Neither. There isn't any such notion, since, in phase space, invariance under canonical transformations implies that no preferred basis exists. 

so are the everettian then adding to the formalism by suggesting that there is one, presumably; onto which or across which the worlds branch

No. For on any branch, invariance under canonical transformations implies that no such preferred basis exists, either.

What the many worlds approach of Everett does is consider exclusively the classical configurations, but does not consider the superpositions, that are not classical. 

The basis upon which the wave function collapses depends on the measuring apparatus, not on the state.  Indeed, in the projection postulate, the apparatus is represented by an operator, and the wave function collapse onto one of its eigenfunctions, whose corresponding eigenvalue is the result of the measurement.

Dear Stam, are not in effect then selecting or prefering by not selecting the classical configurations. And how do you mean by classical, do you mean that they reduce to a deterministic system (or a reduction into singular worlds) so that in any world classical logic is respected; ie so that only one orthogonal outcome occurs in each world. I presume they consider just those bases on which this is possible due to decoherence effects...

There are several "quantum mechanisms" - Lagrange/Hamilton/Poisson approach and more... - not being equivalent. States and observables are not (completely) isomorphic in all possible formulations. The same is tru in classical mechanics. I consider those "problems" as part of metaphysics.

Classical configurations are those that satisfy the classical equations of motion-that are deterministic (though they need not be, e.g. when describing clssical thermodynamics).  The many worlds formulation does not perform any selection-that's its point. It's the consequence of the uniqueness of the solution to the equations of motion that, in any such ``world'', a unique outcome is observed. For classical thermodynamics, the defining property is that configurations can be labeled, once and for all. 

However it is possible to experimentally produce superpositions-and to describe their effects mathematically-that do not have any classical description. They don't satisfy the classical equations of motion, nor can the labels be consistently assigned, as in classical thermodynamics.   That's why the many worlds formulation does not describe the observed quantum effects. It's an experimental outcome, not a theoretical one. 

In all cases, however, there isn't any preferred basis. 

(The formalisms of Hamilton (or Poisson) and Lagrange are equivalent in classical and quantum mechanics-that's why it doesn't make sense to discuss which one is ``preferable'', either.) 

All this is textbook stuff. Absent a definition of equivalence, the first statement is meaningless. The second statement is wrong. The third is meaningless. And none has anything to do with the question discussed.

Lagrangians that produce the same equations are equivalent.  They may differ by a mere additive or multiplicative constant.

Dear stam,

"when you say, that i is possible to experimentally produce superpositions-and to describe their effects mathematically-that do not have any classical description. They don't satisfy the classical equations of motion, nor can the labels be consistently assigned, as in classical thermodynamics. That's why the many worlds formulation does not describe the observed quantum effects. It's an experimental outcome, not a theoretical one."

Do you just mean indeterminism here?; and when you labels do you mean the indistinguishability of outcomes (or which one is labelled yes/no)

I thought that the whole point of everettian quantum mechanics was to make sense "non classical states; thats why there is branching  (not just states where you measure the state its prepared in, returing an outcome with probability 1).

That is what it means for a state to be in super-position (a non degenerate one where there are at least two outcome (eigenvalues) with positive probability; that is the the world branches into both 'eigenvalue' worlds with the two branches having corresponding weight/measure of existene equal to the amplitudes mod squared. I am not talking about a preferred outcome, when I mean a preferred basis I mean should it branch along the x basis, where say the amplitudes 1/sqr2 spin up x + 1/sqrt 2 x down, or some other angle where its say alpha where the amplitudes are say 1/sqrt 3 spin up alpha + sqrt(2/3) spin down alpha. Generally in an experiment this is dictated by an apparatus setting (the pre-measurement setting of the angle of the magnetic field in the gerlach device which determines the basis (not the state of said basis)onto which the one of two in-deterministic outcomes will be found). And in the absence of that, many everettians suscribe to something to like decoherence or eigenselection (or that the environment selected/assisted selection).

I am not talking about a preferred outcome in a superposition but which 'super-position'. IF the everettian pick out the deterministic states (which are not in super-positiions) this is in effect picking out a preferred basis (and of course there is no question about the preferred measurement outcome, but neither is there in everettianism, really that problem in the indeterministic cases. And if they pick out the deterministic states, they would not even need branching at all

I

Hi Dr. Nicolas, si tacuisses, PHYSICUS mansisses!

Textbook? How about the Langrangian to my H? 

Meaningless? This is called Foundation of classical and quantum mechanics. 

You state: the algebra of observables is meaningless! eventually you think about it

And that's the problem with Everett's approach: it doesn't  describe superpositions as intermediate states. These, however, do contribute, by the superposition principle. So it doesn't get the same measure as in usual quantum mechanics.

In other words: whereas branching is part of quantum mechanics, quantum mechanics realizes branching in a specific way. What's interesting is that this can be, and has been, checked, in real experiments. That's how it's possible to deduce that Everett's approach isn't correct. 

There isn't any such notion as ``deterministic states'', just classical states and states that don't have a classical limit.  The classical states are those of the classical approximation. Quantum mechanics describes all possible linear superpositions. For a spin 1/2 object, the classical states are those at any two antipodal points  of the Bloch sphere; the non-classical states are all the other points of the Bloch sphere. 

These don't have a classical limit. But they do contribute to transition amplitudes in well-defined ways. 

So there isn't any ``preferred basis'', once more. All bases are equivalent-in the example, any coordinate system on the sphere can't be distinguished from any other- and the results obtained by one apparatus can be related to those obtained by another, precisely because there exist quantities, deduced from the measurements, that can be shown not to depend on the arrangement of the apparatus.