We exist in space and time. These concepts are so familiar that we don't realize that the nature of space and time lies at the the heart of some of the deepest mysteries of physics.
Take a concept like position. You learn in kindergarten how to measure position with a ruler. Later on, you learn to say where something is in space by giving coordinates--- numbers like street addresses. You say where something is in time by giving, well, the time. What could be mysterious about that?
Physicists have found that when you study very small things, they behave in highly unexpected ways, not at all like everyday objects. For one thing, everything is made of particles, tiny, discrete packets of energy that can't be divided up. For another thing, you can't actually pin down exactly where the particles are in space, or how exactly how they move. In fact, they act in many ways like waves--- a kind of sloshing around of energy that doesn't happen at just one place, but is spread around in space, and even in time. This dual, particle/wave character applies to all forms of ``stuff'', like atoms and light--- everything whatever.
What we haven't found out is whether it also applies to space and time. Could it be that space and time are also made of waves and particles? Could there be ``particles of time''? What does that even mean?
You can see that things get mysterious pretty fast.
The Fermilab Holometer is machine designed to study the properties of space and time at the very smallest scales. We shine light in different directions, through tubes 40 meters long, to measure whether space and time stand still, or whether they slosh around a tiny bit. The experiment is designed not to be affected by normal sloshing of particles. It can detect a sloshing of spacetime by a tiny amount--- a billionth of a billionth of a meter, almost a billion times smaller than an atom, in about a millionth of a second. That corresponds to an extremely slow motion, about ten times slower than continental drift.
If we find the motion we are looking for--- sometimes called ``holographic noise'', because it resembles the blurring in a hologram--- it will help us understand the nature of reality at the deepest level.