Would studying MWI be a waste of time?

[vanhees71]

To me, what you're saying is just nonsensical. When Alice measures spin-up for her particle along the z-axis, she knows that Bob will measure spin-down along the z-axis. So the statement

"Bob will not measure spin-up along the z-axis"

is new information about Bob that she didn't know prior to her measurement. Either that information was true before Alice performed her measurement, or it became true at the time she performed the measurement. What third possibility is there? (Well, MWI has the third possibility that the statement just isn't true--Bob might measure spin-up in a different "branch")

Saying that Alice's and Bob's particles are entangled is not an answer. That's the reason that Alice can confidently know that the statement is true. But it doesn't answer the question of whether it was true beforehand or became true as a result of Alice's measurement.

My answer is completely sensical, and I've explained this very many times in this forum, in which sense I mean it, but here it's again. Obviously we discuss the following case:

A spin-0 particle at rest decays into two spin-1/2 particles. So the spin part of the two particles must be in the singlet state $|\psi \rangle \langle \psi|$ with
$$|\psi \rangle=\frac{1}{2} (|1/2,-1/2 \rangle - |-1/2,1/2 \rangle.$$
The single-particle spin state is described by the partial trace, and both partices are "unpolarized", i.e.,
$$\hat{\rho}_{A}=\hat{\rho}_B =\frac{1}{2} \hat{1}.$$
So the single-particle spins are completely undetermined.

However, there's the correlation that, if A measures $\sigma_z^{(A)}=+1/2$ then necessarily B measures $\sigma_a^{(B)}=-1/2$. This is due to the preparation of the two-particle system in the spin-entangled state as described and not due to any measurement A does on her particles. Of course, A gains information on her and thus due to the entanglement also B's particle, but nothing else happens at the instant A's detector registers her particle, particularly nothing happens instantaneously to B's particle which might be very far away if both experimenters are placed far away from each other and the place at which the decay of the original particle happened (i.e., the two-particle state was prepared).

 

[Demystifier]

It's not a nonlocal effect since Alice's measurement only reveals something about Bob's particle (and indeed according to standard QT it does), because of the entanglement of the measured observables, and the entanglement is due to the preparation of the two-particle system in this state. So the correlations (one-to-one correlations for some entangled observables on A's and B's particles) are inherent from the beginning before A's measurement and is not due to any action at a distance due to A's measurement!

So you disagree with Ballentine (see post #90 above).

 

[stevendaryl]

I don't understand, what you mean by fundamental here. I use the term only for theories/models, and I call something a "fundamental law" if it is not derivable from some other law (like an axiom in mathematics) but is assumed to define the theory in the first place.

No. To me, a fundamental law is one that is defined in terms of the fundamental objects of the theory: particles and fields and maybe geometry. A measurement is not a fundamental object of physics. Whether something is a measurement or not is a matter of engineering: You design a device so that the property being measured is reflected in a macroscopic property that can easily be read off and recorded.

 

[Demystifier]

No. To me, a fundamental law is

See my post #98. Or consider the statement:
"A fundamental property of non-relativistic mechanics is that velocity is not bounded from above".
Do you think that the word "fundamental" is used correctly in this statement? My point is, a non-fundamental theory may have internal fundamental properties which are not fundamental from the external point of view.

 

[vanhees71]

So you disagree with Ballentine (see post #90 above).

It may well be that I disagree with Ballentine. With locality of course I mean it in the usual sense of a local relativistic QFT, and I don't think that Ballentine disagrees about locality in this specific sense. Of course, there are long-range correlations, described by entanglement, in relativistic QFT as well as in non-relativistic QT, but the point is that they must not be misunderstood as "spooky actions at a distance". For me EPR's criticism is just about the collapse assumption but not about minimally interpreted QT.

Also this question about ontology is irrelevant for physicists to begin with, because they deal with real things in their lab or wherever they observe something in nature. Of course the moon is there, even if nobody observes it, because there are conservation laws ensuring that it doesn't simply vanish, and since the existence of the moon is well established from observations in the past, it's pretty save to predict that it is still there, and we even can predict where it is very accurately, but we don't need to even bother about QT here, because Newtonian classical mechanics is sufficient for that purpose.

 

[Demystifier]

A measurement is not a fundamental object of physics.

Depends on the definition of physics.

 

[Demystifier]

It may well be that I disagree with Ballentine.

But you still think that his book is one of the best books on QM, right?

 

[stevendaryl]

My answer is completely sensical, and I've explained this very many times in this forum, in which sense I mean it, but here it's again...

You're just repeating what it means to say that two systems are entangled, or that their values for particular observables are correlated. But that wasn't the question.

