Erik Verlinde by Ilvy Njiokiktjien for Quanta Magazine

Ilvy Njiokiktjien for Quanta Magazine

The Dutch theoretical physicist Erik Verlinde argues that dark matter does not exist.

For 80 years, scientists have puzzled over the way galaxies and other cosmic structures appear to gravitate toward something they cannot see. This hypothetical “dark matter” seems to outweigh all visible matter by a startling ratio of five to one, suggesting that we barely know our own universe. Thousands of physicists are doggedly searching for these invisible particles.

But the dark matter hypothesis assumes scientists know how matter in the sky ought to move in the first place. This month, a series of developments has revived a long-disfavored argument that dark matter doesn’t exist after all. In this view, no missing matter is needed to explain the errant motions of the heavenly bodies; rather, on cosmic scales, gravity itself works in a different way than either Isaac Newton or Albert Einstein predicted.

The latest attempt to explain away dark matter is a much-discussed proposal by Erik Verlinde, a theoretical physicist at the University of Amsterdam who is known for bold and prescient, if sometimes imperfect, ideas. In a dense 51-page paper posted online on Nov. 7, Verlinde casts gravity as a byproduct of quantum interactions and suggests that the extra gravity attributed to dark matter is an effect of “dark energy” — the background energy woven into the space-time fabric of the universe.

Read the related Abstractions post:
Quantum Gravity’s Time Problem

Instead of hordes of invisible particles, “dark matter is an interplay between ordinary matter and dark energy,” Verlinde said.

To make his case, Verlinde has adopted a radical perspective on the origin of gravity that is currently in vogue among leading theoretical physicists. Einstein defined gravity as the effect of curves in space-time created by the presence of matter. According to the new approach, gravity is an emergent phenomenon. Space-time and the matter within it are treated as a hologram that arises from an underlying network of quantum bits (called “qubits”), much as the three-dimensional environment of a computer game is encoded in classical bits on a silicon chip. Working within this framework, Verlinde traces dark energy to a property of these underlying qubits that supposedly encode the universe. On large scales in the hologram, he argues, dark energy interacts with matter in just the right way to create the illusion of dark matter.

In his calculations, Verlinde rediscovered the equations of “modified Newtonian dynamics,” or MOND. This 30-year-old theory makes an ad hoc tweak to the famous “inverse-square” law of gravity in Newton’s and Einstein’s theories in order to explain some of the phenomena attributed to dark matter. That this ugly fix works at all has long puzzled physicists. “I have a way of understanding the MOND success from a more fundamental perspective,” Verlinde said.

Many experts have called Verlinde’s paper compelling but hard to follow. While it remains to be seen whether his arguments will hold up to scrutiny, the timing is fortuitous. In a new analysis of galaxies published on Nov. 9 in Physical Review Letters, three astrophysicists led by Stacy McGaugh of Case Western Reserve University in Cleveland, Ohio, have strengthened MOND’s case against dark matter.

The researchers analyzed a diverse set of 153 galaxies, and for each one they compared the rotation speed of visible matter at any given distance from the galaxy’s center with the amount of visible matter contained within that galactic radius. Remarkably, these two variables were tightly linked in all the galaxies by a universal law, dubbed the “radial acceleration relation.” This makes perfect sense in the MOND paradigm, since visible matter is the exclusive source of the gravity driving the galaxy’s rotation (even if that gravity does not take the form prescribed by Newton or Einstein). With such a tight relationship between gravity felt by visible matter and gravity given by visible matter, there would seem to be no room, or need, for dark matter.

Even as dark matter proponents rise to its defense, a third challenge has materialized. In new research that has been presented at seminars and is under review by the Monthly Notices of the Royal Astronomical Society, a team of Dutch astronomers have conducted what they call the first test of Verlinde’s theory: In comparing his formulas to data from more than 30,000 galaxies, Margot Brouwer of Leiden University in the Netherlands and her colleagues found that Verlinde correctly predicts the gravitational distortion or “lensing” of light from the galaxies — another phenomenon that is normally attributed to dark matter. This is somewhat to be expected, as MOND’s original developer, the Israeli astrophysicist Mordehai Milgrom, showed years ago that MOND accounts for gravitational lensing data. Verlinde’s theory will need to succeed at reproducing dark matter phenomena in cases where the old MOND failed.

