MOND Also Lurks out There—The Infamous Dark Matter

Ninety-five percent of the universe has gone missing. Or has it? By Mordehai Milgrom OF ALL THE MANY MYSTERIES of modern astronomy, none is more vexing than the nature of dark matter. Most astronomers believe that large quantities of some unidentified material pervade the universe. Like a theater audience that watches the herky-jerky gestures of a marionette and infers the presence of a hidden puppeteer, researchers observe that visible matter moves in unaccountable ways and conclude that unseen matter must be pulling the strings. Yet this dark matter has eluded every effort by astronomers and physicists to bring it out of the shadows. A handful of us suspect that it might not really exist, and others are beginning to consider this possibility seriously. The dark matter problem arose because of a mis- match in the masses of galaxies and larger cosmic structures. The constituents of these systems—stars and gas in the case of galaxies, gas and galaxies in the case of galaxy clusters—move about but do not escape, because they are checked by the gravitational pull from the rest of the system. The laws of physics tell us how much mass has to be present to counterbalance the motions and thereby prevent the dispersal of the system. Disconcertingly, the tally of mass that astronomers actually observe falls far short of that. This mass discrepancy is ubiquitous. It appears in practically all systems, from dwarf galaxies through normal galaxies and galaxy groups on up to the vast superclusters. The magnitude of the discrepancy ranges from a factor of a few to a factor of hundreds. The need for extra matter arises not universe, a phenomenon that neither nor- tested. Might it go amiss? If the laws only in well-formed galactic systems but mal nor dark matter can explain [see break down, then modifying them might also through the universe at large. Long “The Quintessential Universe,” by Jere- obviate dark matter. before galaxies even formed, the universe miah P. Ostriker and Paul J. Steinhardt; Such a modification would not be was filled with a plasma of atomic nuclei Scientific American, January 2001]. without precedent. Two drastic changes and subatomic particles. Radiation suf- In sum, astronomers widely believe to Newtonian physics have already fused the plasma and kept it extremely the current energy content of the universe proved necessary. The first upgraded smooth. Fluctuations in the density of this to be roughly 4 percent ordinary (or “bary- Newtonian dynamics to the theory of rel- plasma did not have a chance to grow and onic”) matter, about a tenth of which is ativity—both the special theory (which develop into galaxies until after the plas- seen as stars and gas; a third dark matter changed Newton’s second law) and the ma had turned into a neutral gas, which in some unknown form; and two thirds general theory (which altered the law of does not interact with radiation as strong- dark energy, the nature of which is even gravity). The second led to quantum the- ly. We know when this neutralization oc- less understood. ory, which accounts for the behavior of curred and what the strength of the den- microscopic systems and even macro- sity fluctuations was then. The problem is Under Cover of Darkness scopic systems under certain circum- that there just wasn’t enough time for DARK MATTER is the only explanation stances. The two proven extensions of those fluctuations to become the galaxies that astronomers can conjure up for the Newtonian dynamics come into play un- we observe. Dark matter would help in various mass discrepancies, if we cleave to der extreme conditions, such as extreme that, being neutral by definition, it would the accepted laws of physics. But if we ac- speeds (special relativity) or extremely not be homogenized by radiation. There- cept a departure from these standard laws, strong gravity (general relativity). The fore, it would have been contracting all we might do away with dark matter. bulk of the phenomena connected with along. Dark matter would have had The diverse appearances of the mass galactic dynamics involves none of these enough time to form galaxy-mass bodies. discrepancy, as reflected in the motions particular conditions. Common knowledge has it that part inside galactic systems, stem from the use What attributes of galactic systems of this extra mass consists of ordinary of a single formula in Newtonian physics. are so extreme that they might require yet matter that gives off too little radiation This formula combines two basic laws: another modification? The first possibil- for present technology to detect: planets, Newton’s law of gravity (which relates ity that comes to mind is size. Perhaps dwarf stars, warm gas. Such material is the force of gravity between bodies to the gravity departs from the Newtonian law more precisely called dim matter. It could bodies’ masses and separation) and New- at large distances. As early as 1923, Eng- represent up to 10 times as much matter ton’s second law (which relates force to lish astronomer James H. Jeans proposed as astronomers see, but even so it could acceleration). The acceleration of a body modifying the distance dependence of the account for only a small fraction of the in orbit depends on the velocity and size law of gravity on galactic scales. But the missing mass. When researchers refer to of the orbit. Putting all this together, one discrepant observations he sought to ex- dark matter, they usually mean an exotic derives the connection among mass, ve- plain were unrelated to dark matter and, breed of matter that makes up the differ- locity, and orbital size or distance. in any event, were later refuted. ence. To add to the confusion, they also These laws accurately explain the Another modified distance depen- suspect the existence of dark energy, a dis- flight of a ballistic missile and the mo- dence was proposed in 1963 by Arrigo tinct type of energy that would produce tions of the planets. But their extrapola- Finzi, then at the University of Rome, as the observed accelerated expansion of the tion to galaxies has never been directly a possible solution to the dark matter ) Overview/Alternative to Dark Matter this page ■ Astronomers have two ways to determine how much matter fills the universe. They tot up everything they see. And they measure how fast the visible objects move, apply the laws of physics and deduce how much mass is needed to generate the gravity that restrains those objects. Vexingly, the two methods Newton's give different answers. Most astronomers conclude that some invisible mass second law MOND also lurks out there—the infamous dark matter. ); BRYAN CHRISTIE DESIGN ( ■ units) (arbitrary rce

