by Lee Smolin
Indeed, as cosmologists have examined the large-scale modes in the microwave background, they have found more mysteries. It’s an item of faith among cosmologists that at the largest scales the universe should be symmetric—that is, any one direction should be like any other. This is not what is seen. The radiation in these large-scale modes is not symmetric; there is a preferred direction. (It has been called the “axis of evil” by the cosmologists Kate Land and João Magueijo.3) No one has any rational explanation for this effect.
These observations are controversial because they disagree profoundly with what we would expect on the basis of inflation. Since inflation explains so much of cosmology, many prudent scientists suspect that there is something wrong with the microwave data. Indeed, it is always possible that the measurements are just wrong. A lot of delicate analysis is applied to the data before they’re presented. One thing that’s done is to subtract the radiation known to come from the galaxy we live in. This may have been done incorrectly, but few experts familiar with the details of how the data are analyzed believe that to be the case. Another possibility, as noted, is that our observations are just statistical anomalies. An oscillation at a wavelength of the scale R takes up a huge part of the sky—about 60 degrees; consequently we see only a few wavelengths, and there are only a few pieces of data, so what we are seeing may just be a random statistical fluctuation. The chances of the evidence for a preferred direction being a statistical anomaly have been estimated at less than 1 part in 1,000.4 But it may be easier to believe in this unlikely bad luck than to believe that the predictions of inflation are breaking down.
These issues are currently unresolved. For the time being, it is enough to say that we went looking for strange physics on the scale R and found it.
Are there any other phenomena associated with this scale? We can combine R with other constants of nature to see what happens at scales defined by the resulting number. Let me give an example. Consider R divided by the speed of light: R/c. This gives us a time, and the time it gives us is roughly the present age of our universe. The inverse, c/R, gives us a frequency—a very low note, one oscillation per lifetime of the universe.
The next simplest thing to try is c2/R. This turns out to be an acceleration. It is in fact the acceleration by which the rate of expansion of the universe is increasing—that is, the acceleration produced by the cosmological constant. Compared to ordinary scales, however, it is a very tiny acceleration: 10−8 centimeters per second. Imagine a bug crawling across the floor. It manages to go perhaps 10 centimeters per second. If the bug doubled its speed over the lifetime of a dog, it would be accelerating about as much as c2/R, a very small acceleration indeed.
But suppose there is a new universal phenomenon that explains the value of the cosmological constant. Just by the fact that the scales match, this new phenomenon should also affect any other kind of motion with an acceleration this tiny. So anytime we can observe something moving with such a tiny acceleration, we would expect to see something new. Now the game starts to get interesting. We do know things that accelerate this slowly. One example is a typical star orbiting in a typical galaxy. A galaxy orbiting another galaxy accelerates even more slowly. So, do we see anything different about the orbits of the stars with accelerations this tiny, compared to the orbits of stars with larger accelerations? The answer is yes, we do, and dramatically so. This is the problem of the dark matter.
As we discussed in chapter 1, astronomers discovered the dark-matter problem by measuring the acceleration of stars in orbit about the center of their galaxies. The problem arose because, given the measured accelerations, astronomers could deduce the distribution of the galaxy’s matter. In most galaxies, this result turned out to disagree with the matter observed directly.
I can now say a bit more about where the discrepancy arises. (For the sake of simplicity, I’ll restrict the discussion to spiral galaxies, in which most stars move in circular orbits in a disk.) In each galaxy where the problem is found, it affects only stars moving outside a certain orbit. Within that orbit, there’s no problem—the acceleration is what it should be if caused by the visible matter. So there seems to be a region in the interior of the galaxy within which Newton’s laws work and there’s no need for dark matter. Outside this region, things get messy.
The key question is: Where is the special orbit that separates the two regions? We might suppose that it occurs at a particular distance from the center of the galaxy. This is a natural hypothesis, but it is wrong. Is the dividing line at a certain density of stars or starlight? Again, the answer is no. What seems to determine the dividing line, surprisingly, is the rate of the acceleration itself. As one moves farther out from the center of the galaxy, accelerations decrease, and there turns out to be a critical rate that marks the breakdown of Newton’s law of gravity. As long as the acceleration of the star exceeds this critical value, Newton’s law seems to work and the acceleration predicted is the one seen. There is no need to posit any dark matter in these cases. But when the acceleration observed is smaller than the critical value, it no longer agrees with the prediction of Newton’s law.
What is this special acceleration? It has been measured to be 1.2 × 108 centimeters per second per second. This is close to c2/R, the value of the acceleration produced by the cosmological constant!
This remarkable twist in the dark-matter story was discovered by an Israeli physicist named Mordehai Milgrom in the early 1980s. He published his findings in 1983, but for many years they were largely ignored.5 As the data have gotten better, however, it has become clear that his observation was correct. The scale c2/R characterizes where Newton’s law breaks down for galaxies. This is now called Milgrom’s law by astronomers.
