Imagine that the Universe is not expanding

Wetterich's cosmon claimed to be an alternative to the Big Bang singularity, inflation, and the recent apparent expansion



Image: NASA/JPL–Caltech...

Most papers trying to replace the usual cosmological concepts such as dark matter and dark energy by something entirely different may be shown to be wrong within minutes. As I learned from a Czech server called osel.cz ("osel" is a horse-like animal known as an ass: I don't know of a shorter way to explain that it's not the other ass), a rather achieved cosmologist Christof Wetterich posted an unusual clever yet apparently equally provoking preprint to the astro-ph arXiv at the beginning of this month:

Variable gravity Universe

Be ready for a wild ride: the proposed model claims to explain all the known observations, eliminate the Big Bang singularity, account for the patterns we attribute to inflation, the radiation-dominated era, and the matter-dominated era. And Wetterich also wants to boast that his construction "produces" the arrow of time – as if cosmology were needed for that (but that didn't make me stop reading). A single scalar field – the cosmon – may do all these wonderful things, the gospel say.

It's weird if not exciting, isn't it? ;-)




The idea of a time-dependent Newton's constant (variable strength of gravity) goes back to Jordan and Dirac. The latter man tried to use it to explain the existence of vast and tiny parameters in the Universe. The explanation doesn't really work, especially because dimensionless constants of physics are measured to be really constant.




This is a field – a minefield, to be more precise – that is full of failed and dead bodies. You don't want to go through all these failures because there are too many. This Wetterich guy wants to avoid the basic traps by assuming that the Planck mass is changing with time but the masses of all objects are changing at the same rate so the ratios remain fixed.

Such a claim is already a bit provoking to me because one always has the freedom to define the masses in the Planck units so with the prescription described in the previous paragraph, we may say that nothing is changing in the Planck units. Well, on page 4, he's a bit more specific about the role of his cosmon field \(\chi\) ("chi"). The effective action is\[

\Gamma = \int d^4 x \sqrt{g} \left\{
-\!\frac 12\! F(\chi) R + \frac 12 \! K(\chi) \partial^\mu\chi\partial_\mu\chi +V(\chi)
\right\}

\] To be authentic, I retyped the expression as he wrote it although the sign of the determinant of \(g\) seems problematic and so do other things. He considers two basic models, (A) and (B), which make the following fixed choices:\[

\eq{
(A):& F(\chi) = \chi^2, \,\,V(\chi)=\mu^2\chi^2\\
(B):& F(\chi) = \chi^2+m^2, \,\,V(\chi) = \bar\lambda_c.
}

\] The coefficients in the kinetic terms \(K(\chi)\) are allowed to vary throughout the paper to adjust the models.

Well, you see that Newton's constant depends on the cosmon in some way. The cosmon has some field-dependent kinetic term and some potential. The first thing that comes to my mind is that one could rescale the metric and nonlinearly redefine the cosmon field so that he would effectively eliminate up to two of the three functions above. So unless there are some global constraints or inequalities, wouldn't it become just an ordinary GR coupled to an ordinary scalar field with some potential?

I am confused by this basic point but it's probably because I have only been reading the paper for a few minutes so far. If and when I spend an hour with it – or if a more experienced reader offers his or her thoughts and observations – chances are that all the uncertainty will go away and the ambitious claims by Wetterich will turn out to be either strictly viable or demonstrably wrong.

Which way it is? ;-) I am unlikely to learn the answer tonight because I want to watch the second soccer match Maribor [SI] vs FC Viktoria Pilsen [CZ]. "Our" Pilsner team is likely to win in the aggregate match after the 3-to-1 victory at home last week which would mean that it will earn over $10 million and penetrate to the standard group of the UEFA Champion League for the second time.

Off-topic: graphene \(\heartsuit\) metals and makes them 100+ times stronger. Via Bahamas

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Boddy, Carroll: trying to save physics by sacrificing the Universe

...but no saviors are needed: their irrational Boltzmann Brain alarmism misunderstands what a hypothesis includes...

External discussion: Jacques Distler will write a few critical sentences about the Boddy-Carroll paper tomorrow. I completely agree with Distler – as he will reproduce some ideas from the text below (and others). It's not possible for hypothetical future events to influence the present; and there is no particular framework of probability theory into which sentences of the kind "we're likely Boltzmann Brains" may be justifiably embedded. Each of these two bugs is enough to identify the paper as crap and the authors as nuts.

On his blog, the Preposterous Universe, Sean Carroll promoted a paper by himself and Kimberly Boddy:

The Higgs Boson vs. Boltzmann Brains (his blog)

---

Can the Higgs Boson Save Us From the Menace of the Boltzmann Brains? (arXiv)

Last week, I was giving a popular physics talk in a planetarium in Northern Bohemia. It clearly turned out to be too complicated for the bulk of the audience (philosophers are sometimes annoying but a group of philosophers is more ready to listen to some almost real physics than a selected 1/1,000 fraction of the general public in a medium-size town!) but we've had some fun, anyway.

One of the longest discussions was dedicated to the phase transition that may destroy the Universe; the Higgs field instability is the most ordinary example of such a scenario. In a "seed of doom", the Higgs field (or, more generally, another usually scalar field) may penetrate to a new, lower energy state that is incompatible with life. This "seed of the new lifeless Universe" starts to expand almost by the speed of light and devour everything. You won't feel the pain because your nerves are slower than the inflating nothingness.



I wanted to calm the public. The Universe won't collapse anytime soon. At the end, however, I just couldn't tell them anything else than the truth. And the truth is that empirically, we only know that the approximate lifetime of the Universe after which the "seed of doom" starts to grow somewhere is unlikely to be much shorter than the current age of the Universe, 13.8 billion years. It may be comparable, it may be a bit shorter but it may also be much longer and infinite. If it is finite, it sounds sort of unlikely that it would be comparable to the current age of the Universe which means that it's probably much longer. Don't worry. But there's really no "solid" argument that would prove that the Universe won't start to disappear in the next 1 billion years.

You may find the "Higgs decay" scenario frightening. The Universe may die long before the Sun runs out of fuel in 7.5 billion AD and goes red giant. What a waste! It may be tomorrow. We're not able to present any solid enough proof that it won't happen. However, Boddy and Carroll are scared of something else: that the Universe won't die soon. So they claim that the unstable Higgs field is our savior from the genuine threat: the Boltzmann Brains. This fear is utterly irrational because the Boltzmann Brains aren't endangering us. They aren't endangering physics, either. The won't ever appear on the Earth (much like Category 6 hurricanes which are nothing else than another proof that Al Gore is a liar without any scruples). There's no reason to sacrifice the world (or billions of dollars).

Similar explanations have repeatedly occurred on this blog but here we go again.




Boddy and Carroll – and others – are scared of a competing theory that may "explain" all the observations we have had. It's a theory that doesn't require the usual prehistory that has led to our life – including the Big Bang, the formation of the galaxies, the Solar System, and the lengthy path of evolution, not to mention many less fundamental parts of our life story.

Instead, one may say that there will be infinitely many opportunities in our soon-to-be-almost-empty de Sitter space where brains locally indistinguishable from ours may be created out of pure thermal fluctuations. Carroll and others believe that because the number of such "freak brains" is infinite (when integrated over the whole infinite future of the Universe), they are predicted to be more likely to be "us" than anything else (i.e. the well-behaved brains that have evolved from the Big Bang and evolution).

But this just ain't the case.




If there is an infinite number of something, this infinite number doesn't mean that it "has to be us". For example, \(\pi\) has infinitely many digits in its decimal form but that doesn't mean that you are any of them. The probability that you are just a digit of \(\pi\) is zero which means that not even the infinite number of these digits may force you to become a digit. Even if the probability that you were a digit of \(\pi\) were nonzero, it may still decrease with the location in \(\pi\) so quickly that the overall probability that you are a digit will be tiny.

Let me hope that the previous paragraph sounds trivial to you but be sure that Sean Carroll and others don't understand this simple claim. They confuse the "number of some objects" with "their probability" which are completely different quantities (and in a general situation, completely uncorrelated quantities) because the probability that "you are something" is in no way uniform for all these "somethings".

That's one way to describe the fundamental mistakes in his reasoning.

Another, closely related way to describe the fallacy is to point out that a hypothesis in science is something that explains our observations. To do so, it must not only make assumptions about "how the world works" but also about "where and when we are located or living" i.e. essentially "who we are" (I mean primarily who we are relatively to the rest of the world, not who we are internally and structurally).