Perhaps the fault lies not in the matter but in the laws of physics. The author Fo has proposed a modification to Newton’s laws of motion (see graph at right)— or, equivalently, of gravity—that would explain away the discrepancy. 10–10 3 × 10–10 5 × 10–10 ■ Acceleration (meters per second per second)

The modification, known as MOND, does an amazingly good job of reproducing preceding pages observations—better, in many ways, than dark matter does. That said, MOND NEW THEORY, known as MOND, changes Newton’s has some problems, which may be unimportant or may be fatal. second law of motion at low accelerations. SLIM FILMS (

44 SCIENTIFIC AMERICAN AUGUST 2002 MAKING THE ROUNDS

JUST AS THE PLANETS in the solar system orbit around the sun, stars in a galaxy orbit around the galactic center. For example, the sun completes one circuit of the Milky Way every 200 million years or so. Stars in the disks of spiral galaxies have nearly circular orbits, and their orbital speed depends on their distance from the center. Two effects determine the speed: the distribution of mass and the weakening of the Orbital velocity of stars force of gravity with distance. The first effect is simply a matter of geometry—the amount of mass contained within a stellar orbit increases with distance. This effect dominates in the Galactic center inner reaches of the galaxy. Farther out, the second effect becomes more important. The net result is that the orbital speed initially increases but then levels off and begins to decrease. This relation between speed and distance is known as the rotation curve. According to Newton’s laws, the rotation curve should continue to decrease forever. If MOND is correct, however, it should reach a constant value. —M.M.

problem in clusters. But in the early applies as usual: force is proportional to tained within a certain radius. Then, by 1980s I showed that such modiﬁcations acceleration. But when the acceleration is Newtonian dynamics, beyond this radius

of the distance dependence of gravity fail small compared with a0, Newton’s sec- the speed of objects in circular orbits (such to reproduce the observations. ond law is altered: force becomes propor- as gas or stars) should decrease with in- What, then, can work? After system- tional to the square of the acceleration. By creasing radius. This is what happens in the atically considering different attributes, I this scheme, the force needed to impart a solar system. The bulk of the solar system’s zeroed in on acceleration. The accelera- given acceleration is always smaller than mass is contained in the sun, and the or- tion in galactic systems is many orders of Newtonian dynamics requires. To account bital velocity of the planets decreases with magnitude smaller than in everyday ex- for the observed accelerations in galaxies, distance. Mercury trundles around the sun perience. The acceleration of the solar MOND predicts a smaller force—hence, much faster than Earth does, for example. system toward the center of our galaxy less gravity-producing mass—than New- Where MOND applies, however, the sit- (about one angstrom, or 10–10 meter, per tonian dynamics does [see illustration on uation is radically different. At sufﬁciently second per second) is one hundred-bil- opposite page]. In this way, it can elimi- large distances from the center of a galaxy, lionth the acceleration of the space shut- nate the need for dark matter. the orbital velocity should stop decreas- tle toward the center of Earth (about 10 In the outskirts of galaxies, the accel- ing and reach a constant value. This con- meters per second per second). Nearly 20 eration produced by gravity decreases stant velocity should be proportional to years ago I proposed a modiﬁcation to with distance and eventually goes below the fourth root of the galaxy’s mass.

