Postulates of many worlds interpretation of QM

[cstromeyer]

Ilja, the experiment shows that the wavefunction in QM is non-sequential and non-causal. By definition, Bohmian mechanics is a causal interpretation. Please see:

http://plato.stanford.edu/entries/qm-bohm/

 

[Count Iblis]

First, again, there is no difference between "Wigner's basis" and "Wigner's friends basis". The preferred basis is for everything, and it is uniquely defined given a decomposition of the whole universe into different subsystems. Now, in Wigner's case we have three different subsystems - Wigner, his friend, and the rest of the world - and the decomposition into these three subsystems is the same, therefore the preferred decoherence basis is the same.

Just because in practice the basis is the same doesn't mean that the laws of physics forbid other bases. Suppose a quantum computer is built in which the decoherence basis is the tensor product of the |0>, |1> bases for each qubit. This quantum computer is almost perfectly isolated from the environment so that decoherence effects are negligible.

We switch to the |0'>, |1'> basis:

|0'> = 1/sqrt(2) [|0> - |1>]

|1'> = 1/sqrt(2) [|0> + |1>]

and implement (classical) observers in this basis.

Then why can't this be done?

 

[Ilja]

Ilja, the experiment shows that the wavefunction in QM is non-sequential and non-causal. By definition, Bohmian mechanics is a causal interpretation. Please see:

http://plato.stanford.edu/entries/qm-bohm/

There is nothing in the experiment which contradicts standard quantum theory. And, once there is an equivalence theorem, the results of the experiment cannot contradict BM as well.

Thus, there is only an apparent contradiction. In particular, BM is known to be nonlocal, and naive attempts to find realistic interpretations often assume locality implicitly. Then, in BM it is extremely important to consider the whole experiment - including all measurement and storage instruments, up to the final moment - into the consideration.

This is clearly not done. There is a lot of talk about various measurements of the particles, without any consideration how the choice of these measurments influences the measurement of the photon. But this is an important feature of BM: The choice of measurements for one part influences the actual results of measurements of another part of some superpositional state.

This is not the first experiment which is claimed to be incompatible with causality: The quantum eraser has been interpreted in a similar way, but allows for a causal interpretation in BM (even if the corresponding trajectories have been characterized as "surrealistic"). The situation looks very close, and the outcome is predictable: Bohmian trajectories exist, and nothing in this game contradicts classical causality, but the explanation given by these trajectories will look extremely surrealistic: Probably some ways of particle detection appear to be fooled.

Yes, these are guesses, but similar to guesses of those mathematicians which become confronted with angle trisection algorithms. They know they have a theorem behind them and have some experience considering such examples, so they can give a conclusion without having to consider everything in detail.

A serious angle trisection paper would have to show in detail what is wrong with the impossibility proof for such algorithms. Similar for claims that some standard quantum experiment does not allow for an explanation in terms of causal Bohmian trajectories.

 

[cstromeyer]

Ilja, the experiment contradicts "collapse" interpretations of QM which are supposed to be equivalent to Bohmian mechanics.

I agree with you that Bohmian mechanics is compatible with non-locality, but the experiment shows that the wavefunction of QM is also non-sequential and thus non-causal.

However, the work of Professor Joseph Eberly and colleagues, e.g., see his article in the journal Science, shows that quantum entanglement can suddenly die. One might try to argue that this sudden death might restore some concept of 'causality'.

 

[Ilja]

Ilja, the experiment contradicts "collapse" interpretations of QM which are supposed to be equivalent to Bohmian mechanics.

I agree with you that Bohmian mechanics is compatible with non-locality, but the experiment shows that the wavefunction of QM is also non-sequential and thus non-causal.

First, I doubt that it contradicts collapse interpretations, but this question is not interesting enough for me to spend time evaluating it. But this experiment is clearly standard QM, and in standard QM the wave function follows a causal equation - the Schroedinger equation (if one uses classical causality, with the absolute time used in this equation).

Thus, a contradiction with classical causality cannot follow, it is a purely interpretational artefact.

However, the work of Professor Joseph Eberly and colleagues, e.g., see his article in the journal Science, shows that quantum entanglement can suddenly die. One might try to argue that this sudden death might restore some concept of 'causality'.

I would not even try.

 

[Dmitry67]

First, again, there is no difference between "Wigner's basis" and "Wigner's friends basis". The preferred basis is for everything

No, no, this is much much worse hten you think.

As I said before, for any observer the only valid choice of basis is his own basis. Before box is opened, the world for Wigner and his friends is different.

And even worse, decomposition into systems is made by some observer, hence, it is observer (and basis-) dependent.

And even worse, an observer itself is not clearly defined.

And even worse, there are some branches from, let's call them 'early forks', where Wigner and his Friend did not decide to make an experiment, or where they were not friends, or Earth did not exist. So all we are talking about is relative to some branch.

And even worse (I don't know why it is not stressed) - basis itself must be redefined every time after any macroscopic event, after any act of decoherence. You cant, for example, talk about 'how sad Friend tells Wigner that cat is dead', using the old Friend's basis before he didnot knew cat's fate, because in the old basis he was in a superposition to both outcomes, which is not consistent with his own updated basis (I know that cat is dead/alive).

So you can't as you like to say 'I don't care about branches', because 1 the initial branch, 2 the decomposition of the universe into systems, 3 the definition of what is an observer are branch-dependent. And 2 and 3 are dynamic.

 

[Ilja]

No, no, this is much much worse hten you think.

As I said before, for any observer the only valid choice of basis is his own basis. Before box is opened, the world for Wigner and his friends is different.

And even worse, decomposition into systems is made by some observer, hence, it is observer (and basis-) dependent.

And even worse, an observer itself is not clearly defined.

And even worse, there are some branches from, let's call them 'early forks', where Wigner and his Friend did not decide to make an experiment, or where they were not friends, or Earth did not exist. So all we are talking about is relative to some branch.

And even worse (I don't know why it is not stressed) - basis itself must be redefined every time after any macroscopic event, after any act of decoherence. You cant, for example, talk about 'how sad Friend tells Wigner that cat is dead', using the old Friend's basis before he didnot knew cat's fate, because in the old basis he was in a superposition to both outcomes, which is not consistent with his own updated basis (I know that cat is dead/alive).

So you can't as you like to say 'I don't care about branches', because 1 the initial branch, 2 the decomposition of the universe into systems, 3 the definition of what is an observer are branch-dependent. And 2 and 3 are dynamic.

If it would be as you claim, my article would be unnecessary and many worlds would be simply ill-defined, and nothing worth to care about. As circular as possible.

 

[Dmitry67]

I expected that question.
MWI is circular, but it is much better then CI: check the image.
Now, why I prefer it over BM... wait few mins, I will post a new thread.