I Would studying MWI be a waste of time?

[vanhees71]

And also stronger than any local non-deterministic (but ontic) model.

This must be an extension of Bell's original theorem. Is there any specification of what "non-deterministic" and "ontic" means?

 

[Demystifier]

This must be an extension of Bell's original theorem. Is there any specification of what "non-deterministic" and "ontic" means?

I meant local non-deterministic hidden variables. For instance, particle trajectories exist (hidden variables), but they obey a stochastic law such as random walk (non-deterministic), and motions of spatially separated particles are not correlated (local). Such theories are also excluded by Bell's theorems, as discussed by Bell himself.

 

[stevendaryl]

No! The correlation comes from the fact that the two-particle system was prepared in the entangled state.

I'm not talking about the correlation. I'm talking about the statement

"Bob will measure spin-down along the z-axis"

That statement was not true initially. Then Alice measured spin-up. Afterward, the statement was true. So immediately before Alice's measurement, there were two possible results for Bob. After her measurement, there is one possible result for Bob. That's what people mean by "measurement causes collapse".

 

[vanhees71]

I see. I thought the hidden variables are introduced to save "determinism".

 

[Demystifier]

I see. I thought the hidden variables are introduced to save "determinism".

That's one of the most frequent misunderstandings about hidden variables. They are introduced to save ontology - properties existing even without measurements.

 

[vanhees71]

I'm not talking about the correlation. I'm talking about the statement

"Bob will measure spin-down along the z-axis"

That statement was not true initially. Then Alice measured spin-up. Afterward, the statement was true. So immediately before Alice's measurement, there were two possible results for Bob. After her measurement, there is one possible result for Bob. That's what people mean by "measurement causes collapse".

That it is true after A's measurement is caused by the correlation, not by A's measurement. That's all I'm saying. Before the single-particle spins are completely indetermined anyway; only the correlation is determined (i.e., the total spin being $S=0$ and thus also $\Sigma_z=0$).

 

[vanhees71]

That's one of the most frequent misunderstandings about hidden variables. They are introduced to save ontology - properties existing even without measurements.

Properties of course exist without measurements. I think that's also a common misconception about QT. It's often stated: "Nothing exists if it's not measured". That's nonsense. If you say: "There's an electron" it's specified what it is by its intrinsic properties (mass, charge, spin) and the observables that can be defined (momentum, position, angular momentum, helicity, etc. etc.). Now knowing the state by preparation (maybe even that it is a pure state a pure state which means you have the as complete as possible information about the electron), however does not mean that all observables have determined values. For sure not all observables can be determined at once, only compatible ones. That's all. Why this implies that there's no ontology, I never understood. That an electron is there or not is a clear statement, and it can be checked by detecting the electron. That's pretty much all there is to say something is there or not?

 

[Demystifier]

Properties of course exist without measurements. ... That an electron is there or not is a clear statement, and it can be checked by detecting the electron.

How can measurement (detection) of the electron be used to check that it is there even without measurement?

 

[Demystifier]

For sure not all observables can be determined at once, only compatible ones. That's all. Why this implies that there's no ontology, I never understood.

If one observable cannot be determined (because the other complementary one is measured), does it mean that the value of this observable does not exist?

If it exists, then it's a hidden variable.

If it does not exist, then what if no measurement is performed at all? Does value of any observable exist in that case? If yes, that's a hidden variable again. If not, then there is no ontology.

So either there are hidden variables, or there is no ontology (because hidden variables and ontology in the absence of measurement are the same). Which one do you choose?

 

[stevendaryl]

That it is true after A's measurement is caused by the correlation, not by A's measurement.

But we agree that:

1. At the time the twin pair was created, the statement "Bob will measure spin-down in the z-direction" was not true.
2. It became true when Alice measured spin-up.

So, the correlation may have been an essential ingredient, but it was Alice's measurement that caused the statement to flip from indeterminate to true. If she hadn't performed the measurement, the statement would still be indeterminate.

 

[zonde]

That it["Bob will measure spin-down along the z-axis"] is true after A's measurement is caused by the correlation, not by A's measurement.

