Mysterious messages from the dark side
Big news: the universe has a dark side, completely surprising physicists. First, dark matter. Then, dark energy.
This is the sound bite; the long version now follows.
Dark matter
Don’t shoot for the stars; we already know what’s there. Shoot for the space in between because that’s where the real mystery lies.
—VERA RUBIN EXHORTING YOUNG PHYSICISTS
Imagine sitting at a playground watching your child happily riding on a merry-go-round, holding on tight, as instructed. Your attention wanders. Suddenly, you notice that the merry-go-round is spinning around much faster. You instinctively rush over, fearful that your child is going to fly off.1
This was more or less what the astronomers2 observed starting in the 1920s. A galaxy typically rotates, meaning that the zillions of stars that make up the galaxy move in unison, revolving around the center of the galaxy. Astronomers could measure the speed of the stars, thanks to the Doppler effect for light.
The sound version of the Doppler effect is commonly noticed in everyday life: the pitch of the siren on an approaching ambulance and on a receding ambulance sound different. Similarly, the light emitted by an approaching star is blueshifted (its frequency is raised), while the light emitted by a receding star is redshifted (its frequency is lowered). The amount of the shift is proportional to the speed of the star.
When astronomers examine the Doppler data on stellar motion in rotating galaxies, they react with much of the same horror experienced by the parents in my playground analogy. The stars are moving way too fast for their own good!
Actually, Fritz Zwicky3 first suggested (and coined the term) “dark matter” in 1933 by observing the motion of galaxies in a cluster of galaxies, rather than the motion of stars in an individual galaxy. But the underlying principle is the same. The individual galaxies are moving much too fast, so that, unless a large amount of unseen matter is holding them back by means of gravitational attraction, they would fly away from the cluster.
Observational techniques improved by the 1960s, so that Vera Rubin4 (1928–2016) and Kent Ford were able to measure the collective5 motions of stars in different regions of rotating galaxies and thus firmly established that galaxies were themselves suffused by this unseen dark matter.
As explained in chapter 5, we require contact with the forces in everyday life. The children on the merry-go-round are told to hold on tight to the handrail. The stars do not have anything to hold onto, of course; instead they are kept from flying off into deep silent space by the gravitational attraction exerted on them by the zillions of other stars in the galaxy. It is a collective enterprise: the stars form a conglomerate known as a galaxy by virtue of their mutual gravitational attraction for one another. Notice that although the gravitational force decreases, according to Newton, like the square of the distance and so is minuscule on the galactic scale, the pull of the zillions of other stars in the galaxy really adds up and keeps the stars bound to the galaxy.
This was the expectation. The data show that, yes, the gravitational pull of the other stars on any given star does add up, but the total is not quite enough. The galaxy should have fallen apart with all the stars flying off into deep space, each chasing after its own destiny rather than remaining part of the greater good. I have simplified the story slightly, but only slightly. Astronomers actually had data on how the speed of the stars as they revolve around the galactic center depends on their distances from the center, and this also disagreed with theoretical expectations.6
An important point: note that the dark matter story does not have anything to do with Einstein gravity as such. Newtonian gravity is completely adequate to account for motion on the galactic scale.
Thus was born the notion of dark matter.7 Galaxies, including our very own Milky Way, must be suffused by a mysterious type of matter with quite a bit of mass. This unknown matter is called dark because it neither emits nor absorbs light. Clearly, it can’t emit light (otherwise, we would have seen it), and it can’t absorb light, since we can see the stars on the other side of the galaxy (after accounting for various observed interstellar clouds of dust particles).
Notice that the universality of gravity, in contrast to electromagnetism, that we spoke of in chapter 8, is crucial here. Whatever dark matter is, while it is free not to have anything to do with light, it must listen to gravity, because gravity is just curved spacetime.
