vanesch --We agree on this. My notion was that you were talking about a more formal, precise idea of physical reality or 'what's going on".
In regard to personal styles of reasoning, there's a fantastic book by Jaques Hadamard, The Psychology of Mathematical Invention (Dover). Hadamard interviewed many world class mathematicians as well as Einstein on their patterns of work and thought, and tied things together stimulated by an experience of Poincare -- who worked for months on a problem in Fuchsian functions and made little progress, so he stopped. Several months later, the solution came to him as he was stepping onto a bus. Poincare asked, Why, How...The great mathematician latched onto Freud's idea of the unconscious, and postulated that his unconcsious mind continued to work on the problem even though he had consciously stopped. Hadamard built on Poincare's experience and ideas, and demonstrated that it makes sense to talk about unconscious reasoning and work -- based on his interviews and conversations.
So, why deal with Hadamard? Well, Hadamard also develops the idea of differing views of reality within the creative side of math and physics -- Einstein's trip riding on a light wave is not exactly characteristic of hard-nosed reality. The boundaries between illusion, imagination, and reality can get quite fuzzy -- those who tend to think in images can have a very difficult time translating their thought into spoken or written language, perhaps characteristic of silent or reclusive geniuses. Hadamard gives, I think, a compelling case for the highly subjective nature of internal views of reality, that is, for differing mental pictures.
For example, I think of the double slit experiment with photons, electrons or whatever, in terms of water waves -- I can see what's going on. I prefer to avoid the cognitive dissonance I encounter when thinking about particles in a double slit experiment. We clearly have very different mental pictures, and thus see different realities.
Yes, the whole point of physics is to gain understanding -- by any means possible. Because the mathematics of much of physics is highly difficult, we are forced to operate by intuition a great deal of the time. The "pictures" we have built based largely on classical physics are several hundred years old -- or, at least a whole bunch. These pictures are very much at odds with the "pictures" commonly accepted prior to the Enlightenment.
So the prime mover folks had to be screaming over Newton's ideas; over the heretical idea of a solar centered universe. But, as is pointed out in great detail in Daniel Boorstien's, "The Discoverers", and also in "Longitude" by Dava Sobel, and in countless histories; the shift in viewpoint came from mainly pragmatic impetus. The scientific view of the world made no sense at all to many, not all of them stupid by any means. And, there are still such people around -- they have not caught up with the paradigm ( I use this word about once a decade, it being vastly overused. But I rely on T. Kuhn as my reference here.) shift of roughly four centuries ago.
Many of us have worked out our own approach to building intuition, quantum or otherwise. The fact that notions of a quantum reality do not fit nicely into a 19th century view of an invariant, objective universe simply means, given historical precedents, that the criticisms and discomfort of and with QM will die a natural death.
You say:So the "difficulty" with quantum theory is to find such a picture, which should be suggestive of the entire formalism in a natural way.
What does "suggestive of the entire formalism in a natural way" mean? Who gets to define "natural?" (The way I think about QM is natural to me, and clearly not natural to you.) You talk about the importance of your way to your work, and illustrate an example re slits. You are, I am, and everybody else is, of course entitled to our mental practices, So why require a monolithic picture of QM? I've read and listened to many physicists talking about QM topics in a highly intuitive fashion -- I completely reject the idea that physicists do not understand QM -- the only way to counter my contention is to attempt this understanding with 19th century notions, and such an attempt is, as we all know, fraught with problems.
You state:
I'm supposed to be thinking about "formal tools to predict statistical outcomes of ensembles of experiments". There's no intuition to be gained from that.
Who in the world suggests that you are supposed to be thinking in such terms? What a meaningless statement, a "straw man". And, if you do, better take an applied QM course to get back to daily physics reality. In my experience, I've never heard of such a thing -- but then I was trained to believe the height of physics was to explain a complex phenomena with no math.
Regards, Reilly
