@Pawl -- Re: @RobHib -- We'll see...
Your insightful last post in effect wraps up the discussion I reckon. Your comment succinctly summarises the original point I was trying to make about aspects of fields being incomprehensible except through mathematics. Anyway, it seems what started with my casual and facetious remark about a 'Nobel for 'fields' has generated more words than I expected.
As mentioned, the notion of fields, through various levels of understanding, has troubled me for decades since as a kid I asked what magnetism was, and in ways it still does. Whilst the double-slit experiment rightfully captures popular imagination as a means of demonstrating quantum weirdness, it seems to me a similar case can be made with respect to force fields. Especially so since it's a ubiquitous aspect of physics in the sense that most physics students, electrical engineers, etc., not only can't avoid it, but as with thermodynamics, it's a central pillar of their work/profession.
Moreover, I cannot ever recall any intermediate-level text making a strong point about the striking dichotomy between static, non-excited, force fields (magnetic, electric etc.) and those of far-field EMR. Of course, by that I'm referring to both our perception of and our seemingly quite different explanations of these physical phenomena—yet clearly for nature, they're just manifestations of the same thing; she has no concerns that we've difficulty in explaining them, and or that we often do so using inconsistent or very different approaches for each phenomena.
Ages ago, I recall searching* various classical physics and QM texts for various explanations of what happens at the instant a static magnetic field begins to move (is accelerated) with respect to an electron or current-carrying wire (specifically the classical case—where EMR/photons begin to be emitted and the instant when λ ceases to be meaningless/'infinite'); and it was exceedingly difficult to find any direct references to the matter. One is left to figure it out like an exam question from the more general explanations which can be very difficult. (I ended up in an entangled (no pun intended) mathematical mess; Lorentz and many other such matters to consider, even the relativistic case was in the mix—right, my attempt failed.)
I failed again tackling the problem from the QED end, one easily gets bogged down (well, certainly I do) in complicated conceptual matters, and the maths is persistently mind-boggling (heaven knows why I bothered). The basics of QM photon generation/emission is documented but to fully understand the intricacies of the coupling/interaction of e‾ to the magnetic static force field at the moment of initial acceleration is, pretty much, beyond this mere mortal's capability. We've to consider such notions as virtual photon exchange, perturbation theory, QM's non-relativistic and relativistic Hamiltonian for both free and bound electrons in a static force field etc., etc. If it's not one's primary bread and butter, then it's damn heavy going. (Oh, to have Dirac/Feynman's mind!)
I note also the popular press has recently dipped its toes into the question of what exactly is a field. In a short, somewhat uninformative article on fields New Scientist (No 2999, 13 December 2014, p39) says of a field that "On the one level, it is just a map"; and even MIT's Frank Wilczek gets into the act who's quoted as saying "Ultimately, a field is something that depends on position".
This leaves me little the wiser. I'd have thought that with Wilczek's renowned stature in such matters, he could have put up a marginally better performance. It's hardly very informative given that the article's opening paragraph quotes Newton's dismissive position on the matter of fields. But then, Wilczek, like Newton, is also dismissive.
As Robinson ruefully points out in his post, that speculating over the philosophy of QM phenomena is a waste of time: "[it] is unknowable and likely transcends the limits of Human understanding. That's why physicists don't like to discuss it. It's kind-of pointless." Perhaps so, (and I essentially agree with that position, especially so from the position of getting things done); but I doubt seriously if many (even some scientists) will ever refrain from doing so on the grounds that it's pointless. It's just too alluring for many (and sometimes it actually delivers results).
Of course, the other aspect of this argument is that physicists aren't lily-white either. As a matter of course, they do things that would give philosophers apoplexy. They've little qualms about 'creating' virtual particles that run backwards in time, exceed c and perform other strange 'illegal' non-real-world scenarios, and then there's also perturbation—say no more! [OK, OK, I know!] Moreover, they've been performing these 'kluges' for a very long time, Planck ultimately did it back ca 1900 as a last resort and out of sheer desperation to solve the Ultraviolet Catastrophe and, voila, now very thankfully we've h. So I'm not against such approaches by any means, as it usually works somehow (a bit like those parametric equations one learnt about in one's early schooling). If I'd been Planck, I'd have done exactly the same (but that's nonsense, I'd have never dreamt up such an ingenious solution anyway). What it certainly does show is how truly brilliant and innovative Planck really was.
Thus, it doesn't really matter if people speculate or theorize wildly; scientists will carry on doing their day-to-day work in their usual, procedural, by-the-book way. But very occasionally philosophising will yield results and someone will arrive at a brilliant idea (after all, Einstein famously speculated in a tram if I recall and now look at the results).
Anyway, seems we've come full circle. It's unlikely we've gained a better understanding of these closely-related electromagnetic field phenomena than we had before we started the discussion, but it seems to me what's key and really significant is how vastly different our approach needs to be towards each for our ultimate understanding of the physics that's involved. If nothing else, these two phenomena are an excellent illustration of how seemingly idiosyncratic the quantum world is. Whether or not we want to, they force us to think about the problem.
A great story and great posts.
…Now I can sit back and wait to see whether QM is analogue or not! ;-)
* BTW, during that earlier search, I ended up ferreting out old original copies of that eccentric genius Oliver Heaviside's expansion and reformulation of Maxwell's 1873 masterpiece, 'A treatise on electricity and magnetism'. Heaviside's own three-volume set on the subject titled 'Electromagnetic Theory' (1893 if I recall), is also a masterpiece, albeit dense and heavy going. Those with an understanding of Maxwell's equations and who've an interest in the history of the subject ought to at least peruse them. In the grand schema, this is an extremely important mainstream document, as in it Heaviside essentially modernizes Maxwell into the form that we use today. Also, it introduces much of the terminology (absent in Maxwell) that practical scientists and electrical engineers use today (they'd be forever thankful to Heaviside if they knew these were his ideas, but most don't). There's also Heaviside's earlier work 'Electromagnetic Waves' (1889) which may also be of interest.
Seems these days Heaviside's a little lost to history which is a shame. It's often what happens when you fight the scientific establishment/established orthodoxy, which he did (remember it took Galileo quite some centuries to be 'redeemed' for similar reasons). Nevertheless, he features heavily in my old books on radio theory; had the Kennelly–Heaviside ionospheric E layer named after him; and even the 'Heaviside layer' features as the subject of a song in Lloyd Webber's musical Cats.