# The Reference Frame

## Thursday, May 24, 2012
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### Psychology of dark matter denial

Sean Carroll mentioned some developments concerning dark matter that have been discussed on this blog, too. His short text is another example of the fact that his comments are sometimes right, however rare these events may be.

A month ago, the media overhyped a paper by Chilean astronomers who claimed that their measurements show that there was no dark matter in the vicinity of the Solar System. However, Bovy and Tremaine showed that with a more realistic model for the velocities of the galaxies, the corrected method seems to yield a dark matter density that is fully compatible with the value obtained by more common methods.

Among the media, only Universe Today, Phys Org, and Nude Socialist mentioned the new article which arguably is – unlike the previous, overhyped one – correct. The ordinary non-scientific media remained silent. Theories that work are not too interesting for the journalists; they prefer to write about things that don't work, especially if these "don't work" claims are untrue.

These days, many people – or at least a sufficiently large number of loud people – are literally obsessed by attacks against some key theories contained in the very foundations of modern science. String theory may be just too mathematically abstract for a number of amazingly aggressive "critics" if I have to avoid the term "imbeciles". Quantum mechanics brought the most profound conceptual revolution in the history of physics.

One could perhaps understand the existence of these people – because these theories really dramatically differ from our everyday understanding of the reality or from the expected amount of mathematical depth that is needed to to describe the observations properly.

However, the anti-scientific movement reaches corners of science that seem totally conventional. The existence of dark matter is an example. Many people just get unbelievably emotional when you say something about dark matter. They're as certain as any other religious bigot that dark matter shouldn't exist: it's so dark and blasphemous! The adjective "dark" surely means that it's just a collection of fudge factors that the cosmologists and physicists have to apply in order to hide the truth. The cosmologists and physicists must have signed a contract with the Devil if they promote dark matter.

The actual fact is that dark matter is just pretty much ordinary matter from a physics viewpoint; it's just composed of yet another type of an elementary particle. There are many types of elementary particles. We encounter some of them frequently, some of them less frequently, but all of them are just examples of particles that also behave as waves, quanta of some particular quantum fields which are intrinsically vibrating strings if weakly coupled string theory applies to the real world.

Where are those conspiracy theories about dark matter that surely has to be a fraud coming from?

A part of it may boil down to the name and the hype in the popular science media that dark matter is something totally shocking. People just don't like "dark" things. They're connected with the devil, they feel. And many popular science writers love to oversell the topics they're discussing so they stress that dark matter is something totally unusual, completely otherworldly, crazy. But it's not. It's as conservative as muons or Higgs bosons. It's just a different material but the difference doesn't really require any dramatic paradigm shift away from quantum field theory, our "theory of nearly everything" (TONE), or string theory, our "theory of everything" (TOE).

Many of the anti-scientific movements, whether we talk about quantum mechanics, string theory, or dark matter, boils down to an unbelievable degree of naivety of the critics. They just want all the objects in physics to look like a tree – or something else you encounter in your everyday life. It shouldn't be too small, it should reflect an amount of light that is neither too low nor too high, it should sit in the space without fluctuations, it should only have three dimensions, it shouldn't contract or get heavier when it's moving, and so on.

Except that the fundamental objects and concepts in physics simply aren't any trees! They are different. They get shorter and heavier when they're moving. They may be constructed out of new particles, the particles' internal structure may expose a one-dimensional string or higher-dimensional branes, all these objects live in extra dimensions and follow the probabilistic logic that must be described with the maths of quantum mechanics. The fundamental objects in physics have many properties that differ from the properties of a tree. Get used to it.

Those people can't get used to it. But even smart kids in the kindergarten must be able to understand why these people's criticism is utterly irrational. There is no reason why fundamental things should look like trees – just like there is no reason why the entity that has created the Universe has to look like a grandfather sitting on the cloud. Other possibilities are mathematically consistent so they may be realized in Nature. And indeed, the right ones are realized in Nature. We are just some composite objects, animals that evolved in a particular way and have been trained to perceive and evaluate a certain kind of empirical information. But it's surely not all the information, information in all the forms, that may exist in the real world.

In particular, a big part of the elementary particles (counted as a fraction of the total mass of particles) may be invisible through light. And in fact, we know that a majority of the localized mass/energy in the Universe is invisible via light; that's why we call it dark matter. It just doesn't interact with the electromagnetic field – or the interaction is so impressively weak that the practical outcome is the same. We don't see it.

