While mulling around yesterday before the Thankgsiving festivities, I decided to print off a new paper out in Physical Review X about a novel quantum interpretation and formulation ^{(1)}Quantum Phenomena Modeled by Interactions between Many Classical Worlds.

Phys. Rev. X 4, 041013 – Published 23 October 2014

Michael J. W. Hall, Dirk-André Deckert, and Howard M. Wiseman

DOI: http://dx.doi.org/10.1103/PhysRevX.4.041013. The group, consisting of three members, developed a formulation of quantum theory which they call the Many Interacting Worlds (MIW) interpretation.

Overall the article reads well, and since much of the mathematics is beyond my pay-grade, I can’t critique too harshly. The paper starts out on primarily ontological grounds and establishes a plausible basis for their formulation based on a traditional ambiguity in the basis for more ‘orthodox’ interpretations.

Their *de facto* comparative formulation is the de Broglie-Bohm (dBB) theory, which posits that a universal wave function guides the state of the universe around us. So in essence, the outcome of any interaction is merely a manifestation of the quantum wave function, the primary entity. From the dBB groundwork, they construct their formulation. The basis for the MIW approach is to imagine that every conceivable configuration of particles (i.e. every conceivable universe) exists in a meaningful way.

Each one of the universes within this vast menagerie evolves through time and is influences by the universes around it. The ability for one universe to influence another is the defining element for the MIW formulation since for other quantum theories which also posit a multiverse, these universes are completely independent once separated. The interaction proposed by MIW is quite specific and depends on how similar the two universes are. The more similar two universes are, the stronger the interaction between them is. Therefore you can imagine that only the small subset of universes that ‘border’ our own in composition have any meaningful impact on our own. Additionally, just as many of you know that two particles will not occupy the same space, and will repel each other if brought close enough together, so too do these universes. The force between two nearly identical universes (in fact between any two universes) is repulsive. This is important for the results as you will see.

Now, a classic quantum phenomenon can occur when an electron comes up against a potential barrier^{(2)}See Quantum Tunneling (wikipedia). Imagine an electron is moving down a wire and then comes up against a high-energy potential. In effect the electron is running up against a wall, and just like water we would not expect the electron to flow over the wall unless the electron had enough energy (i.e. the water was deep enough). The quantum phenomenon is that even a very low energy electron can occasionally pass right through the barrier and this is call “quantum tunneling”. In our analogy, imagine a drop of water spontaneously jumping up and out of the tub just to get to the floor—clearly it’s not something we experience.

What does tunneling have to do with the MIW interpretation of quantum mechanics? So now imagine that there are two universes, virtually identical, but one is slightly a head of the other one in time. If we could model these two universes it would look like one was lagging just behind the other. Now when the first universe’s electron gets to the barrier it slows down; but then due to the repulsive force between the two universes, the electron in the second universe repels the first electron up and over the barrier. The result is then that in one universe the electron ‘tunneled’ through the barrier while in the other universe the electron simply bounced off.

So where does this leave us? Looking at this from the outside, I’m surely a proponent of seeing scientists take a new look at long held notions since science without criticism becomes dogma. Let’s use this a model for examining our own beliefs and take inspiration for our playful daydreams.

Notes

↑1 | Quantum Phenomena Modeled by Interactions between Many Classical Worlds. Phys. Rev. X 4, 041013 – Published 23 October 2014 Michael J. W. Hall, Dirk-André Deckert, and Howard M. Wiseman DOI: http://dx.doi.org/10.1103/PhysRevX.4.041013 |
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↑2 | See Quantum Tunneling (wikipedia) |