Let’s introduce the profound controversial issue:
In the mathematical description of quantum mechanics, everything not forbidden is mandatory. A particle moving from A to B takes every possible path from A to B simultaneously. This includes paths that involve highly improbable events like a photon dividing into an electron-positron pair that then annihilates to result again in a photon. A quantum electrodynamics (QED) prediction of the interaction between an electron and a magnetic field correctly describes the interaction to 14 decimal places. For more accuracy, interactions that do not strictly belong to QED may have to be taken into account (QCD or suchlike are similar animals though), and anyway, today’s measurement accuracy is not sufficient to show whether QED predicts still more precisely. However, with those caveats in mind, as far as we know, QED as such is correct to 15, 16, 17 … hell - it is simply correct, period. In order to predict this well with the QED theory, you must take paths into account, paths and interactions that the involved particles could have taken in as far as one can tell from the outcome, paths that seem ridiculously complicated.
Whether or not you do non-relativistic quantum mechanics with path integrals, when it comes to field theory, every allowed way a process can happen does contribute!
If you were nutty enough, you could claim that the mathematical description asks us to put in precisely all the possibilities that are consistent with what the observer knows.
Now that would be nuts, right? Well, there are roughly two main camps: The “nutty nuts camp” supposedly consists of silly freaks that lost their marbles, you know, like me. They ramble about quantum mechanics supposedly showing how observers are ghosts hanging from non existent purple clouds in the sky of transcendent idealism while there is no reality; they call it anti-realism or what not. Yeah – Nuts – I told you so!
Then there is the “real reality camp”, which consists of nice people who stick to “common sense” and who hold science is about uncovering how the reality out there really works. The latter camp has support from quite a number of popular science writers and accomplished scientists, much more than the nutty nuts camp, where scientists usually only go after they got past their sell by date, the age where physicists should be put down for their own good.
The real reality camp holds that those virtual particles, that is those particles that participate in all the complex interactions that must be taken into account as described above, are “real”. Science is about real stuff, they say, QED is proven by experiment, and QED tells us that there are those virtual particles, so they must be there, so they are real. Otherwise, if those virtual particles were not actually there interacting, QED would give a different result, namely one that is not consistent with experiment. QED just calculates what those particles are all doing! Although “virtual” was basically coined in order to say that something is "not real", the real reality camp claims that “virtual” simply means “not directly observable”. Just because we cannot observe them, so they say, that does not mean they are not real – only people from the nutty nuts camp hold that real stuff is only a dream that dreams itself so that what is not in the dream is not in the dream or whatever – Yeah - Nuts – I told you before. In fact, many in the real reality camp even claim that the not observable virtual particles are actually also observable, because you observe the result of their interactions. So there you go silly idealist – “eat our shorts” say the serious guys.
The nutty nuts have a problem with there being in every simple interaction, even in an electron plainly just sitting there doing nothing as far as we can tell, an infinite amount of virtual stuff “actually going on”. Remember, even every single step in a very complicated path is itself a path that can be completed in infinitely many different ways according to QED.
But really nutty nuts like me have other, really crazy thoughts: All those paths that are allowed are precisely all the possibilities that could happen given what we already can know about the system.
All those contributions inside the math match exactly nothing less and nothing more than precisely all that which is possible in as far as it does not contradict what the observer already knows about the system.
You can join whatever camp you like and discuss with great sophistication stuff like “Are superposition states ontological entities or merely epistemological constructs?” (I cannot help you here, because I do not see any difference.)
But let me warn you. If you get close to the nice and realistic guys, it counts as “unprofessional” to ask questions like “do you truly believe that in every little interaction of every little particle in every tiniest moment there are an infinity of “real virtual” particles actually buzzing and bumping around somehow as we speak?” Their answer to that, if it is not the door in your face, is some weaseling around about that certain issues may seem sometimes strange but you should not worry because people much more clever than you are working on it.
I squarely belong to the nutty nuts crazy people. Wittgenstein tells me that the world is all the facts, that totality is all the self consistent arrangements of facts, of what is possibly observed. Modern physics tells me that paradigm shattering progress in understanding the foundations comes from taking the situation of the observer into account (relativity) and questioning the constraints on observation as such (how to measure, does the measurement impact the measured?, …).
Now there is finally a theory, called quantum mechanics, the mathematical description of which asks us to put in precisely all the possibilities that are consistent with what the so called “observer” already knows.
What the theory deals with matches exactly the uncertainty that I have about what happens, and that determines the possibilities I should expect next, no more and no less.
Am I to take this as some super weird coincidence, some misinterpretation that is actually about real stuff that I cannot observe but that happens to involve an infinity of things actually bumping around, interacting so that it coincidentally all together comes out as precisely my uncertainty?
If that is what reasonable commonsense is about, I gladly belong to the nuttiest in the nutty nut camp!