Identifying Dark Matter

By Mark Trodden | August 27, 2006 9:53 pm

Last week’s dramatic evidence in favor of particulate dark matter, and weighing against modifications to gravity, as an explanation for the dynamics of galaxy clusters is another terrific result of observational cosmology. Equally important however, are the implications of these observations, at some of the largest scales in the universe, for the physics of the unimaginably small – particle physics.

The Bullet cluster result, building on earlier measurements, adds a crucial discriminating data point to the already overwhelming evidence that the universe contains matter of a type other than that which we see forming galaxies, stars, planets and us (called baryons). In fact, the evidence shows that there is five times more of this so-called dark matter in the universe than there are baryons. It is observed indirectly through many different cosmological methods and, indeed, is the reason that galaxies are able to form the way they do. This is confirmed not only through observations, but by comparing those to the results of increasingly accurate and beautiful numerical simulations of how cosmic structure crystallizes out of a soup of dark and baryonic matter.

That we are now more certain than ever that a critical component of cosmic dynamics is due to an entirely new type of matter, sharpens the associated particle physics question – how do these particles fit into our greater structure of fundamental physics – what is the dark matter?

There is a good reason that the answer is not yet known. The reason the dark matter is not seen glowing along with much of the rest of the material in galaxies is that it does not experience electromagnetism, the force of nature that leads to light. We think that dark matter particles must be only weakly interacting (electromagnetism is quite a strong force) and a consequence of this is that it is hard to get them to do anything measurable to material on Earth in order to betray their presence.

There are two ways to get around this. One is to build very sensitive detectors to measure even the smallest effects of dark matter on normal matter. After all, if there is five times more dark matter than baryons around, there should be lots passing through the Earth all the time as our solar system orbits the galaxy. There are many people devoted to these efforts and there are reasons to think that success is lurking in the not too distant future. The second way is, rather than waiting for cosmological dark matter to hit something in your detector, to smash particles together hard enough to create some of it all for yourself. If one can do this, then one would be able to measure its properties (its mass and the strengths of its interactions) and study how it fits into the overall structure of particle physics. This is where our colliders are indispensable.

The mere possibility that we may be able to probe the nature of most of the matter in the universe, hitherto undiscovered, using terrestrial machines is, to my mind, breathtaking science that is crying out to be done. However, in the case of dark matter, and the possibility that is made up of weakly interacting massive particles, there is also a relatively general and quite compelling argument, arising purely from particle physics, that there should be candidate particles within extensions of the standard model of particle physics.

The relevant particle physics/cosmology connection has its roots in the hierarchy problem – the problem of reconciling two wildly disparate mass scales; the weak scale (102 GeV) and the Planck scale (1019 GeV). This hierarchy is technically unnatural in particle physics, since, in general, the effect of quantum mechanics (here known as renormalization) is to make the observable values of such scales much closer in size.

One approach to this problem is to introduce a mechanism that cancels many of the quantum corrections, allowing the scales to remain widely separated even after quantum mechanics is taken into account. An example of such a mechanism (and the most popular one, for sure) is supersymmetry (SUSY). Supersymmetry is a beautiful idea that relates seemingly unrelated types of particles – fermions (such as the electron), and bosons (such as the photon) – to each other, and also to the underlying symmetries of space and time. A remarkable property of supersymmetric theories is that subtle cancellations between the effects of all the particles mean that the quantum effects I referred to above are rendered harmless. Even though supersymmetry is not an exact symmetry of our world, if it is exact just above the energy scales of the standard model and broken below, the structure of the standard model remains stable, since quantum corrections can only be effective up to the scale at which SUSY becomes exact (much lower than 1019 GeV in this case).

Another perspective is to view the hierarchy problem no longer as a disparity between mass scales, but rather as an issue of length scales, or volumes. The general hypothesis is that the universe as a whole is 3+1+d dimensional (so that there are d extra spatial dimensions), with gravity propagating in all dimensions, but the standard model fields confined to a 3+1 dimensional submanifold that comprises our observable universe. This submanifold is called the brane (as in membrane).

