The Origin of Force

 

As I have expanded upon lengthily in this previous post, interference is a key phenomenon in quantum theory. In this post, we will see how it can be used to explain the existence of forces between certain objects, using the example of the electromagnetic force in particular. 

The usual popular account of the quantum origin of forces rests on the notion of virtual particles. Basically, two charged particles are depicted as 'ice skaters' on a frictionless plane; they exchange momentum via appropriate virtual particles, i.e. one skater throws a ball over to the other, and both receive an equal amount of momentum imparted in opposite directions. This nicely explains repulsive forces, i.e. the case in which both skaters are equally charged. In order to explain attraction, as well, the virtual particles have to be endowed with a negative momentum, causing both parties to experience a momentum change in the direction towards the other. Sometimes, this is accompanied by some waffle about how this is OK for virtual particles, since they are not 'on-shell' (which is true, but a highly nontrivial concept to appeal to for a 'popular level' explanation).

In this post, after the introduction, I will not talk about virtual particles anymore. The reason for this is twofold: first, the picture one gets through the 'ice-skater' analogy is irreducibly classical and thus, obfuscates the true quantum nature of the process, leaving the reader with an at best misleading, at worst simply wrong impression. Second, and a bit more technically, virtual particles are artifacts of what is called a perturbation expansion. Roughly, this denotes an approximation to an actual physical process by means of taking into account all possible ways the process can occur, and then summing them to derive the full amplitude -- if you're somewhat versed in mathematical terminology, it's similar to approximating a function by means of a Taylor series. The crucial point is that the virtual particles are present in any term of this expansion, but the physical process does not correspond to any of those terms, but rather, to their totality. So the virtual-particles analogy can't give you the full picture.

The Interpretation of Quantum Mechanics

So far on this blog, I have argued that quantum mechanics should be most aptly seen as a generalization of probability theory, necessary to account for complementary propositions (propositions which can't jointly be known exactly). Quantum mechanics can then be seen to emerge either as a generalization (more accurately, a deformation) of statistical mechanics on phase space, or, more abstractly (but cleaner in a conceptual sense) as deriving from quantum logic in the same way classical probability derives from classical, i.e. Boolean, logic.

Using this picture, we've had a look at how it helps explain two of quantum mechanics' most prominent, and at the same time, most mysterious consequences -- the phenomena of interference and entanglement, both of which are often thought to lie at the heart of quantum mechanics.

In this post, I want to have a look at the interpretation of quantum mechanics, and how the previously developed picture helps to make sense of the theory. But first, we need to take a look at what, exactly, an interpretation of quantum mechanics is supposed to accomplish -- and whether we in fact need one (because if we find that we don't, I could save myself a lot of writing).