I want you to understand how weird this observation is. The scale R is the scale of the whole observable universe, which is enormously bigger than any individual galaxy. The acceleration c2/R occurs on this cosmological scale; as noted, it is the rate at which the universe’s expansion accelerates. There is no obvious reason for this scale to play any role at all in the dynamics of an individual galaxy. The realization that it does was forced on us by the data. I recall my amazement when I first learned about it. I was shocked and energized. I walked around for an hour in a daze, muttering incoherent obscenities. Finally! A possible hint from experiment that there is more to the world than we theorists imagine!
How is this to be explained? Apart from coincidence, there are three possibilities. There could be dark matter, and the scale c2/R could characterize the physics of the dark-matter particles. Or the dark-matter halos could be characterized by the scale c2/R, because that is related to the density of dark matter at the time they collapsed to form galaxies. In either case, the dark energy and dark matter are distinct phenomena, but related.
The other possibility is that there is no dark matter and Newton’s law of gravity breaks down whenever accelerations get as small as the special value of c2/R. In this case, there needs to be a new law that replaces Newton’s law in these circumstances. In his 1983 paper, Milgrom proposed such a theory. He called it MOND, for “modified Newtonian dynamics.” According to Newton’s law of gravity, the acceleration of a body due to a mass decreases in a specific way when you move away from that mass—that is, by the square of the distance. Milgrom’s theory says that Newton’s law holds, but only until the acceleration decreases to the magic value of 1.2 × 10−8 cm/sec2. After that point, rather than decreasing with the square of the distance, it decreases only by the distance. Moreover, while normally the Newtonian force is proportional to the mass of the body causing the acceleration times a constant (which is Newton’s gravitational constant), MOND says that when the acceleration is very small, the force is proportional to the square root of the mass times Newton’s constant.
If Milgrom is right, then the reason the stars outside the special orbit are accelerating more than they should be is that they are feeling a stronger gravitational force than Newton predicted! Here is brand-
new physics—not at the Planck scale, and not even in an accelerator, but right in front of us, in the motions of the stars we see in the sky.
As a theory, MOND does not make much sense to physicists. There are good reasons why the gravitational and electrical forces fall off with the square of the distance. It turns out to be a consequence of relativity combined with the three-dimensional nature of space. I won’t go into the details here, but the conclusion is drastic. Milgrom’s theory appears inconsistent with basic physical principles, including those of special and general relativity.
There have been attempts to modify general relativity to construct a theory that contains MOND or something close to it. One such theory was invented by Jacob Bekenstein; another by John Moffat, then at the University of Toronto; and still another by Philip Mannheim, at the University of Connecticut. These are very imaginative people (Bekenstein, you’ll recall from chapter 6, discovered black-hole entropy, while Moffat has invented many surprising things, including the variable-speed-of-light cosmology). All three theories work to some extent, but they are, to my mind, highly artificial. They have several extra fields and require the adjustment of several constants to unlikely values in order to get agreement with observation. I also worry about issues of instability, although the authors claim that such problems are settled. The good news is that people can study these theories the old-fashioned way—by comparing their predictions to the large amount of astronomical data we have.
It should be said that outside the galaxies, MOND does not work very well. There are a lot of data about the distribution of mass and the motion of galaxies on scales larger than the galactic scale. In this regime, the theory of dark matter does much better than MOND at accounting for the data.
Nevertheless, MOND seems to work quite well within galaxies.6 Data gathered over the last decade have shown that in more than eighty cases (by last count) out of around a hundred studied, MOND predicts accurately how the stars are moving. In fact, MOND predicts how the stars move within galaxies better than the models based on dark matter. Of course, the latter are improving all the time, so I will not pretend to be able to predict how the match-up will turn out. But, for the present, we seem to face a delightfully frightful situation. We have two very different theories, only one of which can be right. One theory—the one based on dark matter—makes good sense, is easy to believe in, and does very well at predicting the motions outside galaxies but not so well inside them. The other theory, MOND, does very well with galaxies, fails outside the galaxies, and in any case is based on assumptions that seem to contradict extremely well-established science. I should confess that nothing has kept me awake at night in the past year more than worrying about this problem.
It would be easy to disregard MOND if not for the fact that Milgrom’s law suggests that the scale of the mysterious cosmological constant somehow bears on whatever is determining how stars move in galaxies. Just from the data, it appears that the acceleration c2/R plays a key role in how stars move. Whether this is because of a connection between dark matter and either dark energy or the cosmological expansion scale, or something more radical, we see that new physics can indeed be found at this acceleration.
I’ve had conversations about MOND with several of the most imaginative theorists I know. Often it went like this: We would be talking about some sober mainstream problem and one of us would mention galaxies. We would look at each other with a glint of recognition and one of us would say, “So you worry about MOND, too,” as if admitting to a secret vice. Then we would share our crazy ideas—because all ideas about MOND that are not immediately wrong turn out to be crazy.