This is really a superstring-inspired modification of the Kaluza-Klein idea that the universe may have more spatial dimensions than the three that we observe. As in traditional Kaluza-Klein theories, it is necessary that all dimensions other than those we observe be compactified (wrapped up nice and small), so that their existence does not conflict with experimental data. The difference in the new scenarios is that, since standard model fields do not propagate in the extra dimensions, it is only necessary to evade constraints on higher-dimensional gravity, and not, for example, on higher-dimensional electromagnetism. This is important, since electromagnetism is tested to great precision down to extremely small scales, whereas microscopic tests of gravity are far less precise (although remarkable advances have been made in recent years, prompted in part by these theoretical ideas).

Since constraints on the new scenarios are less stringent than those on ordinary Kaluza-Klein theories, the corresponding extra dimensions can be significantly larger, which translates into a much larger allowed volume for the extra dimensions. This extra volume is a big deal, because the spreading of gravitational flux into the large volume of the extra dimensions allows gravity measured on our brane to be so weak, parameterized by the Planck mass MP, while the fundamental scale of physics M* is parameterized by the weak scale, MW, say.

The problem of understanding the hierarchy between the Planck and weak scales now becomes that of understanding why extra dimensions are stabilized at a linear size (~0.1 mm, for example) that is large with respect to the fundamental length scale (1/M*). This is the rephrasing of the hierarchy problem in these large extra dimension models.

I give the two approaches above as examples, and there certainly exist other approaches to the hierarchy problem. However, an important point is that the connection between dark matter candidates and new particle physics, just above the weak scale, with the power to address the hierarchy problem, is very general one, which is independent of the particular approach one might find most compelling. Here’s the brief argument.

  1. In the absence of extreme fine-tuning, the stability of the standard model demands that there be new physics not far above the weak scale – usually referred to as the TeV scale.
  2. This new particle physics will inevitably involve new particles and symmetries relating them to the standard model particles (otherwise, how are their interactions to help us with the hierarchy problem).
  3. A danger with introducing such new particles is that their interactions may ruin the spectacularly precise and tested predictions of the standard model. To avoid this, one usually needs to introduce a new discrete symmetry – basically saying that all standard model particles have one charge, and all new particles the opposite – to suppress unwanted interactions.
  4. There will inevitably be a lightest one of the new particles and it will be stable because it can’t decay into other new particles because they are heavier than it, and it can’t decay into SM particles, because that wouldn’t conserve the new discrete symmetry.
  5. In large ranges of parameter space, this lightest particle can be electrically neutral.
  6. So now we have a new, weakly interacting, stable particle at the TeV scale (a WIMP), demanded purely from particle physics considerations, that makes an excellent dark matter candidate.

This basic structure applies to the popular ideas for addressing the hierarchy problem that I discussed above. In SUSY, the lightest superpartner of the SM particles (the LSP) can be neutral and rendered stable by the R-Parity symmetry. In extra dimensional models, the lightest Kaluza-Klein particle (the LKP) may be dark matter, and is stable by virtue of KK-Parity, and in little Higgs models, which address the hierarchy problem in a different way, and which I have not discussed, a similar situation holds, with T-Parity playing the relevant stabilizing role.

Thus, although it is important to remember that there are other well-motivated dark matter candidates, such as the axion, discovering what new physics exists at the TeV scale may play a central role in uncovering the nature of the particulate dark matter that the Bullet cluster observations have so clearly revealed. This is one reason that cosmologists, as well as particle physicists, await with bated breath the upcoming operation of the Large Hadron Collider (LHC) at CERN. The world’s largest machine is designed to take us one level deeper into the mysteries of subatomic physics, and to help answer some of the most pressing questions in particle physics, such as the origin of electroweak symmetry breaking and the nature of the solution to the hierarchy problem. But these days, particle physics and cosmology walk hand in hand, and every new discovery at the LHC will help us to sharpen and expand our understanding of cosmic evolution. The Bullet cluster observations have provided a yet clearer hint that we are on the right path.

CATEGORIZED UNDER: Science
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  • Tom Ryan

    This our Kenedey Assassination Sean. Our passions/prefessions 9/11. Man this is our event horizon. Do you remember the day they proved dark matter/energy? Where where you when it hit you that there had ti be a 4th dimention…. and that this matter that we cannot even see, feel, hear or touch excpet at massive huge quabututes and at larger distances to see INTO IT?

    I have been at my abstracts CHANDRA all weekend watching this. This is the day our ubiverse changed. It’s just like 1905. Haha, CHANDRA is our Einstien.

