CMS at 190/pb: LHC avoids black hole production

The CMS Collaboration has published a new paper that also answers the question whether the Earth is going to be swallowed by a man-made black hole.




You can be sure that everything is fine and the Earth isn't being eaten yet. To be sure, here are the webcams near the CMS experiment and the LHC building. You may watch it to get assured that our planet is safe. ;-)



If you want to check that the LHC is safe with some music...

Indeed, even after 190 inverse picobarns, there's no black hole:

Search for black holes in pp collisions at sqrt(s) = 7 TeV

They studied final states with many - e.g. 10 - objects such as jets, leptons, and photons which carry a high energy such as 1 TeV or more. They would be a sign of an evaporating black hole. An agreement with the Standard Model background is found. I choose not to get excited by some occasional 2-sigma-like excess etc.

If there were low-energy string theory in Nature around us, I would still expect the string scale to be of order 3 TeV but the quantum gravity scale - the mass of the lightest black holes worth the name - would probably be significantly greater than that (an order of magnitude or more) and inaccessible at 7 TeV and maybe even at 14 TeV. So I personally view this experiment as a formality. But surprises may come at unexpected times...

MOND and HOND: theories without dark matter

Your humble correspondent's holographic modification of gravity for low accelerations passes a quantitative test

Sean Carroll mentions a preprint arguing that it's been experimentally demonstrated that Kepler's laws fail when the acceleration of orbiting objects is below a certain constant a0:

The Breakdown of Classical Gravity?

X. Hernandez, M. A. Jimenez, and C. Allen looked at wide-orbit binary stars and they claim that for these small accelerations, the Kepler's (i.e. Newton's) formulae for the velocity should be superseded by a constant velocity

v = (G a₀ M) ^1/4.

Such a modification is compatible with the MOND, Modified Newtonian Dynamics, theories whose goal is to claim that dark matter is not needed.

While I find the typical MOND theories with the ad hoc irrational extra vectors and scalars and/or nonlocalities to be awkward enough to be eliminated without tests, I can imagine that the observations above are actually valid and dark matter doesn't have to be exist, after all.

I have developed an explanation of the modified behavior for small acceleration that looks much more convincing than any MOND scheme I have ever seen. Let me call it HOND, Holographic Modified Dynamics.

As you know, gravitational phenomena in a quantum world like ours may be encoded on a holographic screen. In most cases, we expect the usual local dynamics to emerge out of the hologram, anyway. But is there some behavior for which the holographic nature of physics has to be taken into account - when the local bulk physics with the usual scaling laws is not a good approximation?

I believe that the low-acceleration regime is exactly a regime where this could be the case.

Consider a non-accelerating particle. It's connected with some kind of de Broglie wave, exp(-iEt+ipx). This wave is periodic in space and time. But when a particle accelerates with acceleration "a', then it moves along hyperbola whose center C is spacelike-separated from the point where "v=0" and the distance is 1/a, in c=1 units.



Imagining the de Broglie wave, the center C is where the wave may become ill-defined because the hypersurfaces of constant phase intersect at this center. I may need to draw a picture but I believe that many people understand me even without the picture. The existence of this center on the hologram may be needed for the usual Kepler scaling laws to emerge.

OK, I finally added a picture. The Mathematica command was

phase[x_, y_] :=
If[x^2 - y^2 >= 1, 0,
If[Abs[y] >= Abs[x], 0, Sin[10*Re[ArcTanh[y/x]]]]]
DensityPlot[phase[x, y], {x, -2, 2}, {y, -2, 2},
ColorFunction -> "SunsetColors", MaxRecursion -> 5]

However, if the acceleration is too low, 1/a is too large and it may fail to fit into the visible Universe. Only a large enough hologram with many ways - and with the center C in it - produces the usual bulk physics. What is the acceleration for which you start to get deviations? Well, the size of the visible Universe is 8.8 x 10^{26} meters which is 2.9 x 10^{18} seconds.

Its inverse is 3.4 x 10^{-19} inverse seconds. Multiply it by the speed of light to get the acceleration in the usual units and you will get

a₀^HOND = 1.02 x 10^-10 m/s²

That's my holographic prediction for the approximate acceleration below which you may start to get deviations from the usual emergent bulk physics because of the smallness of the hologram relatively to the wave patterns on it. What is their observed value of "a0"? Note that a priori, I could have received a figure that differed by dozens of orders of magnitude from what I got.

Anyway, their value is

a₀^{binary stars} = 1.2 x 10^-10 m/s²

It only differs by the missing zero in the middle of the number which doesn't really matter :-) - the difference is just 20% which led me to scream Wow when I first calculated it. Isn't it a rather amazing coincidence - or confirmed prediction, if you interpret it optimistically?

I will try to derive the new scaling law for the velocity at low accelerations when I have some time. Note that it's enough to show that the orbital velocity stays constant while Newton's force switches from the 1/r^2 law to the 1/r law, more precisely to

GravAcceleration_{low acceleration limit} = (G a₀ M)^1/2 / r.

The switch from the inverse square law to the inverse proportionality looks like an effective decrease of the dimensionality by one - like in holography, indeed. The binary stars are exchanging 3+1D gravitons as long as the hologram including the center of the hyperbola fits into the Hubble-scale holographic screen. If it doesn't, the objects effective live on the boundary only and they attract by a 1/r force only. It sounds OK but there are still many difficult issues that remain to be clarified about this heuristic picture.

For example, why the heck is it proportional to sqrt(M) only where M is probably roughly the bigger of the two masses? In the holographic context, the square root may be similar to one of the relationships in AdS/CFT between the dimensions and masses.

Also, one has to decide what is the useful orientation of the holographic screen, with respect to the orbital plane, that is relevant for a more accurate version of this argument. It may be parallel to the orbital plane.

The Bousso-Susskind hypermultiverse

Leonard Susskind and Raphael Bousso are creative guys and famous physicists. Both of them are well-known for some papers about holography, too. Of course, the first scientist is still a bit more famous. They have just released a preprint to show that they're on crack and they are greatly enjoying it:

The Multiverse Interpretation of Quantum Mechanics

The ordinary multiverse with its infinitely many bubbles whose possible vacuum states are located in 10^{500} different stationary points of the stringy configuration space was way too small for them. So they invented a better and bigger multiverse, one that unifies the "inflationary multiverse", the "quantum multiverse", and the "holographic multiverse" from Brian Greene's newest popular book, The Hidden Reality.

Yes, their very first bold statement is that parallel universes in an inflating universe are the same thing as Everett's many worlds in quantum mechanics! ;-)

Sorry to say but the paper looks like the authors want to stand next to Lee Smolin whose recent paper - as much crackpottish as any paper he has written in his life so far - is about "a real ensemble interpretation" of quantum mechanics. Bousso and Susskind don't cite Smolin - but maybe they should! And in their next paper, they should acknowledge me for pointing out an equally sensible and similar paper by Smolin to them. ;-)




Just like your humble correspondent would always emphasize that the "many worlds" in Everett's interpretation of quantum mechanics are completely different "parallel worlds" than those in eternal inflation or those in the braneworlds, these famous physicists say - On the contrary, they're the same thing!

However, at least after a quick review of the paper, the drugs seem to be the only tool that you can find in the paper or in between its lines to convince you that it's the case. ;-)

It's a modern paper involving conceptual issues of quantum mechanics, so it treats decoherence as the main mechanism to address many questions that used to be considered puzzles. Good. However, everything that they actually say about decoherence is a little bit wrong, so their attempts to combine those new "insights" with similar "insights" resulting from similar misunderstandings of the multiverse - and especially the way how outcomes of measurements should be statistically treated in a multiverse - inevitably end up being double gibberish that is cooked from two totally unrelated components such as stinky fish and rotten strawberries.

In what sense decoherence is subjective

One of the first starting points for them to unify the "inflationary multiverse" and the "many worlds" of quantum mechanics is the following thesis about decoherence:

Decoherence - the modern version of wave-function collapse - is subjective in that it depends on the choice of a set of unmonitored degrees of freedom, the "environment".

That's a loaded statement, for many reasons. First of all, decoherence isn't really a version of the collapse. Decoherence is an approximate description of the disappearing "purity" of a state in macroscopic setups with various consequences; one of them is that there is no collapse. The probabilities corresponding to different outcomes continue to be nonzero so nothing collapses. They're nonzero up to the moment when we actually learn - experimentally - what the outcome is. At that point, we must update the probabilities according to the measurement. Decoherence restricts which properties may be included in well-defined questions - for example, insane linear superpositions of macroscopically different states are not good "basis vectors" to create Yes/No questions.

As first emphasized by Werner Heisenberg and then by anyone who understood the basic meaning of proper quantum mechanics, this "collapse" is just about the change of our knowledge, not a real process "anywhere in the reality". Even in classical physics, dice may have probabilities 1/6 for each number, but once we see "6", we update the probabilities to (0,0,0,0,0,1). No real object has "collapsed". The only difference in quantum physics is that the probabilities are not "elementary" but they're constructed as squared absolute values of complex amplitudes - which may interfere etc.; and in classical physics, we may imagine that the dice had the state before we learned it - in quantum physics, this assumption is invalid.

It may help many people confused by the foundations of quantum mechanics to formulate quantum mechanics in terms of a density matrix "rho" instead of the state vector "psi". Such a "rho" is a direct generalization of the classical distribution function on the phase space "rho" - it only receives the extra off-diagonal elements (many of which go quickly to zero because of decoherence), so that it's promoted to a Hermitian matrix (and the opposite side of the coin is that the indices of "psi" may only involve positions or only momenta but not both - the complementary information is included in some phases). But otherwise the interpretation of "rho" in quantum mechanics and "rho" in classical statistical physics is analogous. They're just gadgets that summarize our knowledge about the system via probabilities. Now, "psi" is just a kind of a square root of "rho" so you should give it the same qualitative interpretation as to "rho" which is similar to "rho" in classical statistical physics.

