Physics StackExchange user QuestionAnswers asked the question “Is the preferred basis problem solved?“, and I reproduced my “answer” (read: discussion) in a post last week. He had some thoughtful follow-up questions, and (with his permission) I am going to answer them here. His questions are in bold, with minor punctuation changes.
How serious would you consider what you call the “Kent set-selection” problem?
If a set of CHs could be shown to be impossible to find, then this would break QM without necessarily telling us how to correct it. (Similar problems exist with the breakdown of gravity at the Planck scale.) Although I worry about this, I think it’s unlikely and most people think it’s very unlikely. If a set can be found, but no principle can be found to prefer it, I would consider QM to be correct but incomplete. It would kinda be like if big bang neucleosynthesis had not been discovered to explain the primordial frequency of elements.
And what did Zurek think of it, did he agree that it’s a substantial problem?
I think Wojciech believes a set of consistent histories (CHs) corresponding to the branch structure could be found, but that no one will find a satisfying beautiful principle within the CH framework which singles out the preferred set from the many, many other sets. He believes the concept of redundant records (see “quantum Darwinism”) is key, and that a set of CHs could be found after the fact, but that this is probably not important. I am actually leaving for NM on Friday to work with him on a joint paper exploring the connection between redundancy and histories.
[Added 2015-1-6: This paper is now available: arXiv:1312.0331.]
You mention Many Worlds and David Wallace. Does this basically mean that you lean towards Many Worlds being right but that there are still details to be sorted out, or are you saying that the problem might be too fundamental and K.O. MWI ?
In general, I don’t think it’s useful to argue about whether the other branches are “real”. However, if the set-selection problem could be solved, then I would say that a MWI description is consistent with our observations, internally self-consistent, and complete. (As I said, I do not consider Copenhagen-like interpretations to be complete.) Any competing interpretation would be either (a) incomplete or (b) observationally indistinguishable from MWI.
It seems to me that you (and Zurek) are quite sure that a set of CHs will be found, but you seem doubtful of the existence of the principle needed to call QM complete?
Zurek and most many-word’ers (of which Zurek is not one!) are quite sure that a set of CHs can be found. I am slightly less sure. I have a back-of-the-enveloped calculation that says that no satisfactory set can exist, but the calculation is suspect (and does not strongly change my a priori Bayesian likelihood). If a set could be found, but no nice principle was used to find it (i.e., if it was basically just intuition or maybe even just a non-constructive existence proof), then I would be very uncomfortable, but I wouldn’t say QM was incomplete. It would be similar to how I feel about simply postulating a low-entropy initial state of the universe without explanation (see Sean Carroll).
So quantum darwinism wont replace this principle, but can only be used to find a set in the first place?
Zurek has great hope for Quantum Darwinism as a fundamental principle, without CHs playing an important role. I believe it is a very useful hint in the search for a principle or at least a CH set, but I am skeptical that Darwinism will play a fundamental role without being substantially modified.
Where does this leave MWI ? Obviously if MWI a la Wallace is correct then there’s no doubt that the other worlds are real. But if this is contingent upon finding a principle that singles out one set does that mean you doubt MWI is correct?
Although I hate when people dismiss discussion as being “just philosophy”—since the actual way we do science is built on an implicit acceptance of all sorts of non-trivial philosophical argument—answers to questions like this one can border on meaningless. (Although, again, it’s not always trivial to know what distinctions are meaningless. See John Bell.) Hopefully I won’t say anything stupid.
As I understand it, Wallace’s claim is that the branches of the wavefunction are just as real as a rock because, like a rock being composed of many atoms which are constantly shed and acquired, the branch structure is “emergent” from more objective/real stuff. If (1) the wavefunction itself is real and (2) an acceptable solution to the set-selection problem exists, then Wallace is probably correct. Addressing these in reverse order,
(2) Suppose there were many totally inequivalent (but equally justified) ways of describing the atoms in the universe of which most did not admit a useful notion of “this rock”. Then I would certainly not be so confident that rocks were “real”, and I would probably be more inclined to say they were purely subjective (i.e a world of solipsism). But still, I’d at least know the atoms were real. With the wavefunction, on the other hand…
(1) I think it’s a bad idea to say “the wavefunction itself is real in exactly the same way that atoms are real”. The wavefunction is just too similar to a purely epistemic (i.e. subjective) probability distribution for anyone to be confident that the whole thing is just as real as the part we experience. As stressed by my great friend and colleague Godfrey Miller, the only thing that separates the wavefunction from merely a probability distribution is Bell’s inequality.
Furthermore, it’s well known that there are many observationally equivalent ways to describe the same physics (whether quantum or otherwise), some doubtlessly undiscovered, and I think it’s presumptuous and probably meaningless to declare a particular mathematical description “real”. At the most, it’s the equivalence class of theories which are observationally indistinguishable and of equal a priori probability (because of beauty or whatever) that has the most claim to that title, if anything does.
What if one just said “all sets of CHs are real”, would that lead to a Many Many Worlds interpretation?
If the answer turns out to be meaningful, then this is a fascinating question. It is explicitly discussed by Dowker and Kent.Starting here, I previously wrote “In short: no. Remember that a set of histories is essentially a catalog of all the worlds. According to the mere requirement of “consistency” (which is currently the only mathematically rigorous principle we have to single out sets) there are many, many consistent but mutually incompatible sets. If all the consistent sets are equally real, then this says there are way more worlds out there than the ones claimed by MWI. So at the very least, MWI would be massively incomplete.” On 2014-8-22, I realized I missed the second “many” in the question, and so completely misunderstood it. So it was re-written.a Yes, if you asserted that they were all real, then there would be many many worlds. But the consistency criterion is very weak, so the vast, vast majority of these worlds would have no physical interpretation. The would also have inconsistent arrows of time, etc. See also IshamC. J. Isham, Int.J.Theor.Phys. 36 (1997) 785-814 [arXiv:gr-qc/9607069.]b .
[Minor edits on 2013-6-16, 2015-1-6, 2016-6-28.]
(↵ returns to text)
- Starting here, I previously wrote “In short: no. Remember that a set of histories is essentially a catalog of all the worlds. According to the mere requirement of “consistency” (which is currently the only mathematically rigorous principle we have to single out sets) there are many, many consistent but mutually incompatible sets. If all the consistent sets are equally real, then this says there are way more worlds out there than the ones claimed by MWI. So at the very least, MWI would be massively incomplete.” On 2014-8-22, I realized I missed the second “many” in the question, and so completely misunderstood it. So it was re-written.↵
- C. J. Isham, Int.J.Theor.Phys. 36 (1997) 785-814 [arXiv:gr-qc/9607069.]↵