  • http://gardnerman.com Michael Gardner

    “baited breath” -> “bated breath”

    That aside, thanks for a very interesting and informative article. This is an exciting time for both particle physics and cosmology!

  • Northwesterner

    There’s something I never understood about the Hierarchy problem. Does it have physical significance? Is it something strange about the world, or is it something strange about the way we perform quantum mechanical calculations?

  • loonunit

    Speaking of dramatic demonstrations, did y’all see last week’s article on Mike Griffin’s comments to the NASA Advisory Council members?

  • Jack

    No, baited breath is right. He’s been eating a lot of seafood.

    Anyway, great post. But aren’t there problems for supersymmetry in the higgs search data? I think I’ll bet on extra dimensions myself.

  • http://eskesthai.blogspot.com/2006/07/right-spin-for-neutrino-superfluid.html Plato
  • http://blogs.discovermagazine.com/cosmicvariance/mark/ Mark

    Ah, you get on a typing roll and before you know it you’ve forgotten your Merchant of Venice. Thanks Michael Gardner – I just fixed it.

  • Aaron S.

    I have a question, this is the first time i have been to this site, and i am very much enjoying the content. I would first like to say thank you for all the good info!

    But here is my question(s?)

    What ISN’T afftected by gravity?

    lol silly question, but with serious intent. is there a substance that we have identified that is not acted on by gravity?

  • http://rantingnerd.blogspot.com/ JD

    Haven’t y’all read The Amber Spyglass (book 3 of His Dark Materials, by Phillip Pullman)? Dark Matter is Angels!

    <voice imitate=”Charlton Heston from Soylent Green“>Dark Matter is ANGELS! IT’S MADE OF ANGELS!<voice>

    More seriously, though, are there any predictions from primordial nucleosynthesis (which predicts the various H/He/etc. ratios) that put limits on what sort of particles could make up dark matter? (Or would that depend too much on coupling constants that are yet To Be Determined?)

    Thanks –

    JD

  • Tom Ryan

    Anything without a mass. Remember photons, electrons, and even neuotrino’s have just the smallest amount of mass.

    Anything that can and does go past the speed of light isn’t effected by gravity. Remember, the faster you get, the more your mass becomes till you hit infinite mass. No mass, you are unrestricted with this fact. When you have mass, you get effected by gravity.

    Gravatationial waves are the one thing I can think of right now. We technically haven’t recorded any yet since our equipment isn’t sensative enough to do so yet (we think at least).

    When stars go nova, or when two super massive blackholes star orbiting each other then eventutally get drawn in, get closer and closer warping space-time more and more till they smash into each other. Since they combine into one object, and you can’t obrit yourself, the excess gravitationial waves get releases and are basically uneffected by matter.

    Hope that helps Aaron.

  • http://cosmicsutra.blogspot.com Subhendra

    One of the dark matter candidates the Chandra-HST-Magellan discovery rules out is the mirror universe (the standard model group G is extended to GxG and each sector interacts with the other only gravitationaly but mirror matter coupling with itself is just like standard model). The fact that the cross section per mass of this drak-matter is found to be 1 cm^2/gm probabaly rules out the mirror matter as a candidate for dark matter-an idea championed by Robert Foot.

  • Aaron S.

    Thanks Tom. I hope you don’t mind, i have another question…

    Since photons have a small amount of mass, how do they travel at C?

    my thoughts on a mass object traveling at C leans toward it having infinite energy, not tangible mass, seeing as energy and mass are really like dollar bills and coins…

    so a photon travelling at C would have infinite energy…

    or am i way out to lunch on this?

    Also WRT Gravity, all things affected by gravity should have some type of mass… right? so would it be safe to assume that hawking radiation is truly a massless substance? If so shouldn’t the things that aren’t affected by gravity be studied to understand what gravity REALLY is?

    I apologize if i am way off the subject… so many questions…

    thank you in advance.

    Aaron

  • anon

    >Anything without a mass. Remember photons,

    Gravity couples to energy, not mass. Photons are massless, but affected by gravity: gravitational fields can deflect light. This phenomenon was the first empirical confirmation of General Relativity.

    Great article by MT, a delight to read. Cheers.

