Would studying MWI be a waste of time?

[zonde]

An idealized polarizer by definition absorbs photons polarized in one direction with 100% probability and let's through photons in the perpendicular direction with 100% probability. It's an ideal filter. Where do I need a collapse here? It's just a device constructed to filter photons according to their polarization.

Yes, this works for first polarizer.
What about second and third? Say first polarizer filters out all V polarized photons. But after third polarizer you have only V polarized photons. How is it reflected in your "no collapse" treatment?

 

[stevendaryl]

Indeed, Demystifier is right in saying that I choose my description according to the preparation procedure. That's also done in classical physics, and nobody talks about a collapse there either.

That's because in classical physics, probability can be interpreted in terms of "hidden variables", where objects have definite values for most physical properties that you would care to measure, but those values are unknown. In QM, it's provable that that's not the case. That's why collapse shows up in QM but not in classical mechanics.

This is the big difference between EPR and a similar-sounding classical experiment.

Classically, you can take a pair of shoes and put each into a box, mix up the boxes and send one to Alice and the other to Bob. Before opening her box, Alice would say there is a 50/50 chance of having a left shoe or a right shoe. When Alice opens her box and sees a left shoe, she immediately knows that Bob received a right shoe. Is this a "collapse" of the probability function? No, it's just updating the probabilities in light of new information. There is a "hidden variable" associated with each box, which is the type of shoe inside.

Bell's theorem shows that there can't be a similar "hidden variables" explanation for EPR.

The claim that, even in the quantum case, observations are simply revealing information is hard to maintain in light of Bell's theorem (unless, as in Bohmian mechanics, the information is nonlocal).

 

[vanhees71]

Yes, this works for first polarizer.
What about second and third? Say first polarizer filters out all V polarized photons. But after third polarizer you have only V polarized photons. How is it reflected in your "no collapse" treatment?

All polarizers work as I described it. Photons going through the 1st polarizer are polarized in $x$ direction $0^{\circ}$. Then I put a polarizer in $45^{\circ}$ direction. Every photon going through is polarized in this direction (this happens for about 50% of all photons prepared by the 1st polarizer). The same argument holds at the 3rd, after which all photons going through are polarized in $y$ direction. There's no more predicted by QT than the corresponding probabilities for a photon to run through the polarizers or not, nothing else. There's no need for collapse assumptions here. Of course, the detailed microscopic description of the working of a polarization filter is very complicated, but I don't see any principle need for dynamics outside of QT and thus for a collapse assumption.

 

[stevendaryl]

I don't need a collapse, I need Born's rule. That's it.

I don't see how it is possible to understand the Born rule without collapse unless one dives into tackling the MWI problem of how to interpret probabilities for a unitarily-evolving wave function.

Let's take the simplest case of measurement, which is just a spin measurement along some fixed axis. So suppose I have a device that measures spin. For definiteness, let's just say that there are two LEDs, one labeled "UP" and one labeled "DOWN"; if a spin-up electron enters the device, the "UP" light comes on, and if a spin-down electron enters the device, the "DOWN" light comes on.

So the Born rule says that for such a device, if we supply it with an electron whose spin state is a superposition of the form $\alpha |u\rangle + \beta |d\rangle$, then the "UP" light will come on with probability $|\alpha|^2$ and the "DOWN" light will come on with probability $|\beta|^2$.

To me, that way of describing the measuring device assumes that the state of the device after interacting with the electron is in a "collapsed" state of either one light being on, or the other light being on. If it were computationally feasible to analyze the device (and the environment, and possibly the rest of the universe) using quantum mechanics, you would not find that it has a state of definite value for which light is on. Instead, you would find that there is some amplitude for the device (plus the rest of the universe) to have one light on, and some amplitude for the device to have the other light on.

But we don't see that. We see that the device is in one of two possible definite states. That sure seems like "collapse" to me. The property "which light is on" takes on a definite value. To me, that seems inconsistent with the minimalist interpretation as applied to microscopic objects such as electrons. For an electron, you don't say (and can't say, as Bell's theorem shows us) that it has a definite value for its z-component of spin at all times. So why does the measuring device have a definite value for the property "which light is on"?