Newton’s second law that changed the a0. Exactly where this happens depends How does MOND fare when con- relation between force and acceleration on the value of a0 and on the mass. The fronted with the data? Orbital velocities when the acceleration is low. This was higher the mass, the farther out the effects in spiral galaxies, instead of declining

the beginning of the idea called MOND, of MOND set in. For the value of a0 that with increasing distance from the galactic for Modiﬁed Newtonian Dynamics. is required by the data, and for a galaxy center, ﬂatten out to a constant value, as of typical mass, the transition takes place predicted by MOND. Moreover, accord- Building Up Speed several tens of thousands of light-years ing to an observed correlation known as MOND INTRODUCES a new constant from the center. For the mass of a typical the Tully-Fisher relation, this constant ve- of nature with the dimensions of acceler- cluster of galaxies, it happens at a few mil- locity is proportional to the fourth root

ation, called a0. When the acceleration is lion light-years from the center. of the galaxy’s luminosity. This, too,

DON DIXON much larger than a0, Newton’s second law Suppose the bulk of a galaxy is con- emerges naturally from MOND. The key

www.sciam.com SCIENTIFIC AMERICAN 45 eration inordinarygalaxiesexceeds barely beseenatall.Whereastheaccel- lar agglomerationssowispythattheycan 46 of low-surface-brightnessgalaxies I formulatedit.Oneexampleisthenature effects thatcouldnotevenbetestedwhen larly intriguingisthatitpredictedmany struction. WhatmakesMONDparticu- indeed, theyfurnishedcluesforitscon- ready insightwhenIproposedMOND; correlation. even tighterthanthevelocity-luminosity tion: adirectvelocity-masscorrelationis cent observationsvindicatetheassump- is proportionaltomassornearlyso.Re- assumption isthattheluminosity,inturn, ward thecenteranddropsbelow THE AUTHOR outskirts, theaccelerationinlow-surface- Glimpses oftheseregularitieswereal- SCIENTIFIC AMERICAN ALL TYPESOFGALACTICSYSTEMS and clusters globular starclusterstodwarfgalaxiesgalaxygroups observed andtheinferredmass.Thisdiscrepancyscales mology andhigh-energy astrophysics. His otherscientific interestsconcerncos- tent ofthealternativestodarkmatter. MOND, themostsuccessfulandpersis- tute inRehovot,Israel.Heisthefather of oretical physicsattheWeizmann Insti- MORDEHAI MILGROM Mass Discrepancy (inferred mass/observed mass) 100 10 1 0.01 Small galaxy groups Small galaxy — suffer fromadiscrepancybetweenthe Dwarf spheroidal galaxies is professorofthe- a 0 — in the a — Dwarf spiral galaxies MO 0 stel- T ranging insizefrom to- ypical Acceleration (inunits MOND of parameter ND IN GALACTIC SYSTEMS light tomass.The inferredvalueofthispa- galaxy: theconversion factorfromstar- parameter thatmustbeadjusted foreach page 50 MOND isremarkable[ dictions. Andthecorrespondence with enough tocomparewiththeoretical pre- tronomers madeobservationsdetailed tance. Onlysincethelate1980shaveas- cise variationoforbitalvelocitywithdis- galactic rotationcurves magnitude ofthediscrepancies. rectly anticipatedthis.Italsoforesawthe American, ies,” by G nary galaxies[see“TheGhostliestGalax- ately largerinthesegalaxiesthanordi- mass mismatchisindeeddisproportion- Since then,theyhavediscoveredthatthe ies andhadanalyzednoneinanydetail. only afewlow-surface-brightnessgalax- pounded MOND,astronomersknewof out suchagalaxy.AtthetimeIpro- mass discrepancyshouldbeseenthrough- everywhere. AccordingtoMOND,the brightness galaxiesissmallerthan Another successconcernstheshapeof CU R Ga VE PREDICTED BYMOND ]. Thesecomparisonsinvolveone la regory D.Bothun; xy February 1997]. MONDcor- February 1997]. clusters 0.1 ag aaycutr.— large galaxyclusters. the correlation.MOND’smainfailureoccursincoresof MOND predicts.Dark-mattermodelshavenoexplanationfor inversely withthecharacteristicacceleration,justas see illustrationon — that is,thepre- Scientific Spiral galaxies a 0 ) a 0 G lobular clusters tional adjustableparameterspergalaxy comparisons involveatleasttwoaddi- tions. Fordarkmatter,incontrast,the rameter agreeswiththeoreticalexpecta- in theformof feeble starsorlukewarm amounts ofdim observations areincomplete. Significant haps thetheoryitselffails,butperhaps the not sweepawayalltheinvisible mass.Per- that amismatchremains.MOND does on theinnerpartsoftheseclusters, wefind can explain.If,however,weconcentrate about afactoroffiveto10,whichMOND they typicallyshowamassdiscrepancyof ters. Ifweconsidertheclustersatlarge, one exceptionisfoundin predictions [ most completelyagreeswithMOND’s the typicalacceleration,patternal- one plotsthemassdiscrepancyagainst NOHRGALACTIC OTHER IN to theException Rule? rotational dataaswell dark mattertheoriesdonotexplainthe matter. Despitethisflexibility,current namely, theextentandmassofdark Cluster cores see illustrationabove matter 1 — as MONDdoes. ordinary matter rich galaxyclus- systems, when AUGUST 2002 M.M. ]. The —

