I'm really not trying to be controversial Dale, and I regret that my characterization of QFT came across as being "misleading at best".
I certainly was not trying to discredit QFT, or quantum theory in general. On the contrary, the remarkable thing about quantum theory is that it has been so convincingly verified by experimentation. Regardless of how counterintuitive some of the implications might seem, physical existence is clearly quantized at a fundamental level.
Further, I was definitely not attempting to suggest that physical theories are "nothing more than math". Yes, these theories are written in the language of mathematical formalism. However, the theories are typically arrived at initially by recognizing patterns of action within observable physical parameters, elucidating the logical relationships between those physical parameters, and then utilizing the theory to make predictions that can be verified experimentally. The theories are also obviously much more than "just math" because their power of predictability allows for real world application of the physical principles in question. In the case of quantum theory alone, the real world applications include lasers, CDs/DVDs, MRI diagnostic imaging, and countless others.
Yet, despite the compelling degree of experimental verification, and despite the incredible value in real world application, I think you'll agree that there is still great debate within the physics community regarding the appropriate interpretation of quantum theory... debate about what's really going on at the quantum level. Still, the debate is largely philosophical, because the predictions of quantum theory remain the same regardless of whatever interpretation you might favor. That is precisely why the "shut up and calculate" attitude is so prevalent in practitioners of quantum theory.
My impression was that the OPs curiosity was similar to this. He (or she) seemed to be asking for an "ontological" definition of "what" space is. I thought your reference to "field" theory was helpful in that it at least offers a mental construct to visualize, but I don't believe it really gets to the heart of the OP's question unless you can define what the field is ontologically.
I do not mean for this to be at all confrontational, and I don't believe it is an overly controversial statement. I'm not even sure that we are in actual disagreement. I think your objection to my previous statement might be largely due to some loose semantics on my part. I did not mean to suggest that a field's "substance" of linkage should be thought of as some type of mystical "luminiferous ether". You stated yourself that "there are good reasons to assume that interactions (in/of/by the field) are mediated by something". That "something" is all I meant by the "substance" of linkage.
Yet, the interested lay person (reasonably, but naively) expects physics to be able tell them, in ontological terms, WHAT that "something" is. I was simply trying to explain to alasange that, ultimately, the science of physics does not provide those types of answers to those types of questions. Those kinds of questions are left to the philosophers.
Again, I think gmax summarized that position much better, and much more succinctly...
gmax137 said:
This is where the physicists point out that physics is, in fact, about predicting not explaining. I know, not very satisfying is it? Actually a lot can be done by "mere" prediction. And really if you think about it hard enough, all "explanations" demand further explanations, it seems ultimately you get to a point where it is "turtles all the way down."