Re: What is the preferred basis problem of the many world's interpretation?

The best example to think about what a "basis" is in quantum 
mechanics is the polarization of a photon.  Photons make up light, 
which is an electromagnetic field that's moving in one direction (z).  
The electric field is oscillating perpendicular to z, but it's not clear if 
it's in the x direction (East), the y direction (North), or perhaps some 
combination of x and y like Northeast or Southeast.  (It can also be 
rotating with time, but let's assume the oscillation is in a constant 
direction.)

The "basis" problem is this: If the polarization is measured by a 
device aligned along the x or y axis, the result will either tell you that 
the photon was polarized "east-west" or "north-south".  No other 
results are possible.  That's a measurement in one "basis".  But 
another device, aligned at 45 degrees to the first, will tell you that the 
photon is either polarized "northeast-southwest" or 
"northwest-southeast".  This is a measurement in another basis.

Note that the two measurement possiblities in each basis are 
"orthogonal" to each other (literally, in this case, perpendicular).  
Orthogonal is just a mathematical way of saying "perpendicular" in a 
multi-dimensional space.

Now comes the "problem".  The Many Worlds Interpretation says that 
if the photon is measured by the first device, the universe splits into 
some universes in which the polarization is "north-south" and other 
universes in which the polarization is "east-west".  But a different 
measuring device would split the possible universes into a different 
"basis"; say that of NW-SE or NE-SW.  The probability posulate 
simply tells you how "many" universes each possibility will end up in, 
and is absolutely untestable.  Note that the orientation of the 
measuring device determines the basis in which the universe splits 
apart.  This becomes a real problem when one considers that the 
wavefunction of the entire universe is never measured at all (there's 
nothing "outside" the universe to choose a basis), so it's not clear 
how one should split the wavefunction of the universe in MWI theory.

The Copenhagen Interpretation also can't deal with the wavefunction 
of the universe, because now there's nothing to 'collapse' the 
universe from the outside.  I think the only type of quantum theory 
which might correctly deal with quantum cosmology is going to have 
to be one that is time-symmetric, and very few people are working on 
time-symmetric interpretations to quantum mechanics.