In the Universe, 73% of the energy density seems to be composed of dark energy which is not localized and has no internal structure. It seems that it's just Einstein's cosmological constant adding some curvature – just a number – to the vacuum (spacetime) at each point. The remaining 27% are composed out of dark matter, 23%, and baryonic i.e. visible matter, 4%, most of which (counted as mass) is composed of protons and neutrons. Among those 27% assigned to localized matter, 85% of it is dark matter.

Is it a large percentage? Is it small? Well, I don't know. There is no a priori, philosophical calculation that would tell you what the right percentage should be. The Universe as we see it is consistent and allows life at this moment. One can show that if we changed some percentages but not others, certain things wouldn't work anymore. There wouldn't be any life at this moment, for example. Some other correlated changes could still be compatible with life at this moment but these alternative possibilities are simply not realized in the world around us even though they could seem acceptable. Our world has unique answers to most of such questions.

Spectrum of rainbow

But the fact that there is matter we don't directly see – by our eyes – just shouldn't be shocking. Our eyes only see light whose wavelength is between 0.4 and 0.8 microns. At the log scale, it's just some interval corresponding to one doubling. Inside the huge interval of interesting wavelengths of electromagnetic waves, going from $10^{-25}$ to $10^3$ meters, the visible interval is located at a seemingly random place in the middle – well, it's not too random: the frequencies we see are close to those that are mostly emitted by the Sun and that make it through the atmosphere. We are directly sensitive to the type of light that is widespread on Earth (although our devices are able to detect the remaining frequencies in the wide interval, too).

It's not an accident that our eyes became able to see the frequencies that are dominant on Earth. It's easier to evolve an observing optical apparatus – an eye – if it doesn't have to deal with one problem, the shortage of light of the detectable frequencies. And at the end, the eyes use similar chemical and electrical processes to detect the light that are employed during the emission of the light by atoms. So you shouldn't be shocked that the frequencies had to be close.

Evolution of the not-only-human eye. Sorry if clicking will produce a creationist page; they were just successful enough to be high-scorers with Google and the picture (in which they present a serious theory) just passed my tests.

However, one simple conceptual point that you should appreciate – and the "critics" of dark matter arguably don't appreciate it – is that the eyes got evolved to adapt to the environment and the composition of the electromagnetic waves in this environment. What I want to say is that the causal relationship wasn't going in the other way around. Some people seem to think that they decide what is the preferred way how they should be seeing the world and things in Nature are obliged to adapt so that they may be seen in this "user-friendly" way.

But Nature isn't obliged to obey such conditions. In particular, it doesn't have to be "user-friendly". Nature isn't obliged to obey any ad hoc man-made conditions whatsoever. By definition (of "natural" and "man-made"), there aren't any fundamental physical processes in Nature that would be man-made, a trivial fact that could drive the climate alarmist crackpots up the wall but that is true, anyway. If we want to understand Nature, our beliefs and our science has to adapt to what has existed in Nature for billions of years, not the other way around. Nature just won't adapt to your beliefs. Feel free to complain against Nature's totalitarian attitude and team up with a few billion of other crackpots who will demand Nature to surrender. She won't.

The electromagnetic spectrum: click. Note how narrow the visible band is on the log scale. And it still allows us to have so much fun with colors, to distinguish millions of them, etc.

Just like there are objects and processes that emit or absorb light at frequencies that are very different from the frequencies of the visible light, there are particles that aren't able to emit or absorb light at all – at least not at rates that would be significant and detectable. That's not shocking.

Light itself (or a photon) is just one elementary particle. Others aren't obliged to interact with it. In particular, electrically neutral particles don't interact with electromagnetic waves and there are many electrically neutral particles. Neutrons and atoms are examples of electrically neutral particles that still interact with light (emission spectra, magnetic moments etc.) because they're made out of electrically charged pieces – pieces that are sufficiently distant from each other. However, elementary particles such as neutrinos or neutralinos are both neutral and tiny so any substructure involving charged sub-particles is unobservable at achievable frequencies. So they just don't interact with light.

There isn't any a priori calculation of the fraction on the Universe's particulate mass that these invisible particles should constitute. It seems we know a lot to conclude that it is a majority of the matter (not counting dark energy). This conclusion is deeply incorporated into our modern picture of cosmology – I mean to the publicly available version of the CV of our cosmos.