 

[stevendaryl]

All polarizers work as I described it. Photons going through the 1st polarizer are polarized in $x$ direction $0^{\circ}$. Then I put a polarizer in $45^{\circ}$ direction. Every photon going through is polarized in this direction (this happens for about 50% of all photons prepared by the 1st polarizer).

But that doesn't make any sense from the point of a pure filtering operation. If it's just a matter of filtering, then a photon could only pass both filters if it simultaneously were polarized in direction $0^o$ and $45^o$.

 

[stevendaryl]

All polarizers work as I described it. Photons going through the 1st polarizer are polarized in $x$ direction $0^{\circ}$. Then I put a polarizer in $45^{\circ}$ direction. Every photon going through is polarized in this direction (this happens for about 50% of all photons prepared by the 1st polarizer).

The collapse hypothesis is that after you measure a property, the system is in some eigenstate for that property. The claim that after going through the 45^o filter, the photon is polarized at angle 45^o is equivalent to the collapse hypothesis. It seems to me that you are being inconsistent.

 

[zonde]

Every photon going through is polarized in this direction (this happens for about 50% of all photons prepared by the 1st polarizer).

See @stevendaryl reply.

 

[Demystifier]

There's no need for collapse assumptions here.

I would go a step further. If the collapse is defined as an objective physical process, and if wave function is interpreted as a thinking tool (not as an objective physical entity), then the collapse assumption is logically incoherent.

 

[vanhees71]

I don't see how it is possible to understand the Born rule without collapse unless one dives into tackling the MWI problem of how to interpret probabilities for a unitarily-evolving wave function.

There is nothing to understand about Born's rule. It's just a fundamental property of QT as a theory of nature. It describes accurately our observations. It's not derived but a postulate in minimally interpreted QT.

 

[vanhees71]

The collapse hypothesis is that after you measure a property, the system is in some eigenstate for that property. The claim that after going through the 45^o filter, the photon is polarized at angle 45^o is equivalent to the collapse hypothesis. It seems to me that you are being inconsistent.

Yes, but in almost all cases after the measurement the system is not in an eigenstate of the measured observable. The systems I deal (theoretically ;-)) with are destroyed after they are measured (hadrons, leptons, and photons from heavy-ion collisions).

In our example of the polarization you have a filter measurement, but there's no collapse, it's just dynamics between the em. field and the polarizer. The important point is that the collapse hypothesis, i.e., instantaneous actions at a distance are in clear contradiction to the very fundamental assumptions upon which QED is built, locality and microcausality (and QED is describing em. fields and their interaction with matter accurately as far as we know today).

 

[Demystifier]

The collapse hypothesis is that after you measure a property, the system is in some eigenstate for that property. The claim that after going through the 45^o filter, the photon is polarized at angle 45^o is equivalent to the collapse hypothesis. It seems to me that you are being inconsistent.

According to the minimal ensemble interpretation, the physical system cannot be an eigenstate simply because the physical system does not live in the Hilbert space. Only our knowledge is represented by a state in the Hilbert space. The physical photon, defined as a click in a detector, is not a state in the Hilbert space. Only our mental knowledge about the physical photon is a state in the Hilbert space. The symbol $|\psi\rangle$ is not a click in the detector. Map is not the territory. That's what the minimal ensemble interpretation is telling us.

Perhaps the only philosophical problem with such an interpretation is the Wigner's unreasonable effectiveness of mathematics. If $|\psi\rangle$ is not the thing that clicks in the detector, then why does it describe the (statistics of) clicks so well?

 

[stevendaryl]

Yes, but in almost all cases after the measurement the system is not in an eigenstate of the measured observable.

For the particular case we're talking about the photon. After passing through the polarizer at 45^o, the photon is in a state of being polarized at 45^o. So it can't be interpreted as simply a matter of filtering. In a pure filter, the state of the thing being filtered isn't changed by passing through the filter. But in this case, it is changed. It wasn't polarized at 45^o beforehand.