Second, is decoherence "subjective"? This is a totally equivalent question to the question whether "friction", "viscosity" (or other processes that dissipate energy) is subjective. In fact, both of these phenomena involve a large number of degrees of freedom and in both of them, it's important that many interactions occur and lead to many consequences that quickly become de facto irreversible. So both of these processes (or their classes) share the same arrow of time that is ultimately derived from the logical arrow of time, too.

First, let's ask: Is friction or viscosity subjective?

Well, a sliding object on a flat floor or quickly circulating tea in a teacup will ultimately stop. Everyone will see it. So in practice, it's surely objective. But is it subjective "in principle"? Do the details depend on some subjective choices? You bet.

Focusing on the tea, there will always be some thermal motion of the individual molecules in the tea. But what ultimately stops is the uniform motion of bigger chunks of the fluid. Obviously, to decide "when" it stops, we need to divide the degrees of freedom in the tea to those that we consider a part of the macroscopic motion of the fluid and those that are just some microscopic details.

The separation into these two groups isn't God-given. This calculation always involves some choices that depend on the intuition. The dependence is weak. After all, everyone agrees that the macroscopic motion of the tea ultimately stops. In the same way, the information about the relative phase "dissipates" into a bigger system, a larger collection of degrees of freedom - the environment - during decoherence. The qualitative analogy between the two processes is very tight, indeed.

But a punch line I want to make is that decoherence, much like viscosity, isn't an extra mechanism or an additional term that we have to add to quantum mechanics in order to reproduce the observations. Instead, decoherence is an approximate method to calculate the evolution in many situations that ultimately boils down to ordinary quantum mechanics and nothing else. It's meant to simplify our life, not to add some extra complications. Decoherence justifies the "classical intuition" about some degrees of freedom - what it really means is that interference phenomena may be forgotten - much like the derivation of equations of hydrodynamics justifies a "continuum description" of the molecules of the fluid.

Clearly, the same comment would be true about friction or viscosity. While the deceleration of the car or the tea is usefully described by a simplified macroscopic model with a few degrees of freedom, in principle, we could do the full calculation involving all the atoms etc. if we wanted to answer any particular question about the atoms or their collective properties. However, we should still ask the right questions.

When Bousso and Susskind say that there is an ambiguity in the choice of the environment, they misunderstand one key thing: the removal of this ambiguity is a part of a well-defined question! The person who asks the question must make sure that it is well-defined; it's not a job for the laws of physics. Returning to the teacup example, I may ask when the macroscopic motion of the fluid reduces to 1/2 of its speed but I must define which degrees of freedom are considered macroscopic. When I do so, and I don't have to explain that there are lots of subtleties to be refined, the question will become a fully calculable, well-defined question about all the molecules in the teacup and quantum mechanics offers a prescription to calculate the probabilities.

The case of decoherence is completely analogous. We treat certain degrees of freedom as the environment because the state of these degrees of freedom isn't included in the precise wording of our question! So when Bousso and Susskind say that "decoherence is subjective", it is true in some sense but this sense is totally self-evident and vacuous. The correct interpretation of this statement is that "the precise calculation [of decoherence] depends on the exact question". What a surprise!

In practice, the exact choice of the degrees of freedom we're interested in - and the rest is the environment - doesn't matter much. However, we must obviously choose properties whose values don't change frantically because of the interactions with the environment. That's why the amplitude in front of the state "0.6 dead + 0.8i alive" isn't a good observable to measure - the interactions with the environment make the relative phase terribly wildly evolving. Decoherence thus also helps to tell us which questions are meaningful. Only questions about properties that are able to "copy themselves to the environment" may be asked about. This effectively chooses a preferred basis of the Hilbert space, one that depends on the Hamiltonian - because decoherence does.

To summarize this discussion, at least in this particular paper, Bousso and Susskind suffer from the same misconceptions as the typical people who deny quantum mechanics and want to reduce it to some classical physics. In this paper's case, this fact is reflected by the authors' desire to interpret decoherence as a version of the "nice good classical collapse" that used to be added in the QM framework as an extra building block. But decoherence is nothing like that. Decoherence doesn't add anything. It's just a simplifying approximate calculation that properly neglects lots of the irrelevant microscopic stuff and tells us which parts of classical thinking (namely the vanishing of the interference between 2 outcomes) become approximately OK in a certain context.

Let's move on. They also write:

In fact decoherence is absent in the complete description of any region larger than the future light-cone of a measurement event.

If you think about it, the purpose of this statement is inevitably elusive, too. Decoherence is not just "the decoherence" without adjectives. Decoherence is the separation of some particular eigenstates of a particular variable and to specify it, one must determine which variable and which outcomes we expect to decohere. In the real world which is approximately local at low energies, particular variables are connected with points or regions in spacetime. What decoheres are the individual possible eigenvalues of such a chosen observable.

But the observable really has to live in "one region" of spacetime only - it's the same observable. The metric in this region may be dynamical and have different shapes as well but as long as we talk about eigenvalues of a single variable, and in the case of decoherence, we have to, it's clear that we also talk about one region only. Decoherence between the different outcomes will only occur if there's enough interactions, space, and time in the region for all the processes that dissipate the information about the relative phase to occur.

So it's completely meaningless to talk about "decoherence in spacelike separated regions". Decoherence is a process in spacetime and it is linked to a single observable that is defined from the fundamental degrees of freedom in a particular region. Of course, the region B of spacetime may only be helpful for the decoherence of different eigenvalues of another quantity in region A if it is causally connected with A. What a surprise. The information and matter can't propagate faster than light.

However, if one restricts to the causal diamond - the largest region that can be causally probed - then the boundary of the diamond acts as a one-way membrane and thus provides a preferred choice of environment.

This is just nonsense. Even inside a solid light cone, some degrees of freedom are the interesting non-environmental degrees of freedom we're trying to study - if there were no such degrees of freedom, we wouldn't be talking about the solid light cone at all. We're only talking about a region because we want to say something about the observables in that region.

At the same moment, for the decoherence to run, there must be some environmental degrees of freedom in the very same region, too. Also, as argued a minute ago - by me and by the very authors, too - the spatially separated pieces of spacetime are completely useless when it comes to decoherence. It's because the measurement event won't affect the degrees of freedom in those causally inaccessible regions of spacetime. Clearly, this means that those regions can't affect decoherence.

(A special discussion would be needed for the tiny nonlocalities that exist e.g. to preserve the black hole information.)

If you look at the light sheet surrounding the solid light cone and decode a hologram, you will find out that the separation of the bulk degrees of freedom to the interesting and environmental ones doesn't follow any pattern: they're totally mixed up in the hologram. It's nontrivial to extract the values of "interesting" degrees of freedom from a hologram where they're mixed with all the irrelevant Planckian microscopic "environmental" degrees of freedom.

They seem to link decoherence with the "holographic" degrees of freedom that lives on the light sheets - and a huge black-hole-like entropy of A/4G may be associated with these light sheets. But those numerous Planckian degrees of freedom don't interact with the observables we're able to study inside the light cone, so they can't possibly contribute to decoherence. Indeed, if 10^{70} degrees of freedom were contributing to decoherence, everything, including the position of an electron in an atom, would be decohering all the time. This is of course not happening. If you associate many degrees of freedom with light sheets, be my guest, it's probably true at some moral level that the local physics can be embedded into physics of the huge Bekenstein-Hawking-like entropy on the light sheet - but you must still accept (more precisely, prove) that the detailed Planckian degrees of freedom won't affect the nicely coherent approximate local physics that may be described by a local effective field theory - otherwise your picture is just wrong.

The abstract - and correspondingly the paper - is getting increasingly more crazy.

We argue that the global multiverse is a representation of the many-worlds (all possible decoherent causal diamond histories) in a single geometry.

This is a huge unification claim. Unfortunately, there's not any evidence, as far as I can see, that the many worlds may be "geometrized" in this way. Even Brian Greene in his popular popular book admits that there is no "cloning machine". You can't imagine that the new "many worlds" have a particular position "out there". The alternative histories are totally disconnected from ours geometrically. They live in a totally separate "gedanken" space of possible histories. By construction, the other alternative histories can't affect ours, so they're unphysical. All these things are very different from ordinary "branes" in the same universe and even from other "bubbles" in an inflating one. I don't know why many people feel any urge to imagine that these - by construction - unphysical regions (Everett's many worlds) are "real" but at any rate, I think that they agree that they cannot influence physics in our history.

We propose that it must be possible in principle to verify quantum-mechanical predictions exactly.

Nice but it's surely not possible. We can only repeat the same measurement a finite number of times and in a few googols of years, or much earlier, our civilization will find out it's dying. We won't be able to tunnel our knowledge elsewhere. The number of repetitions of any experiment is finite and it is not just a technical limitation.

There are many things we only observe once. Nature can't guarantee that everything may be tested infinitely many times - and it doesn't guarantee that.

This requires not only the existence of exact observables but two additional postulates: a single observer within the universe can access infinitely many identical experiments; and the outcome of each experiment must be completely definite.

In de Sitter space, the observables are probably not exactly defined at all. Even in other contexts, this is the case. Observers can't survive their death, or thermal death of their surrounding Universe, and outcomes of most experiments can't be completely definite. Our accuracy will always remain finite, much like the number of repetitions and our lifetimes.

