Is this only me feeling this way or the recent extension of Decoherent Histories Quantum Mechanics with One ‘Real’ Fine-Grained History due to Gell-Mann and Hartle makes a lot of sense? I was very much impressed to see that almost everything I was looking for naturally appears there! Apparently the major interest of the authors in their theory is the fact that it’s compatible with quantum cosmology. But to me the use of the extended probabilities which could have negative values is what’s striking. Since the first day that I became interested in Weak Measurements I was wondering if there could be a formulation of quantum mechanics in which the extended form of probabilities play a defining role! Here we go, there is this new formulation. Paraphrasing Aephraim Steinberg, if you look in the dark you’ll see negative probabilities! All the problems we were wondering about involving Weak Measurements and retrodiction, which gave negative probabilities could be viewed as history problems and now systematically appear in our formulation of quantum mechanics. This is so cool. I guess it’s now time to look at that particular application of quantum theory which has always shed light onto quantum foundations, namely quantum information, and see what can we do with the negative probabilities! Hopefully we’ll find some new stuff.
Nevertheless, there are some arguments that you shouldn’t interpret weak values as probabilities. Which in this case the whole debate goes back to the starting point! But since it looks like I’m the only reader of this blog now, I won’t go into the details.