Adrian Kent in Aeon:
Here’s the basic problem. While the mathematics of quantum theory works very well in telling us what to expect at the end of an experiment, it seems peculiarly conceptually confusing when we try to understand what was happening during the experiment. To calculate what outcomes we might expect when we fire protons at one another in the Large Hadron Collider, we need to analyse what – at first sight – look like many different stories. The same final set of particles detected after a collision might have been generated by lots of different possible sequences of energy exchanges involving lots of different possible collections of particles. We can’t tell which particles were involved from the final set of detected particles.
Now, if the trouble was only that we have a list of possible ways that things could have gone in a given experiment and we can’t tell which way they actually went just by looking at the results, that wouldn’t be so puzzling. If you find some flowers at your front door and you’re not sure which of your friends left them there, you don’t start worrying that there are inconsistencies in your understanding of physical reality. You just reason that, of all the people who could have brought them, one of them presumably did. You don’t have a logical or conceptual problem, just a patchy record of events.
Quantum theory isn’t like this, as far as we presently understand it. We don’t get a list of possible explanations for what happened, of which one (although we don’t know which) must be the correct one. We get a mathematical recipe that tells us to combine, in an elegant but conceptually mysterious way, numbers attached to each possible explanation. Then we use the result of this calculation to work out the likelihood of any given final result. But here’s the twist. Unlike the mathematical theory of probability, this quantum recipe requires us to make different possible stories cancel each other out, or fully or partially reinforce each other. This means that the net chance of an outcome arising from several possible stories can be more or less than the sum of the chances associated with each.
More here.