Postulates of many worlds interpretation of QM

[Dmitry67]

The shadows on the wall seen by Plato's prisoners are real shadows. Because they follow from the really existing objects, the really existing source of light, and the really existing wall. Naming them illusion explains nothing. An explanation has to describe how the illusion emerges, in a logically consistent way.

This is a good example. Yes, shadows on the wall. And it is not well defined what is a wall. And these walls are not flat. And to analyze their shape, we use the shadows.

BTW, returning to the 'observables' which are not obserables at all: can you see elementary particles with your naked eye? You do you use some devices to get values of these 'observables'?

 

[Ilja]

BTW, returning to the 'observables' which are not obserables at all: can you see elementary particles with your naked eye? You do you use some devices to get values of these 'observables'?

I don't - I'm a pure theorists. Your point being? Of course one has to use devices. My argument was that for pure quantum systems one can use very different devices measuring very different observables, in simple cases all of them. Without any contradiction with decoherence.

 

[Dmitry67]

I don't - I'm a pure theorists. Your point being? Of course one has to use devices. My argument was that for pure quantum systems one can use very different devices measuring very different observables, in simple cases all of them. Without any contradiction with decoherence.

My point is that you can't observe them. You can read some numbers from your device. Hence you never get the true value of your 'observable', but just a result of a decoherence of a particle or other QM system with a measurement device. Again, you can never get values of p, r DIRECTLY.

 

[Ilja]

My point is that you can't observe them. You can read some numbers from your device. Hence you never get the true value of your 'observable', but just a result of a decoherence of a particle or other QM system with a measurement device. Again, you can never get values of p, r DIRECTLY.

I can never get even the color of the tomato I like to eat DIRECTLY. So I don't see a point. All measurement results are indirect, depend in their interpretation on our theories.

 

[Dmitry67]

My point isthat in your article you have proven the tautology (you call it a "different physics"). The culmination of your proof is the point what you say that p, r have different values based on the basis, so it mean "different physics". But it is predicted by MWI!

1. In Wigners friend experiment, p,r of the cat is different in the basis of the Wigner and in the basis of his friend inside the box. This is how this experiment is explained in MWI
2. Different 'branches' of the same observer might have different values of 'observables', for example, the same observer have have different values for the cat (dead and alive version/branch).

 

[Ilja]

My point isthat in your article you have proven the tautology (you call it a "different physics"). The culmination of your proof is the point what you say that p, r have different values based on the basis, so it mean "different physics". But it is predicted by MWI!

1. In Wigners friend experiment, p,r of the cat is different in the basis of the Wigner and in the basis of his friend inside the box. This is how this experiment is explained in MWI
2. Different 'branches' of the same observer might have different values of 'observables', for example, the same observer have have different values for the cat (dead and alive version/branch).

No. In Wigners friend, the basis is the same: the positions (or something close to it which is decoherence-preferred) of Wigner, his friend, and the remaining part of the universe. And all their observations are compatible with standard QM laws of physics, with the standard Hamiton operator.

And different branches see different results, but all results are results compatible with the same laws of physics. Instead, the different phyisics related with my non-uniqueness examples means different laws of physics, where Hamilton operators are different, even if they have a similar form in the canonical variables.

 

[Dmitry67]

I am trying to understand, are you talking about 'different laws' relative to different decoherence basis or relative to the different 'branches'?

Different basis and bracnhes form 2 levels of hierarchy: we can have different decoherence basis and for each basis we can have different branches. For example, in Wigners friend experiment we have:

*** Before the box is opened:

1. Wigners friend basis
1.1 Wigners friend branch - observing a dead cat
1.1 Wigners friend branch - observing a cat which is alive
2. Wigner's basis (not decoherenced yet with the inside of the box)

*** After the box is opened:

1. Wigners friend basis
1.1 Wigners friend branch - observing a dead cat
1.1 Wigners friend branch - observing a cat which is alive
2. Wigner's basis
2.1 (in sync with 1.1) Dead cat
2.2 (in sync with 1.2) Alive cat

 

[Ilja]

I am trying to understand, are you talking about 'different laws' relative to different decoherence basis or relative to the different 'branches'?

Different basis and branches form 2 levels of hierarchy: we can have different decoherence basis and for each basis we can have different branches. For example, in Wigners friend experiment we have:

*** Before the box is opened:

1. Wigners friend basis
1.1 Wigners friend branch - observing a dead cat
1.1 Wigners friend branch - observing a cat which is alive
2. Wigner's basis (not decoherenced yet with the inside of the box)

*** After the box is opened:

1. Wigners friend basis
1.1 Wigners friend branch - observing a dead cat
1.1 Wigners friend branch - observing a cat which is alive
2. Wigner's basis
2.1 (in sync with 1.1) Dead cat
2.2 (in sync with 1.2) Alive cat

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.

The non-uniqueness has nothing to do with different branches. Branches depend already in their definition on the choice of a decoherence-preferred basis.

The non-uniqueness is below that level. There are different decompositions into systems, which lead to different choices of the decoherence-preferred basis, and, as a consequence, to different definitions what it means to be a "branch".

 

[cstromeyer]

Hi, this paper by S. Dolev and A.C. Elitzur shows that the results of their experiment are not compatible with a "collapse" (or "wave guide" interpretation of QM such as Bohmian mechanics) on pages 3-4:

http://arxiv.org/abs/quant-ph/0102109

Additionally, this paper by G. Castagnoli et al. also argues against a MWI of QM:

http://arxiv.org/abs/quant-ph/0005069

 

[Ilja]

Hi, this paper by S. Dolev and A.C. Elitzur shows that the results of their experiment are not compatible with a "collapse" (or "wave guide" interpretation of QM such as Bohmian mechanics) on pages 3-4:

http://arxiv.org/abs/quant-ph/0102109

As an argument against pilot waves this is clearly not conclusive. Pilot wave trajectories are known to behave strangely (which is sometimes used as an argument against them).

 

[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.