In the next sentence, they agree that the assumptions fail - but because of the holographic principle. One doesn't need a holographic principle to show such things. After all, the holographic principle is an equivalence of a bulk description and the boundary description so any physically meaningful statement holds on both sides.

At the end, they define "hats" - flat regions with unbroken supersymmetry - and link their exact observables to some approximate observables elsewhere. Except that this new "complementarity principle" isn't supported by any evidence I could find in the paper and it isn't well-defined, not even partially. In the quantum mechanical case, complementarity means something specific - that ultimately allows you to write "P" as "-i.hbar.d/dx" - a very specific construction that is well-defined and established. In the black hole, complementarity allows you to explain why there's no xeroxing; the map between the degrees of freedom isn't expressed by a formula but there is evidence. But what about this complementarity involving hats? There's neither definition nor evidence or justification (unless you view the satisfaction of manifestly invalid and surely unjustified, ad hoc assumptions to be a justification).

If you read the paper, it is unfortunately motivated by misunderstandings of the conceptual foundations of quantum mechanics. In the introduction, they ask:

But at what point, precisely, do the virtual realities described by a quantum mechanical wave function turn into objective realities?

Well, when we measure the observables. Things that we haven't measured will never become "realities" in any sense. If the question is about the classical-quantum boundary, there is obviously no sharp boundary. Classical physics is just a limit of quantum physics but quantum physics fundamentally works everywhere in the multiverse. The numerical (and qualitative) errors we make if we use a particular "classical scheme" to discuss a situation may be quantified - decoherence is one of the calculations that quantifies such things. But classical physics never fully takes over.

This question is not about philosophy. Without a precise form of decoherence, one cannot claim that anything really "happened", including the specific outcomes of experiments.

Oh, really? When I say that it's mostly sunny today, it's not because I preach a precise form of decoherence. It's because I have made the measurement. Of course, the observation can't be 100% accurate because "sunny" and "cloudy" haven't "fully" decohered from each other - but their overlap is just insanely negligible. Nevertheless, the overlap never becomes exactly zero. It can't. For more subtle questions - about electrons etc. - the measurements are more subtle, and indeed, if no measurement has been done, one cannot talk about any "reality" of the property because none of them could have existed. The very assumption that properties - especially non-commuting ones - had some well-defined properties leads to contradictions and wrong predictions.

Decoherence cannot be precise. Decoherence, by its very definition, is an approximate description of the reality that becomes arbitrarily good as the number of the environmental degrees of freedom, their interaction strength, and the time I wait become arbitrarily large. I think that none of the things I say are speculative in any way; they consider the very basic content and meaning of decoherence and I think that whoever disagrees has just fundamentally misunderstood what decoherence is and is not. But the accuracy of this emergent macroscopic description of what's happening with the probabilities is never perfect, just like macroscopic equations of hydrodynamics never exactly describe the molecules of tea in a teacup.

And without the ability to causally access an infinite number of precisely decohered outcomes, one cannot reliably verify the probabilistic predictions of a quantum-mechanical theory.

Indeed, one can't verify many predictions of quantum mechanical properties, especially about cosmological-size properties that we can only measure once. If you don't like the fact that our multiverse denies you this basic "human right" to know everything totally accurately, you will have to apply for asylum in a totally different multiverse, one that isn't constrained by logic and science.

The purpose of this paper is to argue that these questions may be resolved by cosmology.

You know, I think that there are deep questions about the information linked between causally inaccessible regions - whether black hole complementarity tells you something about the multiverse etc. But this paper seems to address none of it. It seems to claim that the cosmological issues influence even basic facts about low-energy quantum mechanics and the information that is moving in it. That's surely not possible. It's just a generic paper based on misunderstandings of quantum mechanics and on desperate attempts to return the world under the umbrella of classical physics where there was a well-defined reality where everything was in principle 100% accurate.

But the people who are not on crack will never return to the era before the 1920s because the insights of quantum mechanics, the most revolutionary insights of the 20th century, are irreversible. Classical physics, despite its successes as an approximate theory, was ruled out many decades ago.

I have only read a few pages that I considered relevant and quickly looked at the remaining ones. It seems like they haven't found or calculated anything that makes any sense. The paper just defends the abstract and the introduction that they have apparently pre-decided to be true. But the abstract and and introduction are wrong.

You see that those would-be "revolutionary" papers start to share lots of bad yet fashionable features - such as the misunderstanding of the conceptual issues of quantum mechanics and the flawed idea that all such general and basic misunderstandings of quantum physics (or statistical physics and thermodynamics) must be linked to cosmology if not the multiverse.

However, cosmology has nothing to do with these issues. If you haven't understood a double-slit experiment in your lab or the observation of Schrödinger's cat in your living room and what science actually predicts about any of these things, by using the degrees of freedom in that room only, or if you haven't understood why eggs break but don't unbreak, including the degrees of freedom of the egg only, be sure that the huge multiverse, regardless of its giant size, won't help you to cure the misunderstanding of the basics of quantum mechanics and statistical physics.

The right degrees of freedom and concepts that are linked to the proper understanding of a breaking egg or decohering tea are simply not located far away in the multiverse. They're here and a sensible scientist shouldn't escape to distant realms that are manifestly irrelevant for these particular questions.

And that's the memo.

Gravity Probe B final results: frame dragging within 20 percent

Stanford's $0.76 billion satellite mission to test Einstein's theory of gravity, Gravity Probe B (Wiki), has announced the final results during the press conference aired by NASA TV a few hours ago. The results will be published in Physical Review Letters:

Gravity Probe B: Final results of a space experiment to test general relativity

If you read the abstract of the paper above, you will see that their measured geodetic effect is -6,602 mas/yr (milli-arcseconds per year), while the prediction of GR is -6,606 mas/yr (an excellent agreement within 0.06 percent or so; however, their official error margin, 18.3 mas/yr, is larger - 0.3% of the figure).



The more difficult measurement of the frame-dragging drift rate gave them -37.2 mas/yr, to be compared with -39.2 mas/yr according to GR. The discrepancy is just 7 percent or so. However, their actual announced error is closer to 19 percent (7.2 mas/yr), so they can barely prove that the frame-dragging effect is nonzero at the 5-sigma confidence level.




The accuracy of the frame-dragging measurement by Gravity Probe B has been a major disappointment; the previous, incomplete results from the probe were not even able to prove at the 5 sigma level that the effect was nonzero. Instead of a 19% error, the plans expected a 1% error; the main source of trouble has been electric polarization of the gyroscopes that contaminated the signal with lots of Coulomb forces whose harmful impact was amplified by irregular patches on the surface of the spheres. Because of that, Gravity Probe B actually turned out to be less accurate than the LAGEOS experiment that measured frame dragging within 10% in 2004.

Nevertheless, if you ask whether the probe has helped to dramatically eliminate doubts that GR is correct once again, the answer is a resounding Yes.

Remarkably, I first learned about the final results from Anthony Watts' climate blog. He is a fellow skeptic and my bookmarks equally contain the "mainstream scientific" blog Real Climate. Despite this equal status, I have learned about dozens of interesting hot news from Anthony Watts - not only about the climate - but I have never learned anything about science from Real Climate. That's not a surprise. The newest article on Real Climate is concerned with the proposition that deniers are deniers and denialism is a common trait.

See also The New York Times, Science Now, and dozens of others at Google News.

Constraints from Einstein's equations as Navier-Stokes equations

In January, Andy Strominger and friends posted a very interesting paper

Geometry for every solution of Navier-Stokes (TRF)

Today, Andy Strominger and Vyacheslav Lysov offer their extraordinary concise related preprint

From Petrov-Einstein to Navier-Stokes (hep-th)

In the paper, they start with a flat p+1-dimensional hypersurface that has 1 temporal direction and p spatial directions. However, it may be embedded into a p+2-dimensional curved spacetime.




Strominger and Lysov impose the Petrov type I condition for this p+2-dimensional spacetime - something that has been studied in GR for purely relativistic reasons, and something that uses Newman-Penrose vector fields, among other things - and they find out that it reduces the degrees of freedom near the hypersurface to the hydrodynamical degrees of freedom.

Now, they look at Einstein's equations near this p+1-dimensional hypersurface. Normally, we evolve the geometry in time. Whenever we're doing so with some partial differential equations with local symmetries, we find out that some of the equations are "constraints" which means that they restrict possible initial states - but they don't tell us anything else about the evolution because they don't contain time derivatives.

Maxwell's equations contain the equation "div D = rho" which is a typical constraint equation. It may be linked to the electromagnetic U(1) gauge invariance of the states in the quantized version of the theory of electromagnetism; after all, you get it from the variation of the action with respect to A_0. A similar constraint part exists for Einstein's equations - variations with respect to g_{0,mu}, roughly speaking - and it restricts the possible exterior curvature on the "t=const" slice.

However, Lysov and Strominger look at the constraint equations in a different way. Instead of studying a purely spacelike hypersurface - a "t=const" slice - they study a (flat) hypersurface of the type "x=const" that has a time-like direction in it. It's still possible to separate Einstein's equations to the "dynamical" ones (in space, in this case) and the "constraint" part.

And the two physicists find out that in the limit in which the extrinsic curvature goes to infinity, the constraint part of Einstein's equations reduces to the Navier-Stokes equations! So this is a pretty natural holographic embedding of hydrodynamics in general relativity, indeed.

Cute.

Of course, general relativity expects us to extrapolate the geometry to long distances away from the p+1-dimensional hypersurface. This is a procedure that people studying hydrodynamics would probably not do but it is a pretty natural one, and assuming it can be done, it should tell us something about the Navier-Stokes equations - and perhaps even lots of things about turbulence.