  • http://blogs.discovermagazine.com/cosmicvariance/mark/ Mark

    Hi Aaron S.,

    Actually, Tom Ryan’s answer isn’t correct. Everything experiences gravity because gravity is due to the warping of spacetime due to energy (not mass). Photons therefore, just like gravitational waves, are precisely massless, yet experience and affect gravity because they have energy.

  • http://predelusional.blogspot.com/ Stephen Uitti

    What if there is no single particle? There are tons of nuetrinos out there, but due to their low mass, they can only make up 3% (or some such) of dark matter. Are there lots of other candidates? Perhaps they could add to near 100%. I doubt neutrinos could be even part of it. They fly like light, only with less obstruction. Light does not orbit galaxies.

  • Tom Ryan

    @ Aaron: Glad I can help at all! I’m really really excited about this stuff, especially about it with this profound moment we are in the history of cosmology, and particle physics. I’ve been chomping at the bit since I got out of undergraduate (I’m taking care of my sick father for the past year and a half, otherwise I’d like to tihnk I’d be in graduate school). Also, anyone who thinks I’m missing something, forgot to mentiontion something, or am misunderstanding something, please pop in and let me/us know.

    On the subject before of gravationial waves, NASA just FINALLY got a decent, stable simulation of two equal massed blackholes starting from random locations. Here is the page. They have a MPEG and Quicktime download of like 7mb showing you what it would look like on the space-time plane:
    http://www.nasa.gov/vision/universe/starsgalaxies/gwave.html

    Great fucking question by the way, I wondered this myself for a bit! Photons have zero rest mass, however when in motion they have a non-zero mass as does all forms of energy including charge (M). Gravatationial waves.

    I’ll get to the Energy turning into Mass thing, and why it wouldn’t make infinite mass, after lunch. The short answer is that you aren’t remember to keep things relative. The faster something moves, the harder it is to further increase their kinetic energy.

    ~Tom

  • Tom Ryan

    Sorry, sorry, my computer scrambled the order of stuff. Let me retype the last part.

    Great fucking question by the way, I wondered this myself for a bit! Photons have zero rest mass, however when in motion they have a non-zero mass as does all forms of energy including charge.

    I’ll get to the Energy turning into Mass thing, and why it wouldn’t make infinite mass, after lunch. The short answer is that you aren’t remember to keep things relative. The faster something moves, the harder it is to further increase their kinetic energy.

    @The Above People: Thanks for correcting me. I’m a little rusty and sometimes I don’t understand things as well as I think I remember!

    ~Tom

  • Aaron S.

    thanks guys, here is some more ignorance on my part.. lol ok just silly questions really. further into the looking glass…

    after looking into the gravity thing (lol dry humor… oops) it seems that the curvature of space-time is due to the pressence of mass, and that the mass itself is the reason of the curvature…

    and this makes sense that energy on a vector would appear to be straight, while in actuality it follows the curvature of the space time…

    however, i have one thing to note on this and i find nothing about it in anything i read as far as gravity goes.

    isn’t the effects of gravity instantaneous? for instance, if i were to create a planet and put it into space, it would take billions of lightyears for the light radiation to reach the edge of space, but its gravitational effects would be seen immediately.

    and if so wouldn’t it be possible that the gravity that scientists are associating with dark matter could actually be gravity signatures of celestial bodies that we are not able to see yet?

    and if gravity isn’t istantaneous, then couldn’t it be signatures of celestial bodies that have long since been destroyed and we are seeing residual effects of gravity?

    please shine some light on this for me!

    thanks

    Aaron

  • Chris W.

    Aaron S.,

    Instantaneous propagation of gravitational effects is incompatible with the special theory of relativity. That was one of the main reasons Einstein pursued the development of what turned out to be the general theory of relativity (1905 – 1917).

    (He realized in the course of this effort that gravitation is best understood as a manifestation of the curvature of spacetime (not just space!). The idea of spacetime itself was originally introduced in the context of special relativity.)

  • http://countiblis.blogspot.com Count Iblis

    Subhendra, it makes it unlikely that mirror matter in the form of a mirror gas accounts for a large fraction of the dark matter. But there are some other mirror matter models proposed by e.g. Mohapatra and Berezhiani in which sterile neutrinos form the bulk of the mirror matter.