"correlation" can make Bob's measurement certain? But then it can make Alice's measurement certain as well?
So how the cause goes? Like this?

Bob's measurement <--is caused by-- "correlation" --causes--> Alice's measurement

But this then contradicts what you said earlier:

both single-particle spin-z components are as indetermined as they can be.

 

[Jilang]

Doesn't the wave function reflect a partial probability, with the full actual probability dependent on the measurement? The relationship between amplitudes and probabilities would suggest this as would the ability to describe the wave function in different bases.

 

[martinbn]

But we agree that:

1. At the time the twin pair was created, the statement "Bob will measure spin-down in the z-direction" was not true.
2. It became true when Alice measured spin-up.

So, the correlation may have been an essential ingredient, but it was Alice's measurement that caused the statement to flip from indeterminate to true. If she hadn't performed the measurement, the statement would still be indeterminate.

Couldn't one say that it became true after Bob's measurement? Just because Bob's and Alice's measurements are simultaneous, and technically the statement became true after Alice's measurement, it doesn't mean that Alice's act has anything to do with it.

 

[LeandroMdO]

If it's really true that MWI is nonsense--well, it's the usual QM with certain assumptions removed. Logically, if a theory is nonsensical, then it can't become more sensible by adding additional assumptions. If MWI is nonsense, then so is QM.

A few assumptions are removed, a few more are added. The failure of MW proponents to produce a suitably minimal procedure for interpreting quantum states in terms of quasiclassical parallel worlds makes these frequent boasts a bit perplexing: yes, I know that you would like to interpret quantum mechanics in this way, but can you? So far I have seen no evidence that this is possible---the projection postulate is removed only to reappear in some other disguised form.

One does not introduce "parallel universes" (very polemic, by the way), one simply accepts them as predictions of quantum mechanics! These "branches" are there microscopically, their effects are well-known, visible and testable (e.g. double-slit).

Exactly!

What one introduces by hand is a magical collaps to get rid of macroscopic parallel branches, simply b/c one does not like them.

And they are there microscopically in a rather trivial manner, e.g. |spin up> + |spin down>. All what happens is that this somehow induces a kind of "branch structure" macroscopically, but of course in one single quantum state.

You can certainly write them like that, but to interpret them like parallel quasiclassical worlds requires more work and additional assumptions. In particular, since unitary evolution takes a pure state to a pure state, the decision to throw out small off-diagonal terms in the density matrix (because they are small) is just a tacit collapse postulate. It is otherwise illegitimate to neglect such terms: their smallness only corresponds to irrelevancy if one is armed with a probabilistic interpretation, that is, attempts to derive a many-worlds ontology from the oft-quoted set of minimal postulates have a tendency to assert the conclusion.

 

[vanhees71]

If one observable cannot be determined (because the other complementary one is measured), does it mean that the value of this observable does not exist?

If it exists, then it's a hidden variable.

If it does not exist, then what if no measurement is performed at all? Does value of any observable exist in that case? If yes, that's a hidden variable again. If not, then there is no ontology.

So either there are hidden variables, or there is no ontology (because hidden variables and ontology in the absence of measurement are the same). Which one do you choose?

It's a strange formulation to ask whether a value exists or not. QT simply says that an observable's $A$ value can be determined to be $a$. That's the case if the state is given by
$$\hat{\rho}=\sum_{\beta} P_{\beta} |a,\beta \rangle \langle a,\beta|, \quad \sum_{\beta} P_{\beta}=0, \quad P_{\beta} \geq 0.$$
Here $|a,\beta \rangle$ denotes a complete set of orthonormalized eigenvectors of the self-adjoint operator $\hat{A}$ of eigenvalue $a$ that represents $A$ (dependent on the concrete $\hat{\rho}$. Of course analogously you can have continuous sets for $\beta$.

For other states the value of $A$ is undetermined. That's it.

The observable of course always exists, because you can measure it. An observable is not a self-adjoint operator in Hilbert space nor are states statistical operators but an observable is defined by an equivalence class of measurement procedures (by a concrete device to measure it; the official definition is given by the buereaus of standard like NIST in the USA in such terms). A state is defined as an equivalence class of preparation procedures.