This picture is still "unusual" in the realm of stringy dualities because both sides of the "duality" are completely classical. I still don't know how to think about it. Is it really analogous to the usual string dualities where one side always assumes the quantum effects of the other side to be huge? And if it is not a duality in this sense, shouldn't it mean that it's vacuous in some sense?

John Baez, octonions, and string theory

John Baez has always been obsessed by octonions. He sees them everywhere. I love octonions but I realize that they don't play much role in most of physics - and not even in most of string theory.

In 2009, I wrote a related article

John Baez, M-theory, and spinors

Scientific American has just published a text by John Baez and his student John Huerta,

The Strangest Numbers in String Theory (demo; free version in 1 month)

The first fact I find utterly crazy is that two people who manifestly and demonstrably don't understand string theory - not even at the undergraduate level - are writing articles for widely read journals pretending to be scientific magazines with "string theory" playing the role of one half of the title. As I will argue, they are really abusing the stellar brand of string theory to promote their idiosyncratic bullshit.




The SciAm article is a simplified version of this more technical article

Division Algebras and Supersymmetry II by John Baez

posted at Jacques Distler's n-category and marijuana coffee shop. As sketched in my 2009 blog entry, Baez is obsessed by the observation that the classical string theories in D=3,4,6,10 - which use spinors with different reality and chirality projections - can be mapped to R,C,H,O, the four division algebras of dimensions 1,2,4,8.

In some sense, SL(2,O) may be interpreted as SO(9,1).

However, that's it. The actual structure of the octonions - their multiplication table whose characteristic automorphism group is G_2 - is not really used in SO(9,1) in a useful way. And if this table and the G_2 symmetry appears at a certain stage, it immediately disappears.

Moreover, the minimal superPoincaré algebras in 3,4,6,10 dimensions are far from being the only four superalgebras in their class. They're not even the most interesting or most symmetric ones. They're just algebras in four dimensionalities D such that D-2 - the number of physical polarizations of a gauge boson - is a power of two. It has to be a power of two in a minimal supersymmetric gauge theory because the number of bosonic polarizations has to match the number of fermionic polarizations and the latter come from a spinor; I don't need division algebras to prove that. Also, I don't need division algebras to prove that minimal super Yang-Mills theories can only exist in these four dimensions.

Also, the "other remarkable structures" that directly come from the R,C,H,O sequence are not that interesting. He also talks about membranes in 4,5,7,11 dimensions (not surprising that they have the same counting of physical degrees of freedom - it's just double dimensional reduction). Except for the last one, they're not terribly interesting theories or vacua. So the detailed data refute Baez's hypothesis; he clearly doesn't care. Also, the R,C,H,O argument doesn't really show why/that only the 10- or 11-dimensiona case is consistent at the quantum level (as a separate theory). This whole R,C,H,O perspective on the landscape of string/M-theory vacua is naive at the level of a kindergarten kid. You simply can't understand the secrets of string theory by learning the sequence 1,2,4,8.

In the slow comments under the 2009 blog entry, Robert Helling argued that there is a lot of interesting fog about the closure of the supersymmetry algebra etc. I find this whole approach to these issues irrational.

There's lots of fascinating, still poorly understood mysteries about string theory's internal mathematical consistency. But the topics that Baez, Huerta, Helling, and others are talking about are pretty much exactly those where the mystery has already been fully eliminated. The mysterious links to pure mathematics continue to exist but you must get much deeper to uncover them.

There are simple ways to prove that 3,4,6,10 are the relevant dimensionalities for the classical superstring - but only D=10 is the actual dimension that is allowed at the quantum level. However, counting of the dimensions is one of the most elementary facts about string theory. All the cancellations that Baez et al. hype can be easily proved - in many different ways, in fact. Joe Polchinski boasts that volume I of his book derives the critical dimension of the bosonic string theory in 7 different ways. So why is there so much ado about nothing? Our ability to derive results in 7 different ways shows that we kind of understand it. Those ways also connect different portions of mathematics - but it is the whole structure of string/M-theory, and not a division algebra, who unifies all this stuff.

Moreover, as hinted in the previous sentence, what I am really irritated by is Baez's obsessive tendency to reduce all the mathematical cleverness of string theory to the division algebras in general and octonions in particular. His way of looking at all these things shows that he is nothing else than an irrational numerologist who can never distinguish real insights from superficial distractions - and who apparently doesn't want to distinguish them.

The division algebra is just one way to look at all the issues linked to 7 imaginary units with the G_2 automorphism group, and all the associated algebraic structure. The octonions as an algebra are just one possible corollary or intellectual projection of the structure behind it. And even all these structures combined are just a totally minuscule portion of the string theory's wisdom, much like John Baez's knowledge of string theory is an infinitesimal fraction of the knowledge of a good graduate student.

So the article hyping a set of a few simple mathematical observations is just pathetic. It's not really demonstrably wrong - unlike Garrett Lisi's pseudoscientific "theories of everything" that can't agree with the most elementary facts of particle physics such as parity violation. But it's still morally wrong because it totally distorts what is understood and what remains mysterious about the remarkable mathematical structure we still call string theory.

This distortion shouldn't be unexpected from authors who don't have a clue about string theory. But this is no real excuse because Scientific American shouldn't be publishing stuff written by people who don't know what they're talking about.

Leonard Susskind: String theory and M-theory

If you have something like O(10 x 100 minutes) = O(1000 minutes) and you want to learn the basics of our only candidate for a theory of everything, here is the playlist with ten Prof Susskind's lectures on string theory and M-theory for the Californian pensioners.



Lenny Susskind is much more than just one of the early fathers of the field.

I hope that some of you will try to watch at least a part of this symphony and we will hear some comments about the people's impressions and insights.




Thanks to Adam O.

Sidney Coleman's QFT lectures: TeX, PDF

E-mail from Bryan Chen

Dear Lubos,

It's been a few years since I wrote you. I thought you might be interested that the LaTeXing of Coleman's notes has had quite a bit of recent progress.  Indeed, the project was more or less stalled in 2008, until last year, when Ting Yuan Sen (a student at National University of Singapore and Ecole Polytechnique) began writing me that he was continuing the typesetting. Indeed, within a few months, he finished all the rest of the lectures!

Earlier this week, I wrote Brian Hill (who originally wrote the handwritten version), and at my request, he gladly contributed a short preface to the project, giving a bit of context to the notes, and I've compiled it with all the lectures into one 338 page PDF file.




The files are in the same place they've always been.  There are various readmes in that directory as well, saying basically the same things as this email:

www.physics.upenn.edu/~chb/phys253a/coleman

Here're the links to some specific files:

The PDF of the full notes (338 pages, Google Docs Viewer):

www.physics.upenn.edu/~chb/
phys253a/coleman/coleman.pdf

A convenient ZIP file containing the source files:

www.physics.upenn.edu/
~chb/phys253a/coleman/
coleman_latex_
source_20110314.zip

The TeX project should surely be improved with (at least) two more things, which I don't have the energy for:

1. The formatting between lectures is rather inconsistent, especially with regard to "section" headings and the like.
2. The lectures would benefit greatly from an index.

I'd appreciate it if you might spread the word on your blog!

Best,
Bryan

---

P.S. (by LM): Just to be complete, videos from the lectures are available at Harvard:

Physics 253: Quantum Field Theory: Lectures by Sidney R. Coleman

They cover both semesters, 253a and 253b, and were recorded in 1975-1976.

Japan, physics, string theory, and me

Fundamental physics has traditionally been a part of the Euro-Atlantic culture. So the Japanese physicists may be viewed as relative newbies but they have already imprinted their skills onto our collective body of knowledge.

Hideki Yukawa became the first Japanese Nobel prize winner and, in some sense, he founded the Western theoretical physics in Japan as we know it. His description of the nuclear force - when the difference between the strong force and the weak force wasn't quite understood - was arguably the most important step in the physicists' understanding of short-range forces.

It helped the people to figure out that massive particles mediate short-range forces. Pions in his original model play this role when it comes to an approximate description of the strong interaction; W-bosons and Z-bosons generalize this logic and describe the weak interaction.

But I think it's right to mention three more older Japanese physicists who belong to the same league: Sin-Itiro Tomonaga (thanks, Robert!), Yoichiro Nambu, and Tamiaki Yoneya.

Sin-Itiro Tomonaga benefited from interactions with Werner Heisenberg and his group while in Leipzig, Germany in the 1920s - a decade before their countries would become close "axial" allies ;-) - but he became a powerful independent weapon who focused on the cancellation of divergences in quantum field theory. He discovered the old-fashioned renormalization independently of Schwinger. Tomonaga, Schwinger, and Feynman shared the 1965 physics Nobel prize.

Of course, Nambu joined two other Japanese physicists, Makoto Kobayashi (K) and Toshihide Maskawa (M), when they formed the trio of the 2008 Nobel prize winners.




Of course, many people had expected the Nobel-winning trio to reproduce the names behind the CKM matrix - we're used to it, after all. However, Nicola Cabibbo (C), while a very important physicist, wasn't quite in the same league as Nambu, I think. That's why I found the purely Japanese 2008 selection to be creative and fair. Unfortunately, Cabibbo died last Summer so he won't be able to get his own prize.

Nambu is a giant of theoretical physics. As a co-father of the Nambu-Goto action, he carved the cradle of string theory. As a key name behind the Nambu-Goldstone bosons, he was a critical man to uncover the secrets of the spontaneous symmetry breaking. And he is a co-father of the color, quarks' new charge, too.

