Saturday, October 22, 2011

Faster than nothing

"Mr Nothing", whose ideas were first discussed on this blog back in July, has released a paper on OPERA's superluminal neutrinos. He actually has an equation which fits OPERA, MINOS, and SN1987A, something which only a few other theorists can do. :-)

(The equation is on page 5, number 6.1. All the energy dependence is in the factor "ln(E/Eμ)".)

Saturday, September 24, 2011

The question no-one is asking

What are the implications for physics if neutrinos are slower than light?

Wednesday, July 13, 2011

Inspiration strikes!

What is the situation? We have a functioning field theory, the standard model, in which there are over a dozen numbers that are just input parameters. We have a supposed derivation of a few of those parameters, in terms of quantities associated with the icosahedron. How are we to give these derivations causal significance in a more fundamental theory?

The basic idea is as follows. We have an icosahedron associated with each point in space. (The exact nature of the association doesn't matter at this stage.) Then, we have a field whose expectation value has a specific functional dependence on the properties of the icosahedron. Or rather, we have several such fields, each with its special functional relation. Then, we combine those fields so as to give rise to the standard model parameters. And we're done!

For example, consider the problematic relationship: dihedral angle equals sum of three physical parameters (let's overlook the peculiarity of mr nothing's "GUT angle" for now), plus another quantity. If you were "measuring" an icosahedron through, say, a TQFT, there's simply no reason why the TQFT would directly detect the existence of that decomposition.

So instead, we suppose there is a "dihedral angle field", with a VEV equal to the icosahedron's dihedral angle, and a "Weinberg angle field", which gets its VEV from, say, that DFQ angle (we may suppose that it's a slightly non-Euclidean icosahedron). And then we have a "Cabibbo angle field", whose VEV equals "d.a.f. VEV - W.a.f. VEV - 'GUT angle' - pi/3" - with this relationship being enforced, not by any property of the icosahedron, but simply by algebraic fiat. Voila, we now have the Cabibbo angle as an output from our "icosahedral theory of nothing", ready in turn to be an input to the set of relationships which reproduces the standard model.

Analysis of nothing, part 2

So, let's recapitulate. The dihedral angle of the icosahedron is supposed to be the sum of three angles of physical significance, plus 60 degrees. The exponential of the surface area of the icosahedron, divided by the mass of all leptons expressed in units of electron mass, allegedly equals ... another whimsical expression relying on the Weinberg angle. And, counting all the fermions and gauge bosons, we get 24, and this has something to do with SU(5) and the icosahedron.

Also, there are a bunch of alleged identities involving the Weinberg angle, which I have not yet bothered to check numerically, nor have I checked whether a simultaneous solution to these equations is even possible. Also, I suspect that the closeness of the "DFQ angle" mentioned in the previous post, and the experimentally measured value of the Weinberg angle, may subliminally be at work here. (Let me note in passing that if you embedded an icosahedron in a slightly non-Euclidean geometry, it should be possible to make the DFQ angle exactly equal to the measured Weinberg angle - at one's preferred energy scale, that is, since the value of the Weinberg angle flows.)

The attentive reader may recall that the premise of this blog was, that abstracts from the snarxiv could - if used in moderation - serve as genuine inspiration for physics. The current experiment is to see whether an authentic bit of numerological physics, found in the wild (the physics blogosphere), can similarly provide inspiration. So rather than proceed with the numerological analysis, for a moment I want to switch tracks and ask, in what sort of physical theory could the relationships listed at the start of this post actually exist and actually play a role in physical causation and explanation?

Since Weinberg angle, Cabibbo angle, Higgs VEV, etc., all acquire physical significance on account of the roles they play in a particular quantum field theory (the standard model), we are presumably looking for a beyond-standard-model theory which reduces to the standard model in some limit, and in which icosahedra matter. Perhaps there are compact dimensions shaped like icosahedra; perhaps there are icosahedral branes. Perhaps there are interaction vertices dual to icosahedra, or perhaps we calculate certain amplitudes by integrating over icosahedra.