DON DIXON

tem, thelargebackgroundacceleration erence. OnEarthorinthenearsolarsys- with respecttoanabsoluteframeofref- MOND criterionisthefullacceleration ble. Theaccelerationthatentersthe fortunately, laboratorytestsareinfeasi- well asastronomicalobservations.Un- MOND usingphysicsexperimentsas MOND forhighaccelerations of Pluto.Tobesure,thestructure the sunasEarthis,farbeyondorbit one goesabout10,000timesasfarfrom Newtonian dynamics the theorydepartsonlyminutelyfrom phenomena at hand. it cannotyetbeappliedtoallthe relevant veloped. AndMONDislimited, because indeed, theconceptofdarkmatter) de- tions, muchasquantummechanics (and, scribe andexplainabodyof observa- ples. Itwasbornfromadirectneedtode- not constructedon,fundamentalprinci- that ithasnotbeenmotivatedby,andis theory. Byphenomenological,Imean the moment,alimitedphenomenological diverse appearances. 50 value the successoftheorythatsame dictions forgalacticsystems.Itispartof appear inmanywaysMOND’spre- other factors revolution aroundthesunandmyriad caused byEarth’sgravity,itsrotation, gas second per many rolesinquantumtheory,sodoes December 1998]. and theCitizen, Gas Leak?”byGeorgeMusser;Science plained withinMOND[see“Pioneering craft, ifverified,couldbenaturallyex- anomaly inthemotionsofcertainspace- duce observableeffects.Theclaimed very small,isstilllargeenoughtopro- It mightbethatthedeparture,though ing thesundoesnotfallbelow planets. Theaccelerationofbodiesorbit- MOND bystudyingthemotionsof nally. Similarly,itwouldbehardtotest with smallrelativeaccelerationsinter- MOND evenifwecouldcreateasetup — Ideally, onewouldliketocheck The mainreason isthatMONDhas Successful asitmaybe,MONDis,at Just asPlanck’sconstantappearsin SCIENTIFIC AMERICAN — could belurkinginthesesystems. approximately oneangstromper — would masktheeffectsof Scientific American, — works forallthese — is notyetknown. — a 0 where until a — 0 compatible withgeneralrelativity. theorists havenotmadequantumphysics today, despitelong,concentratedefforts, compatible withspecialrelativity.Even equation, andmoretimestilltobemade be encapsulatedintotheSchrödinger Max Planck,EinsteinandNielsBohr,to for thequantumidea,asputforthby ter oftime.Afterall,ittookmanyyears ble todoso;perhapsitissimplyamat- special orgeneral.Perhapsitisimpossi- obeys theprinciplesofrelativity,either not beenincorporatedintoatheorythat smaller than involve, ontheonehand,ac present purviewofMONDarethosethat H PHENOMENA THE Beyond the Ken MOND galactic center. speed varieswithdistancefromthe for variousgalaxies,showinghoworbital the MONDprediction. the measurementprecision,matches A straightlinefitsthedataand,within is correlatedwiththegalaxies’brightness. outskirts speed ofstarsinthegalaxies’ sample ofspiralgalaxies,theorbital is theso-called with remarkableprecision.

