Why aren't we on maverick branches?

[Quantumental]

This one is dedicated to my dear Everettians: http://arxiv.org/abs/1511.08881

What is interesting to me is that Stephen Hsu has previously been a very outspoken proponent of Everett.

 

[bhobba]

This one is dedicated to my dear Everettians:

Why you are stuck on this decision theory stuff in MW has me beat.

Its simply an elegance thing to derive it in the formalism rather than assume it.

You can assume its true and MW doesn't change at all.

That's without delving into this supposed disproof of the decision theory approach - once can still use Gleason. And having studied Wallace's book that's what it amounts to anyway - showing non contextuality which implies the Born Rule via Gleason.

From the paper:
Everett defined maverick branches of the state vector as those on which the usual Born probability rule fails to hold -- these branches exhibit highly improbable behaviors,

If the Born Rule fails to hold you have disproved QM. Since MW is deliberately cooked up to be equivalent to the QM formalism that's not logically possible.

Added Later
After a bit of investigation it turns out maverick branches are branches with a very small probability - not violating the Born Rule - which of course it cant.

Thanks
Bill

 

[bhobba]

Reading a bit more of the paper I came across this little gem:
'In the previous section we illustrated the drastic differences resulting from two choices of measure: the counting distinct histories measure vs the Hilbert (norm-squared) measure. The former leads to predominance of maverick branches, the latter to the usual quantum mechanics and the Born rule. Obviously, there is an infinite set of possible measures over the space of state vectors. Yet, there is not even a natural place in the theory to impose a measure. Everett claimed (erroneously) that the Hilbert measure emerges naturally, but in fact the measure problem remains unsolved.'

The measure problem was resolved by Andrew Gleason:
https://en.wikipedia.org/wiki/Andrew_M._Gleason

His famous theorem shows that there is only one measure that is basis independent - the Born Rule. If you have any others its not basis independent and is very strange in a theory based only on vector spaces - one of key things about vector spaces is its properties are basis independent. BM for example introduces the quantum potential which means its more than vector spaces - but such is not the case in MW. The counting of distinct histories is not basis independent and if you use it you run into issues. This is examined closely on page 189 of Wallace's book (The Emergent Multiverse) where a number of alternative strategies such as naive counting are looked at. They all have issues. In fact that's what the decision theory approach is all about - only basis independence makes sense.

I think the author needs to understand QM a bit better.

Thanks
Bill

 

[DrClaude]

As far as I can see, the paper mentioned in the OP has not been published in a peer-reviewed journal, so it is a not proper for discussion on PF. If I am mistaken, please PM me with the reference.

Until then, thread closed.