Many Worlds and quantum fungibility

This image, by Joakim Berglund, graces the cover of Many Worlds? Everett, Quantum Theory, & Reality. The photo, taken by Berglund from a Cessna, depicts the damage wrought to a section of Swedish pine-forest by hurricane Gudrun in January 2005. The dendritic pattern is created by logging trucks, employed to remove the fallen dendritic growths...

The book itself contains a decent collection of papers, based upon the contributions delivered by various philosophers and physicists at a pair of conferences hosted in 2007 to commemorate the 50th anniversary of Hugh Everett's famously dendritic Many-Worlds Interpretation (MWI) of quantum theory.

Whilst most of the papers are highly technical, David Deutsch expounds a manifesto for the MWI which is more accessible to the non-specialist. Deutsch, it should be emphasised, is something of an extremist when it comes to the MWI. As explained previously on this blog, there are various strains of the MWI. One version of the MWI claims that a measurement conducted on a particle in a superposed state, literally causes the universe to split into different branches, so that each possible measurement outcome is recorded in at least one branch. In this version, there is one copy of the particle prior to the measurement, but multiple copies afterwards of both the particle, and its associated space-time.

A different version of the MWI claims that quantum theory is a theory of interfering classical universes, and that a particle in a superposed state is composed of numerous interfering branches even before it is subjected to a measurement. On this account, the measurement does not create any more branches than were already present. Rather, it is claimed that the measurement causes two things to happen: (i) the state of the measurement device becomes correlated with the respective state of the particle in each of the branches; and (ii) because the measurement device is macroscopic, a decoherence process subsequently suppresses the interference between the different branches, thereby ensuring the absence of macroscopically-detectable superpositions.

This latter version of the MWI provides not only an interpretation of the dynamics of quantum theory, but a radical compositional metaphysics, and one might imagine the wave-function splitting into decohered branches in the same way that a prism splits white light into the colours of which it is composed.

The radical formulation of the MWI is the version which I take David Deutsch to be the principal exponent of. This much is clear from the following excerpt, (where Deutsch refers to the branches as 'universes', and the interfering collection of branches as the 'multiverse'):

"Consider a single, free particle in empty space. It's described by a wave-packet...Which means that, as far as universes go, it's at different positions in different universes. You might think that a non-interacting particle, at least, is something that happens in each universe independently of the others, so that we can forget about the multiverse when describing it. But no. Again because of the uncertainty principle, and because of the linearity of quantum mechanics, there is no region of the multiverse in which both the position and velocity are behaving independently of what's happening elsewhere in the multiverse. That means that there are no autonomous information flows that would be universes. So in fine detail, even a free particle is an irreducibly multiversal object, not just a parallel-universes' one.

Furthermore, at a later time, the shape of the wavepacket will have changed. The instances of the particle in the multiverse will be at different positions. But none of them, individually, will have moved to where it is - because there is no such thing as one of them individually. When the universe approximation breaks down, the autonomy of the instances of a single particle in the multiverse breaks down too. They are then fungible," (p546).

In other words, the branches of a quantum state possess an identity consisting entirely of their interference relationships to the other branches, rather than any self-sufficient existence.