Velocity Velocity Below isasampleofrotationcurves

(kilometers per second) (kilometers per second) reproduces keygalaxyobservations 150 150 100 100 50 50 0 0 a Distance (kiloparsecs) Distance (kiloparsecs) 0 024 051015 (so thatMOND Tully-Fi MOND G 09NC20 UGC 128 NGC 2403 UGC 7089 531NC27UGC 6399 NGC 247 F563-1 that falloutsidethe THEORY VERSUS DATA hrrelation.Ina sher N ewton 80510152068 010203040 At theright celerations plays a — 0510 M.M. er than acceleration nearablackholetobesmall- second criterionbutfailthefirst:for ty isalsocalledfor).Blackholesmeetthe extremely stronggravity(sothatrelativi- role) and,ontheother,extremespeedsor can explainthedisparityinbothcases. But wedonotyetknowwhetherMOND that observationsofgalacticdynamicsdo. lensing exhibitthesamemassdisparity servations thatmakeuseofgravitational tific American, scope,” byJoachimWambsganss; itational lensing[see“Gravity’sKaleido- treat thismotion,whichpertainstograv- both criteria.MONDcannotproperly galactic systems,however,doessatisfy propagating inthegravitationalfieldsof er thantheobservableuniverse.Light Galactic Luminosity (solar units) 10 10 10 11 10 9 01020300 200 100 50 a 0 , theholewouldhavetobelarg- (kilometers persecond) Ro ta 246 02 t ional Velocity November 2001].Ob- AUGUST 2002 Scien-

top: DON DIXON; SOURCE: ROBERT H. SANDERS Kapteyn Astronomical Institute AND MARC A. W. VERHEIJEN University of Wisconsin–Madison; bottom: BRYAN CHRISTIE DESIGN; SOURCE: STACY S. MCGAUGH University of Maryland COMMENTARY Not a Bad Idea MOND is out of the mainstream, but it is far from wacky By Anthony Aguirre

