American Scientist

The amount of matter that astronomers can detect with their instruments doesn't seem to be nearly enough to explain why some of the big-ticket items in the cosmos behave the way they do. Spiral galaxies spin faster than they should, and clusters of galaxies stick together even though the velocities of their constituent galaxies suggest they should be flying apart. The standard solution to the problem posits the existence of some hidden mass in the universe—often called dark matter (sometimes abbreviated DM)—that's holding everything together by the force of gravity. Most astronomers believe that dark matter exists—even though it has never been seen, and no one knows what it might be.

But a 20-year-old alternative to dark matter has been getting an increasing amount of attention lately. The idea, called MOND (for Modified Newtonian Dynamics), was proposed back in 1983 by physicist Mordehai Milgrom, now at the Weizmann Institute of Science in Rehovot, Israel. Milgrom had seen the data like everyone else, but instead of thinking about new kinds of matter, he decided to question the physical laws that describe how ordinary matter behaves.

The laws in question are the law of gravity and Newton's second law, f = ma, which simply tells us that the amount of force you need to accelerate a mass increases linearly as you increase the mass or its acceleration. MOND says that Newton's law still holds true for the kinds of accelerations that take place inside our solar system, but that it's different when the mass is accelerating very, very slowly—precisely the way that bodies in galaxies and systems of galaxies move. MOND employs an acceleration constant, a₀, roughly equal to 10^–8 centimeters per second per second, and it kicks in when the accelerations are this slow.

With this modification to standard Newtonian dynamics, MOND has proved to be every bit as successful at explaining the astronomer's observations as dark matter has. Yet it has relatively few adherents. Why?

The question of how scientific ideas get accepted or rejected is one that philosophers and historians of science have been exploring for decades, of course. But what is it like for a scientist who is in the middle of such a debate? I interviewed Milgrom this past November to get his thoughts on why MOND has gotten such a cold (and dark) reception.—Michael Szpir

Why did you decide to reconsider Newton's second law?

It wasn't that I was struck by a conviction that there must be something wrong with DM. I just thought it would be legitimate and interesting to explore this possibility. I tinkered with modifying the distance dependence of gravity, and also with the idea of adding a new 1/r² force that couples not to mass, like gravity, and not to charge, like electricity, but to angular momentum. These attempts didn't go very far. Toward the end of a sabbatical year, in May 1981, I hit upon the idea of departing from standard dynamics at low accelerations.

How was MOND first received by the scientific community?

I did encounter much opposition and sheer disregard, and this was against my expectation. I was surprised that people thought that this was not a legitimate avenue to explore. Many times I heard people say that it is too early to start considering such heretical ideas. Why? I wondered. I thought it was legitimate to consider anything.

People were much more comfortable with dismissing MOND, back then, than they can be today—now that we know so much more about the regularities and patterns shown by the mass discrepancy. The nice thing is that MOND has not had to change or adjust itself to the many observations that came after it was proposed. Rather, these observations have fit themselves into the predictions made by MOND. [Editor's note: MOND accurately predicted how the orbital velocity of the stars in a spiral galaxy will change with their distance from the center, nearly a decade before astronomers were able to make such precise measurements.]

There is, of course, some precedence to modifying Newtonian dynamics: Einstein showed that Newton's laws of gravity don't hold when the velocities approach the speed of light or when the gravitational field is very strong. Do you think that things might be different now if MOND had been suggested before dark matter was proposed?

Certainly the historical order in which things occurred has much to do with it. Taking things to an extreme, if all that we know now about the mass discrepancy was known to Newton, it is difficult to conceive of him formulating his laws the way he did with the addition of huge quantities of "materia obscura" to bridge the large discrepancy his laws encounter in galaxies. He would have been laughed off the stage. Any sensible person would have tried to formulate a set of laws that fit all the known data without adding hypothesized ingredients. Remember that Newton's laws were based purely on phenomenology, just the encapsulation of the known data. They were not derived on the basis of some fundamental principles.

In a less extreme situation, suppose MOND had been propounded a few years before the mass discrepancy came to light, and that it predicted that mass discrepancies should appear in galaxies, etc. I am convinced that it would have been treated with more respect.

But it is understandable why people find it difficult to accept that these very useful and reliable tools—Newton's laws—break down in yet another realm of phenomena (after the breakdowns connected with relativity and quantum theory). I actually think this is a healthy attitude. There are many, many suggestions made all the time to modify this or that cherished idea. It would be unthinkable to treat them all seriously from the start.

