May 5, 2009
The previous blog post (I recommend that you read it first) ended with Sidney Coleman's argument in favor of the 'many worlds interpretation', which really is an argument that a 'collapse' of the wave function is not necessary to explain our usual conscious experience. As we shall see there is a problem with that argument.
Max Tegmark provides for a good (and easy to read) explanation of the 'many worlds interpretation' in this paper. In the last section he discusses the issue of 'quantum immortality', considering a quantum suicide experiment and in my opinion this raises an important question.
In general we have to assume that the wave function |Y> of You the Observer always contains components associated with an alive human being, even thousands of years in the future and even if classical physics would describe you as long dead; The wave function never 'collapses' and preserves all components, even those which describe absurd freak events. It is an important question what conscious experience is associated with such states.
But in order to discuss this further I prefer to modify Tegmark's thought experiment so that the experiment does not use bullets which may kill you, but pills (the "red pill or the blue pill") which may or may not contain drugs to knock you unconscious for a while. We may want to call the thought experiment Schroedinger's Junkies and instead of his cat we place You the observer in an experiment where you have to swallow a pill which either contains harmless water or a strong drug (e.g. LSD), depending on a measurement of the quantum state |s>.
If |s> = a|u> + b|d> we have to assume that after the experiment You are best described by the wave function |Y> = a|U> + b|D> , where the component |U> means that you are unharmed, while |D> means that you are heavily drugged.
Again we consider Coleman's operator C, but this time we have to assume that C|D> = 0 (heavily drugged you will not have a normal conscious experience) while C|U> = |U>. The problem is that now C|Y> = aC|U> + bC|D> = a|U> and the state |Y> is no longer an eigenstate of C. In other words, Coleman's consciousness operator indicates that after the experiment You are not in a normal conscious state [*]; This contradicts the fact that for a = b in approximately half of the cases Schroedinger's Junkies will always experience a normal conscious state (and for a >> b almost all of them !).
Does this counter example to Coleman's argument indicate that something like a 'collapse' (e.g. decoherence) from the superposition |Y> to either |U> or |D> is necessary after all?
I have to admit that trying to understand quantum physics feels like trying to find the solution to x² + 1 = 0 in the real numbers!
[*] One could argue that there is no problem if the total state is not an eigenstate of C, since the "psychophysical parallelism" of m.w.i. assigns consciousness to the components of the wave function only. However, we can split any component into subcomponents and even if C|U> = |U> we can split |U> e.g. into two subcomponents |U> = ( |U> - |D> ) + ( |D> ) so that none of the subcomponents (..) is an eigenstate of C.
Coleman's argument seemed to provide for consistency across different ways to split the wave function into components, but indeed it fails in general; In order to rescue "psychophysical parallelism" for m.w.i. one would have to find a preferred basis and it has been argued that decoherence might just do that. However, I have explained earlier why I am not convinced.