lthough the great majority of astronomers believe that dark or second view to the third. Why? I think there are three reasons. Amatter exists, an alternative hypothesis—a modification of First, as both its opponents and proponents point out, MOND is Newtonian gravitational dynamics (MOND)—has quietly endured a modification only of Newtonian dynamics. Despite some effort, since its proposal in 1983. As Mordehai Milgrom discusses in the MOND’s proponents have yet to formulate it in a way that can be accompanying article, MOND can claim an impressive number of applied to post-Newtonian phenomena such as gravitational correct predictions regarding the dynamics of galaxies. The lensing and cosmic expansion. Either no such theory exists or it is reactions of most astronomers fall into three categories: inherently difficult to develop. Whatever the reason, MOND has been unable to confront—and hence pass or fail—some key tests. 1. MOND is a tautology. It explains only what it was expressly Second, it is not clear that MOND works well in systems other designed to explain. It has made a few fortuitous predictions, than galaxies. For example, its predictions about the temperature but the success of those predictions has been exaggerated by of hot gas in clusters of galaxies disagree starkly with observations, its proponents. unless clusters are dominated by—what else?—undetected matter. 2. MOND describes a surprising, even mysterious, regularity in the One might hope (as do MOND’s proponents) that this matter could formation and evolution of galaxies. The standard theory of take a recognizable but hard-to-see baryonic form such as small gravity still applies and dark matter still exists, stars or warm gas. Those possibilities are not but somehow the dark matter emulates MOND. currently ruled out, but they are strongly When applied in detail to unusual galaxies or to constrained both observationally and systems other than galaxies, MOND will theoretically. And it is rather disquieting that eventually be shown to fail. dark matter (even if in a prosaic form) must be 3. MOND replaces Newtonian dynamics under postulated to save a theory devised to certain conditions. It is one aspect of a theory of eliminate dark matter. gravitational dynamics that will supplant The third reason, related to the first two, is Einstein’s general theory of relativity. that standard dark matter theory has scored some impressive triumphs in recent years. The first view, through uncharitable, was the Numerical simulations predict a spatial one held by most astrophysicists for much of distribution of intergalactic gas that is in MOND’s history. In recent years, however, exquisite agreement with observations. outright rejection has become much less Independent estimates of the mass of dark tenable. MOND’s myriad predictions have been matter in clusters all agree with one another. The confirmed. Many of these studies have been performed by those predicted growth of structures correctly links the galaxy distribution critical of, or neutral toward, Milgrom’s hypothesis. Moreover, MOND we see on large scales today with the tiny temperature ﬂuctuations in reproduces the statistics of galaxy properties at least as well as the cosmic microwave background radiation from 13 billion years ago. dark matter models do, even though these models describe crucial So what are astronomers to do? Those who are most sympathetic aspects of galaxy formation in an ad hoc way. to Milgrom’s hypothesis should continue the search for a fundamental Most impressively, MOND can predict the details of galaxy theory of MOND, without which the idea will never draw the majority rotation using only the distribution of visible matter and an of physicists away from the standard paradigm. For others, I think assumed (fixed) ratio of mass to luminosity—a feat beyond the that it is productive to study, test and use MOND as a convenient ability of dark matter models. These predictions and the rule of thumb whether or not one accepts a modiﬁcation of Newtonian observations they are compared with go far beyond what was dynamics. Perhaps we could call it Milgrom’s Fitting Formula, or MIFF, available at the time of MOND’s formulation. MOND is no tautology. to emphasize that we are using it as a practical tool while reserving Meanwhile standard dark matter theory has run into difficulty judgment about whether standard physics is indeed wrong. when applied to galaxies. For example, it predicts that the dark matter If general relativity is correct, and dark matter real, then as the cores of galaxies should be far denser than observations indicate. precision of measurements increases, MIFF will ultimately fail. In Such problems could be an artifact of computational limitations; the meantime, MIFF can provide a compact summary of a great deal researchers still lack computers powerful enough to simulate galaxies of knowledge concerning galaxy formation and evolution. in full. But many theorists have taken the discrepancies seriously enough to consider modifications of the properties of dark matter. Anthony Aguirre is a theoretical cosmologist at the Institute for The successes of MOND and the difficulties for dark matter Advanced Study in Princeton, N.J. He is the lead author of two have converted a number of astronomers from the first view critical studies of MOND, available online at arXiv.org/abs/astro-ph/

SLIM FILMS to the second. Relatively few, though, have gone from the first 0105184 and arXiv.org/abs/hep-ph/0105083

