Note that I am not an expert on Many-Worlds theory. The whole reason I was reading Price's FAQ, which obviously has a lot of work put into it, was to learn about this subject. So my questions must be treated at least as much as misunderstandings on my part as actual problems with the theory.
Decoherence occurs when irreversible macro-level events take place and the macrostate description of an object admits no single description. (A macrostate, in brief, is the description of an object in terms of accessible external characteristics.)
Are the "superpositions of base states" just in the minds of the "observers" in the worlds, or is there some physical branching of worlds going on?
Worlds do not exist in a quantum superposition independently of each other before they decohere or split. The splitting is a physical process, grounded in the dynamical evolution of the wave vector, not a matter of philosophical, linguistic or mental convenience.
This sounds very bizarre! What, does the theory have "splitting axioms" to explain when and how worlds split? This sounds much more complicated than Copenhagen.
If this splitting is a physical process explained by this theory, it's going to have to specify precisely what the states are that are split into, and your method specified above, as you say, "does not uniquely select a basis".
So we're back to my original question: Who selects the basis, and how?
And since you have claimed that this theory explains a physical process of splitting, you can no longer leave the splitting as being in the eye of the beholder, which might almost have been reasonable.
Although Q32 doesn't discuss or even correctly identify the "spooky" correlations of the EPR experiment, it is indeed possible to resolve this "spookiness" with ideas from Price's document.
I will include just one paragraph from my previous tirade:
The claim that Many-Worlds does not have CFD (contra-factual definiteness) is obviously wrong; any theory has CFD; that's what makes it a theory. If you can describe an experiment and predict what the outcome would be (and this is what makes a theory), then you have CFD by definition. CFD just means that it makes sense to talk about measurements that you haven't done. Every prediction of any theory is an example of CFD. But even if Many-Worlds did not have CFD, this would not be relevant.
Now, rather than complain further, point by point, about Q32, I will give an explanation like I wish Q32 would have done:
Here's how it works:
(I won't try to explain the theory in full or in a convincing way,
but rather just explain how it goes about preserving locality.)
First, we need to clarify the notion of a world "splitting" into
two or more worlds.
The splitting can be imagined as a fairly real phenomenon, that
starts wherever a measurement is made (the measuring apparatus
splits into several apparati, one showing each possible result),
and progresses from there as necessary, at the speed of light or
slower.
(The "measurement" need not be intentional, and the "apparatus"
need not be human-made. You can pick your favorite definition
of what constitutes a measurement; it doesn't really matter here.)
As "split" information propogates, it splits the world as it goes.
For example, right before Schroedinger opens the box, the
contents of the box have split into two states, but the split
has not yet progressed beyond the box.
When he opens the box, photons from both of the two new states
come pouring out, thus splitting the world outside the box,
including Schroedinger's eyes and brain.
Then one world has a sad Schroedinger mourning his dead cat,
while a parallel world has a relieved Schroedinger and cat.
A splitting of the world can be thought of much like a zipper,
though on the unsplit side there is just one thing, and on the
split side there are two full copies of the one thing.
____________________
process that photons\
"may" have >---------------------------------
turned on light__________________/ as yet unsplit part of world
no photons
Here a process may have emitted rightward photons. This
means there are two "worlds", one in which it did emit the
photons, and one in which it did not. These two worlds are
represented here by horizontal lines at different heights.
As the photons, and lack thereof, travel to the right, they
"unzip" the world they meet into two distinct worlds, so
their future consequences can be completely independent.
Now, what happens if we make two measurements in different places?
We can have zippers that are racing towards each other, unzipping.
Assuming that the measurements are not related to each other
(and this is almost always the case), the zippers are unzipping
in "orthogonal" ways, completely independently of each other.
___________
\ _______________
>-----<______________ If you have a
___________/ high-speed internet
two zippers about to meet connection, take a
look at an animation
of this "meeting of
_____,--------------------. the zippers". But
`----------------. \_______ don't say I didn't
\___/_____ warn you it's 1.3
_____,-----------------/--' megabytes! It is at
`----------------' http://www.wolfram.com
each zipper has been split in two by the /~cook/html/Zippers
other zipper; now 4 zippers are leaving /BigZipper.html
Thus, two independent splittings that each split one world into
two will combine to result in four coexisting worlds, each with
the appropriate "weight" (likelihood of you winding up in it).
Now, all that's needed to take care of quantum correlations is
that zippers should produce the new worlds' weights according
to the proper quantum mechanics rules.
In order to do this, zippers will need to "know" what measurement
they are based on, since they need to know whether they are
correlated or not.
For example, if we have two correlated photons as in an EPR
experiment, and we send each photon through a vertically polarized
filter, then each measurement causes a split to start. But when
these splits cross each other, they do not form four worlds, but
just two, since the zippers recognize upon meeting that they should
"correlate". The two halves of one split "line up" with the two
halves of the other split, so only worlds containing the correct
correlation are formed:
___________ _____________
\ /
>-----<
___________/ \_____________
two correlated zippers about to meet
_________________________________
_________________________________
after they meet, two worlds are matched up
If there is a correlation which is not perfect, then four worlds
do form, but their weights are determined by the appropriate
quantum mechanical laws. The zippers are free to form pretty
much whatever correlation they like, and quantum mechanical
correlations are well within the bounds of what they can do.
The case where only two worlds form is really just the case
where the quantum mechanical laws assign a weight of zero to
the other two worlds.
Notice how in this model, there isn't really any relation at
all between two measurements unless you are considering regions
where both experimental results are known. The relationship
between two events is worked out when and where the knowledge
about them meets.
This model seems to pull the rug out from under Bell's inequalities.
I haven't found any way to make Bell's reasoning apply to this system.
I don't see any specific problems that arise with this analysis
of the EPR experiment, and it seems quite extendable to more degrees
of freedom, more zippers, etc.
-Matthew Cook
This whole section seems to be assuming that non-quantum gravity would imply that we are gravitationally affected by parallel worlds with which we do not interact in any other way. Now why on earth would that be?
To see why many-worlds predicts that gravity must be quantised, let's suppose that gravity is not quantised, but remains a classical force. If all the other worlds that many-worlds predicts exist then their gravitational presence should be detectable -- we would all share the same background gravitational metric with our co-existing quantum worlds.
What?? This absolutely doesn't follow!
That gravity must be quantised emerges as a unique prediction of many-worlds.
No, it emerges as a unique prediction of whatever it is you're assuming that lets you make the nonsequitorious conclusion in the previous paragraph.
This means that we are completely capable of "living with superpositions" -- if there is a superposition of states, it means you just can't tell which of the superpositioned things happened or is happening, and we see this all the time! The extent to which a superposition approaches a base state is the extent to which you can tell what happened.
It seems to be getting ever more important to be able to pick our base states "correctly", not arbitrarily!
written 12/97 by Matthew Cook
matthewc@caltech.edu