See, this is the fun part: take the work of mr nothing, and try to hybridize it with the conventional apparatus of physical theory. But I must say that the "sum of angles" worries me. We are supposed to be using the icosahedron to explain the standard model, not vice versa. And while the dihedral angle is certainly a natural property of the icosahedron, the peculiar decomposition into a sum of four angles does not appear to be natural. Even supposing that an icosahedral structure appears at some level of our theory, why would the theory be sensitive to the existence of that decomposition of the dihedral angle? Unfortunately, the similarity of the DFQ angle and the Weinberg angle doesn't seem to help, because the DFQ angle isn't a natural part of the dihedral angle, so far as I can see. I shall need to meditate on the geometry of the icosahedron for a little while...

Analysis of nothing, part 1

What are we dealing with here? An attempt to derive various basic parameters of physical theory from quantities associated with the icosahedron. Which quantities? The dihedral angle (angle between two faces), and what I'll call the "inscribed radius" and the "circumscribed radius" (really, these are distances from the 3d center of the icosahedron to the middle of any face and to any vertex, respectively).

I'm a bit puzzled by "angle w". Although it's close to the "DFQ" angle in the link above, I can't see that it corresponds to any natural property of the icosahedron. Yet we have these two alleged identities

5 x ( 1 + sin^2(W) +sin(W) ) = cos ( 2pi/10 ) / [ cos( 2pi/5 ) ]^2

(3 + sqr(5) ) x [ sqr(3)/12] = cos(w)/[ (1 + sin(w) )^2 -1]

If these are both genuinely, exactly true for some w, then that's interesting... OK, duh, I bet "angle w" is supposed to be the Weinberg angle. In fact, mr nothing says so explicitly: "mW/mZ = cos(W)"

Because I'm lazy, I will not try, right away, to see if a w does exist that exactly satisfies the two equations above, or to otherwise guess what the geometric inspiration for those formulae might be. Instead, let's continue identifying the physical interpretation of the three icosahedral quantities proposed. For example, we are told that

The dihedral angle of the icosahedron = Weinberg angle + Cabibbo angle + "GUT angle" + pi/3

Despite its name, the "GUT angle" appears to be mr nothing's discovery, rather than, say, the value of the Weinberg angle in some GUT - it is defined as the dihedral angle divided by the square root of "one plus (half the Higgs VEV in units of electron mass)".

The other crucial element of the physical interpretation of the icosahedron turns out to involve its surface area A:

exp( A ) / (sum mass all leptons/ electron mass ) = [ ( sin(w) + cos(w) ) x sin(w) ]^-1

The "inscribed radius" and "circumscribed radius" don't seem to be playing much of a role...

Conceptually crucial, I believe, will also be the statement that

6 leptons + 6 quarks + 8 gluons + 1 fotón + 3 B ( w+, w- , z ) = 24 = 4! ===> SU(5)

followed by the introduction of the icosahedron. This is where mr nothing is trying to turn his identities into physics.

The numerology of mr nothing

Of course, physics can't just be elegant mathematical constructions without quantitative output. And so today we shall pause to consider the observations of a commenter at Lubos's blog, called "mr nothing". Presently I will make some remarks about how much sense can be extracted from them (or else I will tire of the exercise and delete this post). But for now, let's just hear from mr nothing himself.