The visible matter – protons, atoms etc. – is just a cherry on a pie, some parasitic exceptional stuff that decided to live, get ignited, and burn on the peaks of dark matter halos, the primordial environment where the galaxies were born. You could say that the visible matter is a "higher species" than the dark matter; after all, life is composed of visible matter. But the mass stored in the dark matter, the lower species, may be naturally larger. The number of insects is higher than the number of humans, too.

(I apologize to insect American readers and their environmentalist advocates for my suggestion that the insect Americans are a lower race than homo sapiens.)

We may observe the motion of stars in our galaxy and compare it with the theoretical predictions – either from Newton's theory or Einstein's theory i.e. the general theory of relativity. Without the dark matter, we find a disagreement. The Milky Way is rotating almost like an LP, with a velocity that doesn't depend on the center from the center. According to Newton's theory, the motion should be much closer to the Solar System in which the innermost planets are much faster because their centrifugal acceleration has to compensate the much stronger Sun's gravity they feel.

There are two classes of solutions to this discrepancy: the theory – Newton's or Einstein's theory – is fundamentally wrong; or we have just overlooked some sources of the gravitational field. Of course, the latter option – one leading to the concept of dark matter – is much more conservative from a physics viewpoint. It is favored by detailed observations, too.

But even if we're open-minded about both possibilities, we could try to reconstruct the metric tensor in our galaxy. Just imagine that you try to find a configuration of the metric tensor – the geometry – whose geodesics coincide with the observed world lines of the celestial objects. Assume that this task has a solution and our (imperfect but already nontrivial) observations suggest that it does. So we have something like $g_{\mu\nu}(x,y,z,t)$. Out of this metric tensor, we may calculate the Ricci tensor $R_{\mu\nu}(x,y,z,t)$.

We may use this Ricci tensor to calculate the stress-energy tensor from Einstein's equations,\[

R_{\mu\nu} - \frac 12 R g_{\mu\nu} = -8\pi G T_{\mu\nu}^\text{includes c.c.}

\] In our treatment, you may view Einstein's equations above to be a definition of the stress-energy tensor $T$ which I have defined to include the dark energy term $\rho g_{\mu\nu}$, too. (More often, it would be written as an extra term and moved to the left hand side.) You see that in this approach, we may always obey Einstein's equations. We just define the stress-energy tensor to be the usual multiple of the Einstein tensor constructed out of the curvature components.

In this setup and so far, the question whether the dark matter explanation is the right one remains vacuous. We may always calculate the stress-energy tensor and the difference between this gravitationally calculated stress-energy tensor and the stress-energy tensor from the observed matter may be called the stress-energy tensor of "dark matter". A pure fudge factor.

However, if we assume that the stress-energy tensor of the dark matter is really calculated out of some particular form of matter – such as a cloud of new particles, WIMPs, behaving as a particular kind of dust – which have some particular relations between the pressure and energy density and which evolve according to the same laws as the visible matter – we may already make nontrivial predictions about the stress-energy tensor contributed by the dark matter. And what we observe is already a nontrivial consistency check: the observed cosmology is compatible with the idea that the dark matter whose distribution was decoded from its gravitational influence – i.e. from the motion of the stars etc. – does seem to obey the otherwise known laws of physics, too.

This check is a huge argument in favor of the dark matter paradigm. Analogous consistency checks trying to verify the MOND theories – theories that want to avoid dark matter and blame the anomalous motion on Nature's hypothetical refusal to obey Newton's or Einstein's laws at cosmological length scales – don't work this well. One may continue with other, more detailed checks and the dark matter paradigm just seems to work fine. In fact, it allowed us to decide that most of the dark matter should really be a cloud of a new particle, either WIMP or axions or their mixture or something similar. These theories seem to make sense. Their implications for the early cosmic history seem to make sense, too.

The only "new thing" about this dark matter is that it is dark: we can't observe its presence via light. But we may still observe its presence by other tools, especially by its gravitational influence on other celestial bodies – and if we're lucky, also from its impact on the direct search experiments such as LUX discussed in the previous blog entry.

So where does the emotional opposition to the dark matter come from? There is no observation that would really contradict it; the theory has passed many nontrivial consistency checks; the overall cosmological picture including dark matter makes sense; and the very assumption that some particles don't interact with light is no heresy because it obviously follows from pretty ordinary theories in particle physics. After all, we know that neutrinos have the same property although they're too light to account for the relatively compact and "slowly changing" dark matter halos. But the neutrinos may have heavier cousins. There's clearly absolutely no simple enough way to show that the dark matter paradigm is insane or impossible. All the people who try to convince themselves that they have such a proof are just deluding themselves and others.