Kathryn Zurek, a dark matter theorist at Lawrence Berkeley National Laboratory, said Verlinde’s proposal at least demonstrates how something like MOND might be right after all. “One of the challenges with modified gravity is that there was no sensible theory that gives rise to this behavior,” she said. “If [Verlinde’s] paper ends up giving that framework, then that by itself could be enough to breathe more life into looking at [MOND] more seriously.”

The New MOND

In Newton’s and Einstein’s theories, the gravitational attraction of a massive object drops in proportion to the square of the distance away from it. This means stars orbiting around a galaxy should feel less gravitational pull — and orbit more slowly — the farther they are from the galactic center. Stars’ velocities do drop as predicted by the inverse-square law in the inner galaxy, but instead of continuing to drop as they get farther away, their velocities level off beyond a certain point. The “flattening” of galaxy rotation speeds, discovered by the astronomer Vera Rubin in the 1970s, is widely considered to be Exhibit A in the case for dark matter — explained, in that paradigm, by dark matter clouds or “halos” that surround galaxies and give an extra gravitational acceleration to their outlying stars.

Lucy Reading-Ikkanda for Quanta Magazine

Searches for dark matter particles have proliferated — with hypothetical “weakly interacting massive particles” (WIMPs) and lighter-weight “axions” serving as prime candidates — but so far, experiments have found nothing.

Meanwhile, in the 1970s and 1980s, some researchers, including Milgrom, took a different tack. Many early attempts at tweaking gravity were easy to rule out, but Milgrom found a winning formula: When the gravitational acceleration felt by a star drops below a certain level — precisely 0.00000000012 meters per second per second, or 100 billion times weaker than we feel on the surface of the Earth — he postulated that gravity somehow switches from an inverse-square law to something close to an inverse-distance law. “There’s this magic scale,” McGaugh said. “Above this scale, everything is normal and Newtonian. Below this scale is where things get strange. But the theory does not really specify how you get from one regime to the other.”

Physicists do not like magic; when other cosmological observations seemed far easier to explain with dark matter than with MOND, they left the approach for dead. Verlinde’s theory revitalizes MOND by attempting to reveal the method behind the magic.

Verlinde, ruddy and fluffy-haired at 54 and lauded for highly technical string theory calculations, first jotted down a back-of-the-envelope version of his idea in 2010. It built on a famous paper he had written months earlier, in which he boldly declared that gravity does not really exist. By weaving together numerous concepts and conjectures at the vanguard of physics, he had concluded that gravity is an emergent thermodynamic effect, related to increasing entropy (or disorder). Then, as now, experts were uncertain what to make of the paper, though it inspired fruitful discussions.

The particular brand of emergent gravity in Verlinde’s paper turned out not to be quite right, but he was tapping into the same intuition that led other theorists to develop the modern holographic description of emergent gravity and space-time — an approach that Verlinde has now absorbed into his new work.

In this framework, bendy, curvy space-time and everything in it is a geometric representation of pure quantum information — that is, data stored in qubits. Unlike classical bits, qubits can exist simultaneously in two states (0 and 1) with varying degrees of probability, and they become “entangled” with each other, such that the state of one qubit determines the state of the other, and vice versa, no matter how far apart they are. Physicists have begun to work out the rules by which the entanglement structure of qubits mathematically translates into an associated space-time geometry. An array of qubits entangled with their nearest neighbors might encode flat space, for instance, while more complicated patterns of entanglement give rise to matter particles such as quarks and electrons, whose mass causes the space-time to be curved, producing gravity. “The best way we understand quantum gravity currently is this holographic approach,” said Mark Van Raamsdonk, a physicist at the University of British Columbia in Vancouver who has done influential work on the subject.

The mathematical translations are rapidly being worked out for holographic universes with an Escher-esque space-time geometry known as anti-de Sitter (AdS) space, but universes like ours, which have de Sitter geometries, have proved far more difficult. In his new paper, Verlinde speculates that it’s exactly the de Sitter property of our native space-time that leads to the dark matter illusion.

De Sitter space-times like ours stretch as you look far into the distance. For this to happen, space-time must be infused with a tiny amount of background energy — often called dark energy — which drives space-time apart from itself. Verlinde models dark energy as a thermal energy, as if our universe has been heated to an excited state. (AdS space, by contrast, is like a system in its ground state.) Verlinde associates this thermal energy with long-range entanglement between the underlying qubits, as if they have been shaken up, driving entangled pairs far apart. He argues that this long-range entanglement is disrupted by the presence of matter, which essentially removes dark energy from the region of space-time that it occupied. The dark energy then tries to move back into this space, exerting a kind of elastic response on the matter that is equivalent to a gravitational attraction.