Comment #1

The Mass Higss bosón: the mass is 119,61 Gev
There are five Higgs Bosons: 2 charged ( +1, -1 ) and 3 not charged
Fermi constant/ sqr(sqr(2)) = 246 Gev [246 Gev x cos ( 2pi/5)]/(1+cos(2pi/5)]= mH= 119,61 Gev
( 246 Gev)^2 = ( Sum mass all leptons )^2 + (Sum mass all quarks)^2 + (mW)^2 + (mZ)^2 + (mH )^2

Comment #2

5 x ( 1 + sin^2(W) +sin(W) ) = cos ( 2pi/10 ) / [ cos( 2pi/5 ) ]^2 ; angel w = 28,15648º ; mW/mZ = cos(W)
6 leptons + 6 quarks + 8 gluons + 1 fotón + 3 B ( w+, w- , z ) = 24 = 4! ===> SU(5)
Icosahedral symmetry : very important

If the edge length of a regular icosahedron is a, the radius of a circumscribed sphere (one that touches the icosahedron at all vertices) is : sin(2pi/5); thus: 1-sin^2 (2pi/5) = cos (2pi/5)

Comment #3

and the radius of an inscribed sphere (tangent to each of the icosahedron's faces) is
(3 + sqr(5) ) x [ sqr(3)/12] = cos(w)/[ (1 + sin(w) )^2 -1]
The surface area A
of a regular icosahedron of edge length a are: 5 x sqr(3) ; exp( A ) / (sum mass all leptons/ electron mass ) = [ ( sin(w) + cos(w) ) x sin(w) ]^-1
diedral angle = 138,189685º = angle w + cabibo angle + angle GUT + angle ( 360/6 )
diedral angle / sqr[ In ( mass vacuum higgs/ ( 2 x me ) ) +1] = angle GUT
Mass Vacuum Higgs / 2 x electron mass = 481841,46525 / 2

Thursday, June 16, 2011

Lessons learned

What has this exercise in treating the snarxiv as oracle revealed?

First, it confirms that the snarxiv could serve as an idea generator for physicists in search of inspiration. Particle physics contains a large number of possibilities, and one can easily discover whole new classes of model just by combining these possibilities. Perhaps no-one has ever thought to examine whether T-duality is possible in new inflation, or whether the AdS/CFT/unparticle correspondence can be adapted so as to employ the topological A model in the bulk, or whether cosmic rays might be generated by instantons in the interstellar medium, or whether neutralinos in a generalized RS1 scenario might show up as a TeV-scale fluid - but now, those ideas are out there, ready for the scrutiny of a skeptical world! This is the amazing fact: the space of possibilities in physics is extremely large, and it seems there is no end of work to be done in exploring them.

Second, it confirms that a few hours studying papers from the snarxiv might be a productive way to kill time. This may sound like the previous point repeated, but here I'm talking about a psychological perspective. Of course it would be possible to overdose - I am not about to conduct the experiment of reloading snarxiv and interpreting its output until I can't bear it any more - but employed judiciously, snarxiv may provide the weary physicist with a form of recreation which nonetheless stimulates their professional imagination in a helpful way.

I still find it somewhat disturbing that a mindless computer script can perform this stimulating function. But perhaps if I was a computer scientist, more familiar with the difficulties of large search spaces, it would seem less surprising.

"Entropy at the Planck Scale" by D. Kobayashi and U. Hawking

"Partial progress has been made in recent years on models of spacetime foam. Therefore, in the 20th century, work on models of cosmic rays has opened up a modified class of patch inflationary models. We determine a crucial correspondence between nonzero integrability and the non-special lagrangian brane MSSM. Anomaly constraints are also recalled. After deriving extremal black holes, we check that Geometric Langlands-duality in models of quarks relates to renormalization. Thus, there is much to be done."

The final paper on today's snarxiv. I think this one speaks for itself. Obviously, models of spacetime foam are relevant for entropy at the Planck scale. One can see why new models of cosmic rays (if they are primordially produced... or produced by primordial instantons in the interstellar medium) would have an impact on models of inflation. It's always worthwhile to discover new mathematical properties of realizations of the MSSM, and it's great to see Langlands duality being applied to phenomenology. There is much to be done, indeed.