Different assumptions about "where we are" and "when we are living" obviously lead to different predictions of what we should be seeing (the world looks different if you manage to live inside the Sun, inside the Moon, or million of light years from the nearest galaxy). So these assumptions distinguish different scientific hypotheses and they may be tested and falsified separately from each other. As a hardcore Marxist, Sean Carroll clearly wants to confirm or falsify all these different hypotheses simultaneously, as a collective, but science just can't work like that.

This simple point has been discussed using many different words on this blog. Several years ago, Hartle and Srednicki introduced the catchy term "xerographic distribution" to emphasize that the assumptions about our location within the spacetime incorporated in a theory is a part of the hypothesis that is being tested i.e. validated or falsified.

Imagine that our Universe will converge to an empty de Sitter space – everything indicates it is so (the world is already dominated by the cosmological constant and each 11 billion years of the cosmic time or so, the linear distances will double which means that the particle-based mass density of the Universe will decrease by a factor of 8 or so). This de Sitter space has a certain Poincaré recurrence time comparable to \(\exp(S_{dS})R_{dS}\) after which it has to repeat up to arbitrarily small errors and people have said many things about the question whether the repetitions should be viewed as independent episodes (the ER-EPR correspondence is surely another conceptual reason to think that these repeated stories should be thought of as being "in the same region of the spacetime" i.e. not independent).

But I don't really think that such questions about the identification influence how science chooses the valid hypotheses.

Fine. The Universe will continue as a nearly empty de Sitter space which is still filled with the thermal radiation at the temperature which is tiny (the typical thermal wavelength is comparable to the curvature radius of the de Sitter space) but nonzero. And because it's nonzero, every state of matter has a nonzero probability and when it's given infinitely many opportunities to be realized, it will be realized. In particular, freaky Boltzmann Brains that perceive the same things as we do even though they haven't evolved through the nice scientific big-bang-evolution path are guaranteed to appear at some very distant moment in the future.

But that doesn't mean that our best theories (assuming that the de Sitter space won't collapse) actually predict that we are the Boltzmann Brains. Even though the Boltzmann Brains will be repeated infinitely many times, science can say – and actually does say – that we're not belonging to their transtemporal society. Again, the number of objects is a different thing than the probability that you are one of these things, stupid!

The usual physical theories with the Big Bang and an infinitely long-lived empty de Sitter space are compatible with our having evolved by the "almost straightforward history" involving the usual events after the Big Bang and evolution, among others, without some exponentially unlikely events. Why? Because these assumptions are a part of the standard physical theory combining cosmology and particle physics! Like most good theories in science, the standard cosmology says that life has evolved without a dependence on some super-unlikely fluctuations or events. As a good scientific theory, our Big Bang cosmology explicitly says that we are not Boltzmann Brains. This claim isn't incompatible with any other assumption of the theory just like the claim that you are not a digit of \(\pi\) (even though there are infinitely many such digits) is not incompatible with the biology of mammals.

So the standard cosmological theory is a different theory than any theory that claims that we are Boltzmann Brains. They are totally incompatible with each other because the standard cosmological theory says that everything we see is a result of a nearly inevitable evolution that was picking the most likely outcomes almost all the time – and that depended on no "super-unlikely" events or fluctuations.

Different hypotheses may be compared with each other. You may compare the standard cosmological theory with the Boltzmann Brain hypothesis of any kind. Needless to say, the standard cosmological theory wins because the Boltzmann Brain hypothesis predicts that whenever you look a bit further than before, you should almost certainly see a disorder that will leak the fact that your brain and its vicinity is just a giant thermal fluctuation. (By the Boltzmann Brain hypothesis, I mean the hypothesis that our brains/civilization etc. appeared from a thermal fluctuation that only began to resemble the usual evolution at times much shorter than the usual age of the Universe or in a region much smaller than the usual size of the visible Universe but is truly thermal elsewhere; if you include large fluctuations that have evolved "ordinarily" in the whole visible Universe for 13.8 billion years, then such a "generalized Boltzmann Brain" hypothesis isn't falsified and may in fact be a good description or philosophical incarnation of our observations.)

The standard cosmological theory predicts that the next galaxy you are going to observe with your next-generation telescopes will be similar to those you already know. And of course that the standard cosmological theory's predictions are pretty much right while the totally different predictions of the Boltzmann Brain hypothesis are falsified.

A scientific hypothesis working with the assumption that we are Boltzmann Brains is empirically falsified – by totally elementary observations, in fact. Simple observations (combined with simple logic) are the easiest ways to falsify a hypothesis in science. But it shouldn't be shocking that one needs at least some empirical data to falsify a hypothesis. That's how science has always worked. Science chooses the right and wrong hypotheses by looking at the empirical data. There's no reason to be ashamed of this fact. It is true and it has to be true, otherwise it wouldn't be science.

So we don't need to assume that our Universe will die in a few billion years if we want to protect our physical theories from the Boltzmann Brains' being us. The empirical evidence is overwhelming that we are not Boltzmann Brains. Because we know that we're not Boltzmann Brains, we may immediately eliminate every hypothesis or its part that would force us to believe that we are Boltzmann Brains. It's that simple. That's why we just don't have to be afraid of "being" Boltzmann Brains or postulate some "liberating doomsday" to protect the good feelings about our identity against some crazy ideas.

At the end, I really think that Carroll's totally wrong reasoning is tightly linked to an ideology that blinds his eyes. As a hardcore leftist (or at least a person pretending to be one in order to improve his social status in a hard left-wing environment), he believes in various forms of egalitarianism. Every "object" has the same probability. Also, much like climate "scientists" (and I am only talking about "scientists" in the quotation marks here, not about genuine scientists), he wants to "collectively test" (and "collectively trust") models (e.g. climate models) whether they are right. But none of these things is scientifically true. Objects, people, and their categories are created unequal, probabilities aren't proportional to the numbers of objects in any reasonable sense, and hypotheses must be validated individually and not "in collectives" because at most one of the inequivalent theories or models may be right at the very end and it's just wrong to clump a right theory with the wrong ones because the very purpose of science is to be disentangling the right ones from the wrong ones.

Let me offer you an analogy that should hopefully clarify why Boddy's and Carroll's way of thinking is totally silly.

Imagine that we discover a stone that looks like a display and it displays one decimal digit every hour. Such a stone looks like a result of Intelligent Design but it doesn't matter whether it's man-made, UFO-made (OK, I meant ET-made), or natural. Assume it's natural but your task is to predict what the object will do. Once people begin to watch the digits and remember them, they record the following sequence:

4,1,5,9,2,6,5,3,5,8,9,7,9,...

It looks like a random sequence of digits. However, someone realizes that they look like digits (starting from the third one) of \(\pi\):\[

\pi\approx 3.1415926535897932384626\dots

\] This person will predict that the next digits will be 3,2,3,8 and the prediction is confirmed. It's great. Note that by now, 17 hours after the records began, people have recorded 17 digits from the stone so far.

But someone will start to claim that there is no reason why the digits should be taken from the beginning of \(\pi\). The same sequence of 17 digits appears roughly once in a sequence of \(10^{17}\) digits of \(\pi\) and because \(\pi\) has infinitely many digits, the same 17-digit sequence is bound to appear infinitely many times somewhere.

In fact, someone else will change the statement and say that they will appear somewhere in\[

e\approx 2.718281828459045235360\dots\qquad\\
\qquad \dots 28747135266249775724709369995\dots

\] or somewhere in its powers \(e^n\) where \(n\) is a nonzero integer. Because there are infinitely many numbers of the form \(e^n\) and just one number \(\pi\), someone else may even claim that it's more likely that the stone emits random digits from a number of the form \(e^n\) and not from \(\pi\).

Needless to say, such a claim is unjustified because there's no reason why the \(e^n\)-based explanation should be "equally likely" as an explanation based on \(\pi\). And indeed, the empirical evidence will keep on accumulating (new digits are coming every hour!) that the \(\pi\)-based explanation is the right one while the other hypotheses are just wrong.