Tamiaki Yoneya is two decades younger but I still included him among the great Japanese physicists of the older generation. Independently of Scherk and Schwarz, he realized that string theory automatically implies gravity as painted by general relativity. For many years, he would be working on various stringy versions of the uncertainty principle (for space and time etc.). As far as I can say, the details of this research never became conclusive - and holography has de facto showed that the ultimate correct logic of the inequalities is different - but his philosophy was important to shape the new "lore" of quantum gravity and string theory.

Let me get to two newer developments - linked to string theory: covariant string field theory and covariant matrix theory. It just happens that both of them are "covariant" versions of descriptions of string theory that happen to be working more reliably when they're not covariant. ;-)

Kyoto group and string field theory

When I was a high school student, I didn't have much access to serious books and articles about string theory. Although I knew everything that the Czech popular magazines had ever written about string theory, I couldn't really study it at the technical level. At most, I could read all (mostly misguided) Einstein's papers about the unified field theory - in the Pilsner Scientific Library where I have spent a lot of quality time. I didn't speak German well but you know, a dictionary helps and the actual key language were the equations. ;-)

That situation changed when I got to the Charles University in Prague at the end of 1992. It just happened that the first stringy book I borrowed from the library was a brown book called "Quantum String Theory" - if I remember well - with some proceedings from a 1987 conference. It reproduced several talks and two of them were accessible to me (and became very important in shaping my interests).

The first chapter of the book was about the light-cone superstring field theory. I think that it was written by Michael Green, John Schwarz, and Lars Brink (or Holger Nielsen?). I think that this early exposure has made it much more natural for me to learn the light-cone gauge versions of string theory when I began to study the subject with proper textbooks (especially Green-Schwarz-Witten).

The other chapter that greatly influenced me was one about the Kyoto group string field theory - designed by Hata, Itoh, Kugo, Kunitomo and Ogawa (HIKKO). It was meant to be analogous to Witten's cubic open string field theory but it was supposed to describe closed string interactions. The interaction vertex was able to merge two O-shaped strings into one 8-shaped one. In particular, the chapter also discussed the background-independent version of this string field theory whose action only has the cubic term, namely "A*A*A". I found that beautiful - for quite some time. The equation of motion is really "A*A = 0" which I found to be a perfect Ansatz for a theory of everything (on a T-shirt); I no longer think that this simplicity is the right cause for excitement.

Much of the maths in the HIKKO string field theory is analogous to Witten's cubic open string field theory - which I only encountered much later. Correspondingly, it took lots of time for me to understand that string theory doesn't necessarily have to be formulated as a string field theory. And it took an even longer time to understand why the Kyoto group string field theory is actually less consistent a description than the purely open string field theory by Witten.

Because of this incomplete information, I had believed for many years that the Japanese physicists had made the most advanced discoveries in string theory. It is no longer my exact belief today but the influence has been great.

The IKKT matrix model

A similar event got repeated four years later, at the end of 1996. Although I was monitoring the hep-th abstracts of the arXiv preprints on a daily basis, I had missed the BFSS matrix model paper in October 1996. What I couldn't miss, however, was a November 1996 paper by Vipul Periwal whose title was Matrices on a point as the theory of everything.

As far as I can say, the paper, while ambitious, wasn't right but the title revealed a good piece of marketing and it allowed me to re-discover the one-month-old BFSS matrix model which I began to investigate intensely. It turned out that in the decoupled world of Central Europe, I had mostly missed the duality revolution - focusing on (mostly free-fermionic) heterotic string phenomenology for years instead. However, the BFSS matrix model was a rather straightforward way to fill all those gaps. I don't want to discuss my own exciting adventures here.

But there was one more matrix model that was published soon, in December 1996, the IKKT matrix model by Nobuyuki Ishibashi, Hikaru Kawai, Yoshihisa Kitazawa, and Asato Tsuchiya. I would refer to it as the Japanese matrix model.

Well, it was rather a reproachful word than an expression of admiration but the model has been important because it was promising to become a covariant version of a BFSS-like map. However, the IKKT matrix model would probably be relevant as a non-perturbative (covariant) description of type IIB string theory instead of a non-perturbative (light-cone) description of M-theory offered by the matrix model.

Despite dozens or hundreds of hours I spent by checking this model and attempts to prove it - and reading of other people's papers about it - I am still undecided whether the model actually works or it is just hogwash that looks like something that is right but it is not right.

One thing is clear: Nathan Seiberg-like proof of this model remains non-existent and the papers written about the IKKT matrix model are much more sloppy and much less careful than papers written about the BFSS matrix model. Most of the people who think that the IKKT model is established at the same level as the BFSS matrix model simply have no clue what they're talking about.

I could tell you my strategies how to prove that the IKKT model is right if it is right - ways to reorganize all type IIB configurations into a small perturbation of a collection of N type IIB D-instantons by some "large" (and possibly complexified) SL(2,Z) U-duality transformations, replacing Seiberg's boost used to prove the BFSS matrix model. But it has never quite worked.

It still seems crazy to me that this very important question - whether the only semi-viable proposed covariant non-perturbative description of a superselection sector of string theory is right - hasn't been clearly settled by some good enough physicists and solid enough arguments. Of course, in the late 1990s, many people began to write papers on idiocies such as the anthropic principle so the number of people who could think hard about important but somewhat technically demanding problems - and I surely don't mean just this one - has decreased considerably.

Japan still hasn't managed to get to the top of theoretical physics but many very good people in the field are working in Japan, greetings to them. And I am confident that the average quality of the papers produced in the land of the rising Sun is much higher than the quality of the Chinese papers, for example - no offense to China, please, this is just a piece of reality.

Of course, Japan also has some serious experimental particle physics. The KEK accelerator center is known to many people because SPIRES offers the scanned version of all particle physics papers that were digitized by the KEK library; and Kamiokande has done lots of work in the search for proton decay and in neutrino physics.

ICTP talks by Polchinski, Vafa, Green, Schwarz, and others

I just discovered the YouTube channel of ICTP, i.e. Abdus Salam's International Center for Theoretical Physics in Trieste, Italy.

During the last month or so, they have posted a number of recent lectures (November 2010) by the winners of the Dirac Medal that they have distributed every August since 1985.



A significant fraction of the Dirac Medal winners are string theorists and I have chosen a sequence of 30-minute lectures by Joseph Polchinski (2008), Cumrun Vafa (2008), Michael Green (1989), John Schwarz (1989): two hours in total.




Note that Polchinski is being introduced by a young East Asian female physicist. Most other folks who introduce the speaker are much closer to the Muslim world, as appropriate for a center founded by Abdus Salam who was Pakistani.

Joe Polchinski talked about holography and unification. Cumrun Vafa chose to clarify the physical role of compact extra dimensions. Michael Green looks at string theory as a UV-finite extension of supergravity and he explains why SUGRA isn't enough. John Schwarz focused on superconformal field theories and their role in string/M-theory.

I also recommend to you talks by Roman Jackiw, Helen Quinn, John Iliopoulos, Jogesh Pati, Giorgio Parisi, David Gross (it has probably been shown on TRF), Shiraz Minwalla, Sergio Ferrara, Stephen Adler, and others.

NPR: Brian Greene on The Hidden Reality

Ira Flatow interviews Brian Greene for 17 minutes if you have time (audio). It's not only about Brian's new book.

Somewhat controversial hypotheses but as Brian says, the book is not an uncritical manifesto for the multiverse.

Nima Arkani-Hamed on spacetime, QM, and Large Erect Collider

Nima Arkani-Hamed gave a 90-minute public lecture on unification, relativity, QFT, scales in physics, the LHC, and other key things. I have modified the name of the collider in the title because this blog is way more polite than the prícks at Princeton. ;-)



You may also go to high-resolution and low-resolution MP4 file.




Nima focuses on the hierarchy problem (the Higgs' unbearable lightness of being) and the cosmological constant problem - and their solutions, including supersymmetry etc.

Bonus: admissions at USC

An interesting story: Clifford Johnson has been bullied by a mediocre physicist who nevertheless wanted to become a USC graduate student, despite having totally lousy scores and other objective parameters, in order to improve the weather (he lives in a very cold state now).

Clifford wasn't able to tell him to f*ck off, and as a result, he has missed a talk by a Nobel prize winner.

That's how it works: if you can't authoritatively deal with obnoxious, pushy, and stupid as*holes, they will beat the battle for your time - and influence in general - against the Nobel prize winner or anyone else who has something to offer.

Four reasons why I like string theory (guest blog)

Guest blog by Phil Gibbs

It is exactly one year since I started this blog, so to celebrate I will give my four top reasons for liking string theory.

This is partly a response to a recent survey on Cosmic Variance which included a question about what likelihood people gave to string theory being correct. With about 170 people responding, about half of them gave string theory 10% or less, many said 1% or even 0%. Now, science isn’t settled by democratic votes especially by a random sample of commenters on one particular blog. Nevertheless it is a revealing outcome and there are plenty of other physicists who think the same. The reasons people gave were roughly along the lines of “It has not had any experimental success after a long time” or “it is unfalsifiable”. I dont agree that these are real issues but instead of talking about that I want to review why I think it is still a theory worthy of being excited about.




(1) My top reason for thinking that string theory is a correct approach to unifying physics is that it provides a consistent perturbative description of particle physics with the inclusion of gravitons, and there is no known alternative. Gravity is a very weak force and spacetime is nearly flat on small scales. There must be some perturbative description of the quantized interaction of particles with gravity as a series of approximations. A direct quantisation of GR cannot do this, but string theory can.

