We don’t know how space-time looks when you get really really small – about 0.000000000000000000000000000000000000000000001 metres. Some theories say that it looks foamy as matter and antimatter are continually created and annihilated (killed off by each other). This bubbling broth of creation and death looks similar to a foam, or like the bubbling on top of boiling water.
Einstein’s theory of general relativity describes gravity really well. So far, nobody has found any experimental evidence that disagrees with it. The theory says that mass bends space-time and when things move around in this bent space they appear to move in curves, as if they were being pushed by something. That push is what appears to be gravity. It’s a “smooth” theory with no quantum lumpiness or uncertainty.
Quantum mechanics, or particularly quantum field theory, explains all the other forces apart from gravity really well. The “standard model” of particle physics is a quantum field theory that explains everything we know about sub-atomic forces _except_ gravity.
So, naturally, people want to try and join the two theories together, to make a quantum theory that includes gravity. It’s really difficult to do though, and nobody has yet got something that looks like a winner.
Back to the quantum-foam: in the quantum field theoretic description of things, like Ben says, you can picture empty space as being filled with “virtual” particle-antiparticle pairs that randomly appear and disappear. Now, remember that these virtual particles have mass and energy, and that mass and energy bend space-time. This means empty space should be constantly bending back and forth as the virtual particles appear and disappear. All of space-time would be rippled and constantly changing, like a frothing foam.
Also remember though, that this is just a crazy theory and there isn’t yet a bit of experimental evidence to support it!
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