Because of the long-range nature of the entanglement, the elastic response becomes increasingly important in larger volumes of space-time. Verlinde calculates that it will cause galaxy rotation curves to start deviating from Newton’s inverse-square law at exactly the magic acceleration scale pinpointed by Milgrom in his original MOND theory.

Van Raamsdonk calls Verlinde’s idea “definitely an important direction.” But he says it’s too soon to tell whether everything in the paper — which draws from quantum information theory, thermodynamics, condensed matter physics, holography and astrophysics — hangs together. Either way, Van Raamsdonk said, “I do find the premise interesting, and feel like the effort to understand whether something like that could be right could be enlightening.”

One problem, said Brian Swingle of Harvard and Brandeis universities, who also works in holography, is that Verlinde lacks a concrete model universe like the ones researchers can construct in AdS space, giving him more wiggle room for making unproven speculations. “To be fair, we’ve gotten further by working in a more limited context, one which is less relevant for our own gravitational universe,” Swingle said, referring to work in AdS space. “We do need to address universes more like our own, so I hold out some hope that his new paper will provide some additional clues or ideas going forward.”

Ilvy Njiokiktjien for Quanta Magazine

Video: Erik Verlinde describes how emergent gravity and dark energy can explain away dark matter.

The Case for Dark Matter

Verlinde could be capturing the zeitgeist the way his 2010 entropic-gravity paper did. Or he could be flat-out wrong. The question is whether his new and improved MOND can reproduce phenomena that foiled the old MOND and bolstered belief in dark matter.

One such phenomenon is the Bullet cluster, a galaxy cluster in the process of colliding with another. The visible matter in the two clusters crashes together, but gravitational lensing suggests that a large amount of dark matter, which does not interact with visible matter, has passed right through the crash site. Some physicists consider this indisputable proof of dark matter. However, Verlinde thinks his theory will be able to handle the Bullet cluster observations just fine. He says dark energy’s gravitational effect is embedded in space-time and is less deformable than matter itself, which would have allowed the two to separate during the cluster collision.

But the crowning achievement for Verlinde’s theory would be to account for the suspected imprints of dark matter in the cosmic microwave background (CMB), ancient light that offers a snapshot of the infant universe. The snapshot reveals the way matter at the time repeatedly contracted due to its gravitational attraction and then expanded due to self-collisions, producing a series of peaks and troughs in the CMB data. Because dark matter does not interact, it would only have contracted without ever expanding, and this would modulate the amplitudes of the CMB peaks in exactly the way that scientists observe. One of the biggest strikes against the old MOND was its failure to predict this modulation and match the peaks’ amplitudes. Verlinde expects that his version will work — once again, because matter and the gravitational effect of dark energy can separate from each other and exhibit different behaviors. “Having said this,” he said, “I have not calculated this all through.”

While Verlinde confronts these and a handful of other challenges, proponents of the dark matter hypothesis have some explaining of their own to do when it comes to McGaugh and his colleagues’ recent findings about the universal relationship between galaxy rotation speeds and their visible matter content.

In October, responding to a preprint of the paper by McGaugh and his colleagues, two teams of astrophysicists independently argued that the dark matter hypothesis can account for the observations. They say the amount of dark matter in a galaxy’s halo would have precisely determined the amount of visible matter the galaxy ended up with when it formed. In that case, galaxies’ rotation speeds, even though they’re set by dark matter and visible matter combined, will exactly correlate with either their dark matter content or their visible matter content (since the two are not independent). However, computer simulations of galaxy formation do not currently indicate that galaxies’ dark and visible matter contents will always track each other. Experts are busy tweaking the simulations, but Arthur Kosowsky of the University of Pittsburgh, one of the researchers working on them, says it’s too early to tell if the simulations will be able to match all 153 examples of the universal law in McGaugh and his colleagues’ galaxy data set. If not, then the standard dark matter paradigm is in big trouble. “Obviously this is something that the community needs to look at more carefully,” Zurek said.