 

[zonde]

According to the minimal ensemble interpretation, the physical system cannot be an eigenstate simply because the physical system does not live in the Hilbert space. Only our knowledge is represented by a state in the Hilbert space. The physical photon, defined as a click in a detector, is not a state in the Hilbert space. Only our mental knowledge about the physical photon is a state in the Hilbert space. The symbol $|\psi\rangle$ is not a click in the detector. Map is not the territory. That's what the minimal ensemble interpretation is telling us.

Wave function does not represent photon but rather polarization of photon in particular example.

 

[Demystifier]

Wave function does not represent photon but rather polarization of photon in particular example.

I don't see the point of that comment.

 

[zonde]

I don't see the point of that comment.

You said:

The symbol $|\psi\rangle$ is not a click in the detector.

Yes, $|\psi\rangle$ is not a click in the detector. But it does not even represent the click in detector. It rather represents polarization of the click in detector so to say.

 

[Demystifier]

Photons going through the 1st polarizer are polarized in $x$ direction $0^{\circ}$.

The important point is that the collapse hypothesis, i.e., instantaneous actions at a distance are in clear contradiction to the very fundamental assumptions upon which QED is built, locality and microcausality

I think those two statements can be misleading in the context of minimal ensemble interpretation. What do you mean by "photon", do you mean a state in the Hilbert space, or do you mean a physical photon in the laboratory? What do you mean by "action", do you mean action on states in the Hilbert space, or do you mean action on physical objects in the laboratory?

 

[A. Neumaier]

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

No it doesn't. There is as much branching in a wave function represented as superposition of basis elements as there is branching in a polynomial written as a superposition of monomials.

Whether something appears as a superposition is basis dependent. But QM predictions are basis independent. Just like polynomials - it makes no semantic difference whether you represent them as a superposition of powers or as a superposition of Chebyshev polynomials but the implied ''branching'' is very different. Hence completely spurious from a semantic point of view.

 

[vanhees71]

According to the minimal ensemble interpretation, the physical system cannot be an eigenstate simply because the physical system does not live in the Hilbert space. Only our knowledge is represented by a state in the Hilbert space. The physical photon, defined as a click in a detector, is not a state in the Hilbert space. Only our mental knowledge about the physical photon is a state in the Hilbert space. The symbol $|\psi\rangle$ is not a click in the detector. Map is not the territory. That's what the minimal ensemble interpretation is telling us.

Perhaps the only philosophical problem with such an interpretation is the Wigner's unreasonable effectiveness of mathematics. If $|\psi\rangle$ is not the thing that clicks in the detector, then why does it describe the (statistics of) clicks so well?

Hm, but in classical mechanics an ordered triple of points is also not the body I try to describe with it. Nobody has a problem with that. I think the problem with QT is the probabilistic nature. It's still hard for us to swallow the message that at a fundamental level "god plays dice", as Einstein famously put it. All we know after all the Bell tests and other tests of QT however is that this is indeed the case, and that's way endless papers on the philosophy of QT are produced. From the pure physics point of view, it's all wasted. Maybe there are some interesting ideas for philosophers in it, but to be honest, I doubt it.

 

[A. Neumaier]

As I read this argument, it appears to prove that it is impossible

Everett's argument or mine? I only pointed out that his argument is circular, and hence faulty. In particular, my argument there implies nothing at all about measuring.

Independent of Everett's particular analysis, which is just a particular case:

Whatever microscopic description of measurement is used it must take into account that approximations are made at some point since we can neither observe exact observables nor compute exact dynamics. This invalidates all arguments that don't involve a consideration of approximation errors.

Once approximation is accounted for, and the meaning of a reading from a macroscopic device is specified in terms of statistical mechanics (rather than in term of an ominous collapse to an exact number created by an irreducible quantum random number generator) the Born rule follows without difficulty. See Chapter 10.5 of my online book. The rules of statistical mechanics themselves can be introduced axiomatically without any recourse to measurement issues; see my thermal interpretation of quantum mechanics.