The guy or babe who invented the \(\pi\) theory of the stone used \(\pi\) and not \(e^n\) and he or she did claim that the digits are taken almost from the beginning of \(\pi\), too. He or she isn't "obliged" to consider some faraway sequences in \(\pi\) (or even in other numbers) to be "equally justified" predictions of his or her theory because the theory includes the statement that the digits are taken almost from the beginning. The place in \(\pi\) from which the digits are being taken isn't "obliged" to be "typical" – on the contrary, it's a point of the explanation that it is a very special point, the beginning. So every inequivalent statement is a competing hypothesis and it will finally lose. Too specific theories based on specific enough locations in other numbers will be strictly falsified; theories explicitly or effectively claiming that the digits are random will be "fuzzily" (but increasingly robustly) falsified because they predict that (very/extremely) long \(\pi\)-like patterns are (very/extremely) unlikely. But they're being observed which makes these random explanations increasingly falsified.

In this analogy, Boddy's and Carroll's claim about the "desirable" Higgs decay of the Universe is analogous to the statement that \(e\) is a rational number. If the digits of \(e\) start to get repeated, then the same is true for \(e^n\) as well and the numbers \(e^n\) won't have the sufficient infinite diversity of sequences of digits to match the observed digits emitted by the stone. In this way, the analogous Boddy and Carroll will argue, the \(\pi\) theory is protected against the Boltzmann Brain explanation – the explanation assuming that the digits are being taken from a random faraway place of one of the numbers \(e^n\).

Indeed, academically speaking, the Boltzmann Brains-like \(e^n\) theory of the stone could be falsified in this way: if \(e\) were rational, it just couldn't generate an aperiodic sequence of digits. But what Boddy and Carroll (and others) don't understand is that it is not neccessary for \(e\) to be a rational number if we want to scientifically establish that the digits are actually being taken from \(\pi\). The empirical evidence is enough. And indeed, \(e^n\) for \(n\neq 0\) aren't rational numbers which means that the strategy to disprove the \(e^n\) theory of the stone is hopeless because it depends on propositions that are wrong. And indeed, the evidence from the stone keeps on arriving and confirming the \(\pi\) theory while falsifying any other simple enough hypothesis.

Also, I want to mention that we may know a reason or we may not know any reason why the stone prefers \(\pi\) over \(e^n\). But even if we don't know any such deeper reason, it doesn't mean that the \(\pi\) and \(e^n\) explanations are equally likely. Instead, the empirical data heavily break this symmetry and imply that \(\pi\) is vastly preferred. That observation really means that deeper theories about the inner workings of the stone are either "encouraged" or "totally required" to prefer \(\pi\) over \(e^n\). You may believe that \(\pi\) and \(e^n\) are equally good for the stone but much like any belief in science that has observable consequences, your belief may be proved to be wrong and indeed, it is proved to be wrong in this case, too. There's nothing "holy" or "infallible" about egalitarianism; in fact, it's one of the crappiest ideologies around.

We know that we aren't Boltzmann Brains and we don't need to assume a "doomsday scenario" – a Higgs vacuum decay or any other doomsday scenario one could talk about (the very fact that Boddy and Carroll single out the Higgs vacuum decay is a piece of demagogy or a hint that they're unable to localize the actual reasons that lead to certain conclusions) – to be sure that we aren't Boltzmann Brains because the observations we have already made are enough to be absolutely sure. The state-of-the-art scientific theories claim that we are results of a nearly inevitable evolution involving a very dense and hot Universe after the Big Bang, structure formation, and evolution of species and these scientific theories are explicitly stating that we are not random thermal fluctuations that would have to be super-exponentially unlikely.

Someone may think he has reasons to think that we should be Boltzmann Brains or it should be likely that we are Boltzmann Brains. But "where we are" represent a part of the scientific hypotheses – the xerographic distribution – that needs to be tested much like any other part of a scientific theory. The tests are very easy, have been done long before we became homo sapiens, and the result is that the Boltzmann Brain xerographic distribution is safely falsified. So why do people keep on talking about it? It's as safely falsified a scientific hypothesis as any other falsified scientific hypothesis. In fact, more so. It's one of the key principles of the scientific method that we are gradually ceasing to discuss scientific hypotheses and paradigms that have been falsified.

So Boddies and Carrolls of the world, please stop emitting this crap and attempting to raise the stakes by incorporating ever more irrational and ever more megalomaniac "requirements" concerning a doomsday. No doomsday is necessary for the science we have learned to work.

And that's the memo.

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LIGO: improving sensitivity by squeezed states

Gravitational waves could become visible next year

On Friday, SciTechDaily wrote about an interesting recent article in Nature:

Improvements to LIGO Detector Will Allow Scientists to ‘Listen’ to Black Holes Forming (SciTechDaily, Daily Galaxy)

---

Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light by J. Aasi and 24 co-authors (Nature Photonics: full PDF paper here)

---

LIGO.org press release

LIGO, the Laser Interferometer Gravitational-Wave Observatory, a large L-shaped instrument to detect the gravitational waves, hasn't seen anything yet but it may change soon and dramatically.



The authors of the new Nature paper – the whole LIGO collaboration – is sending special packets of light, the squeezed states, to one of the LIGO detectors and this modification is improving the sensitivity.




Sometimes it sounds like they are claiming that they are circumventing the Heisenberg uncertainty principle but I hope that they're not being completely silly. They're apparently improving a suboptimal technique that has been used so far.




With the upgrade, the facility could become able to observe black holes that are just being born. The gravitational waves could provide us with completely new "eyes" to see many phenomena in the Universe.

LIGO is now being upgraded to Advanced LIGO, scheduled to be operational in 2014. Correct me if I am wrong but I think that the current usage of the squeezed states isn't completely new but what's new is that the squeezed states are being used for the frequency range 150-300 Hz.

Also, my understanding is that this improvement should be ready when Advanced LIGO begins its operations. That's why another article in The Daily Galaxy claims that the direct detection of the gravitational waves is imminent. It sounds pretty exciting.

Just to be sure, state-of-the-art theorists don't have any realistic doubts about the existence of gravitational waves as predicted by GR. It seems impossible for GR to work in all the situations where it has been tested while failing in the case of the gravitational waves. Also, the discovery of a binary pulsar that generated the 1993 Physics Nobel Prize allowed one to verify that the celestial system is losing the same energy each second (the loss is measured from the accelerating frequency of the orbits) that is carried away by the GR-calculable gravitational waves. This consistency check has actually been repeated using independent celestial objects (which have different parameters) so it's almost certainly not a coincidence. We're only waiting for a direct detection of the waves and the applications of these new "eyes".

Hat tip: Bahamas

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Krauss-Dent small C.C. from a Higgs seesaw

This idea is known to most physicists but it's not a full solution to the C.C. problem

Nude Socialist (via Joseph S.) published an article called

Dark energy could be the offspring of the Higgs boson

which mainly discusses a June 2013 preprint by Lawrence Krauss and James Dent,

A Higgs-Saw Mechanism as a Source for Dark Energy.

Funny and not terribly serious. And no, no followups to the paper appeared in the first two months.

The story quotes Frank Wilczek – without even mentioning his remotely related recent paper on Multiversality (which is somewhat more substantial). We learn that Lawrence Krauss was actually "a Higgs sceptic until the very end". What a poetic way to say "a stubborn moron".

At any rate, now Mr Krauss has apparently kindly accepted the belief that there exists a Higgs boson – something he should have learned and understood as an undergrad – so he and James Dent became convinced that they may solve all big problems of physics, too.




The first problem they have "solved" is nothing else than the cosmological constant problem – why is the observed cosmological constant (C.C.) so small in the Planck or other natural units – and they immediately self-confidently sent the solution to PRL, a prestigious journal.




The "solution" is something that every other physicist has thought about: a seesaw mechanism. Numerically, it looks like the C.C. is smaller than the fourth power of the Higgs mass by the same factor by which the fourth power of the Higgs mass is smaller than the fourth power of the Planck or GUT mass, i.e.\[

\rho_{\rm C.C.} \sim \frac{m_{\rm Higgs}^8}{m_{\rm Planck}^4}

\] On the log scale, the Higgs (electroweak) mass scale is in between the tiny mass scale calculated from the dark energy (as the fourth root of the dark energy expressed as an energy density in the \(\hbar=c=1\) units) and the huge Planck scale.

The identity above may be derived – in analogy with the neutrinos – from a pair of fields. If the matrix entries are\[

\pmatrix{ m_{\rm Planck}^2& m_{\rm Higgs}^2\\m_{\rm Higgs}^2 & 0 },

\] i.e. one entry is huge (Planckian) and the off-diagonal ones are intermediate (Higgs-like), then the eigenvalues of this squared mass matrix are of order \(m_{\rm Planck}^2\) and \(m^4_{\rm Planck} / m^2_{\rm Higgs}\), respectively. The latter formula arises because the product of these eigenvalues has to be equal to the determinant of the \(2\times 2\) matrix above which happens to be \(-m_{\rm Higgs}^4\).

