's the limit right now.

    Of course that it may happen that people will actually measure the curvature of the spatial slice and find that it's nonzero. It would be equivalent to "the density's not being equal to the critical density". You just try to sort the galaxies on a map, uniformly, and you will find out that their relative distances nicely fit on a sphere or a hyperboloid rather than a flat space. So far everything is compatible with the flat 3D space. (I must emphasize that the full 4D spacetime is surely curved, with typical curvature radii comparable to 14 billion [light] years.)

    More speculatively, people may also find out that things on the sky get repeated, but it's unlikely to occur for the next 500 billion years. ;-)

    Solidifcation of theories may lead us to get persuaded that we must have K=-1, noncompact hyperbolic geometry, due to tunneling but the theory behind that is arguably too abstract and shaky at this moment.

  19. Yep, true, or you can't make an omelette without breaking some eggs ;-)

  20. I found Matt Strassler blog post to be very well written actually. Does he write that the universe did not begin with an initial singularity? I was under the impression that he was being careful, his position being that the current data do not allow us to answer this question.

  21. Right, that's his position and it is nothing else than the denial of the evidence of general relativity and the big bang theory.

  22. Uncle - I fully agree. When reading a following passage from John Preskill's Inflation on the back of an envelope:
    "A nearly homogeneous scalar field called the inflaton (denoted by ϕ) filled the very early universe. The value of ϕ varied with time, as determined by a potential function V(ϕ). The inflaton rolled slowly for a while, while the dark energy stored in V(ϕ) caused the universe to expand exponentially." I have an even greater sense of wonder than
    "Once upon a time there was a prince who wanted to marry a princess; but she would have to be a real princess. He traveled all over the world to find one, but nowhere could he get what he wanted. There were princesses enough, but it was difficult to find out whether they were real ones. There was always something about them that was not as it should be" can convey.

  23. Dear Lubos,
    I may be wrong but I think the key distinction between the big bang and an ordinary explosion with a center is not the curvature of space time. After all general relativity is perfectly consistent with a totally flat space time. Rather the key distinction is that in GR space can be createt so no center of the explosion is needed. In Newtonian physics it is surely impossible to have an explosion without a center despite of Galilean invariance. I would be surprised to learn if special relativity provides a way around this.

  24. Dear Mikael, nope, the presence of galaxies in the Universe implies that the (cosmological) spacetime *cannot* be flat. This is what Einstein's equations (Einstein/Ricci curvature tensor = stress-energy tensor, roughly speaking) - the main equations governing general relativity - imply. (We often consider simplified cosmological equations derived from Einstein's equations for a homogeneous Universe, the FRW equations.)

    I have never mentioned Newtonian physics or Galilean invariance in my blog post so you are fighting a straw man. The word "explosion" doesn't mean that one must stick to Newtonian physics and Galilean invariance. After all, all explosions in the real world respect relativistic physics and (locally) Lorentz invariance!


  26. Great, I hope you have enjoyed posting all this breathtakingly idiotic junk on my website. Now it's time to ban you.

  27. Here's a refereed paper about how the interpretation of explosion or not is an artifact of the coordinate system:

  28. Of course that you can do it. The damn galaxies just move along trajectories "x = vt" where the vector "v" uniquely labels the galaxies. In Newtonian physics, this collection of infinitely many galaxies is invariant under any Galilean transformation. In relativity, it is invariant under Lorentz transformations.

    In relativity, "|v|" is smaller than "c", and the "cosmological time from explosion" is the proper time from the origin (0,0,0,0) - it is constant on the hyperboloid shells of the spacetime.

    What is the actual problem is how to compute forces from this infinite array of galaxies - the forces to the "left" and "right" are infinite, so the total force is an "infinity minus infinity" indeterminate form. But this problem is exactly equivalent to the nonzero average mass density in this Universe. General relativity solves this "anomaly" by making the spacetime curved.

