That paper is dubious and confused. Their arguments revolve around infinite product states, representing an infinite number of causally disconnected copies of some physical entity. The whole argument is (i) in such states, the observable states of an individual entity appear as infinitely repeated factors with asymptotic frequencies equal to Born probabilities (ii) the basis decomposition of such infinite product states produces other infinite product states with the same property. From (ii), they wish to argue that the very notion of a cosmic superposition is redundant, and so there is no need for many worlds in the Everett sense. Or at least, they claim that there is no difference between the notion of one Everett world and many Everett worlds.
The first thing to note is that their whole construction really needs to be placed in a bigger context. The universe does not just consist of infinitely many causally disconnected copies of the same thing. Each copy is interacting with its environment, which (supposing the inflationary cosmology that they also assume) is in turn entangled with the degrees of freedom of its cosmological environment, all the way back to the beginning of inflation. There is no mention of entanglement prior to inflation, whether that is an issue, and how it could not be an issue if it is real. This lack of a larger framework makes it difficult to sensibly discuss what they have written. But their infinite product states really need to be embedded in some larger thing, the wavefunction of the universe, which is not a product state. The paper is dubious because it does not address this point.
The second thing to note is the total confusion regarding what the actual message of the paper is. Their technical argument is that a superposition of their special infinite product states is itself just another infinite product state. From this mathematical fact they conclude (page 9) that they don’t know if it’s a superposition any more. This isn’t “adding up to normality”; this is like spinning on one spot so fast that you lose all sense of direction, and then concluding that all directions are the same direction, because you can no longer tell the difference between them.
To really take apart a paper like this one, it’s not enough to show that it contains nonsensical statements; you have to figure out the philosophical genesis of the authors’ mistake, and then show how they employed the formalism in the service of their mistake. In such a diagnosis, first you establish explicitly what constitutes valid reasoning about the aspect of the theory that they propose to address, then you show how they spin mathematically valid manipulations into wrong, tendentious, or meaningless statements about physical reality. This is a tiresome thing to do and I hope to avoid doing it in full for this paper. But meanwhile, I am quite confident that it belongs in the rogues’ gallery of papers which falsely assert that they are now, finally, really-truly, solving the problems of MWI.
That paper is dubious and confused. Their arguments revolve around infinite product states, representing an infinite number of causally disconnected copies of some physical entity. The whole argument is (i) in such states, the observable states of an individual entity appear as infinitely repeated factors with asymptotic frequencies equal to Born probabilities (ii) the basis decomposition of such infinite product states produces other infinite product states with the same property. From (ii), they wish to argue that the very notion of a cosmic superposition is redundant, and so there is no need for many worlds in the Everett sense. Or at least, they claim that there is no difference between the notion of one Everett world and many Everett worlds.
The first thing to note is that their whole construction really needs to be placed in a bigger context. The universe does not just consist of infinitely many causally disconnected copies of the same thing. Each copy is interacting with its environment, which (supposing the inflationary cosmology that they also assume) is in turn entangled with the degrees of freedom of its cosmological environment, all the way back to the beginning of inflation. There is no mention of entanglement prior to inflation, whether that is an issue, and how it could not be an issue if it is real. This lack of a larger framework makes it difficult to sensibly discuss what they have written. But their infinite product states really need to be embedded in some larger thing, the wavefunction of the universe, which is not a product state. The paper is dubious because it does not address this point.
The second thing to note is the total confusion regarding what the actual message of the paper is. Their technical argument is that a superposition of their special infinite product states is itself just another infinite product state. From this mathematical fact they conclude (page 9) that they don’t know if it’s a superposition any more. This isn’t “adding up to normality”; this is like spinning on one spot so fast that you lose all sense of direction, and then concluding that all directions are the same direction, because you can no longer tell the difference between them.
To really take apart a paper like this one, it’s not enough to show that it contains nonsensical statements; you have to figure out the philosophical genesis of the authors’ mistake, and then show how they employed the formalism in the service of their mistake. In such a diagnosis, first you establish explicitly what constitutes valid reasoning about the aspect of the theory that they propose to address, then you show how they spin mathematically valid manipulations into wrong, tendentious, or meaningless statements about physical reality. This is a tiresome thing to do and I hope to avoid doing it in full for this paper. But meanwhile, I am quite confident that it belongs in the rogues’ gallery of papers which falsely assert that they are now, finally, really-truly, solving the problems of MWI.
Noted; I will lower my confidence in its ultimate sense-making-ness.