Furthermore it achieves this in a way that did not have to work, but it does because of surprising cancellations. There are five consistent string theories in 10 dimensions which are all related by non-perturbative dualities. The reductions to 4 spacetime dimensions is a consistent process which is now reasonably well understood, except we dont know the correct compactification manifold. The only alternative way to get a consistent perturbative theory is possibly from supergravity, but by now we understand that supergravity too is just another limiting case of string theory. Some physicists have suggested that there may be a chance of finding other non-perturbative solutions to the quantum gravity problem, but no complete solution of that type has been found yet. Until it has, this reason alone is a very strong indication that string theory is on the right path.

(2) Supersymmetry! There are many ways that string theory can reduce to low energy particle physics and not all of them would result in observable supersymmetry. On the other hand, supersymmetry is a natural byproduct of string theory and if it does exist in nature at scales currently being probed by the LHC then it can explain several mysteries. These include the hierarchy problem, dark matter, a light Higgs and the convergence of the running coupling constants at the GUT scale where SUSY says they all have a value of around 1/24. In the last few weeks we have seen the exclusion limits for SUSY greatly extended by CMS and ATLAS. They say that if you throw a frog into hot water it will quickly jump out, but if you put it in cold water and gradually heat the water up it will stay there until it is boiled to death. You should not try this experiment at home but it seems like nature is trying it on physicists who like supersymmetry. In the 1980s we thought that supersymmetric partners would have light masses to avoid fine tuning. If this was right they would have been seen at LEP or the Tevatron. Now the LHC has pushed the minimum masses to uncomfortably high values implying quite a lot of fine tuning. The water is heating up but we will stay put because we now know that the multiverse allows for such fine tuning provided it is in the best interests of our existence. Perhaps the higher masses were needed to allow dark matter to form galaxies or some such.

(3) My third best reason for supporting string theory is that it provides a solution to the black hole information paradox via the holographic principle. This is a much more theoretical argument but it is still quite convincing, I find. Although there may never be any evidence for Hawking radiation from black holes, we know theoretically that it has to be there. Some reasoning using semiclassical quantum gravity tells us the laws of entropy for a black hole, and this should remain correct for any complete theory of quantum gravity such as string theory. Further arguments also tell us that the rules of thermodynamics must obey a holographic principle to avoid the paradox of thermodynamic information being lost inside a black hole. Again, any theory of quantum gravity worth its salt has to comply. It is therefore a triumph for string theory that the AdS/CFT correspondence shows that string theory does (or can) realize the holographic principle. It is another indication that string theory is on the right track.

(4) My final reason for liking string theory is that it comes with a multiverse. For some people this is the favourite reason for not liking string theory and my reasoning for thinking otherwise is partly philosophical, so only people with similar philosophical leanings will agree with me. Ten years ago I did not favour anthropic reasoning. That was because the anthropic principle requires a range of theories that the universe can choose from so that one customised for intelligent life can be selected. I am comfortable with the platonic view that all mathematically consistent universes exist and we just inhabit some part of that realm, but in order to explain the symmetries that govern the laws of physics I think you need to invoke a further principle. For me that principle is universality in the sense of universal behavior seen in complex dynamical systems such as those seen in critical phenomena. I think there is a universal behavior of some type in the realm of complex mathematical systems which overwealms all other possible laws of physics so that only one unique possibility complete with all its beautiful symmetries can be what we experience. You can see that this does not fit well with the anthropic principle. However, there are good indications that the laws of physics are somehow selected to promote intelligent life in a way that would not be consistent with a single unique set of physical laws, contradiction! Luckily the multiverse comes to the rescue in the form of the string landscape. It turns out that string theory does indeed follow from some unique over-arching M-theory, but it can be realized in many forms in lower dimensions by a choice of vacuum determined by the compactification manifold. A wide range of these vacua are stable and there could be as many as 10^500 of them, plenty enough to account for anthropic reasoning. In my view it is the perfect outcome.

So those are my four best reasons for liking string theory. This does not mean that I don’t value other approaches to quantum gravity. We still need to find its complete non-perturbative formulation andIi am sure that such a thing must exist even if string theory has nothing to do with the laws of physics. Other theories such as Loop Quantum Gravity, Non-Cummutative Geometry or Group Field Theory lead to rich mathematical concepts. I see this as a sign that they are telling us something about our world, but I think you have to look for what it says about possibilities for non-perturbative string theory. For example, Loop Quantum Gravity tells us that knot polynomials and spin networks should be important. I like the fact that recently Witten has explored implications of high dimensional generalisation of the knot polynomials (Khovanov homology) to branes from M-theory. This is the kind of outcome I expect from alternative approaches.

So what of the problems people say are issues for string theory? I see the multiverse landscape as an asset, not a problem. It means that string theory cannot tell us much about low energy physics so we will have to look for Planck scale effects instead. Such predicted effects may not be known until the non-perturbative side of string theory is understood, and after that it may be a long time before technology allows us to test them. That I am afraid is the nature of the game. We have no automatic right to expect nature to be kind to us and provide an easy test of any theory of quantum gravity. We are suddenly in a position where almost anything we can observe seems to be covered by the standard model + general relativity so it should be no surprise that testing string theory is very difficult. Any other theory of quantum gravity is likely to have the same problem.

The Hodge-minimal Calabi-Yau three-fold

Today, I recommend you this preprint by Herr Volker Braun of Dublin:

The 24-Cell and Calabi-Yau Threefolds with Hodge Numbers (1,1)

He constructs the "simplest" six-dimensional Calabi-Yau manifold we know.



Click to zoom in.

This diagram shows all the known Calabi-Yau spaces with small Hodge numbers, h^{1,1}+h^{1,2} < 25. The colors indicate how those spaces were constructed. Note that both of these numbers have to be positive. The world's catalog of known Calabi-Yau spaces indicates that h^{1,1}+h^{1,2} < 503 for all Calabi-Yau shapes.




The left-right symmetry of the graph above is nothing else than the mirror symmetry: it exchanges h^{1,1} and h^{1,2} which means that it preserves their sum (y coordinate on the graph) but changes the sign of their difference (x coordinate).

The new entries, showed as purple disks or pieces of disks on my version of the graph above, were constructed by Braun as free quotients of the 24-cell hypersurface; this hypersurface is a "Platonic 24-hedron" in 4 spatial dimensions, analogous to the regular Platonic polyhedra in 3 dimensions. (There are six such polytopes in 4 dimensions.) Its boundary is composed out of 24 mundane octahedra.



The 24-cell polytope. Click to see Wikipedia.

If you look, the minimum entry with the values h^{1,1} = h^{1,2} = 1 was missing so far. Now the hole is filled. Note that the anthropic people wouldn't be interested in such manifolds because they're too constrained; there are not too many cycles that may carry a large number of fluxes. The misanthropic people such as myself think that these "minimal" surfaces are the most important ones - and arguably the most relevant ones physically and cosmologically - because they are very constrained. ;-)



The singer, Jonathan Mann, wants to understand string theory and maths. He wants to hang up with Edward Witten, too. :-) Thanks to Sarah Kavassalis.

LIGO: no waves seen so far

The world's 700 best LIGO scientists ;-) have gathered and published new upper bounds:

Search for gravitational waves from binary black hole inspiral, merger and ringdown (PDF)

No gravitational waves have been seen so far. However, this particular analysis has de facto looked at pairs of black holes only - with masses of 25-100 solar masses - and moreover, they could only find nearly spinless binary stars which are pretty unlikely, too.




You bet that gravitational waves exist - after all, they have been observed indirectly through frequency changes of a pulsar that won the 1993 physics Nobel prize - but that doesn't mean that they're easy to be found directly.

The same comments apply to SUSY and many other things.

People often misunderstand this point - that there is no reason whatsoever why the technical abilities of the experimenters should be synchronized with the theoretical advances. They're surely not synchronized. And throughout the history of physics, they were rarely synchronized.

In many cases, theory is well ahead of the experiments.

In particular, if you want to study effects that are experimentally located just an order of magnitude beyond what has been seen so far, you often need "just a slightly better theorist" who is usually not paid too much more money than his colleague who only deals with easily accessible physical phenomena (but maybe he should be paid much more, in order to erase a part of the discrepancy). However, if you want to access the related phenomena experimentally, you need to increase the spending by an order of magnitude - and sometimes several of them.

In other cases, it may happen that the experiment is years ahead of the theory.

When experimenters were collecting lots of data about the hadrons and their interactions in the 1960s, the theorists had no clue what was going on and why the zoo of the new particles was so rich and messy. Of course, it took just a decade for them to figure out what was going on - QCD - but in more distant chapters of the history of science, you could find eras when theorists had misunderstood the observations for centuries or, if you count ape theorists, millions of years. ;-)

The asynchronism is quite inevitable in science. That's one of the key differences between science and, for example, bread baking. Impatience is not enough to falsify a hypothesis. And the opposite kind of impatience is not enough to understand confusing observed phenomena.

Via Cosmic Variance

The enigmatic cosmological constant

The cosmological constant remains one of the most mysterious players in the current picture of the world.



A building of the Faculty of Natural Sciences of the Charles University in Albertov. In those buildings, where the Velvet Revolution began on November 17th, 1989, Einstein spent a few years but he (and Mileva) didn't like Prague much. Just to be sure, the place had been called Albertov well before Einstein came there: it's named after Prof Eduard Albert MD (1841-1900), a Czech surgeon and poet.

In 1915, after a decade of intellectual self-torture in Prague and elsewhere, Einstein managed to write down the final form of Einstein's equations:



They're pretty. Please imagine that there is a minus sign in front of "8.pi". The convention above is bad.

