THIS may sound like heresy, but did Newton get his law of gravity wrong? Mordehai Milgrom thinks so, and he says he has the proof. The way that some stars and galaxies move so fast and yet remain in their orbits defies all accepted theories, he says. But tweaking Newton’s laws of motion can sort the problem. “Ten years ago, this was a rather disreputable claim,” says Stacy McGaugh of the University of Maryland in College Park. “Now a sizeable minority is taking it seriously.”
Milgrom’s theory is still one that most cosmologists love to hate, however. That is partly because it waves away “dark matter”, a mysterious substance that, according to many physicists, fills the Universe. Mostly, though, this animosity arises because the idea is pretty much plucked out of the air. No one – including Milgrom – knows why it should be true. But while scientists have had over 20 years and a wealth of astronomical data to try to disprove Milgrom’s theory, so far no one has. Even the latest results from NASA’s orbiting Chandra X-ray Observatory, widely publicised by NASA as evidence against Milgrom’s controversial theory, failed to kill it off. “I haven’t lost a minute’s sleep over them,” says Milgrom. His theory simply refuses to go away.
Milgrom first put forward his idea in the early 1980s when he was working at the Institute for Advanced Study in Princeton. He became intrigued by mysterious results from spiral galaxies: the best telescopes in the world were revealing that stars in the outermost reaches of galaxies are orbiting far faster than Newton’s law of gravity predicts.
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According to Newton’s law, the force of gravity drops by a factor of four every time you double the distance from the core of the galaxy, where most of the massive stars and gas are concentrated. Stars skirting the edge of a galaxy should feel a much weaker gravitational pull than ones near the centre, and this means they should orbit the galaxy more slowly. But observations showed that stars’ velocities do not plummet with distance as Newton’s law predicts they should. Instead, the velocity stays constant out to the edge of the galaxy.
It was such a puzzling finding because gravity is the only force that holds all the matter in a galaxy together. “If Newton were alive today and saw the evidence, I’m convinced he would have come up with different laws of dynamics,” says Milgrom, who is now at the Weizmann Institute in Rehovot, Israel. Other theorists explain this by invoking a huge mass of mysterious, invisible matter – dark matter – that exerts enough gravitational pull to correct for the anomalous speed of stars in the outer reaches of galaxies (see “The new dark age”). Milgrom has always found this approach unconvincing, however, which is why he came up with an alternative theory, a tweak to Newton’s idea. He called it modified Newtonian dynamics (MOND).
At first glance, breaking the most cherished rules in physics may not seem like a good idea. After all, Newtonian gravity works in Earth-bound laboratories and in the rest of the Solar System. But Newtonian dynamics does break down under extreme conditions. For objects whizzing around close to the speed of light, for instance, Newton’s laws of motion give way to Einstein’s special theory of relativity.
So Milgrom listed all the differences between the Solar System and galaxies to see if any of them could produce a change in the laws of dynamics in the outer reaches of galaxies, and hence the force of gravity. The obvious one was distance. Milgrom wondered if the relationship between the mass of an object and its acceleration due to the force of gravity suddenly changed at a fixed distance from the centre of the galaxy, but he quickly discovered that this did not work. When he compared the velocities of stars in different spiral galaxies, he found that their speeds became uniform at different distances from the galactic core.
After trying other quantities, such as angular momentum, Milgrom speculated that above some critical acceleration, Newton’s law of gravity holds true: the gravitational force that whirls a star around falls precipitously with the square of the distance from the galaxy’s core. Below this critical value for acceleration, however, gravity weakens only slowly – in direct proportion to the distance. So, according to modified Newtonian dynamics, the galaxy has a stronger grip on some stars than Newton predicts.
This means that stars on the outskirts of a galaxy whizz around with a velocity that hinges simply on the the mass of all the other stars and gas inside the galaxy – not on the distance to the galactic centre, as Newton’s law dictates.
Milgrom’s idea looked promising. And to his excitement, when he applied the theory to observations it seemed to pan out. Every galaxy that had been measured in detail became a new testing ground for MOND. He only had to create one parameter, the critical acceleration at which Newton’s law changes. By setting the critical acceleration to 10−10 metres per second per second – 100 billion times weaker than the gravitational force on a falling apple here on Earth – Milgrom found he could describe the relationship between stars’ velocity and their distance from the centre for a number of spiral galaxies. Certain that there must be some flaw in his reasoning or calculations, Milgrom spent days going over them. “But everything fitted,” he says.
His first notable success was a prediction about a class of galaxies that were virtually unknown in the 1980s, “low surface brightness” galaxies. These objects are so faint that astronomers found it impossible to take detailed images of them until the 1990s.
Because they contain very few stars, the gravitational force in such galaxies is much weaker than it is in bright galaxies packed full of stars and gas. Moving outwards from the centre of these faint galaxies, you soon find that the acceleration falls below the critical value. In bright galaxies, such low accelerations are only experienced by stars at the very outskirts. Milgrom predicted that MOND would succeed in describing the motion of most stars in low surface brightness galaxies. Newtonian dynamics would fail. Radio telescopes finally managed to detect hydrogen gas roaming inside these faint galaxies, and this finally revealed the stars’ velocities. “The prediction was confirmed,” says Milgrom. “MOND passed the test.”