    And it is, of course, possible that an “empty” mirror world exists. The existence of the mirror world can contribute to invisible decay of orthopositronium via orthopositronium-mirror orthopositronium oscillations, see here, but Randall-Sundrum type extra dimensions can also lead to the same effect. Neutron-mirror neutron oscillations is another possible signature of the mirror world.

  • http://gardnerman.com Michael Gardner

    Tom, the concept you are referring to is “relativistic mass,” which is not what most physicists mean when they use the word “mass.” When old physics textbooks used to say that “mass” increases with velocity they were really referring to relativistic mass; but that usage is deprecated. The word “mass” is now used to refer only to the rest mass of an object, and by that usage it is incorrect to say that a photon has mass when in motion (which it always is).

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  • http://www.pieterkok.com/index.html PK

    Great post, Mark! But I’m afraid I do not quite understand your description of the Hierarchy problem:

    This hierarchy is technically unnatural in particle physics, since, in general, the effect of quantum mechanics (here known as renormalization) is to make the observable values of such scales much closer in size.

    What do you mean by observable values and the effect of quantum mechanics? Isn’t everything quantum mechanical (particles as excitations of relativistic fields)? And is your use of renormalization here the same as the one in QFT? I suspect I’m missing something profound here.

    Also, I know next to nothing about SUSY. Can you recommend a good introduction at the basic QFT (and GR) level?

    cheers,
    PK

  • http://countiblis.blogspot.com Count Iblis
  • Aaron S.

    I am still missing some insight on the gravity question i mentioned earlier.

    Perhaps i missed something?

  • http://blogs.discovermagazine.com/cosmicvariance/mark/ Mark

    Aaron S.: The effect of gravity is actually not instantaneous. When a mass or energy distribution changes in a way that the gravitational field far away must change, it takes time for that change to be communicated to the far away place. How much time? Well, the infomation is carried by gravitational waves, moving at the speed of light. this follows directly from general Relativity.

    PK: I am indeed using renormalization in the QFT sense. The hierarchy problem is the following. Write down a classical Lagrangian containing all the fields of the standard model, including the Higgs field, with its mass set at the GeV or TeV scale. Then compute the quantum loops in the system (do renormalization). The Higgs, because it is a scalar particle, picks up quadratic corrections to its mass. If the standard model holds unchanged up to the Planck scale, then the Higgs mass will be renormalized up to that scale. The only way to avoid it is to fine tune the original bare mass you put in the theory to many, many decimal places. This doesn’t really happen for the other particles because if they’re fermions they only experience logarithmic running, which doesn’t require fine tuning to fix. Hope this helps.

    Unfortunately I don’t know of an intro to SUSY that springs to mind – maybe someone else has a favorite.

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  • http://www.pieterkok.com/index.html PK

    Hi Mark, yes this makes it all clear, thanks! Let’s hope another reader knows of an introduction to SUSY. BTW, am I correct in thinking that it is essentially an SU(5) symmetry (12 particles + 12 superpartners = 5^2 – 1), just like QCD is SU(3)?

  • http://countiblis.blogspot.com Count Iblis

    A Supersymmetry Primer

    Authors: Stephen P. Martin
    Comments: 126 pages. Version 4 (June 2006) contains very numerous additions, updates and improvements throughout. Previous versions are obsolete. Errata and a version with larger type (12 pt, 140 pages) can be found at this http URL

    I provide a pedagogical introduction to supersymmetry. The level of discussion is aimed at readers who are familiar with the Standard Model and quantum field theory, but who have had little or no prior exposure to supersymmetry. Topics covered include: motivations for supersymmetry, the construction of supersymmetric Lagrangians, supersymmetry-breaking interactions, the Minimal Supersymmetric Standard Model (MSSM), R-parity and its consequences, the origins of supersymmetry breaking, the mass spectrum of the MSSM, decays of supersymmetric particles, experimental signals for supersymmetry, and some extensions of the minimal framework.

  • http://blogs.discovermagazine.com/cosmicvariance/mark/ Mark

    Good choice – thanks!

  • http://www.pieterkok.com/index.html PK

    That looks like something I can understand, thanks Count Iblis!

  • http://eipipuz.blogspot.com Guillermo Alcántara

    Hi guys, I don’t have any real background on physics, but have always been interested in it. So I wonder, can anyone explain to me why does extra dimensions leave enough space for gravity to irradiate while electromagnetism doesn’t? Is it because there are no magnetic monopoles?