 

[Demystifier]

Hm, but in classical mechanics an ordered triple of points is also not the body I try to describe with it. Nobody has a problem with that. I think the problem with QT is the probabilistic nature. It's still hard for us to swallow the message that at a fundamental level "god plays dice", as Einstein famously put it. All we know after all the Bell tests and other tests of QT however is that this is indeed the case, and that's way endless papers on the philosophy of QT are produced.

I think the problem is not the probabilistic nature. The problem is (the lack of) ontology.

First, even though in classical mechanics an ordered triple of points is not the body, we imagine that there is a body at a position represented by an ordered triple of points. In QM, on the other hand, it is not clear whether there is something like a body represented by quantum mathematical formalism.

Second, Einstein had a problem with "god plays dice" only at the beginning of development of QM. Later he famously asked "Do you really believe that Moon does not exist until you observe it?", which much better describes his later concerns about QM.

Third, and most important, the Bell tests do not exclude determinism. They exclude local realism.

See also Sec. 20.7 of the Ballentine's book. Here are some quotes from it:
" ...they seem to imply that quantum mechanics is incompatible with Einstein’s principle of locality"
"Many assumptions, other than locality, that seem to be implicit in Bell’s original argument have been identified, but in every case it has been possible to deduce a contradiction of quantum mechanics without that assumption."
"Therefore determinism cannot be the cause of the contradiction."
"The issue here is subtle, but fortunately it is now irrelevant, since the new proof in Sec. 20.6 does not make use of probability."
Obviously, your view of minimal ensemble interpretation is very different from that of Ballentine.

 

[AlexCaledin]

The problem is (the lack of) ontology.

Why not assume the "toy onthology" of the Great Game suggested by Feynman in the Character of Physical Law? It seems explaining absolutely everything. The collapse could be a game event ("move"), the branches of reality constituting the mathematical Tree of the Game, so we just safely return to FAPP-Copenhagen .

______________

Sorry! I've got that Feynman book in Russian

 

[Demystifier]

Why not assume the "toy onthology" of the Great Game suggested by Feynman? It seems explaining absolutely everything.

I have no idea what is toy ontology of the Great Game by Feynman. Reference?

 

[stevendaryl]

According to the minimal ensemble interpretation, the physical system cannot be an eigenstate simply because the physical system does not live in the Hilbert space. Only our knowledge is represented by a state in the Hilbert space.

That's fine. The wave function is just some kind of summary of our information about the system, and the information is incomplete, which is why it only gives probabilistic predictions. Now, we perform a measurement/observation and we learn something that we didn't know before--that an electron is spin-up in the z-direction, for example. The question then is: Is this information that already existed beforehand, and the observation just revealed it, or was the information created by the act of measurement? The first option seems like a hidden-variables-type assumption, while the second option seems like a collapse-type assumption.

 

[Demystifier]

The question then is: Is this information that already existed beforehand, and the observation just revealed it, or was the information created by the act of measurement? The first option seems like a hidden-variables-type assumption, while the second option seems like a collapse-type assumption.

The first option, that information existed before the measurement which only revealed it, corresponds to non-contextual hidden variables. It is certainly wrong (even in Bohmian mechanics) due to the Kochen-Specker theorem.

The second option, that measurement somehow created the information, can be realized even without the collapse. In fact, all consistent interpretations (Copenhagen, Bohm, MWI, ...) involve some kind of creation of information by measurement. They must, due to the Kochen-Specker theorem.

 

[stevendaryl]

There is nothing to understand about Born's rule. It's just a fundamental property of QT as a theory of nature.

That cannot possibly be true. A measurement is simply a special kind of interaction whereby microscopic properties are magnified to make a macroscopic difference. Presumably, facts about measurements should be derivable from facts about the particles making up the measuring devices. So a claim about measurements cannot possibly be fundamental.

