#### A. Neumaier

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Correct.(b) The description in the thermal interpretation papers seems to claim that, in fact, if I had a good enough description of the details of the initial state of the microscopic systemandthe measurement apparatus, I would be able to deduce which of the two possibilities "really happened", and that I could do this, again, using only ordinary unitary quantum mechanics with no collapse.

No. Decoherence tells the same story but only in the statistical interpretation (using Lindblad equations rather than stochastic trajectories), where ensembles of many identically prepared systems are considered, so that only the averaged results (which must feature all possibilities) can be deduced. The thermal interpretation refines this to a different, more detailed story for each single case. Averaging the latter recovers the former.Since both stories use the same initial condition and the same rule for evolving in time, these seem to be two different claims about the exact same mathematical object --- the density matrix of the final state of the system. If that's true, then one of them ought to be wrong.

Correct.My understanding of the thermal interpretation (remember I'm not its author so my understanding might not be correct) is that the two non-interfering outcomes are actually a meta-stable state of the detector (i.e., of whatever macroscopic object is going to irreversibly record the measurement result), and that random fluctuations cause this meta-stable state to decay into just one of the two outcomes. An analogy that I have seen @A. Neumaier use is a ball on a very sharp peak between two valleys; the ball will not stay on the peak because random fluctuations will cause it to jostle one way or the other and roll down into one of the valleys.

I explained how the nonlinearities naturally come about through coarse graining. An example of coarse graining is the classical limit, where nonlinear Hamiltonian dynamics arises from linear quantum dynamics for systems of sufficently heavy balls. This special case is discussed in Section 2.1However, the dynamics of this collapse of a meta-stable detector state into one of the two stable outcomes can't be just ordinary unitary QM, because ordinary unitary QM is linear and linear dynamics can't do that. In ordinary unitary QM, fluctuations in the detector would just become entangled with the system being measured and would preserve the multiple outcomes. There would have to be some nonlinear correction to the dynamics to collapse the state into just one outcome.

of Part IV, and explains to some extent why heavy objects behave classically but nonlinearly.

As you can see from the preceding, this is not necessary.Exactly, that's why I'm confused! My impression is that @A. Neumaier is somehow denying this, and that somehow the refusal to describe macroscopic objects with state vectors is related to the way he gets around this linearity argument, although I don't see how.

If we're supposed to be positing nonunitary dynamics on a fundamental level, then that would obviate my whole question, but from the papers I understood A. Neumaier to be specifically not doing that.

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