In these dark matter discussions, I still think that most of the people's irrational attitudes boil down to their dogmas, to their inability to impartially and rationally compare competing hypotheses that are assigned comparable prior probabilities. All the "critics" just start with the assumption that the dark matter paradigm has to be super insanely unlikely for some emotional reasons – some completely unjustifiable would-be argument that there is something contrived about dark matter – and no amount of evidence is capable of convincing them that the answer differs from their dogmas.

It's very important that qualitatively different theories must be given non-negligible, mutually comparable prior probabilities. You may only falsify theories by showing that they disagree with the evidence; you may only falsify them a posteriori. Many critics – and this is true for the dark matter denial just like it is true for the staggeringly shitty anti-stringy imbeciles or for the anti-quantum, anti-Copenhagen zealots - just don't want to obey this basic rule of science that falsification has to boil down to the evidence and not some a priori emotions.

If one has a theory that tells you something about every element of a class of phenomena, the only way to weaken this theory is to find a disagreement between the theory and some observations; or to show that it is totally vacuous and doesn't have any implications whatsoever. This is clearly not case of the Copenhagen quantum mechanics; it's not the case of the dark matter paradigm; it's not the case of string theory. All the people who say that they have some evidence against those things are just lying to themselves.

And that's the memo.

Posted by Luboš Motl
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#### snail feedback (9)
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reader PN said...

I would warmly recommend reading through both papers in question. I'm not particularily impressed by Bovy & Tremains paper. They focus on the approximation Moni Bidini et al. makes in section VIII but seems to entirely ignore the discussion MB has on this topic in section 4.2. Even though I'm an astronomer (high energy astrophysics) I'll readily admit I'm no expert on stellar kinematics and DM halo models and would need to read a number of papers to check the validity of what MB claims in 4.2. But the fact is that they DO explore the parameter space Bovy & Tremaine suggests. Some highlights;

- Observational knowledge of azimuthal velocities for stars high above the galactic plane is scarce. Hence it is a bit disingenious to claim that the values Bovy & Tremain show are required for standard DM halo models are "more realistic".

- High azimuthal velocities on the one hand agrees with current DM halo models but on the other hand (apparently) requires that the total amount of DM is much higher than the standard models suggest so you end up with a conflict if you assume high velocities. As far as I know Bovy & Tremain does not at all explore this problem.

- Other researchers also approximate the term in question to zero.

Any which way, Moni Bidini is by no means proof of no DM at all, that's just media spin. We'll still have the (pretty old) problem of galaxy rotation curves to explain. What they do show, if proven correct, is that the current model of DM halos might be incorrect and might require other forms of DM than are currently considered as the most likely particles.

Bovy and Tremain would have done a better job if they had explored section 4.2 of the original paper in much more detail. As it stands it looks like they really didn't add much at all to the discussion as MB already covered the issues B&T brings up.

reader Luboš Motl said...

Dear pn,

I know that comments formulated such as yours sound convincing to many ears but mine aren't among them.

I just find your attitude lacking in impartiality and ultimately illogical.

First, the big claims by Moni Bidin et al. that are needed for someone to say that the paper is "important" (whether or not it is a "disproof" of the dark matter paradigm) do depend on the section 4.1 so if there's a significant bug in it, it would invalidate the Moni Bidin paper. To write a valid derivation of something, one needs all the steps in the chain to be right.

But we don't really have to solve this partial question because Bovy and Tremaine aren't just correcting an isolated error. They offer their own calculation using the same but corrected methodology as Moni Bidin et al. They end up with a density of dark matter that seems totally compatible with other methods. So the more logical approach now is to take the calculation that looks most comprehensive and takes all the previous observations and corrections into account - the Bovy's and Tremaine's calculation - and try to find problems with it (or confirm it).

You don't seem to be doing this at all. Your comment sounds to me as if you don't want papers of this kind to be read and studied at all. It surely sounds as you want such papers to be viewed as heretical ones. You haven't found any particular problem with Bovy's and Tremaine's paper but your description of it still sounds negative. This looks like a disconnect between the evidence and the conclusions to me. Your judgement sounds prejudiced to me. You want some people to study a section 4.2 of a paper that seems wrong as a whole. Why should the people be doing so? Why are you still trying to sell the Moni Bidin et al. paper to be the holy scripture that should be the benchmark for all these discussions forever? As far as I can say, it is already in the trash bin.

