the wave function of a photon

Every now and then a discussion of quantum theory and its interpretation involves photons, perhaps propagating in some interferometer; e.g. when I wrote about the interpretation problem I used the picture of a Mach-Zehnder interferometer.
And then a discussion of the many worlds or the 'collapse' of the wave function often follows.



But notice that the wave function of a photon is actually a problematic concept, e.g. "...it is possible to define position operators and localized states for massive particles and for massless particles of spin 0, but not for massless particles with spin."

Certainly, the electromagnetic field is not the wave function of a photon, as sometimes implied by discussions of interference in (quantum) optics experiments.



Why do I mention this? Well, it seems to me that some people consider wavefunctions as something very real, while others (including me) think of them as descriptions of reality; It might be helpful to consider single photons before discussing the many worlds.

a classical anthropic Everett model

"..the only kinds of entities we know for sure to be
real are our mental feelings and perceptions (including dreams). The material
world in which we have the impression of living is essentially just a theoretical
construct to account for our perceptions."



This was not written by Ernst Mach but is from a remarkable paper by Brandon Carter, dealing with the classical limit of the Everett many worlds interpretation.



"Assuming ... that mental processes have an essentially
classical rather than quantum nature, this essay has the relatively modest
purpose of attempting to sketch the outlines of a simpler, more easily accessible, classical unification ... as an approximation to a more fundamental quantum unification that remains elusive."



As every other many worlds interpretation, it struggles with the issue of probabilities and proposes a solution "based on the use of an appropriate anthropic principle in conjunction with the Everett approach...".

I really like the way the problem is posed, but I don't find the answer very convincing [x]. If one acknowledges our perceptions as being necessarily
classical realities, does Bohr's interpretation of quantum theory (or something similar) not make much more sense?



You, as a sentient being with q=1 (or as just another one of my theoretical constructions), be the judge of that...





[x] One problem I have with it (p.6ff) is this: Once we assume that the outside world is only my theoretical construct, how can the number of sentient beings (which are only theoretical constructs as well) make a difference to the calculated probabilities? Also, would the anthropic argument not indicate that it
is always more likely to survive a certain situation than to be killed?

really the best of all possible worlds?

Given two equally good roads, the majority of drivers will pick the more crowded road...

... and of course I have fewer friends than my friends have on average.



So the following is not too surprising: We assume that we can assign a "quality of life" value Q to each world in the multiverse of all possible worlds, with Q=0 meaning "boring as hell" and Q->infinity meaning a world "approaching heaven". But then we either live most likely in a world of less quality than the average world - or the total Q grows (less than) linear with the sample size, which means the multiverse as a whole is of low quality...



inspired by Marginal Revolution

under my umbrella

"I would like to know whether it is likely to rain tomorrow. However, when I ask an Everett follower, all she will tell me in direct response to my question is that `it will rain and it won't rain.'
Nevertheless, she is willing to tell me whether or not it is rational for me to take an umbrella. I suppose that if she tells me that it would be highly irrational for me to take an umbrella, I can take the hint and deduce that it is very unlikely to rain.

However, there does seem something wrong with the fact that she is not allowed to say this directly."



Robert Wald reviewed Many Worlds?: Everett, Quantum Theory, and Reality