A. Neumaier said:
You can proofread it now and post your comments here.
It's still dated May 11, 2019, but I now see your modified sentence.
[
@Greg Bernhardt: is there a way for a "last-modified" date to be automatically included in these Insights, as well as the original date?]
I now replaced it by the more accurate
new version said:
Even Ballentine 1998, who rejects rule (7) = his process (9.9) as fundamental, derives it at the bottom of p.243 as an effective rule.
I see no such derivation at the bottom of p243. Rather, the last paragraph on that page talks about how an imperfect apparatus could give rise to the "reduced" state eq(9.18) by environmental decoherence mechanisms. This is not a "
non-destructive projective measurement" of the type addressed by Rule 7. Hence it is incorrect to link the two, as you currently do.
On p.241, Ballentine writes: ''Some evidence that the state vector retains its integrity, and is not subject
to any “reduction” process, is provided by [...]''. No state reduction is his basic credo that he wants to support here. He says on the next page that state reduction should produce a mixed state, (9.18), and on p.243 that in a spin recombination experiment, only the pure state (9.21) is compatible with the experimental results. This is his ''evidence''. Since there was no measurement at the point B/C of investigation - only unitary 2-state dynamics happens -, this is no surprise, anyone would agree. It is not a situation where state reduction should be invoked. Thus his ''evidence'' is bogus.
I think you misread Ballentine's sect 9.5. As I read it, Ballentine's point (starting at the 2nd paragraph on p242) is this:
IF one supposed that all coherence were lost between the wavefunctions at points B and C, then the spin state should be (9.18), i,e., $$\rho^{inc} ~=~ \frac12 \; \Big( |+\rangle \langle +| ~+~ |-\rangle \langle -|\Big).$$ But then, the spin-recombination experiment (with sufficiently good apparatus) described on the rest of p242 and over onto the top of p243, would reveal one's error.
That's what he means by "evidence" (in my humble opinion, of course, since I'm not a mind reader, though neither is anyone else around here, afaik). In other words,
IF one (mistakenly) assumed reduction at points B and C, the actual experiment furnishes
evidence of one's mistake.
