I Would studying MWI be a waste of time?

[atyy]

... like no clue for quantum field theory?

QFT is only an effective field theory. So to the extent that QFT can be captured by lattice gauge theory, Bohmian mechanics should be able to get QFT. The main problem is that we still don't have lattice gauge theory for chiral fermions in non-abelian gauge theory.

 

[atyy]

Gleason's theorem tells us that if we want to introduce a probability measure in QM then it has to comply with Born's rule; it's the unique probability measure in Hilbert space.

Gleason's theorem does not force us to introduce a probability measure at all, nor does it explain why we should do so.

The problem is not the probability measure - even a deterministic process can be described by a probability measure (eg. Liouville evolution in classical mechanics).

The problem with Gleason's is it assumes non-contextuality.

 

[tom.stoer]

No. What is there are wave functions, not parallel worlds.

I was not talking about worlds but about "branches":

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).

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.

Please note the quotes when talking about "branches".

 

[bhobba]

The problem is not the probability measure - even a deterministic process can be described by a probability measure (eg. Liouville evolution in classical mechanics). The problem with Gleason's is it assumes non-contextuality.

Sigh. Someone gets it.

Really - is it an assumption that the outcome will occur with some probability? I mean - really? Is it an assumption it will rain or not tomorrow with some probability - is that an assumption? I suppose you could argue it but it would be really hair splitting. I think people, including my professor, in my old probability modelling class would look at you rather strange going that route. Still to each his/her own I suppose.

The key point is non-contextuality. But as I pointed out there is a theorem in MW that it must be non contextual. Is it faulty? People argue about the decision theory approach, but I haven't seen anyone argue about that theorem. I have been through it - it looks OK to me - but then again so does the decision theory approach so I may have goofed.

Thanks
Bill

 

[Demystifier]

... like no clue for quantum field theory?

See http://lanl.arxiv.org/abs/1703.08341 Sec. 4.3 for an ambitious clue.

 

[vanhees71]

You are right regarding the answers, but not regarding the questions.

Reading the debates of Einstein, Bohr, Heisenberg and Weizsäcker you find - and I am sure you know - that they have been concerned with "why-questions".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.

That's OK when looking at quantitative and testable predictions, but it does not tell us anything else but "quantum mechanics is working in practice". Since we know for decades that this is true, it might be the right time to ask new questions to get a deeper understanding on the meaning of quantum mechanics. This is what the Everett interpretation does.

I don't need a collapse, I need Born's rule. That's it. There's no necessity for any additional "interpretation" to what's known as the minimal interpretation. The double-slit experiment with, say, electrons doesn't show anything additional than the probability distribution predicted by minimally interpreted QT. There's no additional input necessary to predict its outcome than Born's rule and solving the Schrödinger equation with the appropriate boundary conditions to get the wave function (or transition matrix elements if you treat it as a scattering problem in QFT) to apply Born's rule to.

 

[zonde]

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

How do you deal with three polarizers experiment? The one where we place three polarizers (first at 0°, second at 45° and third at 90°) in the path of light beam.

 

[Demystifier]

How do you deal with three polarizers experiment? The one where we place three polarizers (first at 0°, second at 45° and third at 90°) in the path of light beam.

Bayesian update of information encoded in the wave function interpreted as a thinking tool, and not as an objective physical entity. This is what @vanhees71 means when he says that there is no collapse.

 

[vanhees71]

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. 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. To call this "Bayesian" is just to make the argument sound more hip ;-)).

 

[Demystifier]

That's also done in classical physics, and nobody talks about a collapse there either.

Indeed, classical physics can be formulated in a quantum-like language and using a quantum-like philosophy, as I presented in
https://arxiv.org/abs/quant-ph/0505143

 

[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.