Can QM interpretations be reconciled?

[Dirk Pons]

Why should QM exclude "all NLHV solutions"?

QM does't, but it sometimes tries to. QM is incompatible with NLHV solutions, because QM requires its particle to be a 0-D point with intrinsic parameters, whereas hidden variable solutions propose internal structure at the sub-particle level. There have been many deliberate attempts via the inequality methods and loop-hole free entanglement tests to disprove the viability of hidden variable solutions on theoretical and empirical grounds respectively. These results favour QM, and rule out local hidden variable solutions. However no proof or experiment has ruled out all non-local hidden variable solutions.

I'm not aware of any such scheme working in the same realm of validity as QT

True, there are no NLHV solutions that are as quantitatively robust as QM. That does not mean that no partial solutions exist.

 

[kvantti]

But without that special role for measurements, which says that a measurement produces an eigenvalue with a probability given by the Born rule, then it's hard to relate the mathematics of QM to what we actually observe. You can rephrase the Born rule, as you suggest, to the probability of finding yourself in a possible world, but what is the "yourself" in that phrase, and how do we divide up the wave function into possible worlds? Those notions don't appear in pure quantum mechanics.

In the MWI "measurement" is just the entanglement of the environment/measuring device with the decohered states of the state function and all the possible decohered entangled states continue their own evolution within the (state function of the) universe. "Yourself" also continues to evolve with all the possible worlds, so it is just a random luck of "who" of those "YOU" are (if that makes any sense, you can also think that when the worlds decohere/split that you are cloned with the worlds and the square of the probability amplitude tells you the statistical proportion of the the worlds within the state function, ie. if the probability of measuring a certain eigenvalue is eg. 0.15 then in 15% of the decohered worlds that is the outcome of the measurement).

bcrowell gave a nice link explaining the basics of it on the first page of this thread:
http://www.preposterousuniverse.com...hanics-is-given-by-the-wave-function-squared/

Any other questions should be answered by the Everett FAQ.

I like this explanation as it intuitively dovetails with the path integral formulation. The worlds converging rather than diverging so to speak.

Indeed, the path integral formulation explicitly shows how the "parallel worlds" interfere with each other at the quantum level and that the worlds can also converge rather than just diverge as long as the quantum state of the system in question remains coherent.

QM is incompatible with NLHV solutions, because QM requires its particle to be a 0-D point with intrinsic parameters, whereas hidden variable solutions propose internal structure at the sub-particle level.

de Broglie-Bohm theory is a NLHV solution which is compatible with QM and the particles are regarded as 0-D with the pilot wave guiding them in accordance with the Schrödinger equation.

Anyway in quantum field theory, even tho the basic mathematics deals with point particles, it is hardly correct to say that eg. an electron is a "point particle": rather, the closer you zoom into the electron the more of a "fuzzy cloud" of energy it looks like. You start your calculations with a point particle but after you take into account all the possible probability amplitudes going on with the electron you end up with a mess of virtual photons, virtual electron-positron pairs and all the interactions between them, so the electron is "really" a mess of interacting quantum fields - a quantized oscillation of the fields, so to speak.

 

[Dale]

It seems like everyone has had a chance to say their piece, so we will close it here.