Has your experience made you think differently about science and the history of how ideas are accepted or rejected?

I did wonder whether the attitudes I encountered, and the stages of acceptance I have seen MOND going through, were typical. One of the relevant books I read several times is Thomas Kuhn's The Structure of Scientific Revolutions. It is certainly too early to call MOND a scientific revolution, as we are not even sure that it is a fundamental truth, but the pattern I see in connection with MOND is very much like that described by Kuhn.

For example, there is now an intermediate opinion forming that says basically: "Yes, MOND works well in explaining that data, but it is just a clever formula that summarizes many of the properties of DM, for reasons that we do not yet understand." The history of new ideas in science is replete with examples of such a temporary shift from an old paradigm to a middle ground. The claim is that the new paradigm works well, but it is not a fundamental truth, just a scheme to "save the phenomena." As a student, I remember how the quark model was admitted to work well, but there were people saying that quarks are not real, just mathematical auxiliaries.

Do you think it's easier for scientists to accept the idea that there might be new, unknown types of matter because they've been primed by the explosive discovery of elementary particles over the past few decades?

Particle proliferation has had a psychological effect. Certainly people have lost the timidity they used to have to invent, or hypothesize, new kinds of particles. This has helped to promote particle-DM, with candidates such as axions, neutralinos and other cold DM particles, as well as warm DM, and self-interacting DM, whose nature is not even specified. I think this is a reasonable approach. Nothing wrong with new particles if they can be made to work. [Editor's note: These DM models propose the existence of exotic particles that interact with normal matter (baryons, such as protons and neutrons) mainly through the force of gravity.]

What are the biggest challenges to MOND?

MOND does not yet explain all the mass discrepancy in galaxy cluster cores [where galaxies move too fast even for MOND], so we have to say that these cores contain as yet undiscovered quantities of normal matter. I don't see this as a grave problem if all else works.

The biggest challenge we face now is to come up with a more fundamental theory for MOND that includes general relativity. This is similar to the challenge facing practically every live theory. We know the standard model of particle physics is not the final word, and quantum theory has yet to be married to gravity—neither is complete without the other. And we are still very far from this, even after many years of attempts by good physicists. So MOND is in good company, but it certainly leaves much to be desired in this department.

What is the significance of MOND's acceleration constant?

We think that MOND, as it is now formulated, is the tip of some iceberg. Why? Because the acceleration constant, which marks the boundary between the validity regions of MOND and Newtonian dynamics, turns out to have a value that matches accelerations appearing in the context of cosmology. It is roughly the acceleration that will take an object from rest to the speed of light in the lifetime of the universe. It is also of the order of the recently discovered acceleration of the universe. [See "The Hubble Constant and the Expanding Universe"]

We take this as a hint that MOND is somehow connected with the state of the universe at large, and that a0 is not a constant of nature, but a calculable quantity in the underlying theory we seek. This is similar to the "constant" g, the free-fall acceleration near Earth's surface, as it appears, say, in Galilean mechanics. The deeper theory in this case is Newtonian universal gravity, which tells us that g can be calculated from the mass and radius of the Earth.

What kinds of experiments or observations could help scientists to decide between DM and MOND?

It is quite easy to disprove MOND. For example, if the problem in cluster cores were the reverse, if MOND predicted less mass than is seen, that would be difficult to circumvent. Of course, if people find individual cases that seem to disagree with MOND, it could be just due to the fact that astronomy, and its interpretation, is fraught with uncertainties and unjustified assumptions. Dark matter is much more elusive and difficult to refute.

It's been said that dark matter theory is beginning to resemble the celestial mechanics of Ptolemy, who continually added epicycles to his models as the observations failed to conform to a geocentric universe. What would it take for scientists to abandon dark matter?

DM is encountering difficulties in the face of observations, and people keep inventing new DM with new properties to try and circumvent these difficulties. Over the years I have refrained from attacking DM, but others have started finding faults with it and that trend is increasing.

I think few people appreciate that the main difficulty for DM is that the host of regularities pointed out by MOND, if taken as just a summary of how DM behaves and interacts with normal matter, suggests that these two matter components are coupled and correlated very strongly in many ways. This is quite unimaginable. It would be a tall order for DM to explain this, and no one has even tried. This is what, to me, makes DM so difficult to swallow.

In the end, the process that might sway people's minds could be a slow one, in which they become disillusioned and dissatisfied with DM, while MOND explains more and more of the observations. And, if MOND does turn out to have some truth to it, the fact that it encountered so much opposition will just show how nontrivial a thought it was.