    If I make no sense, sorry.

    Thanks to all the writers, this is a great blog!

  • Annie

    Mark — I’ve heard you’re coming to my school on Sept. 11! I’m in the ‘wrong’ department — over here in astro we don’t always hear too much about physics colloquia. What will you be speaking about?

  • http://blogs.discovermagazine.com/cosmicvariance/mark/ Mark

    Hi Annie. I’ll be talking about “Gravitational Approaches to Cosmic Acceleration”. Although I’m speaking in Physics, when I come to Cornell (pretty often), I spend a lot of time in astronomy with my collaborators there. Hope to see you at the talk.

  • Bob E.

    Can we suppress the profanity (Tom Ryan)? This has been a very “classy” (can’t think of a better adjective, but you all know what I mean) blog IMO, as are most of the physics blogs. I read this blog regulary and as a physics grad student learn a lot. I don’t need to read gutter language – I already know that, and it adds nothing.
    Bob E.

  • http://quantumnonsense.blogspot.com/ Qubit

    I’ve got a feeling that dark matter is something to do with pairs of virtual particles, appearing near black hole(s?). One escapes and one falls in. The escaping particle is pushed passed the observable horizon of the one that falls in, which then falls towards the lower energy state of the universe. The lagrange points of black hole(s?) (Through its own imaginary duality (which should have a non zero difference) are projecting its mass through the escaping particle). Sort of an optical illusion that has become real.

  • Jeff

    Qubit, isn’t that just Hawking radiation? Anyway, a baryonic particle formed out of the vacuume at the event horizon of a black hole would still be baryonic, hence, something we could “see”, not dark.

  • http://eskesthai.blogspot.com/2005/11/oh-my-god-particle-revisited.html Plato

    Gerard t’ Hooft:

    In particular the gravitational interactions are responsible for the unitarity of the scattering against the horizon, as dictated by the holographic principle, but the Standard Model interactions also contribute, and understanding their effects is an important first step towards a complete understanding of the horizon’s dynamics. The relation between in- and outgoing states is described in terms of an operator algebra. In this paper, the first of a series, we describe the algebra induced on the horizon by U(1) vector fields and scalar fields, including the case of an Englert-Brout-Higgs mechanism, and a more careful consideration of the transverse vector field components.

    http://arxiv.org/PS_cache/gr-qc/pdf/0504/0504120.pdf

    High energy photons at the time of? You needed ways in which to see this?

    You develope a science and a “quantum” computer?

    So the technology has to be developed to see ever deeper as we “ponder the energy” of our reductionistic views in the early universe?

  • http://quantumnonsense.blogspot.com/ Qubit

    Jeff, I know that is true of current thinking, but I don’t think that idea it entirely right. I think Hawking radiation is about to get an overhaul.

  • http://arunsmusings.blogspot.com Arun

    Question – just how weakly interacting can dark matter be? E.g., if dark matter only interacted gravitationally with itself and normal matter, it would be very difficult to clump it.

  • http://arunsmusings.blogspot.com Arun

    Another question – with lots of weakly interacting dark matter around, wouldn’t black holes grow much faster? Would black hole evaporation be the most efficient way to convert dark matter into ordinary matter?

  • http://arunsmusings.blogspot.com Arun

    Yet another question/remark regarding the following:

    Mark wrote:

    PK: I am indeed using renormalization in the QFT sense. The hierarchy problem is the following. Write down a classical Lagrangian containing all the fields of the standard model, including the Higgs field, with its mass set at the GeV or TeV scale. Then compute the quantum loops in the system (do renormalization). The Higgs, because it is a scalar particle, picks up quadratic corrections to its mass. If the standard model holds unchanged up to the Planck scale, then the Higgs mass will be renormalized up to that scale. The only way to avoid it is to fine tune the original bare mass you put in the theory to many, many decimal places. This doesn’t really happen for the other particles because if they’re fermions they only experience logarithmic running, which doesn’t require fine tuning to fix. Hope this helps.

    This is a good argument if and only if we view a QFT model as a theory that are effective only upto a certain scale. Since the Standard Model is not a theory of everything it is legitimate to expect new physics to kick in at some scale, and then the bare Higgs mass at that scale may require fine tuning.