When I was 15, I would write them about 50 times in my notebooks, in beautiful fonts. ;-) Both sides describe 4 x 5 / 2 x 1 = 10 functions of space and time - a symmetric tensor field. The left-hand side is the "Einstein tensor", describing some information about the curvature of the spacetime. (The term "R_{mu nu}" itself is called the Ricci tensor.) The right-hand side is proportional to the stress-energy tensor "T_{mu nu}". It encodes the density and flux of mass/energy and momentum - which are the sources of the spacetime curvature.




Einstein quickly realized that there was a price to pay for the dynamically curving spacetime: it wasn't able to sit at rest. Instead, the total size of the Universe - or the typical distance between two galaxies - would behave just like the height of a free apple according to Newton's equations. It can fly up and decelerate; or it can fly down and accelerate. But it can't sit in the middle of the room.

For Einstein, this was unacceptable. Much like everyone else in the (de-Christianized) physics community, he was convinced that the Universe has always existed. It had to be static, he thought. (He could have predicted the expansion of the Universe but he didn't. It had to wait for experimenters such as Edwin Hubble. We will mention this point later.)

In 1917, in order to make the Universe static, he added the term

+ Lambda g_{mu nu}

to the left hand side of his equations. The value of the positive cosmological constant "Lambda" he needed for his static Universe - whose geometry is "S^3 x R" (three-sphere times time) - was

Lambda = 4.pi.G.rho_matter

where "rho_{matter}" was the average mass density of the Universe as envisioned by Einstein. The negative value of the pressure would become more important than the positive energy density, and it would prevent the Universe from collapsing, keeping the curvature radius of the 3-sphere equal to "1/sqrt(Lambda)". (The fixed size would be unstable, much like a pencil standing on its tip, but I won't discuss these extra pathologies of Einstein's "solution" in any detail.)

This value of "Lambda" had the right sign and was actually comparable to the currently believed value of the cosmological constant, as I will clarify below. It's either rather accurate or more accurate, depending on what you substitute for "rho_{matter}". Our Universe is not Einstein's static Universe, so we can't measure the right "rho_{matter}" to substitute to these wrong equations ;-) or more precisely right equations with wrong assumptions about the parameters (driven by desired solutions).

You may also move the cosmological constant term to the right-hand side of Einstein's equations which would become

-8.pi.G.(T_{mu nu} + Lambda/8.pi.G g_{mu nu}) =
= -8.pi.G.(T_{mu nu} + 2.rho_matter.g_{mu nu})

Note that in this way of looking at Einstein's equations with the cosmological constant, the cosmological constant is nothing else than a correction to the stress-energy tensor. This correction is proportional to the metric tensor. A positive cosmological constant is nothing else than an addition of a positive energy density and a negative pressure, "p = -rho".

For Einstein's universe to be static, the required "rho" is actually equal to "2.rho_{matter}" where "rho_{matter}" is the average density of matter (assumed to be approximately dust) in the static Universe. Note that if Einstein had known dark matter and visible matter, and if we neglected that they're not quite dust, "rho_{matter}" would be 4+23=27% of the critical density, and this times two is equal to the 54% of the critical density. That would be needed for our Universe to be static.

Because the actual value of the energy density stored in the cosmological constant is about 73% of the critical density which is more than the figure 54% mentioned above, our Universe is actually accelerating its expansion. But you see that the difference between 54% and 73% is not too high. In fact, it's not a long time ago when the acceleration was zero - when the Universe was gradually switching from decelerating expansion to accelerating expansion.

But in that moment, the Universe wasn't static because it still had a positive value of the "velocity" of the expansion. Just the acceleration - another derivative of the velocity - was zero. If you wonder when was the moment when the acceleration was zero, it was approximately six days before God created the Sun and the Earth, about 4.7 billion years ago. ;-)

I ask the Christian readers not to get carried away. It's a complete coincidence - believe me more than the Bible even though it may be hard :-) - and I admit that the six-day accuracy was a little bit exaggerated. The error margin of the figure 4.7 billion years is below 10 percent, however.

Blunder

Of course, when the expansion of the Universe was found by Hubble in the late 1920s, Einstein was upset that he had failed to predict it. If he had predicted it, he could have become more famous than Isaac Newton if not Juan Maldacena. ;-)

That's why Einstein swiftly identified the addition of the cosmological constant term as the greatest blunder of his life. Of course, this was far from a great blunder. In fact, we currently know that the term is there. The greatest blunder of Einstein's life was that he didn't give a damn about quantum mechanics in particular and empirically based science in general in the last 30 years of his life.

Let's look at the reasoning that led Einstein to think that the addition of the term was the greatest blunder. Of course, Hubble had showed that the term wasn't needed because the Universe was expanding, exactly the possibility that Einstein wanted to avoid rather than to predict. But Einstein surely had an a posteriori theoretical reason to think that the term was bad, hadn't he?

Well, the term was "ugly", he thought. It was spoiling the beautiful simplicity of the original Einstein's equations, Einstein would say.

However, we must be extremely careful about such subjective emotional appraisals of the beauty. They may easily be wrong. The sense of beauty is only a good guide for you if it is perfectly correlated with Nature's own taste. Even Einstein has failed to achieve this perfection correlation at many points of his career.

Do we have a more scientific reason to trust Einstein's equations, instead of saying that they're "pretty"? The "counting of the number of terms on the paper" is surely an obsolete criterion for the beauty, especially because the maximally supersymmetric supergravity has many terms, despite being the prettiest theory in the class. So why would we rationally think that Einstein's equations are "prettier" than similar equations in which we would add e.g. squared curvature terms, among others?

Well, we have understood the reason at least since the 1970s - when the ideas of the renormalization group in particular and the organization of the laws of Nature according to the scale in general became a key pillar of the physics lore. The actual reason why the "squared curvature" and even more complicated terms are "bad" is that these terms only become important at short distances. Each factor of a curvature in each term of such equations is approximately adding a factor of "1/squared_curvature_radius". So to protect the right dimension of the terms, it must be multiplied by a coefficient that goes like "length^2".

What is the "length"? Well, it's some special length scale where the behavior of physics changes - and some new terms become important or negligible, depending on the direction where you go in the length scale. The general experience in particle physics indicates that all such scales "length" are microscopic: the size of the atom, proton, electron. And the Planck length is the shortest one.

So at all distances much longer than this macroscopic "length", all the higher-derivative terms - such as the powers of the Ricci tensor - may be neglected. That's really why Einstein's equations, without those extra terms, are a good approximation for long-distance physics. That's why we shouldn't add the "ugly terms".

What about the cosmological constant term?

Well, it actually has fewer derivatives than the curvature tensor: it is even more important at long distances than the curvature tensor in the original Einstein's equations! So we can't neglect it. According to the modern replacement for the "beauty criterion", you can't eliminate it. Einstein's decision to call the cosmological term "ugly" was an example of his flawed sense of beauty.

Quantum physics

And indeed, as we have known from 1998 or so, the cosmological constant is positive because the expansion of the Universe is actually accelerating (it was a big surprise). In fact, it's bigger than what would be needed for the acceleration of the Universe to vanish - what would be needed for Einstein's static Universe. That's why the expansion of the Universe is accelerating. The greater positive cosmological constant you add, the more capable it will be to accelerate the expansion.

(The term "dark energy" is sometimes used instead of "cosmological constant". Dark energy is whatever drives the accelerating expansion and the nature of "dark energy" is deliberately vague. However, accurate observations indicate that "dark energy" has exactly the same properties as a positive cosmological constant, so you may pretty much identify the two terms.)

The energy density carried by the cosmological constant is about 3 times larger than the energy density carried by dark matter and visible matter combined.

Now, you have to realize that the cosmological constant is the energy density of the vacuum. Use the convention in which the cosmological constant term is moved to the right hand side of Einstein's equations. And define the tensor "T_{mu nu}" in such a way that it vanishes in the vacuum. But there's still an extra term added to "T_{mu nu}" which is, therefore, the stress-energy tensor in/of the vacuum.

Can our theories explain that this energy density of the vacuum is nonzero? Well, they can. Too well, in fact. ;-) They explain it so "well" that their predictions are wrong by 60-123 orders of magnitude. :-)

Needless to say, the value of the cosmological constant can't be calculated from "anything" in a classical theory. You need to assume a value and any value is equally legitimate.

In quantum field theory (at least a non-supersymmetric one), you may decide that the classical value of "Lambda" inserted to the equations is zero. But even if the classical value is zero, the total value of the cosmological constant is not zero.

As you should know, quantum field theory produces quantum effects - temporary episodes in which particle-antiparticle pairs emerge from the vacuum and disappear shortly afterwards. These quantum effects modify the masses and energies of all objects (aside from other properties). They change the mass of the Higgs (that's why there's the hierarchy problem) and everything else; they move energy levels in the atoms (by the Lamb shift and many other shifts), and many other things.

They also change the energy density of the vacuum. In particular, if you consider Feynman diagrams without any external lines, they determine the quantum mechanics' contributions to the vacuum energy density. Because of the Lorentz symmetry of the original theory, this quantum-generated energy density is automatically promoted to a stress-energy tensor that has to be proportional to the metric tensor - the only invariant tensor with two indices - so the pressure is always "p=-rho", just like for the cosmological constant.

The simplest diagrams without external lines are simple loops (circles) with a particle running in it. They contribute to the vacuum energy density by something proportional to

+-mass⁴

where "mass" is the rest mass of the corresponding particle species. The bosons contribute positively; the fermions contribute negatively.