The disagreement about the behavior of the velocities is very clear - and clearly stated in the Bovy-Tremaine paper, even in the abstract. Near the mid plane, the Chilean folks need a constant mean azimuthal velocity; Bovy and Tremaine say that a constant circular speed is more realistic. That's what I've been hearing about the observed speeds since the first moment I've heard about dark matter. So I find it bizarre for you to attack the assumption of constant circular speeds as a fringe speculation. It's what's been said about the dark matter models since the beginning and it's pretty much true for any distribution of the dark matter halo - and even largely true in models without dark matter.

"Other researchers also approximate the term in question to zero."

Well, you surely don't think that this sociological fact proves that this is a legitimate approximation for all purposes, do you?

You may find people and papers thinking it's essentially zero and you may find a justified paper explaining that it's nonzero and the nonzero value is justified by arguments. The result is compatible with other methods to determine the dark matter distribution and you can't find any mistake except for insisting on unjustified approximations written in some papers. So the appraisal of this situation is pretty clear, isn't it?

You and the Chilean have *no* genuine evidence against the model including the calculation by Bovy and Tremaine at all. Am I wrong? If I am not wrong, why are you implicitly suggesting that you have such evidence?

Best wishes
LM

reader PN said...

I was going to write a more thorough reply, but it is sadly clear that you haven't bothered to read the papers much at all beyond the abstracts.

Suffice it to say that MB does not make simple errors on the level of a physicist not knowing his Newton. No one, me included, are making claims to the contrary of observations from Oort in the 1930's onward (I did mention the problem of galactic rotational curves, didn't I?)

All I can do is, once again, to encourage a thorough reading of both papers. MB doesn't succumb to beginners errors. A more thorough discussion of their paper is clearly in order but the assumption that they mixed up their velocities is childish.

reader Luboš Motl said...

Dear PN, the Chilean folks screwed the velocity dependence on the radial coordinate.

Not only this fact was clearly demonstrated in Bovy's and Tremaine's paper but I have described everything that one needs to verify this claim in my previous comment. It's the absolute circular speed, and not the angular velocity, that is approximately constant in the Milky Way (and other galaxies). It's very clear which answer is right, which answer is wrong, and the Chilean answer is the wrong one while the Bovy-Tremaine answer is the right one.

You must be illiterate if you haven't been able to detect this self-evident error of the Chilean paper.

Since the effects of dark matter on the curves have been calculated, and it was many, many decades ago, there hasn't been any outstanding "problem of galactic rotational curves". By your repetition that there is this non-existent problem, you are just re-emphasizing your utter incompetence.

Cheers
LM

reader boguta said...

what is the evidence to suggest that dark matter in the Milky Way is made of particles? s

reader Luboš Motl said...

Dear Boguta, the stability of the required dark matter distribution implies that most of the dark matter has non-relativistic velocities, it's "cold dark matter".

The only type of cold dark matter that isn't composed of a gas of particles are MACHOs (Massive Compact Halo Objects) and they're pretty much excluded because if they existed, they would produce lots of gravitational lensing for galaxies behind them which is not observed.

So the dispersed particle-like dark matter is left. It may be composed out of WIMPs or axions, among less plausible choices I can't even enumerate.

Cheers
LM

reader rn said...

ultra-relativistic hot dark matter cannot clump fast enough to produce the small scale structure observed earlier in the universe and cannot have a big effect on galaxy rotation curves.

primordial fluctuations at the end of inflation grew and attracted dark matter and gas. this is supported by galaxies at higher redshifts that are more than present, smaller and their emission lines indicate star birth. this bottom-up growing of structures could happen only of the dark matter is cold with non-relativistic velocities.

i don't know much about dark matter but i think the neutralino is one of the most popular candidates. i don't know much about it but i think the axion was more popular 15-20 years ago but i don't hear it as much being a candidate now or much research done about it but this is something i am not sure about.

reader Rosy Mota said...

the invisible matter and e energy doesn't exist.all is based in deep mathematical divergences. believe that a scalar and vectorial , tensorial fields.the metric tensor as placed "distances" doesn't appear,but yes,sets of vectorial or complex numbers must to be fundamental entities in the universe.so as quaternions and octonios that are discrete and continue fields.that unify quantum theory and STR and GTR

reader Shannon said...

...and PMS.
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