    But if we take the Standard Model purely as a mathematical model with no concern about physics at a higher energy scale, then the cutoff goes to infinity, and the question of fine tuning to many decimal places is as bad or as irrelevant for logarithmic running as for quadratic running. Either this model can have non-zero, non-infinite masses naturally, or not.

    If the model can have non-zero, non-infinite masses naturally, then there is no hierarchy problem in a fundamental sense, it is purely an artifact of our limited computational methods. We may have a secondary hierarchy problem, which is how does the model generate mass scales from the fraction of a eV to a TeV, but the finite small (compared to infinity!) Higgs mass is not a problem. In other words, why doesn’t everything weigh the same as the Higgs?

    If the model cannot have non-zero, non-infinite masses, what we’re saying is that our model as a physical theory has finite GeV-TeV masses purely because of the intervention of new physics at some high energy scale, and to me, this is even more mysterious than the original hierarchy problem.

    Another possibility is that the Standard Model is not well defined as a mathematical object.

    The question is – is any of the above correct?

  • http://www.geocities.jp/imyfujita/index.html Iori Fujita

    These galantic clusters are dark. Without X-ray we can not see them. The gas is only an exhaust. Are there any invisible galaxies?

    The spherical harmonics are the angular portion of the solution to Laplace’s equation in spherical coordinates where azimuthal symmetry is not present. And there are three types of galaxies.
    elliptical galaxy e.g. NGC4881 Three Dimension GM(

  • http://www.geocities.jp/imyfujita/index.html Iori Fujita
  • Ralph Giles

    Guillermo,

    Bee has a nice description of how extra dimensions can make gravity weaker in her post on extra dimensions. As near as I can tell, no one knows of an actual reason for electromagnetism to be confined to 4+1 dimensions while gravity isn’t though, It’s just a way of explaining the discrepancy.

  • http://blogs.discovermagazine.com/cosmicvariance/mark/ Mark

    Am running out, but just a quick answer. Within string theory one can use D-branes to localize standard model particles (since they correspond to the excitations of open strings, which must end on the D-brane), while gravitational modes (which correspond to closed string excitations), can propagate anywhere.

    There are also other, field-theoretic, ways of localizing matter on a submanifold, by using a topological defect.

  • Vince

    Can you have one end on one D-brane and another end on a different D-brane or is that not mathematically allowed? Or maybe I’m taking this picture too literally?

  • http://blogs.discovermagazine.com/cosmicvariance/mark/ Mark

    Yes.

  • http://www.physicsmyths.org.uk Thomas Smid

    I am actually somewhat puzzled why all astronomers are so confident that they know the mass of the ordinary matter (i.e. the mass of stars) in a galaxy so exactly. The ‘known’ figures are largely based on the apparent luminosity of stars and the (more or less empirical) mass-luminosity relationship. It is obvious that any errors in the latter will have a crucial influence: according to the mass-luminosity relationship, a star with half the mass has only 1/10 of the luminosity, so with 10 times as many stars of half the mass, one would have the same overall brightness but 5 times the overall mass. Looking at http://planetquest.jpl.nasa.gov/SIM/science_henry.pdf , one finds indeed that the luminosities for stars less than 1 solar mass are uncertain by about 2-3 magnitudes (i.e. up to about a factor 10). It is quite remarkable that the mass luminosity relationship, which a) is quite uncertain for low mass stars, b) obtained only in the solar neighbourhood and c) obtained only from double stars, is applied to all stars in our or other galaxies regardless. I don’t therefore think that the observations justify the conclusion of dark matter here. There might be much more mass in the form of ordinary stars than thought.

    With regard to the ‘dark matter’ conclusions based on the observations of the motion of gas (rather than stars) in galaxies, see also my webpage Galactic Rotation Curves and the Dark Matter Myth.

    Thomas

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Cosmic Variance

Random samplings from a universe of ideas.

About Mark Trodden

Mark Trodden holds the Fay R. and Eugene L. Langberg Endowed Chair in Physics and is co-director of the Center for Particle Cosmology at the University of Pennsylvania. He is a theoretical physicist working on particle physics and gravity— in particular on the roles they play in the evolution and structure of the universe. When asked for a short phrase to describe his research area, he says he is a particle cosmologist.

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