Even if the simulations can be made to match the data, McGaugh, for one, considers it an implausible coincidence that dark matter and visible matter would conspire to exactly mimic the predictions of MOND at every location in every galaxy. “If somebody were to come to you and say, ‘The solar system doesn’t work on an inverse-square law, really it’s an inverse-cube law, but there’s dark matter that’s arranged just so that it always looks inverse-square,’ you would say that person is insane,” he said. “But that’s basically what we’re asking to be the case with dark matter here.”

Given the considerable indirect evidence and near consensus among physicists that dark matter exists, it still probably does, Zurek said. “That said, you should always check that you’re not on a bandwagon,” she added. “Even though this paradigm explains everything, you should always check that there isn’t something else going on.”

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  • Thank you for the excellent write up – I am merely a statistician interested in physics so trying to read the original paper was difficult, to say the least.

  • Why does this kind of poor science keep getting press here?

    So people can keep looking for MACHOs and WIMPs that don't exist?

    It's axions of some sort, Peccie Quinn QCD axions and/or gravitational Goldstone bosons, sitting down near or below the cosmic background radiation temperature, and/or near the superfluid transition temperature of helium. Everything else is nonsense.

  • The title is (poor) click bait, since there isn't any "case" against dark matter or for any alternative, since there doesn't exist any alternative predicting all the effects cold dark matter does. And in fact it now predicts structures better on all scales down to dwarf galaxy structures and their observed frequency, after supernova flows and what now was included in the models.

    Possibly it could be wrong, but then there is a very long and steep uphill battle for alternatives that we have seen fall off the road for a very long time.

    So, as Thomas Lee Elifritz already asked, why does this kind of poor science keep getting press here? It should be easy to see that it is of little interest among those interested in exciting, aka useful, science.

  • I'm not sure if any of the commenters read the 51 page report. I'm going to try and work my way through it.

    Thomas, Verlinde's theory is trying to do-away with the fruitless searches of WIMPs, etc.

    It's ironic that people will take click-bait as genuine information, even if it has no sources, but when someone takes the time to publish a 51 page report on his ideas, it's called bad science.

    Natalie, thanks for the well written article and link to the source. I will do my best to understand that report. It may be long, but many Quanta articles are long. I don't think people realize information requires reading.

  • It may be that the letter writers complaining about 'poor science' have a point, but they haven't made that point. The article on the other hand gives a splendid and from all appearances a comprehensive overview of the issues surrounding Verlinde's ideas, very much including the possibility that he's wrong. Thank you.

  • Thank you Natalie … a most insightful article; I'm now motivated to try and understand Verlinde's ideas!

  • Having the paper in my hands, it really helps to read through another of Natalie's gems.

    One comment by Verlinde struck me as odd, and it concerns the Bullet Cluster. He said that his theory does not work for Dynamical Systems.

    This strikes me as odd. For the moment gravity appears to be asymptotic, and that is precisely the reason why Einstein continued from Special Relativity, to General Relativity.

    In space all is Dynamical.


  • Solid article as always from Natalie. Not too long. The whole point of Quanta is to learn about science in the making. As such, the bar for junk is inherently subjective within some reasonable bounds.

  • Einstein said that time is an illusion. If time is not an illusion but a fundamental property of the world, the speed of light is not constant and there is no need for GRT.
    Verlinde says that the Big Bang is an illusion, dark matter and dark energy are illusions and gravity is an illusion, gravity being entropic.

    If time is a fundamental property of the world, and I think it is studying the behavior of radiation in the neighbourhood of masses, gravity is not entropic, but entropy is gravitational.

  • Let's not forget, that science is all about making models that can be used to predict the behaviour observed phenomena and, provide means to verify their validity by experiment.

    So far dark matter is still a hypothetical construct, that is used to explain observations, that can't be explained by other means. We still haven't seen any trace of the "dark matter particles", whose existence is implied by the dark matter theory.

    It is not a matter of opinion or personal preference whether Verlinde's theory is better or worse than the theory of dark matter. Only experiment can tell.

  • It's a pretty good article but the author should have let someone respond to this misinterpretation.

    "But that’s basically what we’re asking to be the case with dark matter here."

    No it's not. MOND is not the inverse square law, it was chosen because it fit the data at the time. It's not a conspiracy that something that was built to look like the data looks like the data. Yes it is in new territory but you shouldn't neglect where this began. Not to mention the fact dark matter can explain dozens of cosmological observations while MOND has fallen flat on it's face, you cannot ignore the wider landscape.

  • First of all let me commend those who wrote this article as it was well written and fairly simple to follow, even for someone like me with no formal theoretical physics training.

