A referee report of: Typicality vs. Probability in trajectory-based formulations of quantum mechanics, published on Foundation of Physics

I recommend in the strongest possible terms that this paper be published. It is not often that one finds, in the great mass of papers written on the foundations of quantum mechanics, one that involves a strikingly new idea that not only makes sense, but has been well thought out and has been carefully analyzed. The author in fact proposes a new formulation of quantum mechanics. The proposal involves a new type of physical theory, one that is neither deterministic nor stochastic in the usual sense of the word (i.e., given by a stochastic process). It has several virtues: it involves a perfectly clear ontology, of particles moving in space; for constraining the trajectories it invokes what can arguably be regarded as nothing more than standard quantum structure---and because of this it conforms well with quantum prejudices for how systems should evolve; it arguably recovers all the predictions of quantum mechanics; and it entirely avoids the usual quantum paradoxes such as the measurement problem, as well as many worlds.

This is achieved through the recognition that at the end of the day scientific explanation involving probability makes use, not of the detailed probabilities themselves, but of the much weaker notion of typicality that arises from the probabilities. This opens the door to theories based on a notion of typicality that does not arise from probability, and thus affords
an enhanced flexibility in the formulation of new theories. This paper provides an example of this flexibility in action.

It is true that the new theory might seem a bit odd. It seems odd to me, but genuinely new ideas are likely to seem odd at first. I think it is important that the physics community be made aware of the possibilities afforded by the approach advocated in this paper.

Some minor comments, which the author can address as he sees fit, perhaps by ignoring them: [omitted]

A referee report of: Generalization of the Born rule, published on Physical Review A

The article "A generalization of the Born Rule" by Bruno Galvan is an extremely interesting read. It is well-written, closely argued and supports a new picture of the  link between quantum mechanics and a `quantum' version of Cournot's principle.

The article does not shy away from controversial statements about the foundations  of quantum mechanics, as witness the first paragraph of the introduction. This may  annoy some referees and readers. However, the foundations of quantum mechanics are such that it is impossible to make progress without raising objections from one  camp or the other, and Galvan is explicit and balanced in his comparisons of his  own work and conventional interpretations.

As a referee I cannot check all the details of Galvan's argument, but I can say that I  think that all the appropriate details are there and should be verifiable over time.  The ideas do appear sound and I expect the work to provide an excellent seed  article for the investigation of this new approach.

I highly recommend this article for publication in physical review subject only to the  recommendation that the author recheck the manuscript for typos (particularly  \Delta vs. \cap)