"NS5 Branes in the Early Universe" by S. Argyres

"In the 20th century, work on a model for instanton liquids has opened up a metastable class of large mass models. Unsurprisingly, in recent years, Schwinger derived that the A-model/unparticle physics correspondence is diffractive. In this paper, we take an inflationary approach to trivial metrics, wholly reviewing that general gerbs are related to Lagrange singularities, wholly obtaining that an orientifold plane in the early universe is unconventional. An elaborate part of this analysis is gravitational-duality in topologically twisted TQFTs in the presence of a D1 instanton. Our results establish that a certain notion of localization (excluding general T-duality) is modified. We will provide more details in a future paper."

Despite the title, this is another rather mathematical paper. It's surprising to hear that Schwinger worked on unparticles; and what can it mean, that a correspondence is "diffractive"? It must be one of those highly abstract notions - motivic, or perhaps categorical, given the reference to gerbes. I am tempted to skip this one entirely, but let's make the effort and at least try to figure out what the "A-model/unparticle physics correspondence" might be.

The A model is the version of topological string theory which descends from the Type IIA string. (The later reference to a D1 instanton suggests Type IIB, but that is in the context of a duality, and the NS5-branes of the title occur in both Type II theories.) So far as I can tell, there isn't such a thing as an individual "unparticle"; "unparticle physics" refers to the manifestations of conformally invariant fields coupled to the Standard Model, such as missing energy that looks like it went into a fractional number of particles. They have no discernible connection... But stop the presses! Over at the stodgy old arxiv, there's a paper on "The AdS/CFT/Unparticle Correspondence". Like everything else in field theory, it turns out that unparticles have a holographic counterpart in AdS space. So here is our interpretive salvation: the A-model/unparticle physics correspondence is obviously a mutant form of the AdS/CFT/unparticle correspondence. (Details will be provided in a future blog post.) This even makes it plausible that the peculiar appellation, "diffractive", has at least a semi-literal meaning.

In any case, the significance of this paper is now a lot clearer: it's an application of (mutant) AdS/CFT to ... something ... about the early universe (NS5-branes in the title, an orientifold plane in the abstract). But most of the results are rather technical.

"Reformulating Cosmic Rays at CDMS: Heterotic String Theory Far From a Stack of Canonical Co-isotropic Branes"

Authors: B. Witten, U. S. Fermi, I. N. Sundrum, H. Unruh

"Boundary-dualities on a \Z_9 bundle over m-manifolds unsurprisingly depend on examining bosonic strings surrounded by an instanton. In short, in recent years, Seiberg checked that anomaly constraints are spontaneous. As an interesting outcome of this work for the Hamiltonian in Heterotic string theory, in this paper, in order to establish that instantons in the interstellar medium are primordial, we solve the confinement problem, thoroughly exploring that ghosts turn out to be equivalent to formulating models of hadrons. Our computation of Clebsch-Gordon decomposition on Anti de Sitter Space produces cosmic rays in the interstellar medium. While surveying boundary-duality in superconformal QED dimensionally reduced on n copies of P^1 fibered over S^n, we derive that, whenever perturbation theory in a nonperturbative CFT on R^n is simple, Gromov-Witten invariants in an adjoint Quantum Field Theory on R^2 are useful for demystifying some general illustrations."

Now this sounds promising (and exhausting). Boundary dualities! A Z_9 bundle! Bosonic strings surrounded by an instanton! And that's just in the first sentence. But let's skip over the heavy mathematics and find the essential physical ideas in this paper. These are "that instantons in the interstellar medium are primordial" and that "Clebsch-Gordon decomposition on Anti de Sitter Space produces cosmic rays in the interstellar medium". (Obviously cosmic rays are a theme in today's snarxiv papers.) What Does It Mean?

Let's start by considering what it would mean for these interstellar instantons to not be primordial. Usually, a primordial object or effect is one that has been around since the big bang, but instantons are, well, instant. They don't hang around. Therefore, when we call a contemporary instanton "primordial", it must mean that it derives from a primordial cause, such as a big bang remnant. Parenthetically, let us note that one would not normally expect the interstellar medium to contain instantons, it's not dynamically exciting in that way. We must therefore be talking about an unusual class of models in which instantons do occur and have consequences (such as cosmic-ray production), and in which a further distinction may be made between instantons that are primordially caused and those which have contemporary causes.