 

[Demystifier]

It's a strange formulation to ask whether a value exists or not.

The observable of course always exists, because you can measure it.

I'm not sure I understand you. Are you saying that it's OK to say that the observable exists, but not OK to say that the value exists?

 

[vanhees71]

But we agree that:

1. At the time the twin pair was created, the statement "Bob will measure spin-down in the z-direction" was not true.
2. It became true when Alice measured spin-up.

So, the correlation may have been an essential ingredient, but it was Alice's measurement that caused the statement to flip from indeterminate to true. If she hadn't performed the measurement, the statement would still be indeterminate.

That's true, but this "flip" is not due to "spooky actions at a distance". That's only the case if you make the assumption of collapse, and that's contradicting the fundamental assumptions of locality and microcausality built into QED (and all the Standard Model of HEP physics). The only conclusion can be to give up the collapse assumption and live with the minimal interpretation.

If on top you invent funny unobservable things like parallel universes it up to you, but it's not physics. The original paper by Everett is enigmatic to me. As Arnold already said in this thread, it looks as if he puts in as an assumption what he gets out, of course using nothing else than standard QT and thus the minimal interpretation.

 

[A. Neumaier]

it's OK to say that the observable exists, but not OK to say that the value exists?

The standard NE coordinates of the observable ''position of Vienna (Austria)'' exist, but their value (48° 12′ 0″ N, 16° 22′ 0″ E) is not a real number. It is an uncertain number undefined beyond a small number of digits. The observable ''spin'' of a quantum particle in a pure spin state exists as well, but its spin coordinates are certain only if measured in a basis aligned or orthogonal to the spin direction; otherwise they may be very uncertain.

As the classical example of Vienna shows, a successful ontology does not depend at all on the ontological fiction that all existing observables have infinitely precise values.

Only this fiction must be given up in orthodox quantum mechanics, not the notion of ''existence when unmeasured''.

 

[vanhees71]

I'm not sure I understand you. Are you saying that it's OK to say that the observable exists, but not OK to say that the value exists?

The statement "the value exists" doesn't make any sense to me. Within QT an observable can take a definite value (then the observable's value is determined) or not (then the observable's value is indetermined), depending on the state of the system this observable is defined on. I think, such confusing terms are the culprit to give people the (imho wrong) impression that there is a so-called "measurement problem" in QT.

 

[Demystifier]

The statement "the value exists" doesn't make any sense to me.

Then the concept of ontology doesn't make any sense to you. That's fine, as long as you are consistent by not trying to use that concept or ascribe it a meaning.

Within QT an observable can take a definite value (then the observable's value is determined) or not (then the observable's value is indetermined), depending on the state of the system this observable is defined on. I think, such confusing terms are the culprit to give people the (imho wrong) impression that there is a so-called "measurement problem" in QT.

If you dismiss the concept of ontology as meaningless, then there is no measurement problem you need to worry about.

But the problem is that I don't believe that you really dismiss the concept of ontology. I think your state of mind oscillates, so in one moment you want to keep this concept and in another moment you want to dismiss it. That makes you confused about quantum interpretations, and it is this confusion that drags you into discussions of quantum interpretations. And that's OK, there is no progress in science or philosophy without confusion.

 

[zonde]

That's only the case if you make the assumption of collapse, and that's contradicting the fundamental assumptions of locality and microcausality built into QED (and all the Standard Model of HEP physics).

This is very interesting sentence.
Lets make two definitions of "locality":
1) measurement result at one place is unaffected by things happening at spacelike separated place and vice versa
2) statistical properties of measurements commute for measurements made at spacelike separated places
The first part of statement (collapse contradicts locality) is true when first meaning of "locality" is used, but false with second meaning.
But second part of the statement (locality is fundamental assumption built into QED) is true when second meaning of "locality" is used, but false with first meaning.
I guess I need laws of QT to find out if this statement is wrong or not.

 

[A. Neumaier]

Then the concept of ontology doesn't make any sense

Only the concept of ''ontology of exact values''. There are more things that can exist - not only values!