Because the sum of the eigenvalues is equal to the trace \(m_{\rm Planck}^2\), one of the eigenvalues has to be close to this huge value, too. Due to the right determinant requirement above, the other eigenvalue has no choice and has to be insanely tiny to compensate the Planckian mass in the product (determinant).

Just calculate the damn eigenvalues of the matrix above if you don't know what I am saying.

At any rate, it's obvious – and has been explicitly said by many people many times – that the observed C.C. looks like one arising from such a very tiny "Higgs companion". That's all nice that we may produce new terms to the C.C. that have about the right value.

But the true difficult task is to show that except for the term we would like to emphasize, all the remaining terms cancel so that they don't spoil this nicely tiny, tuned result. In fact, this trivial point is even quoted in Nude Socialist – and attributed to Frank Wilczek although pretty much everyone else could tell them the same thing.

Needless to say, they don't have any explanation for such a coincidence (in most theories, this coincidence almost certainly doesn't occur) which means that they haven't solved the C.C. problem (in a non-anthropic way). But if the production of the seesaw-like tiny contribution is one of the steps to actually solve the C.C. problem, it's very interesting. I have thought about this possibility for quite some time and found some other possible solutions but I wouldn't be arrogant enough to send this incomplete stuff to the arXiv or even to the PRL. One must have some extra chutzpah for that.

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Detonation of the Sun

A frequent source of links has sent me the coordinates of a page

Explosion of Sun

introducing a paper by Alexander Bolonkin and Joseph Friedlander urging all the physicists to think about the possibility that a malicious regime will send a thermonuclear weapon into the Sun and speed up the reactions inside the Sun – effectively converting all of our beloved star to a giant H-bomb long before our main source of useful energy is expected to go red giant around the year 7.5 billion AD.



This picture contains just a real-world eruption! Via IO9.

In the authors' opinion, physicists and others have a moral duty to either exclude the possibility, or look for security measures that would protect us against such a rogue regime, or prove that such a protection is impossible.

First of all, is such an explosion possible?




I don't think so. Note that the concern isn't much different from the old concern that some fathers of the H-bomb had to think about – namely whether the H-bomb would start to devour the whole atmosphere and the rest of the Earth as it realized that it's a thermonuclear fuel that may be burned.

Why is it similar?




It's similar because the present authors are afraid of the increase of the Sun's temperature from the current 9-17 million Celsius degrees in the Sun core to temperatures that are at least an order of magnitude higher and allow the reactions to be exponentially sped up. Consequently, the present temperature is negligible relatively to the desired one. In that respect, the comparison of real and "desired" temperatures is analogous to the situation on Earth where the atmosphere is also much cooler than the temperature needed to change the atmosphere to thermonuclear fuel. In both cases, the initial temperature may be neglected and approximated by zero.

Moreover, the Sun density is about 1.4 times the maximum density of water so it is surprisingly comparable to the densities encountered on our blue, not green planet, too.

The arguments showing that such a risk isn't there are somewhat subtle – the "proof" that we're safe is in no way trivial from a beginner's viewpoint. But I am confident it may be formulated. It seems to me that the "detonating Sun alarmists", much like the "detonating Earth's atmosphere alarmists", are neglecting various other quantities describing the environment that go beyond the temperature and density.

It's plausible that you may create much higher temperatures in a cubic meter of the Sun – probably only on the surface because it's implausible that any material will be able to penetrate through the solar matter whose temperature starts at 6000 Celsius degrees or so (all conventional materials melt and/or evaporate around that point). But if you create such huge temperatures in a small region, it doesn't imply that they will spread.

It seems clear to me that the rate of cooling of the "detonatingly hot" region will be too high when the size of the region grows. More importantly, you just never obtain a high density in this way. The density of the Sun is what it is, dictated by the overall solar mass and the solar volume, and an extra bomb doesn't change this counting much. Because the density of the bulk of the Sun will remain fixed, the ultimate near-equilibrium temperature of fusion is pretty much dictated by this density, and this temperature is what we observed in the Sun today.

See also my answer Why Jupiter isn't a star, whether Jupiter may be blown up and what it would mean, how to stop or blow apart a star, why asteroids around us don't have relativistic velocities, or many other questions and answers about related dramatically catastrophic cosmic (im)possibilities. ;-)

For these reasons and others, I am not really afraid of a Khamenei who would like to turn the ancient Egyptian God, the Sun, into an unhinged Allah. ;-)

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Relativity bans faster-than-light warp drive

In recent 24 hours, lots of media outlets including

NY Times, The Daily Mail, Russia Today, The PK Nation, Times of India, Bend Bulletin

discuss the NASA research into faster-than-light spaceships based on "warp drive". The idea is being attributed to Mexican fantasist (rather than physicist) Miguel Alcubierre while Dr (???) Harold White is being mentioned as the most active researcher working on this ambitious project.



The proposed idea is simple: reduce the magnitude of the space-like components of the metric tensor in front of the spaceship and increase it behind the spaceship. So the space will look shorter in front of you and the general relativistic causal limit will allow the coordinate speed to be greater than it is in the vacuum. Consequently, you will move from one place to another faster than light.




Needless to say, Einstein's 1905 insights known as the special theory of relativity show that such a superluminal motion is impossible. In a different inertial system, it would look like a motion directed backwards in time. And such an invalidation of the usual chronology would produce closed time-like curves with all the "grandfather castrated before the first intercourse" logical paradoxes.




My description above indicates that the modified spacetime geometry looks like a gravitational wave of a sort and these waves can't move faster than light, either. That's really a "constructive" explanation why any would-be warp drive gadget will fail to realize its dreamed about job. The front of the wave can't move faster than light. Moreover, one may see that some negative energy density is needed in parts of the arrangement which is prohibited by the energy conditions linked to the vacuum stability, too.

However, the more universal reason why it is impossible to create a warp drive is still nothing else than special relativity. A problem for most armchair physicists, including Mr Harold White at NASA, is that they clearly seem to believe that the general theory of relativity in 1915-1916 has invalidated much of the special theory of relativity from 1905.

The truth is very different. General relativity is a generalization, not invalidation, of special relativity. Its laws may be derived by demanding the equivalence between all coordinate systems, not just the inertial frames that special relativity labels as special. On the other hand, general relativity describes gravity and you may interpret the whole structure of general relativity as the unique realization of spin-two fields, waves, or massless particles that is compatible with special relativity. The fundamental, primary principles are those of special relativity; general relativity is just a solution of certain constraints.

People generally tend to understand – or at least claim to understand – that general relativity reduces to special relativity whenever the gravitational fields may be neglected. But they don't actually understand how powerful this principle is and how diverse are the ways in which it can be exploited. So let me emphasize that the behaviors dictated by special relativity can be reconstructed in systems obeying general relativity at least in two regimes:

• short-distance physics: in freely falling labs that are much smaller than the typical curvature radius of the surrounding spacetime, general-relativity-predicted phenomena will behave just like in special relativity
• long-distance physics: in large enough regions of the general-relativity-based flat Universe that is mostly empty so that all the regions with strong gravity only fill a vanishingly small percentage of the space, one may use special relativity so that all the high-curvature regions are described as objects or composite particles obeying the laws of special relativity

Situations involving black holes will make the claims above clearer.

If you have a very large black hole, it creates a very strong gravitational field. For example, the red shift factor goes to zero or infinity at the event horizon. However, a freely falling observer who is much smaller than the black hole may freely fall to the black hole. As long as her spaceship is much smaller than the black hole, she won't even notice that something special is happening near the event horizon; please, assume along with your humble correspondent that there are no firewalls so that this discussion doesn't turn into complete chaos.

Special relativity appears in the lab simply because the thin tubular region of the spacetime in the vicinity of the spaceship's world line may be flattened and when it's flattened, it looks just like a straight tubular region of the Minkowski space. So in this tubular region, the gravitational field doesn't exist which means that special relativity has to be a good approximation.

The armchair physicists such as the "warp drive engineers" tend to understand this first limiting context in which special relativity emerges from the general relativity. That's why they're talking about the squeezing and stretching space that should allow faster-than-light motion. They're designing this whole story because they are apparently aware of the actual causal restrictions on motion that hold in curved space according to general relativity: massive objects have to move along time-like, and not space-like or null, trajectories.

