by Shane L. Larson
I grew up in the American West, where our self-identity is inexorably melded with a deep romanticism about the Frontier. My family homesteaded near Briggsdale, Colorado, where the Rocky Mountains fade into the vast expanse of the Great Plains of North America. You can still visit the old homestead site, now on my family’s cattle ranch, and see the foundations that were laid down many generations ago. I can remember crawling around those walls as a young boy, trying to imagine the world in those long forgotten days — before cars, before computers, before rockets. What did my old-time relatives think about every morning when they got up? What did they work on every day? Did they stare at the sky, virtually identical to the sky I stare at (except theirs was probably much darker), and wonder?
We portray the Frontier as a place full of adventure, discovery, and possibly undying fame. But Frontiers are in a very real sense the boundary between all the hard-won knowledge of our species, and our ignorance. This is perhaps captured no where better to my mind than in Ortelius’ 1570 Map of the World, known as Theatrum Orbis Terrarum.
Made in the last decades before the dawn of the Age of Enlightenment, the map was one of the first to capture the knowledge of the true sphericity of the World. The map very clearly shows the boundaries of what was known and what was unknown in western culture. Consider: in 1520, Magellan’s expedition passed through what today is known as the Straights of Magellan, between the mainland of South America and the Isla Grande of Tierra del Feugo. Ortelius’ map captures that Frontier of exploration explicitly, showing the path around South America, but also showing complete ignorance of the nature of the Isla Grande. In fact, the entire lower part of this map shows the boundary of European knowledge of this part of the world, showing the farthest south on the globe any explorer had ever been. Even closer to Europe there are boundaries between knowing and ignorance that can be seen as well: the northern fringe of the Scandinavian Peninsula is clearly not correct, nor is the shape of the Caspian Sea.
Frontiers define those regions where explorers for the first time are discovering and documenting what has only been suspected or imagined before. Frontiers are more often than not enabled by technology. In Magellan’s day, access to the Frontier was enabled by great sailing vessels. When my family homesteaded in the plains of Colorado, their journey had been enabled by Conestoga wagons. Technology is almost always helping us push the boundaries of the Frontier outward. It is as true today as it was in the past.
Today, there are frontiers in science, both in terms of our knowledge, as well as in terms of what our technology is capable of. On both fronts, gravity is at the frontier. In the 100 years since the birth of general relativity, our understanding of the Cosmos has grown dramatically, and at each step, gravity has played a role. Einstein showed us how gravity can explain Mercury’s lagging orbit, and suggested it could bend the trajectory of light and change its color — effects that had never been measured. Since then, the frontiers have expanded well beyond those initial speculations. Modern cosmology was born less than 15 years after Einstein’s initial presentation of general relativity, and even today challenges our understanding of the Cosmos. We have explored the gravitational collapse and death of stars, and discovered the skeletons that survive the throes of death. Closer to home, we have harnessed gravity to allow us to navigate and map the world to exquisite precision. Our satellites have measured the gentle warp of the Earth’s gravity to map out the world in ways Ortelius never imagined.
Despite all these discoveries, there is still much to learn. Gravity is right on the boundary between our most exquisite triumphs and the precipice of our deep ignorance about the Cosmos. Science is about looking over that precipice and wondering what is at the bottom; we know there are still great mysteries Nature is hiding behind the facade that we call “gravity.” We have come a long way from the frontier Einstein imagined. What are the frontiers of gravity today?
Consider the interiors of black holes. A black hole has gravity so strong, not even light can escape. It’s boundary, the event horizon, forever hides the inside from the external Universe. If you could somehow peer past the event horizon, deep down inside you would find a point of infinite density and infinitely strong gravity called the singularity.
Perhaps the greatest enigma, the greatest failing of general relativity, is the existence of the singularity. From a classic perspective, gravity is a purely attractive force that can grow without bound when matter is compressed into a small enough space. The limitless growth in its strength means if you squeeze hard enough, it can grow so large than no other known force can oppose it. When nothing can oppose it, everything collapses in a dramatic collapse not unlike the collapse at the end of a star’s life. But nothing can stop the collapse, and mathematically, everything falls into an infinitely small, infinitely dense point that we call “the singularity.”
Singularities — “infinities” — are perfectly fine in mathematics. They are less desirable in physics. There is a strong, prevailing belief that in the physical world, nothing can be “infinite.” Objects and phenomena can be ridiculously large or ridiculously small when compared to the scale of human experience, but never infinite.
The prevailing belief is that the singularity is an indicator that general relativity is a classical theory — it is good for large scale descriptions of the world, not for the microscopic landscape of the Cosmos. For that, we will need a new idea, an extension of general relativity into the quantum regime — “quantum gravity.” Where does the realm of quantum gravity become relevant? At distances separated by the Planck length (10^-35 meters = 0.000 000 000 000 000 000 000 000 000 000 000 01 meters).
What is quantum gravity? Fundamentally it is expected to be a theory that describes the nature of space and time itself at the Planck scale; many believe that using quantum gravity to describe the interior of a black hole will obviate the need for a singularity, but no one really knows how that will happen because we don’t have any working models that make predictions testable with observations. But there are many, many seductive and enticing ideas that are waiting for us to attain a state of understanding sophisticated enough to put them to the test.