Once again, assuming that we have a source of anti-correlated pairs, one particle being sent to Alice and the other particle being sent to Bob. Assume that Alice and Bob agree ahead of time to measure the spin of their respective particle along the z-axis. For definiteness, let's assume that Bob measures his particle after Alice measures hers.

So suppose that Alice measures spin-up.

• Is the statement "Bob will measure spin-down" true, or not?
• If it is true, was it true before Alice's measurement?

 

[vanhees71]

I do. Also Weinberg's book is among the best books on QM, and he is obviously of a different opinion about the "interpretation problem" than Ballentine. So?

 

[vanhees71]

You're just repeating what it means to say that two systems are entangled, or that their values for particular observables are correlated. But that wasn't the question.

Once again, assuming that we have a source of anti-correlated pairs, one particle being sent to Alice and the other particle being sent to Bob. Assume that Alice and Bob agree ahead of time to measure the spin of their respective particle along the z-axis. For definiteness, let's assume that Bob measures his particle after Alice measures hers.

So suppose that Alice measures spin-up.

• Is the statement "Bob will measure spin-down" true, or not?
• If it is true, was it true before Alice's measurement?

I don't see any contradiction to what I said. The answer to your last question is very simply given by QT.

(a) If Alice finds her particle to have spin up, then Bob's particle with certainty has spin down.

(b) If Alice hasn't meaured here particle's spin, the only thing that's known about both measurements are the probabilities, and nothing else. The single-particle polarization is "maximally unknown" in the sense of Shannon-Jaynes-von Neumann entropy as a measure of the missing information. In other words: both single-particle spin-z components are as indetermined as they can be.

The observable determined here is, by the way the total spin, because it's in the $S=0$ (implying $\Sigma_z=0$ of course) of the two-particle system as a whole.

What is determined here due to the preparation is the 100% correlation of outcomes of spin-z measurements but not the value of the spin-z components themselves. I think that's the very difference between classical physics and quantum physics: While in the former all observables always have determined values, while in quantum physics you can have completely undetermined observables (like the single-particle spin in our example) but still have strong correlations about the outcome of measurements.

Bell's great achievement was to show that these correlations can be stronger than in any local deterministic model, and the great achievement of the experimentalists in the recent 3 decades is that they could measure this prediction of QT with astonishing accuracy. It's one of the rare occasions that a completely philosophical question could be put into the realm of hard facts in the sense of the natural sciences!

 

[Demystifier]

I do. Also Weinberg's book is among the best books on QM, and he is obviously of a different opinion about the "interpretation problem" than Ballentine. So?

So it's interesting that you disagree with some parts of your favored books. There is nothing wrong or inconsistent about it, that's just interesting.

But can you answer my questions in post #86? It seems that they could be central to our disagreement about the minimal ensemble interpretation.

 

[stevendaryl]

(a) If Alice finds her particle to have spin up, then Bob's particle with certainty has spin down.

So, you're saying that, in the case in which Alice measured spin-up along the z-axis, the statement

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

is true. Good. The followup question is:

• Was it true before Alice performed her measurement?

(b) If Alice hasn't meaured here particle's spin, the only thing that's known about both measurements are the probabilities, and nothing else. The single-particle polarization is "maximally unknown" in the sense of Shannon-Jaynes-von Neumann entropy as a measure of the missing information. In other words: both single-particle spin-z components are as indetermined as they can be.

I interpret that as saying that it was not true before Alice performed her measurement, but was true afterward. So it sure seems to me that Alice had a nonlocal effect on Bob: The set of possible outcomes went from two possibilities before Alice's measurement to one possibility afterward. That's what "collapse" means.

 

[stevendaryl]

I interpret that as saying that it was not true before Alice performed her measurement, but was true afterward. So it sure seems to me that Alice had a nonlocal effect on Bob: The set of possible outcomes went from two possibilities before Alice's measurement to one possibility afterward. That's what "collapse" means.

It seems to me that you are assuming collapse, but are not taking it very seriously.

 

[Demystifier]

Bell's great achievement was to show that these correlations can be stronger than in any local deterministic model

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

 

[vanhees71]

So, you're saying that, in the case in which Alice measured spin-up along the z-axis, the statement

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

is true. Good. The followup question is:

• Was it true before Alice performed her measurement?

I interpret that as saying that it was not true before Alice performed her measurement, but was true afterward. So it sure seems to me that Alice had a nonlocal effect on Bob: The set of possible outcomes went from two possibilities before Alice's measurement to one possibility afterward. That's what "collapse" means.

No! The correlation comes from the fact that the two-particle system was prepared in the entangled state. That's the "cause" of the correlation but not A's measurement.

 

[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.