However, they seem to misunderstand or neglect the second way in which special relativity emerges from general relativity – even though the second way is, in some sense, even simpler than the first one.

Imagine that you receive a 50-meter warp drive-driven spaceship and decide to travel from the Earth to the Sun which is 8 light minutes away. Can you get there in 5 minutes? The "warp drive engineers" like to look (at most) at the 100-meter vicinity of the spaceship. Because the spacetime geometry is warped over there, it is possible to guarantee that the spaceship moves along a time-like trajectory despite the fact that it will overcome those 8 light minutes in mere 5 minutes. But is it possible that the spaceship along with the required gravitational field around it moves this fast?

To see that the answer is No, we shouldn't look at the short-distance geometry of the spaceship only. Instead, we should look at the "big picture". Cut the 200-meter vicinity of the spaceship out of your spacetime. What is left is a nearly flat spacetime – millions of kilometers of flat emptiness – because all the hypothetical gravitational fields required to make the warp drive work were confined to the region we have omitted.

But if that's so, it must be possible to use the special relativistic approximation for this "remaining space", too. The spaceship itself (including the gravitational field in its vicinity) is just a local perturbation moving on top of a Minkowski spacetime. This Minkowski spacetime allows us to choose the different inertial frames, just like we always have a choice in special relativity. And because things can't move backwards in time in any of them, it follows that the perturbations aren't allowed to move faster than light, either.

You simply can't get to the Sun in five minutes. You may think about wonderful fantasies what is inside the warp drive spaceship or its vicinity. But before you conclude that the superluminal motion of the spaceship is compatible with the causal restrictions imposed by relativity, you should realize that relativity holds not only inside the spaceship and 50 meters away from it; it holds in the millions of miles outside the spaceship, too. The validity of relativity in the "bulk of the empty Solar System" allows you to classify any details of the inner workings of the warp drive as "irrelevant internal details of a point mass". These internal details of a point mass can't overcome the commandment of special relativity that "thou shalt not exceed the speed of light" when you are moving inside the external space. The internal details of the warp drive just don't matter at all from the long-distance, external observer's viewpoint!

Note that this second method in which special relativity emerges is valid for extreme gravitational fields such as the gravitational fields of black holes, too. If there are black holes flying through the outer space, they still behave just like other point masses from the viewpoint of distances that are much longer than the black hole radii. It doesn't matter at all that some local physics near the black holes' event horizons predicts an infinitely extreme red shift and other dramatic effects.

An alternative way to convey the same point is to say that (almost) elementary particles – nuclei, protons, neutrons, electrons, neutrinos – may also be viewed as "tiny models of a warp drive spaceship". If the spaceship were allowed to exceed the speed of light, surely the elementary particles would have the right for a perhaps tiny but nonzero "trace" of the same ability. A proton could be surrounded by warp-drive-like gravitational fields, too. Except that we know that elementary particles can't move faster than light. The same conclusion must clearly apply to spaceships – which are just large, composite elementary particles – as well.

(A much more interesting potential inner structure of a composite particle than cheap tricks and futile efforts to make it superluminal are potential wormholes or Einstein-Rosen bridges connecting the object with another, faraway object. The validity of special relativity in the bulk of the spacetime implies limitations on the possible communication between the two throats, too.)

Loop quantum gravity share the misconceptions with the warp drive crackpots

So the "warp drive engineers" de facto deny some key principles that special relativity taught us. They're not the only ones. A whole class of the laymen – the loop quantum gravitists and similar fans of "broken physics" – are doing pretty much the same thing very often. Whenever you hear these people criticizing the quantum field theory's and string theory's usage of a spacetime background in a calculation, you are witnessing their misunderstanding of the "survival of special relativity within general relativity".

There may be curved gravitational fields and they may be so diverse and extreme that we may be tempted to say that no background is preferred over another background. And some people also add that the physics of the Minkowski background doesn't apply because it's too special (you usually hear these things in a tendentious sentence mentioning that "it is against the philosophy of general relativity to think about the flat spacetime", and similar junk).

While the first assertion is sort of right – there are many solutions to Einstein's equations and you may treat them democratically – the second assertion is undoubtedly wrong. Einstein's equations still admit the Minkowski flat spacetime as a solution. And whenever the spacetime is "close to the Minkowski space" in any sense, physics of special relativity simply has to re-emerge and, according to any valid theory incorporating the ideas of general relativity, does re-emerge.

In particular, weak enough gravitational waves may always be viewed as waves of the field \[

h_{\mu\nu} = g_{\mu\nu} - \eta_{\mu\nu}

\] i.e. the difference of the full (curved) metric tensor and the special relativistic (flat) constant metric tensor. The physics of such weak gravitational waves simply has to respect all the restrictions that you may derive from spin-2 waves propagating in a flat spacetime of special relativity. In plain English, the gravitational waves are spin-2 waves in a pre-existing external spacetime. This is not the only way how the identity of gravitational waves may be described but it is a valid way and all conclusions derived from this valid way of looking at things are right and important.

If your theory contradicts the conclusions arising from this approach, and LQG does, then your theory is dead and you can't "resuscitate" it by confusing or demagogic comments about background independent and similar misinterpreted buzzwords. General relativity is a generalization or deformation of special relativity and if your theory doesn't respect the conclusions of special relativity whenever it should, i.e. in all the appropriate limits, then your theory contradicts the principles of general relativity as well because general relativity is something that must include and does include special relativity as a special case!

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Exothermic double-disk dark matter

Anniversary: On July 16th, not only my namesakes had their name day ;-) but we also celebrated the 68th anniversary of the Trinity Test, the beginning of the nuclear age. See Wikipedia, YouTube, The Bulletin. The concentration and speed of the deaths was scary during the following month or so but the event finally saved millions of lives during the (shortened) World War II as well as the 68 years that followed.

This blog entry is about a very similar topic as the previous one; the paper released today also tries to incorporate the hints from the dark matter direct search experiments, both positive and negative ones. However, in their

Exothermic Double-Disk Dark Matter,

Matthew McCullough of MIT and Lisa Randall of Harvard adopt a very different philosophy about the inner structure of dark matter. It isn't composed of individual structureless particles that arise from some symmetries. Instead, in agreement with two 2013 papers that Lisa co-wrote, this dark matter may be composed of rather symmetry-uninspired particles but what makes them special is that they are subject to internal interactions, they live almost just like the visible baryonic matter we know.




The type of dark matter they propose is DDDM, the double-disk dark matter. A more accurate name of ExoDDDM which combines the virtues of DDDM with the exothermic dark matter is the directly detectable, decomposable, dominantly deexcitable, doubly degenerate, delta-depositing double-disk da-da-da [2010] dark matter or DDDDDDDDDDDDDDDM for short. I guess that this acronym by itself will triple the number of readers who will actually open the paper. ;-)




DDDM refers to "double disks" because unlike ordinary dark matter that forms halos, DDDM tends to form disks similar to the galactic disks of the visible matter we know (stars in the Milky Way) which is only possible because of the mutual interactions between the dark matter particles – they may lose energy while keeping the angular momentum, and therefore rearranging themselves into disks.

When there are interactions inside dark matter, it's also possible to imagine that the dark matter particles come in excited states. If they're long-lived, we may imagine that the extra excitation energy is released when this composite dark matter collides with the nucleons, e.g. in the underground experiments.



Kraftwerk (The Power Plant Band) musically explain that the excitation energy of ExoDDDM may contribute to the observed radioactivity.

You see that there are some parameters here that may be adjusted or fudged. But the nice part of the story is that such a model of ExoDDDM, combining the ideas from both previous paragraphs, may explain the observations from both sides of the dark matter wars. CDMS-silicon events are OK while xenon remains largely blind to ExoDDDM – recall the apparent xenophobia of the dark matter. You will have to read the paper to see why the visibility of ExoDDDM is lower when xenon is used.

An animate, complex dark matter sector is surely a cute idea, something that may be considered natural for many reasons. On the other hand, simple isolated dark matter particles may be viewed as less analogous to the visible matter but more minimal and more economic. I think that we don't have enough data – or sufficiently deep ideas – to reliably pick between these two paradigms.

