The approach has much more in common with Bohmian mechanics than with Everettian many worlds. Basically, in BM, one singles out one of the branches of the wave function as ‘real’—think of this as marking it with a dot. The other branches are then called ‘empty waves’, or sometimes ‘empty universes’.
The many interacting worlds interpretation now essentially proposes to remove the empty waves, replacing them with an ensemble of ‘dotted’ worlds that are each as real as one another. That’s perhaps easiest explained by looking at the traditional interference experiment. If a wave impinges on a screen with two (sufficiently narrow) openings, the partial waves emanating from every opening will interfere, producing a characteristic pattern of bright and dark bands on a second screen, like here.
The odd thing now is that in quantum mechanics, one can show that light actually comes in little packets, i.e. quanta. This can, for example, be demonstrated by attenuating a laser’s intensity, until a detector, rather than a continuous signal, in fact registers isolated events. Indeed, one can, using a weak enough source, watch the interference signal be built up, dot by dot, on a photosensitive screen, yielding a picture like this one.
This strikes us as somewhat strange: if there’s really discrete little particles being aimed at the screen, we’d expect just two maxima behind each slit, rather than the interference pattern we get, since each particle can only traverse either slit. And indeed, once we start taking note of which particle went where, by positioning detectors at the slit, this is exactly the behaviour we observe—however, when we take the detectors out, the original pattern resumes.
In the standard interpretation of quantum mechanics, an appeal is made to wave-function collapse in order to explain this behaviour: particles behave wave-like until they are detected; upon this detection, however, they are immediately localized at one point, with the probability for being found at a certain point given by (the absolute square of) the wave function. This explains the buildup of the interference pattern point-by-point on the screen, and also the behaviour if we position detectors at the slits—upon a detection, the particle is localized at either of the slits, and thus, can no longer interfere.
In Bohmian mechanics, the explanation is somewhat different: basically, at each run of the experiment, there is only one particle; however, this particle is guided by the wave function. Hence, the underlying wave function does the interfering, and tells the particle to move accordingly. Thus, in BM, particle trajectories are not necessarily straight, but may wave around; additionally, they can never cross, but instead, appear to ‘repel’ one another. This leads to a picture such as this one, which shows the aggregated picture of many experimental runs according to BM—that is, for each run, the particle follows one of these trajectories.
Now, basically, the many interacting worlds interpretation simply re-interpretes that picture: what if, rather than being accumulated over many different runs, it actually were a picture of one run, but with only one of these particles being in ‘our’ universe? The Bohmian trajectories repel each other, and thus, if one introduces some kind of interaction between the different worlds, one might hope to get the same kind of behaviour without appeal to an additional quantity such as a wave function to guide particle behaviour.
As it turns out, this works—at least to within reasonable accuracies. Should one be surprised that that’s the case? Well, it depends on your point of view. In a sense, that one can replace the guiding potential used in BM by mutual interaction of the particles themselves is kinda neat—it always was at least strange that in BM, the guiding wave influences the particles, but is itself totally uninfluenced by them—it provides a set of slides for the particles to glide down, but itself remains static background. Mathematically, however, it’s just a neat trick—essentially, the guiding potential is discretized, and re-interpreted as an inter-particle (and hence, inter-world) force. Whether forces between different worlds are really any more sensible than a wave function that particles don’t back-react on is kind of just a matter of taste, I suppose.
Personally, the theory’s not for me—I find interacting parallel worlds (kind of oxymoronic in itself) not any less strange than guiding wave functions, noninteracting worlds, spontaneous collapses or anything else from the zoo of possibilities that have been proposed to rescue some semblance of classicality in the face of alleged quantum weirdness, and to be honest, I think that they’re all just various contrivances shying away from facing up to the deep impact of quantum mechanics; but ultimately, that’s just as much a matter of taste.