 

[vanhees71]

I don't understand your argument. Born's rule is just telling the probabilistic meaning of the state (described as a statistical operator) concerning the outcome of measurements, and of course a measurement device works according to the laws of nature, i.e., QT. Born's rule is as far as I know not derivable from the dynamical laws of QT (see Weinberg, Lectures on Quantum Mechanis, Cambridge University Press). It's a postulate independent of the other postulates making up QT, and it's a postulate on the "kinematics" if you wish, not on the dynamics of quantum systems.

 

[stevendaryl]

The second option, that measurement somehow created the information, can be realized even without the collapse. In fact, all consistent interpretations (Copenhagen, Bohm, MWI, ...) involve some kind of creation of information by measurement. They must, due to the Kochen-Specker theorem.

If you consider an EPR-type experiment, and you want to say that Alice's measurement creates information about Bob's particle, that seems like an inherently nonlocal effect. Whether you want to call it a "collapse" or not, it seems like it amounts to the same thing.

In MWI, you would say that Alice's measurement doesn't reveal anything about Bob's particle.

 

[Demystifier]

That cannot possibly be true. A measurement is simply a special kind of interaction whereby microscopic properties are magnified to make a macroscopic difference. Presumably, facts about measurements should be derivable from facts about the particles making up the measuring devices. So a claim about measurements cannot possibly be fundamental.

Read more carefully what @vanhees71 said. He said "fundamental property of QT as a theory of nature." (my bolding). He did not say "a fundamental property of nature itself", nor he said "fundamental property of the final theory of nature".

 

[vanhees71]

If you consider an EPR-type experiment, and you want to say that Alice's measurement creates information about Bob's particle, that seems like an inherently nonlocal effect. Whether you want to call it a "collapse" or not, it seems like it amounts to the same thing.

In MWI, you would say that Alice's measurement doesn't reveal anything about Bob's particle.

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!

 

[stevendaryl]

I don't understand your argument. Born's rule is just telling the probabilistic meaning of the state (described as a statistical operator) concerning the outcome of measurements

As I said, if a measurement is simply a complicated interaction, then no rule involving measurements can be fundamental, because measurements are not fundamental.

For an analogy, if Newton had given, in addition to his laws of motion, an additional law saying: "Cats always land on their feet", that couldn't possibly be a fundamental law. Any law involving cats in principle follows from the laws governing the particles they are made of.

Any statement about measurements (for instance, that they always produce an eigenvalue of the quantity being measured) cannot possibly be a fundamental law for the same reason.

 

[Demystifier]

If you consider an EPR-type experiment, and you want to say that Alice's measurement creates information about Bob's particle, that seems like an inherently nonlocal effect. Whether you want to call it a "collapse" or not, it seems like it amounts to the same thing.

Are you saying that collapse and, for instance, Bohmian non-locality, amount to the same thing?By the way, I do think that there are alternatives to quantum non-locality. See
https://arxiv.org/abs/1703.08341 Sec. 5.3.

 

[stevendaryl]

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

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.

 

[vanhees71]

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. In physics "fundamental laws" are just formalized rules of experience, and Born's rule, in my opinion, is of this kind.

Also the other kinematical postulate you mention is fundamental in my opinion: An observable is described by a self-adjoint operator on a (separable) Hilbert space, and the possible values it takes are the eigenvalues of this operator. That I need to define the description of states and their relation in the first place, and it cannot be derived from some other assumptions. That's why I call it fundamental.

Whether or not you can measure an observable in the lab is another issue and only empirics can answer the question whether I can measure it with the one or other device and whether the measurements are in agreement or disagreement with the theory. For QT they are indeed in very good agreement, and that's why we bother about QT so much.

 

[stevendaryl]

Are you saying that collapse and, for instance, Bohmian non-locality, amount to the same thing?

For the purposes of this discussion, I think the differences are unimportant. The critical thing, which is true for both "collapse" interpretations and Bohm, is that Alice's measurement effects what happens to Bob.

 

[Demystifier]

The critical thing, which is true for both "collapse" interpretations and Bohm, is that Alice's measurement effects what happens to Bob.

Fine, but it's true even for MWI.