  29. Thanks, anonymous. I hope that Mikael will have a look at this PRD paper, too. Of course that to some extent, it may be done.

  30. Sorry, Lubos, I still don't get it. The Hubble law already completely defines the kinematics, right?. And I agree it is good enough for our discussion to stay near enough to the center where the speeds are small so we can think about the Galilean limit. But this damn thing has a center doesn't it?

  31. Right, the Hubble law describes the motion of all the galaxies - the kinematics.

    But the Hubble law doesn't need a preferred center. On the other hand, every galaxy may be considered to be a center of the explosion - these perspectives only differ by a Lorentz transformation (or, in the non-relativistic limiting description, by a Galilean transformation).

    I don't quite follow what you don't understand about it so it's possible that I can't help you.

  32. Well, I agree for a 1+1 D universe. But what about more than one spatial dimension?

  33. I worked out a solution to the observations attributed to the big-bang theory over 10 years ago. Einstein and Hubble were correct to be skeptical of the assumptions that the theory is based upon, the universe does not have a beginning or an end to it, there is no point in space and time where the universe sprang into being, and a singularity is a quick fix paper fantasy which will always lead to an infinite spiral of incorrect assumptions and newly invented entities which in reality cannot ever be observed.


  34. Hi Lubos

    Do you know the latest status of AdS/CFT treatment of spacelike (cosmological) singularities with AdS boundaries?

    Have we learned something about their nature via AdS/CFT?

  35. I think the world started as an idea?

  36. There is a big difference between fitting facts to theory and fitting theories to facts?

  37. One shouldn't lie about the observations but the *interpretation* of the observations is *always* theory-dependent, so in this sense - what the right interpretation of the observations is - facts must be ultimately "fitted" to some theories, too.

  38. To the host. If war between the States and Russia were unavoidable how would you see it being played out? Would it be simple conventional warfare (armies and navies)? Would nukes be used only against military forces? Or as a simple last resort by the loser since MAD may not matter by that point? Do you think it could be possible that warfare between the countries could exist in a manner as to avoid nuclear warfare?

  39. I'm not even a 'physics layman' nor a qualified philosopher, but I dare say that since the (eternal) 'quantum foaming' [and its philosophically complementary companion, i.e. 'the Platonic potential'] has nothing to do with space-times other than apparently 'giving birth' and being a 'Quantum Mechanically/string theoretically describable and, when looked at closely with common-sensed logic, also a weirdly manifested 'building-ground') to them, it is an exercise in futility to look for or think there is any kind of location for the origin of ours.

  40. Ballad of GordonMar 31, 2014, 8:20:00 AM

    That's the whole point of that line--that heterotrophs evolved from autotrophs.

  41. To me, the biggest problem with the whole mess is that we are reneging on the promises we implicitly made (and Russia on the promises they explicitly made) when Ukraine gave up their nukes.

    On the other hand, nobody was considering giving up any nukes before this happened, so no big deal I guess.

    Also, you're wrong about the US reaction to a major city getting nuked: we would want war. Every american takes for granted in the core of our beings that we are the good guy in a hollywood movie and are therefore invincible. Nobody here is afraid of Russia at all - we've been told they were defeated and are now a sideshow of a country, that the only thing separating them from an Iraq is a handful of ancient nukes that they've probably sold to terrorists by now. Maybe the "decision makers" know better but then again, maybe they believe their own propaganda.

  42. Dear dreamfeed, the only reason you are not afraid of Russia is that you have been brainwashed into thinking that Russia is a small, weak, petty foe. I have been talking to the Americans for decades by now so I can compare what they think with the reality of the USSR - which I know vastly more intimately than they do - and yes, the amount of brainwashing was at least comparable to what people saw in the Soviet bloc (and probably higher than what we had in Czechoslovakia). Most of you don't even know that Russia has almost twice as many nuclear warheads, among other things.

    As soon as San Francisco would be flattened after an unspectacular motion of Putin's finger, you would change your mind. Or maybe after Seattle would be settled down, too.