On the other hand, I would probably bet against the validity of Lisa's and Matthew's particular model. It just seems to add more new fields and parameters than the number of extra features or experimental facts that it explains. The ExoDDDM dark sector requires one to add a new unbroken, long-range \(U(1)_D\) gauge group along with a broken \(U(1)'\) and four fields with the following charges:\[

\begin{array}{c|rrrr}
& C & Y_1 & Y_2 & H'\\
\hline
U(1)' & 0 & 1 & -1 & 2\\
U(1)_D & 1 & 1 & 1 & 0
\end{array}

\] along with the natural kinetic and interaction terms for these fields. The terms are natural but the parameters to adjust are numerous:\[

\eq{
\LL &= \LL_{\rm SM} + \LL_{\rm Kin} +\epsilon' F'_{\mu\nu}F^{\mu\nu}+\delta m^2 Z'_{\mu}Z^\mu - V(H_D,H^*_D)-\\
&- m_C \bar C C - m_Y (\bar Y_1 Y_1+\bar Y_2 Y_2) - (\lambda H' \bar Y_1 Y_2+{\rm h.c.})
}

\] Try to count these parameters. So the animate dark matter paradigm seems to lead to non-robust models and it's somewhat hard to fall in love with a specific one, like this one.

So although the dark matter sector may be given a similar a priori opportunity to form complex structures just like the visible sector, Nature doesn't have a duty to serve this entitlement. It is perfectly possible that interaction-free dark matter is preferred. Different parts of the collection of fields in Nature may have very different fates. We know it's true. For example, in the \(E_8\times E_8\) heterotic string vacua, only one of the two \(E_8\) factors is broken to GUT and then to the Standard Model group. It is perfectly possible that we live in a heterotic world where the other \(E_8\) remains unbroken and its gaugino condensate sparks SUSY breaking instead. Different parts of the physical world may play – and usually do play – different roles so I surely don't think it is our "duty" to think that the dark sector must be fully analogous to the visible one.

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Light Dirac neutralino dark matter

As the TRF readers are regularly reminded (see especially dark matter wars), an increasing number of direct dark matter search experiments indicate that there exists a very light particle of dark matter, \(7\)-\(10\GeV\), that may have been detected underground. Its cross section with a nucleon, if spin-independent, would be close to \(2\times 10^{-41}\,{\rm cm}^2\).

Off-topic, feeds: the former users of Google Reader may try Feedly, try the red feed logo near my photograph in the right sidebar, or The Old Reader, a link to this blog's feed.

---

LHC luminosity will be 10 times higher: new U.S. niobium tin quadrupole magnets capable of focusing the proton beams have succeeded in Fermilab tests. This should allow CERN to increase the luminosity within a decade (not since 2015, unfortunately) one order of magnitude above the maximum designed value! See Red Orbit, E&T.

Most recently, CDMS suggested an \(8.6\GeV\) particle in their three events. It's not impossible that LUX, an experiment in South Dakota that is already running, will reveal some spectacularly clear evidence in favor of this light dark matter particle by the end of this year when they almost certainly publish their first results.



However, the number of papers in the phenomenological literature that are implicitly compatible with such a light dark matter particle remains very low. In May, I talked about the proposed right handed sneutrinos. The third hep-ph paper today,

Phenomenology of Dirac Neutralino Dark Matter,

by Matthew R. Buckley, Dan Hooper, Jason Kumar (I know Jason in person) proposes another possibility, one that is arguably more attractive than the sneutrinos and that overlaps with a possibility promoted on TRF many times in the past: the extended supersymmetry.




Phenomenologists ordinarily talk about the minimal, \(\NNN=1\) supersymmetry in \(d=4\). This supersymmetry is generated by one Weyl (or Majorana) spinor of fermionic generators which consists of four real supercharges – an invariant, dimension-independent way to count them.

This supersymmetry implies the existence of a bosonic species for each fermionic species and vice versa. But it is doing so minimally: a known Majorana or Dirac fermion invites one or two complex scalar partners, respectively, and a complex scalar or a real gauge field brings its Majorana fermionic friend.




Remarkably enough, after SUSY breaking, these extensions of the Standard Model, despite their constraints on the dynamics, are consistent with all observations assuming acceptable – but not "perfectly naturally looking" – values of the parameters (especially masses). However, the required choices of the parameters are not quite aesthetically satisfactory and supersymmetry isn't making down-to-Earth experimenters certain that it is doing something for them.

Some unimaginative people like to think that the reason is that there is no supersymmetry in Nature. However, this conclusion is unwarranted and another, opposite conclusion may actually improve the situation: there may be more supersymmetry in Nature than previously thought!

Supersymmetry must come in whole Weyl spinors so the next amount of supersymmetry that is possible is the so-called \(\NNN=2\) extended supersymmetry which consists of eight real supercharges (components). Theories respecting this supersymmetry may only contain two types of light non-gravitational multiplets, the hypermultiplet and the \(\NNN=2\) vector multiplet. Under the \(\NNN=1\) supersymmetry subalgebra, they decompose into two chiral multiplets; and one chiral and one vector multiplet, respectively.

To require \(\NNN=2\) supersymmetry for the whole particle content would be too much of a good thing. This extended supersymmetry is too strong and implies too many constraints that are incompatible with the basic properties of particle physics as we know it from experiments. For example, \(\NNN=2\) SUSY implies that physics is left-right-symmetric so there can't be any diversity in the charges of the left-handed and right-handed fermions; the couplings are too constrained; there are just too many new particles that should stay light; this SUSY can't really be spontaneously broken by a field-theoretical mechanism.

However, there exists a possibility that \(\NNN=2\) is respected by a part of particle physics, the gauge bosons and their superpartners, while the matter – the chiral multiplets extending known leptons and quarks – only respects the minimal \(\NNN=1\) SUSY as it does in the minimal supersymmetric models. This asymmetric treatment of gauge bosons and matter in generations may be justified by braneworlds in string theory where the gauge bosons may live on higher-dimensional (e.g. codimension-two) branes and preserve a higher amount of SUSY; while the chiral multiplets such as quarks and leptons live on intersections of such branes and preserve a lower amount of SUSY.



So the gauge bosons are extended not just to \(\NNN=1\) vector multiplets by adding their superpartners, Majorana gauginos. Instead, gauge bosons are extended to whole \(\NNN=2\) multiplets that contain two copies of the Majorana gauginos – i.e. effectively Dirac gauginos (the Dirac masses must inevitably arise so it's really wrong to talk about two Majorana fermions in that case) – as well as extra complex scalars, the sgauginos (sgluinos are most frequently discussed in this context).

And it is the Dirac gauginos that are proposed as dark matter candidates in the new paper by Buckley at all. Incidentally, Matt Buckley has a Twitter account where he recently tweeted about 100+ tweets on the recent Santa Barbara LHC phenomenology conference.

Anniversary: Julian Schwinger died 19 years ago.

Their scenario proposes dark matter composed of Dirac gauginos, probably mostly Dirac binos (with almost no flavor of higgsinos added; note that the dominant type of neutralinos in the hep-ph literature are neutral winos instead – I surely don't mean just Gordy Kane) which can be very light, perhaps consistent with the \(7\)-\(10\GeV\) range suggested by the dark matter direct search experiments. (Note that Dirac gauginos have also been argued to naturally admit much heavier masses than the normal Majorana gauginos so they're flexible in both directions.) These dark matter particles may annihilate through slepton exchange and things work well if the squarks are pretty heavy. The \(R\)-symmetry to be discussed below may also be broken and depending on the strength of the breaking, one may interpolate between the normal phenomenology with "just" \(R\)-parity and their new phenomenology with the full \(R\)-symmetry.

That's everything I am going to say about the particular paper. Now, some extra background.

I said that the Dirac gauginos may be imagined as arising from the \(\NNN=2\) supersymmetry. This supersymmetry has supercharges \(Q_A^i\) and their complex conjugates, \(\bar Q_{\bar A}^i\), where \(A=0,1\) is a chiral spinor index and \(i=1,2\) is the extended supersymmetry index. The transformations acting on \(A=0,1\) are \(SL(2,\CC)\sim Spin(3,1)\) while the transformations acting on \(i=1,2\) are \(U(1)\sim SO(2)\) rotations.

