**From:** D. Goel (*deego@gnufans.org*)

**Date:** Fri May 09 2003 - 13:46:36 MDT

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hi

*> Well, the coefficients of "mismatch states" like |x=1>|you=2> should
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*> become very small, compared to those of "veridical states" like
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*> |x=1>|you=1>. But I don't see how that addresses the basis problem.
*

The mismatch state's coefficient was 0 in the first place. I had

added and subtracted a term like that to both sides.

I should go over the argument more carefully:

[1] say, the particle is in a(t)|x_1> + b(t)|x_2>

where a(t) and b(t) are some functions of time.

So the system's total state is (a(t)|x_1> + b(t)|x_2>)*|you>

[2] You perform measurements attempting to observe the position.

The new state becomes:

|x=1>|you_1> + |x=2> |you_2>. ---- (2)

where you_1 is the part of you whose molecules in the brain remember

seeing the particle at x=1.

[3] Eqn. [2] is just a snapshot in time. The time-dependent solution

looks more like:

exp(+it)|x=1>|you_1> + exp(-it)|x=2> |you_2>. ---- (3)

[4] Now, we want to interpret eqn. [3].

If eqn. [3] could be written as:

[a1(t)|f=1>|you_f1>] + [a2(t) |f=2> |you=f2>]

+ [a3(t) |f=3> |you=f3>] + ...

. ---(4)

for some basis of the particle "F". Where you_f1 means "you having

observed the particle in state f=1", then that's a valid

interpretation.

Then we could say, "Well, that's a valid interpretation... and then

the allowed states for the particles which one of the above "you's"

would observe in (4) are the various f's.

[5] Turns out that the only way in which (3) can be put into form (4)

is by choosing the x basis. If time were not an issue (viz. you were

just considering (2), then (2) can be put in the form (4) in *many*

ways). But (3), the time-dependent solution has only one way of being

put in form (4).

Again, note that (2) can be put into (4) in many many ways. But the

issue is to put the time-dependent equation (3) into form

(4)----viz. we want an "interpretation" that is "stable" with time.

[6] That way is

[exp(+it)|x=1>|you_1>] + [exp(-it)|x=2> |you_2>] ---- (3)

Thus, once you entangle yourself with the system in a certain way,

there's effectively only one basis to choose from.

That's just my understanding. I may be wrong. I haven never studied

that math of decoherence. :(

*> So I still think you need an extra postulate in MWI, in order to single
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*> out a basis.
*

Maybe that's true indeed. I really don't know at this point how much

of what I am saying is true and how much i am imagining..

====================================================

unrelated but:

BTW, if one were to survey what most GR/QFT professors believe in, as

regards the "QM problem", I think that Everett intepretation would

outnumber all others combined. It is my observation that most

professors who are puzzled by the "collapse" aspect of QM when growing

up---most GR, QFT, particle physicists, soon gravitate to the Everett

intepretation[1]. And that Everett intepretation is really the

"standard" now.. just not yet taught this way in first year QM

textboks. Since they concluded that their "QM issue" is more or less

solved and there are bigger controversies to tackle in QFT etc., they

move on to QFT.. Once in a while, you find a few professors who got

turned off by the "many worlds hogwash" early on in their lives and

never gave it a chance, end up investigating nonunitary solutions..

And since these professors are the ones being seen as "working on

basic interpretation of QM", this serves to "keep the controversy

alive, at least in the minds of journalists".

[1] BTW, they dislike the "journalists labeling this a Many Worlds

Intepretation" -- because that leads to observations like "this has

got to be ridiculous, exactly how often does the split take place?"

Q. Mechanically, there's just one wavefunction for the universe that's

happily following the Schrodinger's equation.. no splits..

--

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