The Problem of Conceptualism

I have a confession to make, a confession that will probably bar me from theoretical physics forever: I'm a conceptualist. No, not the philosophical kind. Jury's still out on whether universal qualifiers can exist. I'm a physical one. I believe that everything in physics should be understood in terms of physical concepts.

The physical part is important. There are two ways to analyze anything in physics. The first way is with math. If you take the Poynting vector of an oscillating dipole you see that there is energy at infinity. Bam, radiation. But this doesn't tell you why you get radiation. In order to get that you'd have to notice that due to finite propagation time an oscillating dipole creates expanding "kinks" in the electric field. These kinks look like waves. Ergo radiation. This is conceptualizing the problem, recasting it in terms of what the world is actually doing.

Obviously mathematics is important in physics. You can't quantify anything without it, and without quantification you don't know whether your bridge will fall down or explode. What about qualification? Do we need conceptualization? Certainly it helps all physics before 1915 or so. Einstein built special relativity entirely off of gedanken, or conceptualization experiments. Things started getting a little tricky with quantum mechanics, though. It's really goddamned hard to imagine a probability wave, and the uncertainty principle is designed specifically to mess with our heads. Then you get deeper. Cosmology. Particle physics. String theory. The deeper you go the more the qualification becomes math. There is no physical reality happening, just math becoming macroscopics. Do isospin and hypercharge even exist? I have no idea.

I want to believe that conceptualization is still important. Certainly it becomes important in applied physics. If you can't imagine how the physics interacts with your intentions, then you fail as a technologist. I do not know how to rationalize it for pure physics. Surely you can get an understanding of what is going on without caring about it's physicality? But then we're no longer doing physics. We're doing reality math. That does sound pretty cool, but it also seems almost antithetical to the ideas of both reality and math.

There is one possibility to patch it up. We know from special and general relativity that there are things we know are real, but far to complicated for the human mind to comprehend. That's why we represent them entirely mathematically. This bothers me for other reasons that I will not go into now, because it is convention nonetheless. This allows for reality to be happening at the particle level while still requiring that the only qualitative analysis be mathematical. This is probably going to be the way it's going to go.

But what about the skills of conceptualization? Do they simply become useless with the patch? I'd say no, and it's a stance I feel comfortable taking. Conceptualization is simply a manifestation of imagination, and imagination is irrevocably wedded to creativity. And creativity is essential for insight at all levels. Einstein used them all to formulate both relativities. But we're all not Einstein, and we have to show that it also applies to us mere mortals. So let me give an example.

A capacitor is a set of two oppositely charged plates. Obviously they'll attract each other. This gives them potential energy, which for a very long time we've been taught to think of as energy that "balances the checkbook" for conservation. In EM we learned that the energy is in the form of the electric field between them, which carries it's own energy. This was the point where I asked the teacher "so is it field energy or potential energy?" She changed the subject. Later on a friend and I worked out that potential energy was field energy. Any sort of potential energy is actually real energy "trapped" in some kind of field. This has provided a great deal of insight into physics and provided a useful tool for understanding how certain problems interacted with each other. This was a realization that could not have happened without creativity and imagination. Even if you do argue that it could have, you would have to accept that you'd need such creativity to actually do anything with it.

That's my current position on the topic. Creativity in the form of conceptualization may not be necessary to 'get' what's going on in advanced physics, but it's hugely beneficial when you need to create new knowledge and models of reality. It's also necessary to craft the knowledge and models into practical creations for human use. That's why my love of conceptualization keeps me out of theoretical physics. I'd be much much happier doing applied.