The Third Quantum State

Decoherent/Consistent histories, for example, is an alternative to the MWI that takes quantum mechanics seriously as a description of reality.

Some instances of that approach may be intended as elaborations of the MWI, although this is never made very clear. Others states that the multiverse doesn't exist and those typically state that quantum mechanics is not an accurate description of reality. Take Griffith's book "Consistent Quantum Theory" Section 27.5 in which he writes:

"The principle of unicity does not hold: there is not a unique exhaustive description of a physical system or a physical process. Instead, reality is such that it can be described in various alternative, incompatible ways, using descriptions which cannot be combined or compared."

Since there is no complete description of physical reality, it follows that quantum mechanics is not such a description, and so that Griffiths does not take seriously as a description of reality.

You are insisting the mathematical structure of quantum mechanics must be obtained by some deeper conceptualiseable reality (the multiverse).

No. I'm saying that QM describes the multiverse, not that it can be derived from the multiverse.

Instead, quantum mechanics is the description of patterns exhibited by reality that permits us to obtain conceptualiseable approximations.

This sentence doesn't provide a clear description of your position. What's a "conceptualiseable approximation"? What are "patterns exhibited by reality"?

Second, there is no particular reason to think quantum mechanics is inexplicable, and some features of it have been explained, see http://arxiv.org/abs/1405.5563

That paper does not tender an explanation of quantum mechanics or its features.

Yes it does. From the abstract: "It explains the relationship between classical and quantum information, and reveals the single, constructor-theoretic property underlying the most distinctive phenomena associated with the latter, including the lack of in-principle distinguishability of some states, the impossibility of cloning, the existence of pairs of variables that cannot simultaneously have sharp values, the fact that measurement processes can be both deterministic and unpredictable, the irreducible perturbation caused by measurement, and entanglement (locally inaccessible information)."

The only existing explanations of those experiments, of which the mathematics is a precise and easily criticisable expression, involves the existence of multiple copies of the experiment.

That is not the case. One explanation that doesn't involve multiple copies of the experiment is that the terms and features we use to describe reality are only approximately counterfactually definite.

No. That doesn't explain single particle interference. The interference pattern at the end of the experiment is influenced by what is going on in all of the states the particle could occupy. The particle is not just "not counterfactually definite", it is actually in multiple states at the same time.

If you are saying the core of the sun exists, then you are postulating the existence of something you can't observe. So then you are prepared to admit the existence of some unobserved things but not others. So how do you draw the line?

The rejection of unobserved things has nothing to do with the point I am making. I am not saying the MWI is wrong because we cannot observe other decoherent branches. I am saying quantum mechanics does not compel us to adopt the MWI, and the multiverse does not need to be invoked to justify the presence of probability amplitudes and interference terms in the formalism of QM.

QM implies the existence of the multiverse. Nobody has provided any alternative description of what QM says about reality: there is no other explanation.

You have a system in an unsharp state |a>+|b>, it gets measured and the subsequent state is |a>|a>M+|b>|b>M then you look at the measuring instrument and the state is |a>|a>M|a>You+|b>|b>M|b>You and so on until there are multiple versions of everything you see around you.

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