Gear300 said:
Interesting stuff...since it was mentioned that the vacuum state has energy, has there also been consideration of space-time energy (assuming space-time and the vacuum have some commonality)?
In normal quantum mechanics, no because quantum mechanics, in terms of the Schroedinger equation, is non-relativistic. However, quantum field theory does take into account special relativity, which is one of the reasons why some people talk about matter fields in quantum field theory. In field theory, we can create and annihilate particles, even particles with mass, due to special relativity, they just go into energy. So in this case, the matter fields behave like the electric/magnetic fields. That is, the photon is the energy quantum of the electric/magnetic fields. Whenever the fields interact with a system, they do so in the manifestation of a photon. Likewise, an electron (or other particle) has a matter field. Whenever the electron matter field interacts with a system it does so in the manifestation of the electron.
Another example, the creation of a photon is just taking a photon "out" of the vacuum state. If we have an electron and positron collide, create energy, and then create new particles, this can be roughly shown as the electron and positron annihilating, creating a virtual photon (which carries the mass energy of the pair), annihilating the virtual photon, and creating the resulting particle pair (I can't remember what they can be... muons maybe?).
What I am not too sure on is the universality of this interpretation. When you look at quantum mechanics, you will get all sorts of interpretations, like Copenhagen or many-world. But I am not sure if the same goes with field theory (or if field theory is just a really complex interpretation in itself but then are there other quantum mechanics interpretations that cover fild theory) and field theory explains a lot more processes and physics than regular quantum mechanics since it takes into account special relativity. It's really something I have never seen in my readings on the subject when even a simple quantum mechanics text like Griffiths will take the time to mention other interpretations. So I don't know if the whole "matter field" is something that is common to all quantum field theories (though it seems like the name and theory imply it by definition). Particularly since I have only seen a few authors come out and explicitly explain it as thus (Zee in his Quantum Theory in a Nutshell does so).