www.sciam.com SCIENTIFIC AMERICAN 51 A second system that requires MOND This idea falls within the framework of year Manoj Kaplinghat and Michael S. and relativity is the universe at large. It an old concept, Mach’s principle, which Turner, both then at the University of follows that cosmology cannot be treat- attributes inertia to such an interaction. Chicago, claimed that the appearance of ed in MOND. This incapacity extends to Physics abounds with instances in a characteristic acceleration akin to a0 oc- questions relating to incipient structures which the effective inertia of particles is curs naturally in dark matter models. Ac- in the universe. MOND can be applied to not an inherent property but rather is pro- cording to their scenario, these models well-formed systems that are detached duced by their interaction with a back- predict the formation of dark matter ha- from the global cosmological soup, but it ground medium. For example, electrons los of a restricted type around galaxies. cannot describe the early moments be- in solids sometimes behave as if their in- Subsequently, however, I pointed out fore galactic systems became distinct. ertia has been greatly modiﬁed by the rest that this scenario does not work. Kaplin- Researchers have made preliminary of the solid. Might an analogous effect be ghat and Turner based their work on If we accept a departure from the standard laws of physics, we might do away with dark matter. attempts to deal with what these phe- responsible for genuine inertia? If so, what crude approximations that disagree with nomena might look like in a MOND- could be the agent whose presence impedes observed dark matter halos and with de- inspired theory. For example, Robert H. acceleration and thus produces inertia? tailed numerical simulations of dark mat- Sanders of the Kapteyn Astronomical In- An exciting possibility is the vacuum. ter behavior. Those simulations, as they stitute in Groningen, the Netherlands, The vacuum is what is left when one an- now stand, do not reproduce any aspect and Adi Nusser of the Technion–Israel nihilates all matter (or, equivalently, en- of MOND phenomenology. To boot, Institute of Technology have devised sce- ergy) that can be annihilated. According their claimed result accounts for only a narios of galaxy formation by supple- to quantum theory, the remnant is not a small fraction of the successes of MOND. menting MOND with further working complete void but rather a minimal rep- But it is possible that MOND follows assumptions. But it must be said that resentation of all the forms of energy. The from the dark matter paradigm in a dif- without an underlying theory, none of interaction of the vacuum with particles ferent way. Time will tell. these efforts can be fully trusted. might contribute to the inertia of objects. In the meantime, work is proceeding In what directions should one look for Intriguingly, the vacuum also enters cos- on understanding the observational con- the needed underlying theory? A clue may mology as one explanation for dark ener- sequences of MOND and improving the come from the value of a0. One angstrom gy. It remains unknown, however, whether theory itself, with contributions from per second per second would take a body the vacuum can be fully responsible for Sanders, Jacob D. Bekenstein of the He- from rest to near the speed of light in the inertia and whether it can indeed account brew University in Jerusalem and Stacy S. lifetime of the universe. In other words, a0 for MOND. McGaugh of the University of Maryland. is roughly the same number as the prod- Many researchers maintain that al- MOND continues to be the most suc- uct of two important constants: the speed though MOND neatly reproduces galac- cessful and enduring of the alternatives to of light and the Hubble constant, the tic phenomenology, it does not constitute dark matter. Observations, far from rul- present-day expansion rate of the uni- a fundamental truth. The argument goes ing it out, seem to prefer it over dark mat- verse. It is also near the (unrelated) accel- that MOND is perhaps an economical ter. Although people are right to be skep- eration produced by the dark energy. This and useful summary of what we see in na- tical about MOND, until deﬁnitive evi- numerical proximity, if it is not just a co- ture but that these relations and regulari- dence arrives for dark matter or for one incidence, may tell us either that cosmol- ties will one day emerge from the com- of its alternatives, we should keep our ogy somehow enters local laws of physics, plexity of the dark matter paradigm. Last minds open. SA such as the law of inertia, to produce MOND or that a common agent affects MORE TO EXPLORE both cosmology and local physics so as to A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass leave the same mark on both of them. Hypothesis. Mordehai Milgrom in Astrophysical Journal, Vol. 270, pages 365–370; July 15, 1983. Available online from adsabs.harvard.edu/ Resistance How Cold Dark Matter Theory Explains Milgrom’s Law. Manoj Kaplinghat and Michael S. Turner in Astrophysical Journal, Vol. 569, No. 1, Part 2, pages L19–L22; April 10, 2002. Available online at MOND APPEARS to suggest that iner- arXiv.org/abs/astro-ph/0107284 tia—the responsiveness of a body to a Modified Newtonian Dynamics as an Alternative to Dark Matter. Robert H. Sanders and force—is not an inherent property of bod- Stacy S. McGaugh in Annual Reviews of Astronomy and Astrophysics, Vol. 40; 2002. ies but is acquired by the body by dint of Available online at astro-ph/0204521 its interaction with the universe at large. Stacy S. McGaugh’s MOND Web site is at www.astro.umd.edu/~ssm/mond

52 SCIENTIFIC AMERICAN AUGUST 2002