The observed value of the cosmological constant, if expressed as the energy density, is approximately equal to

mass_neutrino⁴,

i.e. the fourth power of the lightest massive particle we know, a neutrino. This relationship is only approximate - as far as I know. It may be a coincidence but it doesn't have to be a coincidence. (In the "c=hbar=1" units I use, the energy density is energy per cubic distance but the distance is inverse energy, so the units are "energy^4" or "energy^d" in "d" spacetime dimensions.)

To get the finite number above, we may have to choose a regularization scheme, and it seems helpful here to assume dimensional regularization. (But the final result is not too compatible with the observations, anyway, so it's questionable whether the method is really helpful. But we will continue to assume that this basic calculation is valid.)

So if the neutrinos were the only particles that would contribute their quantum loops to the cosmological constant, you would get approximately the right vacuum energy density (with a wrong sign because neutrinos, being fermions, contribute a negative amount to the energy density).

However, there are many particle species that are heavier than the neutrinos. In particular, the top quark is approximately 10^{15} times heavier than the lightest neutrino (or the smallest neutrino mass difference; we can't quite measure the absolute neutrino masses today). Because it's the fourth power of the mass that contributes to the vacuum energy density, the top quark loop contributes a negative term that is about 60 orders of magnitude too large.

And then you have all the conceivable contributions to the cosmological constant from the "intermediate" particles between the neutrinos (which are OK) and top quarks (which are 60 orders of magnitude too high). Every effect you may imagine - including confinement, Higgs mechanism, and other things - modifies the value of the cosmological constant.

For the Higgs field, for example, it's important to distinguish the potential energy at the local maximum and the minimum. We live at the minimum but the cosmological constant would be vastly (60 orders of magnitude) higher at the local maximum. And it's just the Higgs field.

And as simple particles as the top quark or the Higgs boson give you contributions that are 60 orders of magnitude too high. In fact, the top quark is almost certainly not the heaviest particle in the world. Particles worth the brand "particle" may exist up to the Planck scale which is 15 orders of magnitude heavier than the top quark. (Particles heavier than the Planck scale are black hole microstates.) Clearly, if you include the heaviest, near-Planckian particle species (e.g. the new particles predicted by grand unified theories), you will get contributions to the cosmological constant that are about 120 orders of magnitude too high.

In fact, the observed cosmological constant is equal to "10^{-123}" in the Planck units - a very unnatural pure number.

How is it possible that the sum of all the effects and loops of particles of diverse masses ends up being so tiny, comparable to the contribution of the lightest neutrino which is ludicrously lighter than the Planck scale?

Supersymmetry

You may have noticed that the contributions of the bosons are positive while the contributions of the fermions are negative. Can you cancel them?

Well, a problem is that the masses of the bosons are some random numbers, and the masses of the fermions are other random numbers. There's no reason for them to cancel exactly or almost exactly. 3-6+9-15+48-98 has a chance to be zero but it's probably not zero.

Things change if you have unbroken supersymmetry. If supersymmetry is unbroken, each boson has a fermionic partner and vice versa. The masses of both partners exactly match. When it's so, it follows that the total quantum correction to the cosmological constant vanishes. (You may still need to be careful about a "classical" term that could have been nonzero to start with. In my opinion, it's rather reasonable to expect or require that the classical term has to be zero in realistic vacua.)

However, supersymmetry in the real world has to be broken. The mass differences between the pairs of superpartners are at least as large as the top quark mass - at least some of them. It follows that you still get an uncanceled contribution that is comparable to the contribution of the top quark we chose as a benchmark. And it's 60 orders of magnitude too high.

At least, you get rid of the larger contributions that could arise from the near-Planckian heavy particles and that would be 120 orders of magnitude too high. With broken supersymmetry, the discrepancy between the measured and "estimated" cosmological constant gets reduced from 120 orders of magnitude to 60 orders of magnitude.

It looks like progress - we have already done 1/2 of the job. While it's true, there is also some sense in which the - smaller - discrepancy obtained in the supersymmetric context (supergravity, in fact, because we want to include gravity as well) is much more "real" than in the non-supersymmetric context.

I still believe that all the physicists are confusing themselves with the "estimates". Particular theories or string vacua - perhaps a bit different than the popular ones; perhaps the same ones with a more correct calculation of the vacuum energy density - could actually lead to a more accurate cancellation than what is suggested by the estimates. The discrepancy of the 60 orders of magnitude could be fake.

There have been many episodes in the history of physics in which people made a very sloppy estimate and they (thought that they) ruled out a correct theory because of this estimate. For example, people would believe that the gauge anomalies in all chiral vacua of string theory (with Yang-Mills fields) had to be nonzero. They believed so until 1984 when Green and Schwarz showed that the complete calculation actually produces an answer equal to zero. That sparked the first superstring revolution.

I find the "generic" estimates of the cosmological constant to be equally sloppy to the arguments in the early 1980s that the gauge anomalies in string theory had to be nonzero. There can also be a contribution from a counterpart of the Green-Schwarz mechanism. The total could be 10^{-120} in Planck units. And much like in the Green-Schwarz anomaly cancellation, there may exist more "profound" and "simpler" ways to show that the cosmological constant cancels much more accurately than people expect.

A big difference is that in the case of the type I string theory's gauge and gravitational (and mixed) anomalies, we know that they cancel. We know the Green-Schwarz mechanism and other things. The "similar" scenario for the cosmological constant remains a speculation or a wishful thinking, if you wish. So we can't say that science has showed that the situations are analogous. I still think that this wishful thinking is relatively likely to be true.

Landscape of possibilities

In quantum field theory, you may adjust the classical value of the cosmological constant to any number you want. So you may adjust it so that when the quantum corrections are added, you get exactly the desired value.

String theory is much more rigid and predictive. You can't adjust anything. Much like quantum field theory, string theory allows you to calculate the quantum corrections to the cosmological constant - and all other low-energy parameters - but unlike quantum field theory, it also allows you to calculate the classical pieces, too. There's no dimensionless continuous static parameter in string theory that would be waiting for your adjustments.

There are only discrete choices you can make - the topology of a Calabi-Yau manifolds; integers encoding the number of branes wrapped on various cycles and magnetic fluxes; and some related discrete data.

If you believe that there's no Green-Schwarz-like miracle waiting for us, then you must probably agree with the anthropic people who say that the most likely prediction of the cosmological constant by a single semi-realistic vacuum is comparable to the Planck scale, about 120 orders of magnitude too high.

If you believe so, then you face a potential contradiction which is "very likely" if the theory produces a small number of candidate vacua. In such a situation, the existence of more than 10^{120} solutions that string theory offers is saving your life. It's saving you from the discrepancy. The large number of solutions de facto allows you to do the same thing that you could do in quantum field theory. In quantum field theory, you could continuously adjust the cosmological constant (and all other parameters). In string theory, you're not allowed to adjust it continuously but the number of solutions is high enough so that you may adjust it "discretely" and "almost continuously".

I still think that one should try not to rely on such mechanisms that are meant to be able to cure any inconsistency by a universal metaphysical trick. (This nearly religious "cure for everything" is common among low-level physicists such as the loop quantum gravitists who think that they can cure "all UV problems" by their spin network aether, without doing any special work. That's too bad because in a consistent framework with a QFT limit, one can prove that e.g. gauge anomalies cannot be cured. So any framework that allows you to argue that even theories with gauge anomalies can be defined is inevitably internally inconsistent.)

There seems to be a disagreement between the observed and estimated value of the cosmological constant so we should work hard to improve our estimates. We should find previously neglected terms and mechanisms that, when accounted for, make our estimates more compatible with the observations.

The opposite, anthropic attitude could have been used to "solve" any puzzle in the history of science. But in every single puzzle we understand (and consider to be solved) today, we have learned that the anthropic solution was wrong. The neutron is "anomalously" long-lived but we don't need a landscape to explain that (even though the longevity could be argued to be important for life); we can calculate the lifetime and it's the "small phase space" of the decay products that makes the neutron more stable than expected.

And I can tell you thousands of such examples of puzzling features of Nature that could have been explained by the anthropic hand-waving but the right explanation turned out to be different and more robust.

Supergravity seems to be rigid when it comes to the calculation of the vacuum energy density and those 60 orders of magnitude of disagreement seem to be real today. But we may be mistreating the vacuum graphs in supergravity. We may be missing the counterpart of the Green-Schwarz anomalous transformation laws. We may be missing some purely quantum effects that only (or primarily) affect the tree-level graphs. We may be missing alternative ways to prove an almost exact cancellation.

The cosmological constant may be linked to

mass_neutrino⁴

as I have suggested above and there may exist a good reason why. For example, the value of Lambda could be running in a bizarre way and the running could stop below the neutrino mass (the mass of the lightest massive particle), guaranteeing that the value of "Lambda" stays comparable to the fourth power of the neutrino mass. (In a similar way, the fine-structure constant doesn't run beneath the mass of the lightest charged particle, the electron.) A value of "Lambda" that is vastly higher than "mass^4" could make the effective (gravitating) field theory defined for the "mass" scale inconsistent for a currently unknown reason.

And because 60 is one half of 120, the observed cosmological constant may also be related to the ratio

m_Planck⁸ / m_Top⁴

where I chose the top quark mass - our previous benchmark - to represent the electroweak scale or the superpartner SUSY-breaking scale which is arguably not far from the electroweak scale. I have about 5 different scenarios how some of these formulae could be shown correct on a sunny day in the future. Needless to say, I realize that none of those scenarios is fully convincing at this point. But people should keep on trying, anyway.

And that's the memo.