The finding convinced McGaugh – who was studying low surface brightness galaxies at the time – that MOND was a serious alternative to dark matter, the favourite explanation for the rapid motion of stars and galaxies.
Since then, we’ve seen MOND work for around 100 assorted galaxies. Astronomers simply add up the mass of all the stars and gas in a galaxy, and feed it into Milgrom’s equations to give a curve ending in a plateau that describes the relation between all the stars’ velocities and distances from the core (see Graph). But MOND does more, describing both the shape and the height of each galaxy’s curve in great detail. That’s impressive for a theory based on a single parameter: the mass of the galaxy. “It’s a very strong test,” says McGaugh.
And it’s not the only test that MOND has passed. It can also predict the masses of galaxies. For each galaxy you simply pick a mass, predict the motion of stars for this mass and see how well it compares with the measured data. If you repeat this with different masses, you eventually find one that describes the data best. This is an important measurement because you can’t weigh a galaxy directly. Instead, astronomers have to estimate the mass of a galaxy from the light that all the stars and gas emit. Over the years, they’ve built up detailed models relating the colour of this light to the mass of the galaxy. The predictions from MOND have been tested against these models and the agreement is pretty good. “I find it one of the most intriguing aspects of MOND,” says McGaugh.
So has Milgrom been vindicated? Not yet, and the challenges keep coming. The most recent one came from a team led by David Buote of the University of California at Irvine. Last year, the team analysed high-resolution images of an elliptical galaxy called NGC 720 taken by the Chandra X-ray Observatory. The astronomers discovered that NGC 720 is enveloped in a hot cloud of gas shaped like an egg. They believe that only the additional gravitational pull produced by a halo of dark matter can squash the gas cloud. It looked like the first hard evidence against MOND.
But supporters of MOND point to flaws in assumptions Buote and his colleagues made when interpreting the data. They assumed that the gas in the galaxy was static, but it might have been spinning. This would also have the effect of squashing the gas cloud, says Milgrom. He also points out that the Chandra telescope might not have a high enough resolution to spot tiny stars beaming X-rays. Such X-rays could blur the image, making NGC 720 appear distorted. For the moment, at least, MOND seems to have won a reprieve.
No one denies that MOND fits a wealth of galactic observations, but the theory certainly isn’t perfect. For one, it breaks down at larger scales – when looking at clusters of galaxies, for example. Even though it can reproduce the observed motion of galaxies in the outer reaches of clusters, it fails in their cores. With their known mass, these are accelerating faster than MOND would predict. “My suspicion is that cluster cores may contain a lot of undetected material in some mundane dark form – for instance, dim stars,” says Milgrom. Cosmologists have ruled out the idea of there being huge amounts of “ordinary” dark matter in the Universe, because it would have utterly changed the conditions shortly after the big bang. Instead they favour “exotic” matter such as mysterious particles called WIMPS. What’s more, invoking dark matter in order to save MOND, a theory that attempts to do away with dark matter, is worrying. It is this failure of MOND to describe the cores of galaxy clusters that people object to so strongly.
And there’s more. MOND was developed in an empirical way and has no fundamental basis in physics. Milgrom admits this is a problem. But he counters that when quantum theory was developed early last century it was in a similar position for many years. He is convinced that there is a deep theory underlying MOND.
A clue might come from the vacuum – the void that permeates the Universe. Far from being completely empty, the vacuum is a frothy sea of particles that pop in and out of existence. Milgrom thinks that the vacuum might modify the mass, or inertia, of objects somehow. If he is right there could be an unexpected and deep connection between the way things accelerate and the age of the Universe. “This is supported by an odd coincidence,” says Milgrom. The critical acceleration in MOND turns out to have the same value you would need to accelerate an object from a standstill to the speed of light in the time the Universe has been in existence. To Milgrom, the connection between these two numbers hints at a deeper theory. It’s a hand-waving argument, he admits.
Critics have another, much more serious objection. “The main reason I don’t like MOND is that it does not fit with the rest of physics as we know it,” says Bohdan Paczynski of Princeton University. He is concerned that MOND breaks down close to the speed of light and near black holes where gravity is strongest and Einstein’s theory of relativity takes over from Newton’s laws. This also worries Abraham Loeb of Harvard University. “It makes it difficult to subject MOND to the wealth of high-quality data we now have in cosmology – including the microwave background data, gravitational lensing data, and data from galaxy surveys on the growth of structure,” he points out. These phenomena can only be explained using relativity.
Milgrom agrees that the lack of a MOND theory that takes relativity into account is a problem. But he believes that, given time, this problem can be overcome. Theorists will eventually accept MOND not because of its successful predictions, he says, but because the various proposals for dark matter will never match observations. He is going to have a hard time silencing his critics, though: they’re using every sense they can to quash his heretical ideas. “Dark matter may not be the right answer,” admits Paczynski. “But MOND just doesn’t ‘smell’ like new physics to me.”
- The MOND website maintained by Stacy McGaugh at