As for the relevance of anti de Sitter space, I suspect that here we have an application of AdS/CFT duality to the exotic interstellar plasma which is the site of these cosmic-ray-generating instantons. Some technical calculations (Clebsch-Gordan decomposition) in the AdS dual of the plasma establish that it does indeed have the necessary instantons. And this is all performed in the context of a heterotic braneworld model.

That one was easy. Next!

"On Neutralino Collisions" by Z. S. Fermi

"We determine an essential correspondence between a resolution of the strong CP problem and some general frameworks. RS1 is also generalized, explaining a holographic superconductor in generalized inflation, as we will see in this paper. Unfortunately, in recent years, minimal progress was made on models of charginos. Reconstructing is made easier by reformulating an entropic resolution of the U(1) problem. We also check agreement with some little-known cases. Three-fluid fluctuations at the LHC follow from the Lagrangian in topologically twisted QFTs."

Initial impression: Z.S. Fermi is easier to interpret than H.R. Gell-Mann, but this is because the abstract contains fewer inherently challenging combinations. Then again, the very plausibility of its blandness could be used to up the ante. Can I come up with a genuine reason why someone writing about neutralino collisions would be generalizing RS1, how they could find a holographic superconductor in "generalized" inflation, what the "entropic resolution of the U(1) problem" might be, or what the "three-fluid fluctuations at the LHC" might be?

But it's all so generic! The "U(1) problem", for example, sounds like a technical problem known only to experts working in a particular sub-sub-field (such as the study of charginos and neutralinos in generalizations of the RS1 scenario). "Three-fluid fluctuations at the LHC" sounds a little more baroque, but obviously it's new TeV-scale physics predicted by the model, and who am I to say that we won't discover three new "fluids" (perhaps they are components of dark energy?) when we do get to that scale?

"A Model for Cosmic Rays" by H. R. Gell-Mann

"In this paper, we present a criterion for geometric transitions. Next, we establish that the T-dual of new inflation depends on formulating an impossible model with solitons. Actually, a flavor Planck large mass extension of String Theory deformed by Wilson lines gives rise to a surprising framework for clarifying some conspicuous paradigms. A holographic superconductor is also analyzed. We therefore disagree with a result of Nelson that instanton liquids at the edge of our universe are transverse. When evaluating Randall-Euler RS1, we deduce that the strong CP problem is microscopic."

This paragraph contains vagueness and unidiomatic expressions which clearly identify it as a fake, but let's focus on the pseudo-content. The title tells us what it's about: cosmic rays.

What I find most intriguing are one of the claimed theoretical results (about T-duality applied to new inflation) and the concept attributed to "Nelson", of "instanton liquids at the edge of our universe" (which are "transverse"). Let's focus on the latter.

My preferred interpretation of transverseness would be in the sense of extra dimensions, forming a "bulk" outside an extended object like a braneworld. The boundary of a space at infinity can be rotating, I have learned today; so why couldn't an entity at such a boundary also be "transverse"? Perhaps the most sensible interpretation of all would be to see it as a statement about the asymptotic properties of a field: that they have a nonvanishing transverse component at infinity. So now we know what Nelson was saying: that certain instanton liquids remain transverse even at the "edge of our universe" (perhaps this refers to the cosmological horizon). But H.R. Gell-Mann disagrees!

Let's now tackle the concept of a "flavor Planck large mass extension of String Theory deformed by Wilson lines". The first few words are admittedly hard to parse. Is it a "flavor Planck" "large mass extension", or a "flavor" "Planck large mass extension"? I'm going to go for the latter, further sub-parsed as a "Planck-large mass extension", and I'll tentatively interpret it as being about adding a Romans mass to supergravity that is as large as the Planck mass. That it is "flavor" must have to do with the way that the Romans mass is introduced - e.g. in a way that involves flavor degrees of freedom, rather than color degrees of freedom. "Deformed by Wilson lines" is an ordinary wholesome concept, but not one we can do anything with (interpretively) unless we know more details. But at least we now know what sort of modification of string theory H.R. Gell-Mann was considering.