These \(U(1)\) transformations are generated by a charge and they're called the \(R\)-symmetry. In even more extended SUSY vacua, the \(R\)-symmetry may become non-Abelian; for example, it is \(SU(4)\sim Spin(6)\) in the \(\NNN=4\) gauge theory known from the most famous example of the AdS/CFT correspondence. Note that the \(R\)-parity may only be \(P_R=\pm 1\) if we adopt the multiplicative form of the group \(\ZZ_2\) and for the Standard Model particles, it may be written as\[

P_R = (-1)^{2J+3B-3L}

\] where the odd coefficients may be replaced by other odd coefficients because the signs don't change (but some choice of the coefficients may be better than others for the beyond-the-Standard-Model particles). You may check that the bosons and fermions in the Standard Model have an even and odd \(2J\) (that's always the case!) as well as even and odd \(3B-3L\) (only in the Standard Model) so the sign above is always positive while their superpartners have a negative \(R\)-parity. The \(R\)-parity generates a group isomorphic to \(\ZZ_2\).

On the other hand, the \(R\)-symmetry is an additive group isomorphic to \(\ZZ\); its charge (generator) generalizes the exponent from the \(R\)-parity above and we suddenly care about its value, not only about its being even or odd. The supercharges \(Q_A^{1+i2}\) carry the unit charge – the sign is reverted for \((1-i2)\) and it is reverted once again for the complex conjugates. So in each multiplet, you find some particles with different \(R\)-charges. Incidentally, theories with an unbroken \(R\)-symmetry may admit several new stable species. If the lightest \(R=\pm 2\) particle (which can be e.g. the new Higgs-like scalars \(R_{u,d}\) in their model which combine with the usual Higgs doublet chiral multiplets to a full \(\NNN=2\) hypermultiplet) is lighter than two \(R=\pm 1\) particles, then both the lightest \(R=\pm 1\) and \(R=\pm 2\) particles will be stable, and so on.

Because the gauge bosons must be neutral under \(R\)-parity because they may be created without limitations (think about extra photons produced while accelerating a proton), the gauginos must be charged under this \(R\)-symmetry. So the Dirac gauginos differ from their antiparticles just like the electrons differ from positrons. In this respect, they are different than the ordinary (neutral, not \(W^\pm\)) gauge bosons and their Majorana gauginos which are their own antiparticles.

This Dirac character of the new particles has various advantages, see the paper. I can easily imagine that people will have found it stupid that they will have studied just the \(\NNN=1\) supermultiplets in phenomenology. Maybe, we will be saying that it was a typical example of not taking a new idea seriously enough. New ideas that seem to work should always be pushed to the limits but the people almost always fail to do so. Because of some counterproductive egalitarian instincts, they have assumed that the same amount of SUSY must be relevant for all particles in particle physics but it ain't so because the gauge bosons may naturally remember a higher amount of SUSY from their stringy or Planckian ancestry.



Czechia timelapse II, released a few weeks ago; see also Part I

If LUX confirms the existence of the light dark matter particle in the results published before the end of this year (or XENON1T later: they only began construction this year), which I personally guess is more likely than not (but I won't say anything stronger because I am not convinced about anything stronger), we may find ourselves in an extremely exciting and interesting situation. Many more people will undoubtedly study things like extended supersymmetry. In that case, I would surely recommend them to study string theory much more carefully than ever before because many beautiful and essential insights have been found by string theorists in the context of extended supersymmetry where it is most straightforward to see string theory's muscles.

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Negligible impact of dark matter on the Solar System

Mike has asked me about the following preprint:

Constraints on Dark Matter in the Solar System by N.P. Pitjev and E.V. Pitjeva (Leningrad, Russia)

This article was celebrated by an impressive title and a "more than just uncritical" article at the Physics arXiv Blog:

The Incredible Dark Matter Mystery: Why Astronomers Say it is Missing in Action

Wow. The only comment over there that isn't preposterous is the comment by S. Seibert. Thankfully, Sean Carroll presents the same stance as your humble correspondent: in his opinion, the expected impact of the dark matter on the Solar System is comparable to the dark matter's influence on NBA three-pointers.

Why?




The Russian authors review some observations of the Solar System in general and planets in particular which lead them to the conclusion that no gravitational impact of the dark matter (which in principle affects the trajectories of everything, including the planets) has been seen. This may be translated to an upper bound on the density of dark matter. The strongest one that we can find in the Table 1 of the paper says\[

\rho_{\rm dm}\lt 3\times 10^{-19}{\rm g/cm}^3

\] For the dark matter around the Earth, the estimate is later improved (i.e. lowered) by another factor of two. Is this upper bound capable of identifying a contradiction between the dark matter theory and the observations?




First of all, the critical density of the Universe for which the Universe is spatially flat – and our Universe seems to be, with an amazing accuracy – is equal to \(9.9 \times 10^{-30}{\rm g/cm}^3\). The dark matter density is about 25% of this figure.

If this were the density in the Solar System, it would clearly be hopeless to try to find an influence of the dark matter on the Solar System: the upper bound derived by the Russian paper only says that the Solar-System-observed dark matter is smaller than 10-100 billion times the correct value. Well, it almost certainly is. One is indeed smaller than 10-100 billion.

However, unlike dark energy, dark matter does clump. It is mostly located in halos around the galaxies – which are somewhat larger than the distribution of the bright stars in the same galaxy. Because of this concentration, the average density of dark matter inside a galaxy such as the Milky Way is larger than one quarter of the aforementioned figure \(9.9\times 10^{-30}{\rm g/cm}^3\).

What is the density of dark matter in the galaxy? The density may depend on the location and these "profiles" aren't quite well-known and the proposed models are somewhat complicated. But to get an order-of-magnitude estimate, it's enough to ask Wolfram Alpha to calculate the following ratio:

mass of milky way / volume of milky way in cubic cm

The result is \(1.3\times 10^{-23}{\rm g/cm}^3\). I tried to use this unit of density (which is the Russian folks' favorite unit) and no other unit throughout this article although it's not my preferred unit in any sense.

So you may see that the upper bound derived from the planetary dynamics is still about four orders of magnitude too weak (i.e. the number is large) relatively to the actual density. The Russian paper says that the planetary-dynamics-observed density of the dark matter is smaller than 10,000 times the right value. Well, 1 is almost certainly smaller than 10,000, indeed.

It shouldn't be hard for you to intuitively understand why dark matter shouldn't have a detectable (or large) gravitational impact on the events inside the Solar System. The main reason is that the total mass of the dark matter inside the Solar System is much much smaller than the total mass of the visible matter in the same volume (which is dominated by the Sun). Why? Because the visible mass is severely clumped while the dark matter isn't that clumped – it is mostly diluted into the vast interstellar regions (volumes in between the stars) whose overwhelming majority is much further from any star than the Saturn-Sun distance.

(There could be some increase in the density of dark matter even in the vicinity of the stars – just like there is an increase around the galaxies – because the concentration of the visible matter that was needed during the birth of the Sun and the Solar System probably depended on a peak in the dark matter distribution. But it's fair to say that this extra increase isn't changing the qualitative story i.e. that the dark matter density inside the galaxy may be assumed to be more or less uncorrelated with the positions of the stars, at least if we only want order-of-magnitude estimates.)

So while the total mass of dark matter in the Milky Way halo is 5 times larger than the total mass of the visible matter, the total mass of dark matter inside the Solar System is incomparably smaller than the total mass of the visible matter: most of dark matter is outside all "solar systems".

If you allow me to advocate the latter point in one more way, note that the closest next star to the Sun is Proxima Centauri, several (4.24) light years from us, while Saturn is just about 1 light hour away from the Sun. One year is about 9,000 hours but to compare the volumes, you have to calculate the third power of this number. You get 729 billion. So the mostly empty interstellar volume that may be "attributed" to the Sun is something like 1 trillion times larger than the ball of the Saturn-Sun-distance radius. This fact means that only 1 trillionth of the solar (or average stellar: but the Sun isn't too far from an average star) mass may be expected in this relatively small ball and this relatively small mass (or density) is compatible with the upper bounds derived from the planetary dynamics even though the possibility to find an impact (or discrepancy) sometime in the future can't be ruled out entirely because we're "just" 4 (or so) orders of magnitude away from the goal.

One may be able to derive or guess the relevant numbers more accurately or less accurately, more quickly or less quickly, but I am disappointed that just a single commenter under the Physics arXiv Blog was able to pinpoint the qualitative idea implying that the hype is completely unjustified – namely that there can't be any observable contradiction because the expected density of the dark matter in the Solar System is way too low. Almost everyone else added his or her own interpretation of the preposterous statement by the blogger that we're facing an "incredible dark matter mystery".