It is obvious (even classically) that a measurement result doesn't exist as long as no measurement is taken. Nevertheless the object to be measured must exist even before the measurement; otherwise it cannot be measured at all! This doesn't change in the quantum realm.

 

[stevendaryl]

That's true, but this "flip" is not due to "spooky actions at a distance". That's only the case if you make the assumption of collapse, and that's contradicting the fundamental assumptions of locality and microcausality built into QED (and all the Standard Model of HEP physics). The only conclusion can be to give up the collapse assumption and live with the minimal interpretation.

I'm just saying that in my opinion, that position is incoherent. You're taking parts of the collapse interpretation and rejecting any implications from it.

 

[vanhees71]

I don't dismiss the concept of ontology as meaningless, but perhaps I have another understanding about ontology than you. For me ontic are the real things in nature, and thus observables are defined by measurement procedures with real-world apparati. I also don't think that I'm too confused about interpretation of QT, also I consider many interpretations to belong rather to esoterics, entertainment for Sci Fi fans, etc.

 

[vanhees71]

I'm just saying that in my opinion, that position is incoherent. You're taking parts of the collapse interpretation and rejecting any implications from it.

Where are there collapse assumptions? I'm just agnostic about what the state of the quantum system might be after measurement. This you can't say in generality, because it depends on how you measure some observable on it.

 

[vanhees71]

This is very interesting sentence.
Lets make two definitions of "locality":
1) measurement result at one place is unaffected by things happening at spacelike separated place and vice versa
2) statistical properties of measurements commute for measurements made at spacelike separated places
The first part of statement (collapse contradicts locality) is true when first meaning of "locality" is used, but false with second meaning.
But second part of the statement (locality is fundamental assumption built into QED) is true when second meaning of "locality" is used, but false with first meaning.
I guess I need laws of QT to find out if this statement is wrong or not.

But 1) follows from 2) (linked-cluster principle; see Weinberg, QT of Fields, vol. I)

 

[zonde]

But 1) follows from 2)

Certainly not. We can consider a toy model. We have a series of boxes where each box contains two identical balls except that one ball is red but the other one is blue.
Alice without looking takes one ball from each box. Bob gets the other one. Clearly which ball Alice takes from the box affects which ball will be left for the Bob. So Alice's action affects Bob's result. But statistical properties for Alice's and Bob's "measurements" do not depend in what order they draw the ball. So this example would satisfy 2) but won't satisfy 1) (if they somehow draw the balls non-localy).

 

[Demystifier]

I don't dismiss the concept of ontology as meaningless, but perhaps I have another understanding about ontology than you. For me ontic are the real things in nature, and thus observables are defined by measurement procedures with real-world apparati.

If I understood you correctly, you say that anything which can in principle be observed by measurement procedures with real-world apparati - is ontology. Even if at the moment we don't have such an apparatus, but will have in the future, it is already ontology - now. And if such an apparatus is impossible even in principle, it is not ontology. Is that correct?

If so, is there any difference, in your understanding, between ontology and observables?

 

[vanhees71]

I don't understand this argument, because you assume that something is non-local to argue that something is non-local. The linked-cluster principle (1) follows from (2) as shown in Weinberg's book. Whether (2) is also necessary for (1) is, as far as I know, not known yet.

 

[vanhees71]

If I understood you correctly, you say that anything which can in principle be observed by measurement procedures with real-world apparati - is ontology. Even if at the moment we don't have such an apparatus, but will have in the future, it is already ontology - now. And if such an apparatus is impossible even in principle, it is not ontology. Is that correct?

If so, is there any difference, in your understanding, between ontology and observables?

Ok, I'm quite sure, I don't understand what you mean by ontology here. To my (admittedly limited) knowledge and understanding of philosophy it's studying the question of existence. According to the natural sciences existing is something that's objectively observable. So for something to exist it must be observable. In physics many things are even quantifiable and then you assign values to observables. According to minimally interpreted QT, not all observables can simultaneously have determined values. Where is a problem with "ontology" here? Only, because the value of an observable is indetermined it doesn't mean that it doesn't exist. That's all I'm saying.