The most intriguing remaining sentence is the last: "When evaluating Randall-Euler RS1, we deduce that the strong CP problem is microscopic." RS1 is already Randall-Sundrum scenario 1, so we would appear to be dealing with a "Randall-Euler" variation on RS1. One would normally suppose that this was introduced in a paper by Randall and Euler, but Leonhard Euler died centuries before Lisa Randall was born. The next hermeneutic tactic, therefore, should be to suppose that "Euler" here is being used to denote a radical postmortem generalization of one of the dead mathematician's concepts. Euler himself furnishes an example, though it comes from outside physics: an Euler filter is a type of data filter, employed in computer animation, which utilizes Euler angles. Euler himself introduced the Euler angles, but computer graphics are definitely a post-Eulerian development. In any case, "Randall-Euler" must then denote a generalization (probably due to Lisa Randall) of the generalization of Euler's original concept, which is at work here. For a space to be Randall-Euler may mean that it has a particular geometric or topological property.

But what can it mean for the strong CP problem to "be microscopic"? The strong CP problem is the question of why QCD doesn't produce CP violation. Most likely, H.R. Gell-Mann is telling us that the reason for this is to be found in the microscopic (fundamental) variables realizing an effective field theory or other low-energy model.

Finally, let us return to the original intriguing conception, the "T-dual of new inflation". New inflation is rather old now - it dates from 1982 - but it is one of the standard inflationary scenarios. One paper succinctly characterizes it as a model "where the inflaton field rolls from a potential maximum at phi = 0 to a minimum at a symmetry breaking value phi = nu", and adds that the original new inflation model employed a Coleman-Weinberg potential. T-duality is a concept in string theory, and it is unsurprising that someone should consider whether string theoretic realizations of new inflation have T-duals, or that they would find that the existence of a T-dual description imposes stringent, perhaps "impossible", constraints.

All in all, then, although H.R. Gell-Mann's phrasing is not the best, we can see rather a lot of meaning in this abstract, and an expert in new inflation might be able to continue the game of interpretation considerably further and deeper than this.

Another bad idea

snarxiv is an imitation of arxiv produced by algorithms similar to those behind the famous Postmodernism Server. I always thought that the essays produced by the Server made rather more sense than anyone acknowledged. The individual statements were rather bland, but considered in whole paragraphs, there was often enough content that one could try to extract an overall sense.

Such an observation could be fodder for the culture wars (now rather passe) over whether postmodern theory is nonsense or just too subtle for its critics. However, here I'm concerned with machine-generated physics ideas rather than machine-generated postmodernism. I read the arxiv daily for inspiration, and I am alarmed that I could be drawing similar inspiration from the output of snarxiv. Here, after all, we are talking about mathematical physics, a subject governed by logical deduction, not by humanistic association.

There are several possible explanations. For example, it could be that all the concepts that typically feature in hep-th abstracts are so tightly linked that even a random collection of them will remind the informed reader of the deeper oneness. Or, it could be that my intellectual development as a physicist is still so primitive that I find it stimulating to see anything at all said about exciting topics like branes and broken symmetries; but if I had the higher-level understanding possessed by the true experts, I would see the superficiality of snarxiv's combinatorial nonsense.

My idea is not to choose one explanation over another, but simply to conduct an experiment. I visited the snarxiv just now and the abstracts looked, as they always do, plausibly like the real thing. So, now we are going to examine them in turn and see just how much sense can be extracted from them. (I will add, by the way, that when I first took the test, in which one is presented with a snarxiv abstract and an arxiv abstract and asked to tell which is which, I scored almost 100% after 20 questions. I can actually read and understand the professional physics literature. But I also have a weakness for entertaining odd ideas, even if they are coughed up unconsciously by a software program.)