I especially feel this way about the epistemic interpretations I’ve tried to read about; I understand that they want to interpret the wavefunction as an expression of someone’s knowledge, but I can never tell what this knowledge is supposed to be knowledge *of*. I know this might be off-topic, but can anyone point to a clear exposition of one of these approaches?

“Spectrum broadcast theory (which has only been worked through for a few idealized cases) ”

is not exactly correct in the following sense. Spectrum Broadcast Structures (SBS) have been theoretically found by the Gdansk group in *all* the models where quantum Darwinism (qD) was earlier predicted, apart from the NV centers (we are working on that). And in several more (QED, gravitational decoherence). Actually one of the pillars of the SBS program is to check as many models as doable to gather a theoretical evidence in their favor. So the SBS “has only been worked through for a few idealized cases” to the very much the same extent as qD. An arXiv search on my name will give the relevant papers. I wrote a comment to Quanta but it didn’t seem to get through to the Editors.

]]>Yes, I think the Wikipedia table is roughly accurate. What’s your point, though? Nobody is disputing that there are interpretations that consider the wavefunction to be real and interpretations that do not.

“I would argue that we formulate our theories in the simplest possible terms, which is why we formulate it in terms of pure states, but we simply don’t know if the world is a pure state or not. Since the mathematical formalism works just as well either way, and since there is no experimental way to determine whether the world is in a pure state or not, “the world is in a pure state” is not a scientific statement.”

So you want to ignore the historical development of our theories, and the fact that mixed states were introduced explicitly to be linear on the probabilities, to consider whether mixed states might be fundamental?

Fine, it is mathematically possible. It doesn’t change the fact that the mixedness that Peter was talking about – the one caused by our ignorance of the precise state and environment – is explicitly a property of the observer, not of the world. Again, map versus territory.

And what if we still end up with a mixed state after removing this subjective mixedness? As you say, there is no experimental way to test whether the state of the universe is pure or mixed. We might as well use Occam’s razor and take it to be pure.

]]>(1) the state of the world and

(2) what an observer observes at a particular time

is fundamentally incomplete. It also needs to explain

(3) how many, and which, observers exist.

Otherwise we would not be able to explain why any observers exist at all, nor why we find ourselves on Earth instead of on another planet or in empty space, nor answer whether other humans feel pain as we do.

If you accept that the universal wave function satisfying unitary evolution is fundamental, and everything else must derive from this, then you run into a problem with quantum measurements. It’s alright to say that an observer, me, exists, and after performing the experiment, I either observed outcome 1 with 60% probability or observed outcome 2 with 40% probability. The problem is that there is nothing in the wave function to distinguish the observer who observed outcome 1 from the observer who observed outcome 2. So if one exists, then both must exist.

If you accept that both exists then I think you essentially accept many worlds. If before performing the experiment there are two scientists Alice and Bob, and afterwards there are Alice-1 and Bob-1 who both observed Outcome 1, and then observed each other discussing it, writing it down, etc., and also Alice-2 and Bob-2 who both observed Outcome 2. etc. etc., then it seems fair to say that Alice-1 and Bob-1 are in some kind of world together and Alice-2 and Bob-2 are in a different world together.

To believe that Alice-1 exists but not Alice-2 you have to believe in some extra information beyond the wave function that helps determine which observers exist. If you want to believe that Alice-1 and Bob-1 exist but not Alice-2 and Bob-2, or vice versa, but never any other combination, it seems like you have to believe in something like objective collapse or Bohmian mechanics.

]]>I would argue that we formulate our theories in the simplest possible terms, which is why we formulate it in terms of pure states, but we simply don’t know if the world is a pure state or not. Since the mathematical formalism works just as well either way, and since there is no experimental way to determine whether the world is in a pure state or not, “the world is in a pure state” is not a scientific statement.

]]>https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Comparison ]]>

I’m glad you enjoyed the discussion. I think Żurek’s relative silence about this is because he doesn’t find Many-Worlds so objectionable. As he put it in his contribution to the “Many Worlds?” volume, his results “fit well within Everett’s relative states framework, but do not require ‘many worlds’ per se”.

]]>All of us take this for granted when we do actual QM problems: e.g., resolving the spin of an eletron along different axes. But, somehow life gets more romantic when people think about MWI in the large.

David Deutsch takes this to its logical conclusion where there is no time either (try to do MWI in GR: the “problem of time” hits you). So, there is, Deutsch has said, just one eternal unchanging wave function with no actual time at all.

Like Peter, this makes my head hurt. Enough that I am willing to consider the possibility that just maybe QM is not the last word.

]]>This is a point that often confuses people. The situation you describe is precisely one where the terms do interfere, and do not evolve independently. Let |0> be the upper path of an interferometer, and |1> the lower path. Then if the photon is in the state |0> + |1>, and passes through a beam splitter, the effect is H|0> + H|1> = |0>, the paradigmatic case of interference.

Now suppose we made a (non-demolition) measurement on the photon, entangling its position with the outside world |W>, ending up with the state |0>|W_0> + |1>|W_1>. Now these terms do not interfere anymore (as long as |W_0> and |W_1> are orthogonal), meaning that any whichever unitaries U,V one applies to the photon, getting U|0>|W_0> + V|1>|W_1>, will not make one term disappear as in the example above. In fact the evolution of both terms is now completely independent of each other.

An interference is only possible if one acts with an entangling unitary on the whole system at once. For a large enough system this is practically impossible, so it is far to regard |0>|W_0> + |1>|W_1> as a sum of two terms that don’t interfere.

]]>Thanks, fixed.

Mateus Araujo,

Thanks! Right now, while I have learned a lot, all of this is causing my brain to hurt, and I have other things to do, may or may not find time soon to think some more. I do wish someone could get Zurek to say more about this. He’s thought deeply about what seems to me the core of the problem, but the thing I quoted is one of the few places he has written about why he is skeptical about “Many Worlds” (in some other places he refers to this one).