There are also challenges for gravity on scales that are enormously large, spanning the size of the Cosmos. Some of these challenges are recent, some have been known for the better part of a century, but they are all unresolved. Part of the story begins in the 1930s with astronomer Fritz Zwicky. In 1933 he was observing the Coma Cluster of galaxies, a group of about 1000 galaxies whose center lies 320 million lightyears away, in the direction of the constellation Coma Berenices. This was less than 10 years after the discovery that galaxies were in fact like the Milky Way, but enormously far away. Astronomers were still trying to learn all they could about galaxies, and studying their behaviour.
Zwicky made a very reasonable assumption: the light of the galaxy is made by all the stars in a galaxy, and since most of the mass is contained in stars measuring the light is a way to get a handle on how much a galaxy masses. If you could measure the mass of all the galaxies, then you can use gravitational theory to explain their motions. But when Zwicky measured the motion of the galaxies, he found they were moving faster than expected — given the speeds they were moving, the cluster should have flown apart long ago. The only explanation is there was missing matter he could not see — more matter would simultaneously make the galaxies move faster, but also provide enough gravitational attraction to hold the cluster together.
By the 1960s, the missing matter problem had yet to be resolved. Astronomer Vera Rubin was studying the rotation of individual galaxies. Stars orbiting the center of a galaxy obey Kepler’s Laws of Orbital Motion, just like planets orbiting the Sun. Kepler’s laws say that the farther you are from the center of gravity, the slower your orbital speed should be. What Rubin found was that the outer reaches of galaxies did not slow in their rotation; in fact they rotated just as fast as stars that were closer to the center. This is known as the “galaxy rotation problem” and the plot of the rotation speed versus distance from the center of the galaxy is described as a “flat rotation curve.” Just as was the case with the Coma Cluster, the galaxy should have flown apart. The only explanation is that there is unseen mass — more matter would simultaneously make the stars move faster, but provide enough gravitational attraction to hold the galaxy together.
Rubin began her investigation with the Andromeda Galaxy, but in surveys of many more galaxies found that it was always true — all galaxies appear to have enormous amounts of unseen matter. Today, we call this dark matter.
This has enormous implications for cosmology. If the Universe is expanding, then the rate it expands, and the ultimate fate as a consequence of expansion, depends on the amount of matter in the Universe. This begs some important questions, like “is there enough matter to slow the expansion?” and “is there enough matter to cause the expansion to reverse?” Gravitational physicists classify the possible futures of the Universe in three ways:
- OPEN: There is not enough matter to slow the expansion of the Universe down at all; it expands forever.
- FLAT: There is just enough matter in the Universe that the expansion is slowing, but it will never halt, instead coasting forever.
- CLOSED: There is enough matter to eventually stop the expansion, and cause the Universe to recollapse in a backward version of the Big Bang that is often called the Big Crunch.
Each of these scenarios has particular signatures in observational data, and astronomers have found strong evidence that the Universe is indeed in the FLAT mode. That being the case, this has spawned a multi-decade quest to make a census of all the stuff in the Cosmos and characterize not only its gravitational influence, but also figure out what it all is!
We are aware of dark matter because of its gravitational influence on the rest of the Cosmos, but we have no idea what it is. And there is a LOT of it. Current estimates suggest that the Cosmos is 27% composed of this dark matter. The stuff you and I and planets and stars are made of — atoms — only make up about 5% of the total amount of stuff in the Universe.
So what is the other 68% of the Universe? Astronomers were perplexed by this for a long time, and began to doubt that the Cosmos was put together the way we thought it was. Maybe the Cosmos wasn’t FLAT but was instead OPEN and our observations were wrong in some way.
But in the late 1990s, there was a breakthrough. Mulitple teams of astronomers were using supernovae to measure the size and expansion of the Universe. Certain supernovae (Type Ia supernovae) are standard candles — they all explode with the same brightness. This means that the brightness of the supernova gives you a way to measure distance — the dimmer the supernova, the farther away it is. But cosmology gives us another way to measure distance, using Hubble’s law — redshift is also a measure of distance. The larger redshift an object has, the farther away it is.
But in 1998, the Supernova Cosmology Project and the High-Z Supernova Search Team discovered that these two methods of measuring the distance to supernovae did not agree — distant supernovae were dimmer than expected given the redshift distance. How can that be? The only explanation seems to be that the expansion of the Universe is accelerating. An unknown something is accelerating the expansion of the Universe, ever so slightly, on the largest scales. Today, we call that something dark energy. Dark energy, whatever it is, makes up the remaining 68% of the expected stuff in the Universe.
At long last, astronomers and physicists have discovered all the stuff we expected to find in the Universe. But we still don’t know what it is. We call this stuff “dark matter” and “dark energy”, but we don’t know anything about their behaviour and properties beyond their gravitational influence. Maybe they are some new, exotic bit of particle physics we have never seen before. Maybe they are some new, exotic behaviour of gravity on large scales. Or maybe they are something completely new, completely unexpected, and completely unexplained. Whatever they are, dark matter and dark energy are clearly at the frontiers of our understanding of gravity and cosmology. The future lies on the other side.
What these discoveries will mean and how they will change the course of human history is not for us to know, just as it was not for Einstein to know how general relativity would change the world. Those are questions for our posterity, our future children, who will have moved on from the simple mysteries that confound us today, and will be challenging their own new frontiers.
This post is part of an ongoing series written for the General Relativity Centennial, celebrating 100 years of gravity (1915-2015). You can find the first post in the series, with links to the successive posts in this series here: http://wp.me/p19G0g-ru.
This post concludes this long series for the GR Centennial. Thanks to everyone who read, commented, and supported this effort! We will certainly talk about gravity again at this blog… :-) This post was completed while in residence at the Aspen Center for Physics.