The most apparent of forces is still far and away the most mysterious of them.
As macro-scale collections of some 7 billion billion billion atoms per human body, our world appears to be dominated by gravity. It is our days and nights, our weather, our thudded footsteps, our fear of heights. The other fundamental forces deal exclusively with the very small—the strong force holds together atomic nuclei; the weak force governs radioactive decay; the electromagnetic force mediates interactions between charged particles—but gravity is like us. It's only interested in big stuff, or so it seems.
Gravity remains a deep mystery, even 100 years after the formulation of Einstein's theory of general relativity—the force's contemporary but not quite complete description. We can say that gravity is the result of mass warping space-time, like weighted balls on a rubber sheet, but physicists still don't understand it at the quantum level, e.g. of interacting particles and forces. Gravity is stubbornly big and imprecise, like human bodies.
While gravity seems crude and primitive compared to the other fundamental forces, it nonetheless remains the most elusive and frustrating of the four. The other forces all have representative particles, which are just quantized forms of the force itself—or, rather, the fields that permeate all space representing these forces. The strong force has its quarks; the electronmagnetic force has photons; the weak force has W and Z bosons.
The gravitational force, meanwhile, has gravitons. Maybe.
Gravity and extra dimensions
The fundamental forces can all be viewed as omnipresent fields. If you were to zoom way in on any one of these fields, you'd eventually get to the point where the field stops looking like a continuous uniform sheet and instead look like a bunch of discrete points. These points, which are what we think of as particles, are the quantizations of a given field.
(Hence: quantum physics.)
Gravity isn't quantum though, or it sure doesn't seem to be. No one really knows for certain how gravity operates when you get down to quantum scales. Quantum gravity is sort of a placeholder theory then. Does gravity have its own particle, like a photon or gluon?
If so, this would be the graviton. The graviton is a nice idea for theorists, but the almost non-existence of the maybe-particle's interactions with matter make it fundamentally impossible to detect. Not just really difficult to detect: impossible.
Freeman Dyson calculated that just building a shield sufficient to block out enough background neutrinos to make gravitons visible to detection would mean that the shield would be so dense and so massive that it would collapse into a black hole.
In other words, nature would seem to have set a limit on our observational capabilities.
Nonetheless, most popular theories of quantum gravity require gravitons. Quantized general relativity is one—where quantum gravity is just a tiny version of gravity mediated by particle quantizations of a field—but string theory usually requires them as well. Here, a graviton is the vibrational state of some one-dimensional object (a string), which is inaccessible to us out here in our regular three spatial dimensions.
The hierarchy problem
Why is gravity so weak compared to the other fundamental forces?
Again, we see and experience gravity in a more personal and immediate way than most any other fundamental thing in physics. It is, however, an almost incomprehensibly weak force. If you'd never experienced gravity first-hand and and maybe lived in some alternate universe of alternate forces and someone came along and tried to explain the relative strength of gravity to you, it would probably seem like it doesn't exist at all!
Fermilab particle physicist Don Lincoln offers a good illustration: "The electromagnetic force between an electron and a proton in a hydrogen atom is 1039 times larger than the gravitational force between the same two particles. Perhaps a more intuitive example is the behavior of a magnet and a paperclip. A magnet will hold a paperclip against the Earth's gravity. Think about what that means. A little magnet, like the one that held your art to your parent's refrigerator when you were a kid, pulls the paperclip upwards, while the gravity of an entire planet pulls downward, and the magnet wins."
But maybe gravity isn't so weak. This is the possibility offered by string theory.
It's fairly obvious that gravity is a three-dimensional phenomenon because we see how its effects vary with respect to three-dimensional geometry (distance between points in three dimensions). But physicists have only observed its effects down to distances of around a millimeter, which leaves open the possibility that gravity might be acting in other dimensions but only at scales below 150 micrometers or so.
So, gravity might be acting in a whole bunch of these tiny extra dimensions in addition to our regular three. We don't have access to these other dimensions, so we experience a form of gravity that seems weak but is really just diluted across many dimensions.
Particle collision experiments like the LHC are actively hunting for signs of these bonus dimensions. Here is the explanation from CERN, the LHC's parent facility:
Einstein's general theory of relativity tells us that space can expand, contract, and bend. Now if one dimension were to contract to a size smaller than an atom, it would be hidden from our view. But if we could look on a small enough scale, that hidden dimension might become visible again. Imagine a person walking on a tightrope. She can only move backward and forward; but not left and right, nor up and down, so she only sees one dimension. Ants living on a much smaller scale could move around the cable, in what would appear like an extra dimension to the tightrope-walker.
If gravitons are real, they can be created in particle collisions. The catch is that they'd still be undetectable, at least directly, before almost immediately slipping into some other dimension. Physicists think they can nab gravitons indirectly as they vanish from our three dimensions by observing small regions of unbalanced energy and mass in particle collision products. Inferring a graviton's existence is better than nothing.
Why haven't we detected gravitational waves?
This one's really troubling. A gravitational wave is the predicted rippling of space-time as a massive body like a star or black hole accelerates. It's analogous to how sound waves propagate through the air in response to a disturbance, like fingers snapping or a violin string oscillating. With gravity, air is replaced by the very fabric of space-time.
But gravity is just so weak as a force that it takes a really extreme event to produce ripples large enough to see. It'd be like if our ears were only able to pick up sounds produced by the largest explosions. And, even then, we don't directly hear the gravitational waves so much as observe their effects as rippling imprints on the errant dust and radiation spread across the universe.
A couple of years ago, physicists at the BICEP-2 experiment, which is based on a sky-scanning telescope array at the South Pole, thought they had a likely observation in the form of periodic or wave-like imprints in the cosmic microwave background, the dim sheet of leftover thermal radiation from the Big Bang. This was a way hyped event.
Eventually, however, it was determined that what they'd seen was nothing more than the effects of cosmic dust, rather than gravitational waves.
Earlier this fall, astrophysicists in Australia using the Parkes radio telescope to hunt for distortions in the rotations of distant pulsars—which may be indicative of gravitational wave influence—likewise came up empty-handed. Many hopes are currently pinned on the massive LIGO project, which looks for millisecond deviations in the arrival times of laser beams fired underground between Washington state and Louisiana. Such an event would indicate the slight distorting effect of passing gravitational waves. In short, we haven't detected gravitational waves because they don't want to be detected, but their existence has hardly been ruled out.
The non-interacting elephant in the room.
Most of the gravity holding the universe and its many structures together is the result of dark matter, a form of matter that makes its presence known only through the gravitational force, ignoring or mostly ignoring the other three. We know it's there because it must be there for the universe to exist as we see it, but we've never seen the stuff directly. Even more so than gravitational waves, dark matter does not want to be detected. It's a whole other (much, much larger) universe filled with nothing but ghosts.
How much larger? Dark matter accounts for some 85 percent of all matter in the universe, which makes us here in the illuminated side look more like the anomaly. We're the ghosts.
It's not quite as simple as imagining two different universes though. The dark matter realm is entwined with ours such that it forms the very foundation of organized existence. Dark matter is how galaxies come together, providing what's often likened to a gravitational lattice upon which light matter can collect and "grow."
Like gravitational waves and gravitons, dark matter remains invisible to us, but hopefully not fundamentally so.