    The shock by the current painful leaders of America when they saw that Russia has no trouble to reclaim its historical territory when the territory finds itself in the state of surrounding anarchy and threats only highlights the fact that they have no clue about the actual Russian capabilities and the actual Russian audacity.

    Of course that Russia didn't hesitate to reclaim Crimea which could have been done peacefully. It wouldn't have serious problems in defeating Ukraine, and if needed, to silence its foes in the U.S.

    But for this moment, things are likely to be smooth. Russia has increased the prices of oil for Ukraine, reverted all previous advantages to disadvantages. The IMF will halve the pensions and some salaries in Ukraine, the life will be mess, and the Kremlin will just root for leaders in the elections that will prefer reunification with Russia. Even if this maximal plan with Ukraine won't work like that, Russia will be the ultimate partial winner of this controversy.

  43. "the only reason you are not afraid of Russia is that you have been brainwashed into thinking that Russia is a small, weak, petty foe"

    I agree.

    "As soon as San Francisco would be flattened after an unspectacular motion of Putin's finger, you would change your mind. Or maybe after Seattle would be settled down, too."

    I doubt it.

  44. McCain would never sacrifice his life. Though he wouldn't hesitate to sacrifice others, especially if it would be to cover his own.

  45. BIG BANG FLAWS: Big Bang scientists extrapolate
    a hypothetical scenario from a few facts. Yes, some galaxies are expanding,
    moving further away, but this is not the case with the entire universe. There
    are galaxies in the universe running perpendicular to the rest of the galaxies.
    That's contrary to Big Bang. If Big Bang really occurred, there should be a
    uniform distribution of gasses. This uniform distribution of the gasses would
    have made sure that the gasses would not have coalesced, due to gravitational
    attraction, into planets and stars. The hypothesis of dark matter providing
    enough gravitational force has been recently discredited. “The (galactic)
    structures discovered during the past few years, however, are so massive that
    even if CDM (Cold Dark Matter) did exist, it could not account for their
    formation” (Dr. Duane T. Gish, “The Big Bang Theory Collapses”). Furthermore,
    an explosion cannot explain the precise orbits and courses of thousands of
    billions of stars in thousands of billions of galaxies.

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  46. Holy crap, literally.

    BTW I just published a text on the poll showing that only 21% of Americans understand-sufficiently-to-believe the Big Bang theory:

  47. Don't be stupid, nuke a Putin!May 22, 2014, 1:57:00 AM

    Hello Ruskey-Lover, your russophile propaganda is more ridiculous than Russian slow & rusty nukes. From my point of view we, the NATO, should nuke your beloved Russia as soon, as possible. Especially know when we have huge amount of drones & faster anti-nuclear shield against Ruskie's ancient nukes. Unfortunately, other NATO states, the USA & rich western EU states don't wanna to admit that Russian's Hitler, Putin will never stop with his disgusting bloodshed against ex-soviet & even ex warshaw pact states, such as Romania, until we finally put that animal for good. The rich cowards in NATO, also don't want to exept that this nuklear war is eminent cause no one can't stop that KGB lunatic, Putin only with moronic economic sanctions, but with sudden, prevential nuclear strike! Maybe after our nuke attack, with a little bit of luck, you, Lubos will be also become crispy like potato's chips, as many other russian's fascists.

  48. extraordinary claims require extraordinary evidence, atheists, you said so yourselves, put up or shut up already you hypocrites

  49. I totally agree with you!

  50. Russia cannot spend more on defence that the soviet union could

  51. McCain followed his father and grandfather, both four-star admirals, into theUnited States Navy, graduating from the U.S. Naval Academy in 1958. He became a naval aviator, flying ground-attack aircraft from aircraft carriers. During the Vietnam War, he was almost killed in the 1967 USS Forrestal fire. In October 1967, while on a bombing mission over Hanoi, he was shot down, seriously injured, and captured by the North Vietnamese. He was a prisoner of war until 1973. McCain experienced episodes of torture, and refused an out-of-sequence early repatriation offer. His war wounds left him with lifelong physical limitations.

