Single-world interpretation, 7

One consequence is that every observation can be thought of as causing the combined observer-object’s wavefunction to change into a quantum superposition of two or more non-interacting branches, or split into many “worlds”.

— Wikipedia on Many-worlds interpretation

That is incorrect.

Let’s consider the double-slit experiment. For simplicity, we regard the event “a person reads the device reading” as a classical event.

Before installing the measuring device, we do not know which slit a photon goes through. The photon state is in a superposition of eigenstates: 

| photon > = a | left > + b | right >

(According to the meaning of probability, |a|^2 + |b|^2 = 1.) In other words, if we send enough such kind of photons through the double-slit apparatus, we get the interference pattern. 

After installing the measuring device, we know which slit a photon goes through. According to the Copenhagen interpretation, when the photon passes through the double-slit apparatus, the photon-state “collapses” to one of the two eigenstates, such as | left >. However, a more accurate point of view is that, according to the quantum decoherence interpretation, the photon-and-device state becomes a superposition of a lot of eigenstates. Most of such eigenstates are corresponding to the macrostate of passing-through-the-left-slit, |left>_macro_state. 

The above many-worlds-interpretation statement assumes that there is a |right>_macro_state.

It is true in a sense that, since the photon-and-device involves a lot of particles, there are so many eigen-microstates. Some are certainly corresponding to the |right>_macro_state.

It is false in a sense that the weighting of the |right>_macro_state is so small that such macrostate is not meaningful in a macroscopic context, for example:

| photon-and-device > = 10^23 |left>_macro_state + 0.001 |right>_macro_state + other possible macrostates

— Me@2012-04-07 11:03:12 AM

2012.04.09 Monday (c) All rights reserved by ACHK