On Wednesday, April 13, 2022 at 8:55:48 PM UTC+3 meeke...@gmail.com (Brent) 

Decoherence has gone part way in solving the when/where/what basis 
> questions, but only part way.

As I wrote at the end of my first reply to your message, I share your 
concern about decoherence but I see the glass as half-full; that is, with a 
little more subtlety I hope that the matter can be formulated in clear 

Surely collapse is easier to handle as a general concept (except, on the 
other hand, that it requires new dynamics). I forgot to mention that *my 
argument for deriving the Born Rule works with collapse, too* -- so it is 
an alternative to Gleason's theorem.

Here I define colapse as an irreversible process, violating unitarity of 
course, and I keep it separate from randomisation. The latter means that 
each outcome is somehow randomised -- an assumption we can do without.

*Collapse can also be described in a many-world formulation!* It differs 
from the no-collapse MWI only in being irreversible. My argument in outline 
1. assessment that MWI-with-collapse is workable;
2. therefore, outcomes of small enough measure can be neglected in practice;
3. now Everett's argument can proceed, concluding that the Born Rule is a 
practically safe assumption (to put it briefly).

So I have replaced two assumptions of Gleason's theorem, randomisation and 
non-contextuality, by the assessment of workability only.

If you don't feel comfortable yet with formulating collapse in a many-world 
setting, let us also assume randomisation (God plays dice), for the sake of 
the argument, in a single-world formulation. That is, we ASSUME the 
existence of probability; then the previous argument just guarantees that 
this probability follows the Born Rule.

Of course I favour the first version of the argument, using the many-world 
formulation of collapse, to avoid the "God plays dice" nightmare.

Thanks for the comments so far, because they stirred my thinking and 
motivated fresh ideas, some of which I hope will prove helpful and worth 
discussing, if and when they mature.

George K.

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