Is matter everywhere?
There are two answers to this question: 1. No, matter is not everywhere and, 2. I don't know.
One of the amazing things that one learns in studying either Particle Physics (the study of REALLY small stuff) or Cosmology (the study of REALLY BIG stuff) is that you realize there is a lot of nothing in the universe. There is a lot of space that really has nothing in it. "Nothing" is sort of a tough and often confusing concept for our little human brains to comprehend. Relative to the size of things in our universe, the space between the things is huge. People are confused because so many popular images and even school science text books often show planets or stars near enough to each other that you can see several at the same time. Other than the moon and the sun, everything else in our universe is so far away that they appear as just points to our naked eyes.
This also applies to subatomic matter. Between the electrons in an atom and the nucleus there is a lot of space filled with nothing. The reason this concept confuses people is that they think of us walking around in nothing. Air is very much something though. To make our accelerators work we have to make little spaces of nothing, also known as a vacuum. Then what is the universe sitting in? The question is even better if you believe The Big Bang Theory and you ask - What is the universe expanding into????? That's the "I don't know" part of the answer, but I sure would like to know. It might be a big nothing also, but if you think about an endless nothing with no limits, it is pretty much beyond our ability to understand!
Brian Kross, Chief Detector Engineer (Other answers by Brian Kross)