Let me mention one widespread laymen's mistake that makes them believe similar conspiracy theories. The laymen tend to think that if a scientific theory XY predicts an object or phenomenon UV, then UV should be visible by pretty much every experiment CD. Most of the uneducated laymen's criticism of string theory reduces to the opinion of this sort. However, this opinion is completely misguided. It is completely normal for UV to be invisible by CD. In many or most cases, CD is just too unrefined or weak to see UV and theories about UV (whether UV is a string or dark matter) often unambiguously predict that UV is invisible by a CD or (almost) all CDs. There's absolutely nothing wrong about a theory just because it predicts that a relevant object or phenomenon will be unobservable. There may exist other reasons why the theory is a good idea or convincing and the only scientific way to eliminate a hypothesis is falsification – the discovery of a measurable contradiction between the theory's predictions and observations. Not observing something that should be unobservable according to the precise predictions of a theory (even if it is very important in the theory!) surely doesn't count as falsification! Too bad that most laymen are incapable of understanding this trivial point.

See also Ethan Siegel.



Just one picture advertising a new CMS paper based on the 2011 data. As you can see, there seems to be a 3-sigma excess in dijet (two jets) events indicating a resonance with a mass near \(300\GeV\), not to mention the 2-sigma excesses near \(1,100\GeV\) and elsewhere. But don't be excessively certain that the former comes from new physics. 3 sigma is not much. Moreover, some extra operations had to be applied to remove some background near \(300\GeV\). Nevertheless, the very fact that no 2012 collisions were incorporated to this 2013 study may look... strange.

BTW the best TRF-rated paper today is Karch-Jensen showing that the Maldacena-Susskind Einstein-Rosen bridges appear for an entangled (color-singlet) quark-antiquark pair in AdS as well because one gets a world sheet with two boundaries along two branches of a hyperbola, so they're causally disconnected from each other. I think that I know how to show the analogous thing for M2-branes in M-theory, or any brane with a wormhole shape, for that matter.

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Hooper: XENON100 may have seen DM candidates, too

...if it's so, LUX will observe 1-6 DM particles a week...

Update 6/24: South Dakota Public Broadcasting tells us that LUX has been turned on. While the data could be interesting in weeks, don't expect official releases before the final months of 2013. You may also check a 14-minute TED talk on LUX from March 2013.

Update 6/19: This astro-ph preprint says that LUX is already doing science and the results of a 60-day run will be out by the end of 2013, promising to brutally beat any competitor in their reach. Except for this short paragraph, this blog entry was posted on 6/10.

Dan Hooper of Fermilab released an interesting new salvo in the dark matter's war on existence,

Revisiting XENON100's Constraints (and Signals?) For Low-Mass Dark Matter.

Recall that the set of underground experiments that are trying to directly catch the particles of dark matter is divided to two violently competing subsets: one of them, the axis, vigorously claims that there can't be any signal in the other experiments. The leader of this axis is the XENON100 experiment whose claimed constraints are far more powerful than the upper bounds on the cross section published by the XENON100's allies.



© XENON100 Collaboration

On the other hand, the alliance of experiments that have already claimed to observe a rather strong signal of a dark matter particle, one whose mass seems to be 7-10 GeV (significantly lighter particles than those in the models that dominate in the phenomenological literature but in no way impossible), is apparently getting stronger every month. It seems that we're somewhere around 1943 in this particular war.




At least since 2010, the traditional leader of this alliance has been the CoGeNT experiment that also claimed to have observed the seasons, sort of confirming previous similar claims by DAMA, another paleomember of the coalition.




Juan Collar and N.E. Fields of the CoGeNT Collaboration have previously claimed that CDMS, formerly a member of the "dark matter is not seen" axis, was actually observing a dark matter signal as well, one that may have reached 5.7 standard deviations, high enough to claim a discovery.

This general claim that CDMS was going to join the "dark matter is seen" alliance was confirmed in April 2013 when CDMS announced that the CDMS was seeing three events that looked like a pretty clear 8.6 GeV or so dark matter particle. It means that we have had almost two months to get used to the notion that CDMS is among those who effectively claim that "something seems to be there", a coalition that also included CRESST-II since 2011, which leaves XENON100 alone as a proponent of the thesis that all the dark matter hints claimed by others have to be bogus. This situation makes it natural to think about air raids on Berlin.



Now, Dan Hooper claims that XENON100, the cornerstone of the dark-matter non-existence claims, is seeing two tantalizing hints of a light dark matter particle, too. The key image looks way too familiar from the recent CDMS charts, especially this one.

On the picture above, once again, you should notice two events that are significantly lower than the bulk of the background events although, for various technical reasons, the XENON100 papers have included them in the background as well. These events seem to be separated by a gap from the group of "clearly background-like events" and they seem to suggest the same mass of a dark-matter particle which would be unlikely if they were parts of some noise. And the mass is compatible with the 7-10 GeV interval indicated by the other experiments.

Based on common estimates, one could have expected up to 50 dark matter particles (which is much more than 2) to have been observed by XENON100. That's why the XENON100 folks are so self-confident in their claim that the dark matter particle with the parameters suggested by others can't exist. Hooper exploits conservative "what if" adjustments of various efficiencies and other boring and mundane parameters of the XENON100 experiment to claim that just 2 events of the sort could still be conceivable.

If this "yes, a particle is there" interpretation is right, then – according to Hooper – the emerging LUX experiment in South Dakota (which is also based on xenon and may be viewed as a superior sibling of XENON100) should see something between 3 and 24 events a month. If the answer is "Yes", then LUX could settle the argument about the existence of the particle rather quickly. Needless to say, dozens of dots near a curve which are sharply separated from the rest would be rather spectacular.



Superman is looking for a glitch in LUX.

The LUX website hasn't been updated for two months but it may be due to the webmaster's laziness or the experimental physicists' having something more exciting to work on these days. L.A. Times ran a fun story about the state of the experiment two months ago.

Incidentally, I must ask you: does any reader who is not Czech use the word "lux" for the vacuum cleaner? If she doesn't, where did we get this word from? Oh, I see, it's the brand called Lux, later Electrolux, founded around 1919. Before that, Lux was producing kerosene lamps, therefore the currently incomprehensible link of the vacuum cleaners to a word for light. ;-)

There was a videochat with the LUX (and Majorana Demonstrator) experimenters today.

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Kip Thorne, a star in a Hollywood movie

You probably know the relativist Kip Thorne as a co-author of the Misner-Thorne-Wheeler book on GR, a co-father of LIGO, Gravity Probe B, and a researcher of black holes, wormholes, proponent of the membrane paradigm for black holes, and many other things in relativistic astrophysics. But as The Guardian told us yesterday,

Kip Thorne: physicist studying time travel tapped for Hollywood film,

he is commuting from Pasadena to a town that is 10 miles away, Hollywood, to shoot a November 2014 sci-fi movie called Interstellar.



Theoretical physicist Anne Hathaway (who is also famous in Hollywood where she has earned $15 million) will be the main female star along with Jessica Chastain. Male actors will include Matthew McConaughey, Casey Affleck, and Michael Caine.




The movie will be about wormholes and other Thorne-related beyond-Einstein topics in general relativity. It was apparently important that Thorne is a "colorful figure who wears jeans, Birkenstocks, Hawaiian shirts and a battered cowboy hat." The description also says that "he regularly makes scientific wagers with Stephen Hawking, a close friend, and invariably wins. (Hawking's penalties have included forking out for a subscription to Penthouse magazine)."

This "permanent winner status" is somewhat bizarre because Thorne was on the losing side, along with Hawking, of their bet against John Preskill concerning the black hole information paradox. Unlike Hawking, Thorne hasn't conceded yet which seems painful to me. On the other hand, it's true that Thorne won a Penthouse-related bet against Hawking.




Incidentally, Pedro Leonardo Mascheroni (77), an Argentinian-born U.S. citizen who worked in Los Alamos as a physicist, finally pleaded guilty that he and his wife were working hard to donate the nuclear bomb technology to the socialist country of Venezuela. He was previously insisting that he was innocent.

I think that Edward Snowden is yet another example of the fact that various institutions that are critical for the safety of the U.S. – and perhaps other Western countries – are routinely hiring activists who have offered others no reason to think that they would be loyal servants of the capitalist countries, their citizens, and their security. Whether Snowden is a loon or a hero is a difficult question but the fact that a person with his known background and with his publicly declared values shouldn't have been hired to his job seems self-evident to me.

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