The orthodox view is that dark matter consists of hitherto unknown elementary particles that do not interact with light. These are in fact very easy to introduce into the standard theory of particle physics; simply do not couple these particles to the electromagnetic field; that is, let them be electrically neutral. Thus began a tremendous effort to detect such particles in earth-bound laboratories. Lately, a bit of skepticism of this view has crept in, merely because, after years of intense search, nothing has been sighted.
Even so, I still much prefer this view of dark matter to the one highly speculative view on the market. Back in 1983, the Israeli physicist Mordehai Milgrom proposed modifying Newton’s laws to account for the rotation of galaxies.8 You might think that after this many centuries, Newtonian physics has been thoroughly tested and verified. Yes, but the acceleration experienced by stars in rotating galaxies is much smaller than any that has been measured on earth and in the solar system.
I remarked in chapter 14 that Einstein’s theory is extremely tight: it cannot be easily modified without messing up the various celebrated tests (such as the bending of light) that the theory has passed with flying colors, not to mention our daily use of GPS, which has to take into account corrections due to Einstein gravity. In contrast, Newtonian laws are quite loose. You feel like modifying Newtonian physics? Go ahead, but make sure that the effects of your modification are so tiny so that they show up only on galactic scales. I personally find such ad hoc modification of Newton’s laws contrived and distasteful.
In becoming theoretical physicists, students are told to keep an open mind and not to dismiss unorthodox suggestions (provided that they are consistent with known facts, of course) out of hand. But still, one’s mind should not be so open that it leaks, possibly leaving an empty mind.
Here I might mention another advantage of the action principle over the equation of motion approach. It is considerably more difficult to modify the action for Newtonian physics than to modify the equations of motion for it.
When Einstein triumphantly completed his theory of gravity, he missed predicting that the universe would expand, as was discovered later by Vesto Slipher, Milton Humason, Edwin Hubble, and others. With the Einstein-Hilbert action given in chapter 12, if we fill the universe with known particles (that is, atoms and molecules, electrons, protons, photons, and what not) it will expand. We simply take the metric describing an expanding universe given in the appendix, plug it into the equations resulting from the action, and solve for the behavior of the function a(t) measuring the size of the universe. In fact, now, more than a century after Einstein gravity was proposed, an advanced undergrad would be capable of doing this calculation. He or she would find that a(t) increases, but at an ever decreasing rate.9 In other words, the universe expands but decelerates in its expansion.
This can be understood heuristically: the known particles, in their uncoordinated motion, exert a pressure outward, leading to expansion, but gravitational attraction between the particles tends to pull everybody back, and hence slows down the expansion.
The big surprise was that observation of distant supernova in the 1990s indicated that the expansion of the universe was actually speeding up rather than slowing down. Contrary to the impression given by some popular media, this effect can be readily accommodated in Einstein gravity. Recall that I explained in chapter 13 that in Einstein gravity, the action has to be composed of geometric invariants, and that besides the curvature, the volume of spacetime is also clearly an invariant. We are free to add to the Einstein-Hilbert action the so-called cosmological constant term, consisting of the volume of spacetime multiplied by a constant Λ. Incidentally, Einstein was quite aware of the possibility of including this term (and I would be exceedingly surprised if Hilbert, being a mathematician, did not know about it).
Including the cosmological term leads to an additional term in the equation governing the expansion of the universe. Again, our bright undergrad could readily show that with the appropriate choice of Λ, he or she could make the universe expand at an ever-increasing rate. This proverbial undergrad10 would also notice that the cosmological constant term, as its name suggests, has an effect only on cosmological distance scales. Thus, it would not affect any of our exceedingly successful calculations involving gravity from the solar system scale all the way up to the galactic scale.
For completeness, I should mention that other explanations for the accelerating expansion of the universe have been floated.11 But since the cosmological constant is ready made and available, I believe that most theoretical physicists prefer, for the sake of simplicity, to use the cosmological constant rather than to have to invent some other far-from-compelling constructs.
