I suggest you don't get too committed to any one model proposed for very small scales. Even if someone can show that their model gives pretty good predictions for a few experimental contexts, they most likely can't show that there's no other model that's as good, or, to throw a spanner in the works, that's better for some experiments but worse for others. Experiments that can distinguish what's happening at scales as small as or much smaller than the Planck scale with the kind of certainty we get from looking through a microscope at bacteria don't seem likely for a few or more generations.
Words like "foam" or "strings" call to mind classical analogies that may be the closest someone can think of for a particular mathematical model, and ideas such as bubbles or knots may have inspired the creation of the mathematical model, but the word "quantum" signals disanalogies that are likely more significant than the analogies.
Even at somewhere like CERN, but certainly in the paper discussed in this thread, the parts of the apparatus, such as photomultipliers, are typically on the order of microns or larger in size. Everything about much smaller scales, down to millionths of millionths of a micron, say, 10-18 meters, is reconstructed from information that we obtain at the micron scale. Intervals of time as well as of length are also very small, but our measurements cannot be more precisely timed directly than to within the time it takes light to travel one micron (we can use attosecond "strobe" lighting, as this Nature article describes, to get to about a thousand times better than that). Experiments at CERN, reconstructing events at smaller than femtometer scales from more than a few centimeters away, are not wholly unlike examining bacteria from the orbit of the moon, but with the added encumbrance that we are only allowed to see results averaged over the course of years to do it; now let's talk about exact details at scales millions of times smaller than the bacteria and the lifetimes of the bacteria, from the orbit of the moon.