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  53. Warheads are only efective when delivered to the target,nowadays technology made it harder for a long range missile to hit its target unless the whole military is asleep.
    Russia will only stop agression after gets nuked ,I hope usa gets a president who has balls like Bush . China has lots of power too,but imports most of its grains and a radioactive conatmination on its main food suplier could easily starve that country,so when comes to war today there are many factors to consider.
    Hitler was not defeated by one country alone ,remember the entire nato are nuclear powers too.

  54. The Secretary of state, Donald Rumsfeld, announced 1 day before the World trade center was bombed that there was over 2 trillion dollars in Government, CIA/Military transactions that could not be tracked... Kinda coincidental, don't you think? Since that day we have spent Trillions of dollars toward a War in multiple countries that would not even get close to costing the amount we've claimed. When Russia and China try to nuke the U.S you will all finally see where that money went! We have been preparing for this for over a decade. It only appears we've been caught with our pants down...because we want them to try it, so we will be justified in our overwhelming retaliation.

  55. Sooo the moral of this story is to let Russia and China take by force whatever country they want or risk war? How's that a good solution? Are we prepared to bend over if they come for us?

  56. Dear Adam, no, the moral of the story is that you should be respectful towards other powers and their completely understandable and sometimes existential spheres of interests even if there were no risk of a war.

    Ukraine undeniably belongs and has belonged for a millennium to the Russian sphere of interest - more so than Puerto Rico belongs to the U.S. sphere of interest or the Falklands Islands belong to the U.K. sphere of interests. If someone doesn't understand this basic historical fact, it's his defect.

    The U.S. and the U.K. don't belong and have never belonged (except for Alaska) to the Russian sphere of interests.

  57. The whole of mad is to wipe out your opponent not take a city here or there

  58. Good thing our government has you to educate them eh? Sigh

  59. It *would* be a great thing if that government were capable of learning - which unfortunately doesn't seem to be the case.

  60. Thinking Russia could even get a nuke to the US is laughable.

  61. Some anti-ICBM secret system?

  62. School boy lol.
    American sent a aircraft carrier (so the principal) to spank russia. And then a plane(one nerd) turned off all the radars and electricity in the aircraft carrier. And then danced around and made fun of them. After 60% of the navy on the ship quit :) well done get your facts right

  63. my gawd you're stupid ....

  64. And USA is clearly not respectful left a war in many countries everything was fine in Iraq USA leaves there and then there is a civil war well done

  65. America uses the media to make you think that Russia is weak one plane turned off USA's aircraft carrier and USA simply does not know how to do that...

  66. Russia can be isolated they can get oil petrol and food it doesn't need other countries idiot

  67. if isa is more accurate then why then can't they turn off one plane with a aircraft carrier

  68. or you know they can't do that

  69. The exact # of nukes will never be known. I don't for a second think that the number shown online and in documents is actual.

    you are also forgetting the fact that the US has nuclear weapons stationed around the world in foreign countries, giving us a major advantage in striking first from all points of the world.

    Canada is bigger than the u.s and right next to our border a war on US, Canada will definitely defend.

    not to mention most of our allies would retaliate with nuclear weapons against Russia if it did use a nuke on US soil.

    nobody trusts Russia they are unstable and unpredictable, most of Russian LAND is inhabitable. if it came to a war only major cities would be striked. I wouldn't be surprised if we have special forces identifying targets in bases in Russia now.

    your opinion is flawed

  70. Another member in good standing of the 'nuclear war is winnable' club. Thank you but go play in the basement, you're upsetting the adults here.

    The fact is that Russia has actually been more stable and predictable these past twenty years than has NATO, which seems to make up the rules as it goes along.

  71. He's one of our "I think Ukraine is in Siberia somewhere' citizens.

  72. Well said, I must admit. You must be a Ha'vard man ;-)