The cosmological constant Λ has a rather convoluted history12 in theoretical physics. As I mentioned, its existence was known to be possible since the time of Einstein. But since its only effect was on the expansion of the universe, for many decades Λ was postulated to be mathematically zero. Unfortunately, while many theoretical physicists tried, nobody managed to come up with a convincing reason why that should be so. Now that observational data has indicated that it is extremely small13 but not zero, the mystery has only deepened.
Here and in chapter 14, I extolled the virtue of Einstein gravity as being an impressively tight theory. But in the present context, one could also say that Einstein gravity is too loose: it allows for two fundamental constants, Newton’s constant G and the cosmological constant Λ. Perhaps the situation echoes a pseudo-philosophical utterance of Niels Bohr, that the opposite of a great truth is also a great truth. Annoyingly, the cosmological constant Λ only reveals itself on cosmological scales.
Leaving these deep issues aside for the moment, I can dispose of a triviality that has confused the lay public a bit for no good reason. The equation of motion for the gravitational field in Einstein’s theory has the schematic form
(variation of the gravitational field in spacetime) = (distribution of energy in spacetime)
When we include in the action a term equal to the volume of spacetime multiplied by a constant Λ and extremize the action to obtain the equation of motion, then of course an extra term will pop up in the equation of motion. This term is usually included in the distribution of energy on the right hand side of the equation. Indeed, that is the origin of the term “dark energy,” a form of energy that can’t be seen except in the expansion of the universe.
But as any high school student could tell you, the equation a = b + c can perfectly well also be written as a − c = b. Thus, some people with nothing better to do prefer to move the dark energy term from the right side of Einstein’s equation to the left side, and regard it as some kind of force other than gravity. A few even go so far as to call it antigravity, a term that is unenlightening at best and misleading at worst. Is it a new form of energy? Is it a new force? Somehow, this debate, which raged for a while in the popular media (or blogosphere, or whatever you call it) barely stirred a ripple in the theoretical physics community. Dear reader, you can understand why. Whether you put a term on the right or on the left of an equation does not change the physics one iota.
The situation reminds me of creative corporate accounting as humorously portrayed: depending on whether you put a tax write-off on the left or right side of the ledger, you could either make a huge profit or sustain a bad loss.
Here then is another advantage of the action formulation of physics versus the equation of motion formulation. There is no left or right side to the action; it is just a sum of a bunch of terms, the fewer the better, according to theoretical physicists hellbent on unification. You tell the universe what the deal is (that is, what the action is), and the universe will do what it takes to find the best possible deal.
The concordance model
Throughout history, our conception of the cosmos has changed a great deal. Currently, the consensus is known as the ΛCDM model, also referred to as the concordance model. You already know what Λ stands for, and CDM stands for cold dark matter, cold meaning that the postulated dark matter particles are moving around much slower than the speed of light. Current measurements indicate that, of the total14 energy and mass of the universe, dark energy contributes 68%, dark matter 27%, and ordinary matter (which you and I are made of) only 5%, as was already mentioned way back in chapter 1.
It was really quite a shock: until recent times, this enormous dark side of the universe was largely unsuspected, although hints of it existed.15
The long history of our growing understanding of the universe has been a humbling process, a steady erosion of anthropocentrism and geocentrism. The ancient Chinese thought that their Middle Kingdom occupied the center of the world. The Greek Anaxagoras was ridiculed for suggesting that the sun may be as large as the Peloponnesus. Eventually, Copernicus instigated a revolution by suggesting that the earth is not at the center of the world. Yet the belief that the sun was at the center of the galaxy persisted until 1915, when Harlow Shapley determined that we are out near the edge. For years afterward, astronomers believed that ours was the only galaxy, thinking that what we now recognize as other galaxies were merely clouds of luminous gas in our galaxy.
But just as we finally came to recognize ourselves as passengers on a smallish planet circling an insignificant star lost somewhere near the edge of an ordinary-looking galaxy drifting inside a relatively sparse cluster of galaxies in some region of the universe resembling any other region, we learn that the matter out of which you and I and stars and galaxies are made may not even be the main component of the universe.
How humble do we have to be?