The only advantage is that this a case where there are lots of data, and the data get better all the time. Sooner or later we will know whether dark matter explains the motions of stars in galaxies, or we have to accept a radical modification of the laws of physics.
Of course, it could just be an accident that dark matter and dark energy share a common physical scale. Not all coincidences are meaningful. So we should ask whether there are other phenomena where this tiny acceleration can be measured. If so, are there situations where theory and experiment disagree?
It turns out that there is another such case, and it, too, is unsettling. NASA has by now sent several spacecraft out of the solar system. Of these, two—Pioneers 10 and 11—have been tracked for decades. The Pioneers were designed to tour the outer planets, after which they have continued moving away from the sun, in opposite directions in the plane of the solar system.
NASA scientists at the Jet Propulsion Laboratory (JPL) in Pasadena, California, are able to determine the velocities of the Pioneer spacecraft by using the Doppler shift and thus can accurately track their trajectories. JPL tries to anticipate the trajectories by predicting the forces on the two spacecraft from the sun, planets, and other constituents of the solar system. In both cases, the trajectories observed do not match those predicted.7 The discrepancies are caused by an additional acceleration pulling the two spacecraft toward the sun. The size of this mysterious acceleration is around 8 × 10−8 centimeters per second per second—bigger than the anomalous acceleration value measured in galaxies by about a factor of 6. But it is still fairly close, given that there is no apparent connection between the two phenomena.
I should point out that the data in this case are not yet fully accepted. Whereas the anomaly is seen in both Pioneers, which is much more persuasive than if it were seen in only one, they were both built and are being tracked by JPL. However, the JPL data have been independently analyzed by scientists using Aerospace Corporation’s Compact High Accuracy Satellite Motion Program, and these results agree with JPL’s. So the data have stood up so far. But astronomers and physicists understandably have high standards of proof, especially when we’re being asked to believe that Newton’s law of gravity is breaking down just outside our solar system.
Since the discrepancy is small, it might possibly be accounted for by some tiny effect, such as the spacecraft side that faces the sun being slightly hotter than the opposite side, or by a small gas leak. The JPL team has taken into account every such effect they can think of and so far has been unable to explain the observed anomalous acceleration. Recently there have been proposals to send out a special-purpose probe, designed and built to eliminate as many such spurious effects as possible. Such a probe would take many years to leave the solar system, but even so, this is a worthwhile mission. Newton’s law of gravity has stood for more than three hundred years; if it takes a few more either to confirm it or prove it wrong, that’s not much to ask.
What if MOND or the Pioneer anomaly turn out to be correct? Might their data be reconciled with some existing theory?
At the very least, MOND is inconsistent with all the versions of string theory so far studied. Might it be consistent with some currently unknown version of string theory? Of course. Given string theory’s flexibility, there is no way to rule this out, though it would be a difficult accomplishment. What about other theories? Several people have tried hard to make MOND come out of a brane-world scenario or some version of quantum gravity. There are a few ideas, but nothing that works impressively. Fotini Markopoulou, my colleague at the Perimeter Institute for Theoretical Physics, and I have speculated about how to get MOND from quantum gravity, but we haven’t been able to show how our idea works in detail. MOND is a tantalizing mystery, but not one that can be resolved now, so let’s move on to other hints of new physics coming from experiment.
The most dramatic experiments are those that overturn universally held beliefs. Some beliefs are so embedded in our thinking that they are reflected in our language. For example, we speak of the physical constants, to denote those numbers that never change. These include the most basic parameters of the laws of physics, such as the speed of light or the charge of the electron. But are these constants actually constant? Why couldn’t the speed of light change with time? And could such a change be detected?
In the multiverse theor
y discussed in chapter 11, we imagined the parameters varying over a range of different universes. But how can we observe such variations in our own? Could the constants, such as the speed of light, change over time in our universe? Some physicists have pointed out that the speed of light is measured in some system of units—that is, so many kilometers per second. How, they argue, can you distinguish the speed of light varying over time in a situation in which the units themselves vary over time?
To answer this question, we have to know how the units of distance and time are defined. These units are based on some physical standard, which is defined in terms of the behavior of some physical system. At first, the standards referred to Earth: a meter was one-millionth the distance from the North Pole to the equator. Now the standards are based on properties of atoms—for example, a second is defined in terms of the vibrations of an atom of cesium.
If you take into account how the units are defined, then the physical constants are defined as ratios. For example, the speed of light can be defined if you know the ratio between the time it takes light to cross an atom and the period of light that the atom emits. These kinds of ratios are the same in all systems of units. The ratios refer purely to physical properties of atoms; no decision about choice of units is involved in measuring them. Since the ratios are defined in terms of physical properties alone, it is meaningful to ask whether these ratios change over time or not. If they do, then there is also a change over time in the relationship between one physical property of an atom and another.