    Secondly, I've eaten nearly 34 hot pockets in the last two weeks and not ONCE did I need the help of "gravity" to do so. If anything it was hindrance.

    Article = 8/10
    My distended abdomen = 100/10

  • I'm still working my way through Verlinde's paper, though certainly not as a physicist (which I'm not), but instead at the hand-waving conceptual "cosmology fan" level.

    I believe Verlinde's paper is the first cosmology paper since the "firewalls" paper to create such an uproar with attendant coverage in the press and online. Which most certainly includes this article. Frankly, as a spectator I'm very much enjoying all the bruhaha.

    However, I'm trying to probe a bit deeper by working my way through Verlinde's references, and the coverage those papers have received in turn. Independent of the paper itself, Verlinde's list of references is well worth reviewing: It's a Who's Who of important physics papers. My goal is to see if (and how) the coverage (and critique) of those papers can be combined to obtain a better understanding of the concepts and conclusions in Verlinde's paper.

    Even setting aside the "No Dark Matter" claim, there are some key features that attracted me to this paper.

    The first is truly fundamental: Verlinde is working in dS, not AdS.

    I've always been dismayed with (and disconnected from) the amount of work being done in AdS, and the comparative lack of equivalent results in dS. Even if Verlinde's final conclusions are eventually shown to be wrong, I believe working is dS is a Good Thing in and of itself, something I'd like to see more physicists pursue.

    The next important feature for me is the notion of Emergent Entropic Gravity (which I failed to grasp from Verlinde's 2010 paper on the subject).

    For years I've been struggling to gain a layman's understanding of Emergent Entropic Time, but I have yet to accept it (despite Sean Carroll's best efforts): It still seems too "magical" to me, especially its non-local uniformity. And yet, even at this early stage of my explorations, Verlinde's form of Emergent Entropic Gravity already seems much more feasible to me (at my admittedly low level of comprehension). Perhaps a better understanding of Emergent Entropic Gravity will help me with Emergent Entropic Time.

    As I work through the references, I'm steadily gaining the impression that Verlinde has created an amazing synthesis that, at the very least, should provide a terrific physics playground for years to come.

  • Thanks for the good article. It helped me better understand the original paper,
    which is quite dense technically. Once more unto the breach.

    A small quibble…
    A problem with this Quanta article's phrasing…
    On pg. 39, section 7, of his paper “Emergent Gravity
    and the Dark Universe”, Verlinde writes:
    The validity of (7.40) depends on a number of assumptions and holds only when certain conditions are being satisfied. These conditions include that one is dealing with a centralized, spherically symmetric mass distribution, which has been in dynamical equilibrium during its evolution. Dynamical situations as those that occur in the Bullet cluster are not described by these same equations.

    Quanta writes “…The question is whether his [..] improved MOND can reproduce phenomena that foiled the old MOND […] One such phenomenon is the Bullet cluster, a galaxy cluster in the process of colliding with another…”

    But Verlinde explicitly notes that the Bullet Cluster is, as yet, outside the grand
    synthesis embodied by his relation (7.40). I believe that he hopes to
    incorporate the non-equilibrium Bullet Cluster collision in future work.

  • MOND is to dark matter as the Copernican heliocentric model was to the geocentric model. Using epicycles to explain the geocentric retrograde motion of the planets is like saying lets explain the observed orbital velocities of perimeter stars in our galaxies by surrounding them with invisible, non-interactive particles.

  • Thank you for this article. MOND and alternative theories will not go away until someone can produce a pound of dark matter to show exactly what it is. In the meantime, anything goes.

    It doesn't seem right to assume that theories that propose a change in the amount of observed matter may be more correct than those that propose a change in the effects of force. Ultimately, either of them give the same result of accounting for anomalous measurements of acceleration.

    I can't help thinking we have been here before: dark matter seems to be the new aether of the very late 1900s, which eventually had to be discarded to give wat to general relativity.

  • Have just finished excellent book by John W. Moffat called Reinventing Gravity which describes his work on a modified theory of gravity that does away with dark matter and dark energy while explaining the rotational behaviours of large galaxies. Further, his theory resolves to relativistic, quantum, and classical solutions in the required contexts.

    Excellent work by a respected physicist!

  • Really interesting article. A complex topic like this deserves as much space at it needs. I did not find the article too long and I found it very balanced. Thank you!

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